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International Migration* Noel Gaston Bond University & Douglas R. Nelson Tulane University Abstract This paper surveys current theoretical and empirical research on international migration with a particular emphasis on the links between trade theory and labor empirics. JEL Classification: F2 * This paper was prepared for the Handbook of International Trade edited by Daniel Bernhofen, Rod Falvey and David Greenaway. The published version was dramatically shortened, resulting in the excision of most of the technical content as well as most of the references. International Migration Like immigration itself, economic research on migration seems to come in waves. The large scale of current global migration, and the sometimes quite ugly politics associated with that migration, has produced just such a wave of research. Theoretical and empirical research on immigration, in particular, occurs across the social sciences, with particularly large bodies in economics, demography/sociology, and political science.1 Within Economics, the study of immigration falls between trade and labor economics, with sizable bodies of both theoretical and econometric work. To limit the field of coverage, and differentiate this survey from others in the field, we will focus on a set of questions framed by standard trade theoretic models and the empirical research that bears on those questions. We begin our analysis with two sorts of background: section 1 provides a brief overview of data on the scale and distribution of global migration; while section 2 provides a brief overview of the main theoretical models that will be used in this chapter. The substantive core of the chapter is the analysis of a set of questions that treat migration as a straightforward case of international factor arbitrage. We consider two broad types of question: those that are essentially international questions; and those that are essentially domestic questions. With respect to the first type, we consider the effect of migration on comparative advantage and trade patterns, and whether immigration and trade are complements or substitutes. Turning to essentially national questions, we will focus on aggregate level effects on production structure and labor markets. All of these topics treat immigration as straightforward factor arbitrage. That is, nothing essential would be lost by switching the theoretical analysis from labor to capital migration. We next turn to two issues in which the analysis really is about labor in an essential way: the role of networks, illegal immigration, and welfare states. We finish with a discussion of recent work on the political economy of immigration. 1. Some Basic Data on International Migration Migration is not a recent phenomenon: people have always migrated in search of food, shelter and fortune (e.g., the gold rushes in California, Victoria, etc.).2 They have left the mother country for the colonies; have fled their countries during war-time, times of persecution, famine and political chaos. Historically, much migration was involuntary: African slaves who were 1 The academic literature on immigration is so large, and so well served by surveys, that one could easily write a survey of the surveys. Most closely related to the approach taken here, there have been several surveys from a trade theoretic perspective. Of particular note are: Ruffin (1984); Ethier (1986c; 1996); Razin and Sadka(1994); Venables (1999); and Schiff (1999). Also of note is Wong‘s (1995) textbook on international trade that seeks to incorporate factor mobility as an essential element throughout the text—chapters 4 (on factor mobility in general) and 14 (on immigration) are particularly relevant. These all focus virtually exclusively on the theory, in this chapter we seek to incorporate coverage of relevant empirical work. 2 See Carter and Sutch (1998), Hatton and Williamson (2006), and Sassen (1999). ~1~ transported to the United States, convicts transported to Australian penal colonies and bonded labour was transported to East Africa and other places. Most modern day migration is voluntary and is driven by the search for a better life. A notable development in the last century was the steady rise of national policies to control immigration – legal and illegal. As Sassen (1999) points out, the development of democracy, nationalism and welfare states have made immigration a politically more difficult, and potentially more explosive, issue in contemporary times compared to earlier times. The policies to affect the levels and patterns of international migration are now quite widespread (see United Nations, 2009a). In developed countries, policies are motivated by issues such as low fertility and demographic ageing, unemployment or skilled worker shortages, brain-drain and brain-gain, social integration and national security. Xenophobia is ever-present as well (Freeman, 1993). According to UNPOP (2009a), in 2010 the number of international migrants in the world will reach almost 214 million, which represents 3.1 per cent of the world population. In the two decades between 1990 and 2010, the world will have 59 million more international migrants (see table 1). Table 1. Estimated Number of International Migrants, 1990-2010 Number of international migrants (millions) Percentage of total population Percentage distribution of international migrants Development group and major area 1990 2010 1990 2010 1990 2010 World More developed regions Less developed regions Africa Asia Latin America and the Caribbean Northern America Europe Oceania 154.8 82.4 72.5 16.4 49.8 7.0 27.6 49.4 4.8 213.9 127.7 86.2 19.3 61.3 7.5 50.0 69.8 6.0 2.9 7.2 1.8 2.5 1.6 1.6 9.8 6.9 16.2 3.1 10.3 1.5 1.9 1.5 1.3 14.2 9.5 16.8 100.0 53.2 46.8 10.6 32.2 4.5 17.8 31.9 3.1 100.0 59.7 40.3 9.0 28.7 3.5 23.4 32.6 2.8 Source: United Nations, Department of Economic and Social Affairs, Population Division. Trends in the International Migration Stock: The 2008 Revision. Notes: 2010 figures are estimates. More developed regions comprise all regions of Europe plus Northern America, Australia/New Zealand and Japan. Less developed regions are Africa, Asia (excluding Japan), Latin America, the Caribbean, plus Melanesia, Micronesia and Polynesia. International migrant stock: Midyear estimate of the number of people living in a country or area other than that in which they were born. If the number of foreign-born was not available, the estimate is the number of people living in a country other than that of their citizenship. While three per cent seems a trifling amount, there are considerable differences across regions and individual countries. Developed countries have absorbed about three-quarters of the increase in the number of international migrants in the past two decades. The major increases in the number of international migrants occurred in Northern America (22.4 million) and Europe (20.4 million). The proportion of migrants in the total population between 1990 and 2010 increased in ~2~ all the more developed regions and declined in the less developed regions. Lowell (2007) notes that these trends actually extend back to at least 1975. In 2010, the countries with at least 20 million inhabitants, where international migrants will constitute more than 20 per cent of the population, are Australia, Canada and Saudi Arabia (table 2). Countries with increases in the last two decades of international migrants of greater than 60 per cent include Canada, Germany, the United Kingdom and the United States. The most dramatic change has been experienced by Spain, where the number of international migrants grew by a remarkable 686 per cent. According to UNPOP (2009b), a relatively small number of countries host the majority of the world‘s international migrants. The United States accepts by far the largest number of international migrants. Table 2: International Migration, by country Total (millions) Percentage of total population Total (millions) 2010 Country Percentage of total population 1990 Saudi Arabia 7.3 27.8 4.7 29.2 Australia 4.7 21.9 3.6 21.0 Canada 7.2 21.3 4.5 16.2 Spain 6.4 14.1 0.8 2.1 United States of America 42.8 13.5 23.3 9.1 Germany 10.8 13.1 5.9 7.5 Ukraine 5.3 11.6 6.9 13.4 Côte d'Ivoire 2.4 11.2 1.8 14.4 France 6.7 10.7 5.9 7.5 United Kingdom 6.5 10.4 3.7 6.5 Source: United Nations, Department of Economic and Social Affairs, Population Division. International Migration, 2009 Wallchart. Notes: Countries with populations greater than 20 million and migrant stock proportions greater than 10 per cent in 2010. During most of the 1990s, while there was no significant increase in legal immigration flows, illegal migration increased steadily. On one hand, these facts point to the effectiveness of policies aimed at restricting immigration (Hanson, 2009). On the other hand, the difficulty in controlling illegal flows has elevated immigration to an important place on the political stage in many developed countries. The ―problem‖ is not just felt in the southern border states of the United States. More than 9 million former Soviet citizens migrated following the collapse of communism. After the fall of the Berlin Wall, Germany absorbed 4 million immigrants, of whom 2 million were ethnic Germans from the former Soviet Union (Dietz, 2000). Migration and population policies are driven by different considerations in source, transit and eventual host countries. However, for the purposes of this survey, the migration policies have changed most notably in many developed countries: from an almost open policy (for whites, at least) to much more targeted programs favouring migrants with higher levels of education, skills ~3~ and human capital. In reality, this policy shift may be illusory. Hatton and Williamson (2006) suggest that any changes in the number of ―high quality‖ immigrants, relative to ―low quality‖ immigrants, has much to do with the countries and regions from which the new residents are emigrating. According to Borjas (1999b), all migration policies address two questions: ‗how many immigrants should the country allow in‘ and ‗who should those immigrants be?‘ Australia and Canada have a ‗points system‘ for the admission of new residents with a desirable set of characteristics.3 Table 3 shows that more than two-thirds of the immigrants in OECD countries come from the low-income regions of the world. While this does suggest that the gains from migration are greatest for those with relatively low incomes, this also suggests that, on average, people migrate from regions with low levels of human capital and labour productivity to regions with labour markets with higher average levels of human capital and labour productivity.4 Lowell (2007) shows that there was a net increase of just less than 7.5 million non-tertiary-educated migrants from less developed and into more developed nations during the 1990s (an increase of 64%). In fact, in the year 2000 almost 96 per cent of all adult migrants with less than a tertiary education settled in Northern America, Europe or Oceania.5 3 In Australia, for example, since the mid-1990s there has been a significant shift toward skilled migrants (and away from migrants entering under the family migration program). This has been justified in the context of alleviating skill shortages in the Australian labour market. Politically, it was also seen as necessary to ‗restore public confidence‘ in the Australia‘s Migration Program, see Khoo (2002). Notwithstanding, it‘s also the case that the migrants from the low income areas tend to have higher skills compared to those people who don‘t migrate. This feature is called ‗positive selection‘. The fact that the more able migrate relates to their lower costs of migration and the greater likelihood of success in their destination countries. This aspect of selection bias has its origins in A. D. Roy‘s (1951) seminal work. 4 5 The fact that most migrants flow to a relatively small number of wealthy OECD countries, is in stark contrast to the effects of liberalised trade which are not so geographically concentrated. ~4~ Table 3: Share of OECD Immigrants by Sending Region, 2000 Low Income Sending Region Mex., Cen. Am., Caribe South & Southeast Asia Eastern Europe Africa Middle East South America Pacific Islands Total 0.202 0.154 0.128 0.080 0.063 0.041 0.004 0.672 High Income Sending Region Western Europe Asia, Oceania North America Total 0.244 0.055 0.029 0.328 Notes: High Income North America includes Canada and the U.S. and High Income Asia and Oceania includes Australia, Hong Kong, Japan, Korea, New Zealand, Singapore and Taiwan. Source: Adapted from Hanson (2008), table 2. More skilled workers usually find legal entry into a new country easier (and less costly) than their unskilled counterparts do. Temporary workers have become increasingly important in Western European countries. For example, Germany recently granted 1,000 new temporary visas for computer programmers and those with ―scarce‖ IT skills. Such workers are thought to enhance labour market flexibility (particularly, when immigration restrictions are in place) and to help meet temporary sectoral shortfalls of particular types of labour. As with the large numbers of ―temporary‖ Turkish workers who sought to remain in Germany, there are some potentially thorny political issues that may need to be confronted in the future (see Zimmermann, 1995). However, the most heated debates are undoubtedly concerned with the immigration of unskilled labour, particularly from developing countries, and the impact on labour market performance. Of course, as is well-known, the 1980s and 1990s were associated with growing wage and income inequality in many wealthy countries. Table 4 shows two different income inequality statistics – the Gini coefficient and the 90-10 income ratio - for the developed countries listed in table 2. The data are from the Luxembourg Income Study (LIS). The latest data are indicated and differenced from the LIS waves closest to 1990 and 1980. Income inequality has increased in all listed countries, with the exception of France. Once again, with the exception of France, the change in inequality since 1980 has been quite large in all the countries. These facts seem to suggest a link between immigration and inequality. Kahanec and Zimmermann (2009) argue that drawing such a link may be misleading due to the fact that the ‗New World‘ countries with a high share of foreign-born population, such as the United States or Australia, also have higher income inequality. Post-transition OECD countries tend to very low shares of foreign population and low Gini coefficients. Western European countries are in between the two extremes. However, they do find that for Northern and Western European countries, which share similar ~5~ histories of immigration and economic institutions, that there is a distinct negative relationship between the Gini coefficient and the share of foreigners in the labour force. Table 4: Change in Household Income Inequality, selected countries LIS Dataset(s) Australia 2003 - wave VI Canada 2004 - wave VI France 2000 - wave V Germany 2000 - wave V Spain 2000 - wave V United Kingdom 2004 - wave VI United States 2004 - wave VI Gini Coefficient 0.312 0.318 0.278 0.275 0.336 0.345 0.372 Change since 1990 0.008 0.037 -0.009 0.018 0.033 0.009 0.034 Change Percentile Change since 1980 Ratio (90/10) since 1990 0.031 0.034 -0.010 0.031 0.018 0.075 0.071 4.241 4.379 3.447 3.366 4.686 4.460 5.683 Change since 1980 0.053 0.602 -0.014 0.376 0.727 -0.208 0.032 0.313 0.329 0.050 0.481 0.318 0.930 1.014 Source: Luxembourg Income Study (LIS) Key Figures, http://www.lisproject.org/keyfigures.htm. While immigration is generally thought to have had a relatively minor impact on national wage levels, there may however, be unwanted effects on the wages of certain occupations or skill groups. As with trade liberalization, these distributional issues are very prominent in the debate about the desirability of immigration. 2. The Basic General Equilibrium Framework: Factor mobility and Factor Returns For most trade economists, the 2-factor × 2-good model of general competitive equilibrium, with the full set of Heckscher-Ohlin-Samuelson (HOS) assumptions, is the first stop for developing intuition on real (as opposed to monetary) international questions. By contrast, most labor economists start with some version of the many-factor × 1-good model of general equilibrium. In this section, we begin by reviewing the basic comparative statics from the HOS model, following which we will examine a variety of models closely related to the models in common use in labor economics. With those results in hand, we will present a general many factor, many final good model of general equilibrium that embeds both of these standard approaches. 6 We start with background assumptions and notation. In common with most applied general equilibrium modeling, we consider a framework with some number of factors of production (# = m, indexed by i I), some number of final commodities (# = n, indexed by j J), and some number of households (# = H, indexed by h H).7 Households are endowed with the economy‘s factors of production and preferences defined It should be clear that even this ―general‖ model is considerably more special than even the abstract general equilibrium model of the Arrow-Debreu-McKenzie (ADM) sort. While the ADM model is a perfectly competitive model, that abstracts from increasing returns to scale, imperfect and incomplete markets, etc., it is well known that it is too general to yield comparative statics of the sort we are interested in this chapter. 7 We will not be doing much with the dimensionality of households, so little is lost with using the label of the set of households to denote the cardinality of the set. 6 ~6~ over final commodities;8 and firms are endowed with a constant return to scale technology, f j(zj), that transforms factors of production into final commodities and cost minimization as an objective.9 Factors of production are assumed to be costlessly mobile between firms within a sector and between sectors; and commodities are assumed to be costlessly mobile between firms and households. The exchanges of factors and commodities between firms and households are assumed to be mediated by a complete set of perfectly competitive markets.10 Given our technological assumptions, cost minimization by firms allows us to represent the technology of the sector with a cost function c j(w), where w is a vector of factor prices. Differentiating the cost function with respect to the elements of w yields a vector of input-output c j w coefficients cij w aij w , where the aij need to be understood as (homogeneous of wi degree zero) functions of the wage vector. We can represent the technology of the economy as the m × n matrix A(w) = [aij] whose columns are the vectors representing the technologies of the n sectors. Following the approach made popular by Jones (1965, pp. 96-97), and detailed on Silberberg and Suen (2001, Chapter 19), letting z the m dimensional vector of factor endowments, y denote the n-dimensional vector of outputs, and p the n-dimensional vector of commodity prices, we can represent equilibrium in the economy with the full-employment and zero profit conditions:11 Ay z Aw p (1) Immigration, minimally, involves mobility of some factors between countries. To consider a world of international migration, we must also have at least two countries. As Markusen (1983) notes, in a world made up of countries of the sort we have just described that is also characterized by identical factor endowments, identical technologies and identical homothetic preferences, even if trade and factor mobility are costless, there will be no basis for trade in goods or factors. Thus, to get the analysis going, whether we are interested in the effects of migration on a single, given country, or on the equilibrium of a trading world, we will need to assume some form of heterogeneity in countries and/or market imperfections such that international exchange is possible. Most research on immigration begins by abstracting from both preference heterogeneity and technology heterogeneity to focus on endowment 8 Preferences are taken to be rational (complete and transitive) as well as well-behaved (continuous, monotone, strictly convex). In addition, it will often be convenient to assume that all households share identical preferences with additional properties that make for ease of aggregation—homotheticity or quasi-linearity. 9 We will consider non constant return to scale technologies later, and then profit maximization will be an appropriate objective function for the firm. 10 All institutional assumptions necessary to ensure existence and competitiveness of all markets are implicitly assumed. 11 We assume that every factor is used in the production of at least two commodities and production of every commodity requires at least two factors. The framework used here, and much of the analysis of the general case, is taken directly from the appendix to Jones and Scheinkman (1977). ~7~ heterogeneity. Work on migration, per se, often also abstracts from trade by assuming either the given country is an economically small free trader or is completely closed to trade in commodities. The first strategy has the advantage of fixing the prices facing the economy, while the second treats factor mobility as the only international linkage. In all three of the specific versions of the general m × n model, immigration is simply a transfer of (some kinds of) foreign factors of production from one country to another. When discussing migration, these factors will be called labor; but in these models there is nothing particularly to distinguish different sorts of labor from one another, or to distinguish labor as a class from other types of factors of production. Later in this chapter we ask what sorts of issues are distinctive to international movement of labor qua human beings. As we shall see, there are two main comparative static questions to be asked in these models: the effect of a change in the endowment of labor on prices; and the effect of a change in the endowment of labor on outputs. 2.1. Factor Mobility in the 2-factor × 2-good, Heckscher-Ohlin-Samuelson (HOS) Model We begin with 2-factor × 2-good HOS model. As with equations (1), letting a bar denote a fixed endowment, we can characterize the equilibrium in terms of the full employment and zero profit conditions.12 a11 y1 a12 y2 z1 a21 y1 a22 y2 z2 a11w1 a21w2 p1 (2) a12 w1 a22 w2 p2 Note that in the even case (i.e. m = n) these conditions are separable. That is, in this case, we can solve for equilibrium factor prices using only the zero profit conditions. This means that, as long as both goods continue to be produced, the endowments do not enter into determination of relative factor prices. In addition to the general assumptions laid out above, we now assume that, both (all) countries have access to the same technological opportunities for producing both goods; and that, for all relative prices that involve both final goods being produced in a given national economy, the factor-intensity ranking of the two industries does not change—i.e. no factor-intensity reversals (―no FIRs‖). [Figure 1 about here] A convenient representation of this model is the Lerner (1952) diagram. Without loss of generality, it is convenient to associate factor 1 with commodity 1, such that for all prices supporting the production of both goods: a11 a12 . a21 a22 12 The classic development of the HOS model is Jones (1965). ~8~ (3) The Lerner diagram involves projection of unit value isoquants into factor input space.13 The slope of the unit isocost line tangent to the unit value isoquants gives the equilibrium factor price ratio. If we measure allocation of factor 1 on the horizontal axis and allocation of factor 2 on the vertical axis, the assumption of no FIRs means that the expansion paths (rays from the origin by CRS) reflecting equilibrium relative input combinations for any given relative factor prices for sector 2 will always lie above those for sector 1. The expansion paths associated with given equilibrium prices describe a cone in input space such that any endowment that lies in the cone permits diversified production consistent with full employment and zero profits at the given prices. As a result, this cone is called the cone of diversification. Starting from endowment point z z1 , z2 , using the properties of vector addition, it is easy to identify the equilibrium allocation of the two factors between the two sectors. Now suppose that the immigration quota for factor 2 is increased such that the new endowment is z z1 , z2 . As long as z remains in the cone of diversification, we can identify the new allocation of factors among sectors. This involves no change in relative commodity prices or factor prices. This is easy to see in the Lerner diagram. With unchanged commodity prices, the unit value isoquants remain fixed in place, and tangent to the unit value isocost, whose slope gives the relative w2/w1 ratio. The expansion paths that intersect these points of tangency define the cone of diversification associated with the equilibrium. Leamer (1995) calls this property of the HOS model the factorprice insensitivity theorem. It is the one country version of the more well-known, and more controversial, factor-price equalization theorem. We will discuss factor-price insensitivity in more detail when we consider the general m × n model. At this point, we simply note that instead of adjustment in relative factor prices, adjustment to the immigration shock occurs on the output margin, with sector 2 (the factor 2 intensive sector) expanding and sector 1 contracting. This adjustment on the output margin is also an essential element of the Rybczynski theorem: at constant relative commodity prices, and under the full set of HOS assumptions, an increase in the endowment of one factor, holding the other endowment constant, will cause an increase in the output of the commodity whose production uses that factor intensively, proportionally greater in magnitude than the change in endowment; and a decrease in the output of the other commodity (Rybczynski, 1955). Note the essential role played by the assumption that commodity prices are unchanged. 14 Given the structure of the HOS model, factor-price insensitivity holds, so with unchanged commodity prices, as long as the endowment change remains in the cone of diversification, factor prices will be unchanged and, thus, endowment changes will be a weighted average of output changes (Jones, 1965). Thus, in figure 1, it is easy to see that the increase in 13 The unit value isoquant for a commodity gives all combinations of factor 1 and 2 capable of producing that quantity of the commodity that sells for $1. That is, it is the 1/pj isoquant. 14 Interestingly, Rybczynski was ultimately interested in the effect of an endowment change on the terms of trade (the title, after all, is ―Factor Endowment and Relative Commodity Prices‖). What we call the Rybczynski theorem is more like a lemma on the way to a conclusion about terms-of-trade. ~9~ the immigration quota for factor 2 zˆ2 0, where a ‗hat‘ denotes a proportional change) results in a decrease in the output of commodity 1 and an increase in the output of commodity 2. Furthermore, given the weighted average property, we must have:15 yˆ 2 zˆ2 zˆ1 ( 0) yˆ1. (4) Factor price insensitivity needs to be qualified in at least two ways. First, if the country is large, so that a change in its pattern of production changes the world relative prices, then standard Stolper-Samuelson effects will apply. Continuing the example of the previous paragraph: the increase in relative supply of commodity 2 induced by the flow of factor 2 will cause the world relative price of commodity 2 to fall; via the Stolper-Samuelson theorem, this produces a fall in the real return of factor 2, and a rise in the real return to factor 1. In figure 2, taking commodity 1 as the numeraire, the fall in the price of commodity 2 will show up as an outward shift in the commodity 2 unit value isoquant (i.e. $1 buys a larger quantity of commodity 2). The new $1 isocost line tangent to the original commodity one and the new commodity 2 unit value isoquants, whose slope is equal to r2/r1, is flatter, reflecting the fall in the relative return to factor 2. The second qualification refers to an endowment change sufficiently large as to move the endowment point outside the cone of diversification. Without changing the dimensionality of the model (i.e. retaining 2 goods), there is now only one good produced, so the economy now behaves like a 2-factor × 1-good economy, and we have a downward sloping factor 2 demand curve. If the overall economy is characterized by 2 factors and m goods, the overall factor 2 demand curve will be characterized by downward sloping portions, where only one final good is produced; and ―flats‖, where two goods are produced. 2.2. Factor Mobility in the m-factor × 1-good model The m × 1 model is the most common framework applied by labor economists working on estimating the effects of immigration, as well as the basis of the two-country model widely used for discussion of international equilibrium of migration. For this model, the commodity is interpreted as gross domestic product, a function of a list of factor inputs: y = f(z), z = (z1,…,zm). Consider, without loss of generality, the 2 factor × 1-good (easily graphable) case. As with the HOS case, we can use the standard representation of the equilibrium in terms of the zero profit and full employment conditions as: 15 Totally differentiating the full employment conditions in (2), and denoting the share of factor i used in sector j by λij i.e. ij aij y j / zi , it is straightforward to derive zˆi jJ ij yˆ j ij aˆij . However, with unchanged jJ relative factor prices, the aˆij are all zero, so endowment changes must be λij-weighted averages of output changes. Thus, with y1 falling, the proportional change in y2 must exceed the proportional change in z2. ~ 10 ~ a11 y1 z1 a21 y1 z2 (5) a11w1 a21w2 p1 It should be clear that the single zero profit condition cannot be used to determine the factor returns without using the full-employment conditions. In fact, the relative endowments will determine the relative factor prices, while the full employment condition determines the absolute value of prices.16 The logic of this claim is easily understood by considering the unit isoquant for production of GDP—shown in Figure 2a. The ray from the origin through the endowment point cuts the unit isoquant, picking out the aij‘s. Thus, in this model, endowments play a role in determining equilibrium factor prices. 17 If we suppose that the country is small, so that the price of the single good is fixed, we can differentiate the production function with respect to the internationally mobile factor, for fixed quantities of the other factors, at every level of allocation of the internationally mobile factor, yielding the economy-wide demand for that factor—i.e. the value marginal product curve. This curve is portrayed for factor 2 in Figure 2b. [Figure 2a and b about here] The area under the curve, from the origin to the endowment of the internationally mobile factor, gives total product (i.e. GDP). The intersection of the vertical supply curve with the demand curve identifies the return to the internationally mobile factor, identifying total payment to the internationally mobile factor as the rectangular area. Because the area under the curve is GDP, if we subtract the payment to the internationally mobile factor from GDP, the remainder is the payment to the other factors. Thus, we have identified the distribution of income in the economy. This is most transparent in the two factor case. If the country now permits an increase in the stock of the mobile factor, say by increasing the immigration quota, it is easy to see that all units of the mobile factor previously resident in the country experience a reduction their return, while all units of the internationally immobile factor experience an increase in their return. Generalizing this result to the case of multiple immobile factors requires that all immobile factors be substitutes for the internationally mobile factor.18 It is straightforward to show that an increase in price of the country‘s good will have no effect on output, but will raise the return to each of the factors in the same proportion as the increase in price. See Woodland (1982, pp. 9697). 17 The analysis above applies here, but factor-price insensitivity would be an unusual case. The (degenerate) cone is the ray through the initial endowment point and any change in endowment that falls on this line will satisfy factorprice insensitivity, but any other pattern of change will result in a change in relative factor prices. As we shall see, when m > n a change in the endowment will generally produce a change in relative wages. 16 18 Most empirical studies find quite complicated relations between immigrant labor and other national factors. This fact will have important implications for conclusions about the distributional effects of immigration. ~ 11 ~ In addition to these distribution effects, the triangular area is called the ―immigration surplus‖ and represents the gain to home factors from immigration. Note from the analysis of distribution effects that this gain is completely captured by the internationally immobile factor. The static analysis of the effect of immigration on output is trivial: with marginal product of labor positive, but diminishing with fixed quantities of other factors, national output rises, but by less than the increase in the endowment of labor. [Figure 3 about here] If we now consider a world made up of two m × 1 countries, we have what Ruffin (1984) calls the MacDougall-Kemp model.19 This has a simple graphical representation in which the horizontal axis gives the world endowment of the internationally mobile factor and the labor demand curves are projected from vertical axes at the limits of the horizontal axis. In a world characterized by free mobility of the internationally mobile factor, the intersection of the two labor demand curves identifies the allocation of the internationally mobile factor between the two countries, and the distribution of income can be identified as in the single country case. We will return to this later, but it is probably useful to note here that figure 3 makes clear the gain to labor from the sending country, and the loss to specific capital from that country. 2.3. Factor Mobility in 3-factor × 2-good models A very closely related model is the 3-factor × 2-good, specific factors (aka Ricardo-Viner) model (Jones, 1971; Samuelson, 1971). In this case, each commodity is produced using one intersectorally mobile factor and one sector specific factor. In this case we have two zero profit conditions and 3 full employment conditions. Letting factor 1 be specific to sector 1, factor 2 be specific to sector 2, and factor 3 be intersectorally mobile, the equilibrium conditions are: a11w1 a31w3 p1 a22 w2 a32 w3 p2 a11 y1 z1 (6) a22 y2 z2 a31 y1 a32 y2 z3 As with the m × 1 case, the zero profit conditions in the specific factors model are a system of two (n) equation in 3 (m > n) unknowns. So, once again, the endowments must be used to solve for relative factor returns; and changes in endowments will affect relative factor returns. 19 The original references, MacDougall (1960) and Kemp (1964), were concerned with capital mobility. However, since both factors were globally fixed endowments, there was no particular distinction between capital and labor. In fact, precisely this model was deployed around the same time to examine labor mobility (Grubel and Scott, 1966; Johnson, 1967; Berry and Soligo, 1969). ~ 12 ~ Recognizing that the aij are functions of the factor returns we can use the full employment conditions for factors 1 and 2 to eliminate the yj‘s from the last full employment condition: a11w1 a31w3 p1 a12 w1 a32 w3 p2 (6') a31 w1 , w3 a w , w z1 32 2 3 z2 z3 a11 w1 , w3 a22 w2 , w3 This system of 3 equations can be used to solve for the 3 factor prices. This model has a graphical representation that looks like Figure 2, but where the figure now represents a single economy. With free mobility of the mobile factor between sectors, the economy-wide equilibrium is picked out in exactly the same way as in the global economy. For the purposes of analyzing international migration and its effects, labor is the internationally mobile factor in the m × 1 model, in the specific factors model the internationally mobile factor need not be the intersectorally mobile factor (although it very commonly is assumed to be). This model tends to be used under either of two interpretations. In the original versions, by Samuelson and Jones, the analyst thinks of the sectors as using specific factors in the long run: immigrants enter a mobile labor force in which one sector (say, agriculture) always uses land and labor, while the other sector (say, industry) always uses capital and labor. On the other interpretation, due to Mayer (1974), Mussa (1974) and Neary (1978), the specific factors model represents a time horizon between the very short run where no factors are mobile and the very long run where all factors are mobile.20 Under the second interpretation, the specific factor is generally sector specific capital, which becomes mobile over (generally unmodeled) time. [Figures 4a & b about here] The income distribution effects of international factor mobility are straightforward. In Figure 4a the internationally mobile factor is also the intersectorally mobile factor, z3. An increase in the quota on the internationally mobile factor expands the base of the diagram, increasing the output of both sectors (as some of the immigrants are allocated to each sector and factor 3 has positive marginal physical product in both sectors), reducing the return to all units of the mobile factor previously resident in the country, and raising the return to both immobile factors (the triangular regions reflecting return to specific factors are both larger and, since the number of units of the specific factors are unchanged, the payoff per unit of specific factor must increase). Furthermore, since the price of the country‘s good is unchanged, this implies a real increase in the return to the specific factors and a real fall in the return to the mobile factor. That is, letting a ―hat‖ denote proportional changes: 20 An alternative representation of the medium term is a model in which both factors are imperfectly mobile (e.g. Hill and Mendez, 1983), but the tractability of the standard specific factors model has made it the much more common choice. ~ 13 ~ rˆ1 , rˆ2 pˆ1 , pˆ 2 0 rˆ3 . (7) A change in the quota for a specific factor, say factor 1, will shift up the value marginal product of factor 3 curve for sector 1, reflecting the fact that mobile factors now cooperate in production with more factor 1. This obviously raises the return to the mobile factor and lowers the return to the specific factor in sector 2. The return to specific factors in sector 1 are a bit trickier: graphically, the triangular area reflecting the total return to factor 1 owners, r1 z1 , is larger, but z1 has increased by the amount of the immigration. However, we know that the price of good 1 is unchanged and, from the general weighted average property of price changes,21 pˆ j ij rˆi , (8) iI so, since there are only two inputs (z1 and z3), and we know that r3 has gone up, it must be the case that r1 has fallen. Thus, for the case of an increase in the endowment of z1, we have: rˆ1 , rˆ2 pˆ1 , pˆ 2 0 rˆ3 . (9) The effects on output are equally straightforward. An increase in the endowment of the intersectorally mobile factor will raise the output of both sectors, but by proportionally less than the endowment increase. The latter fact follows from the fact that, in each sector, there is positive by diminishing return to any factor. Similarly, an increase in the endowment of one of the intersectorally immobile factors will cause the sector using that factor to expand, but by proportionally less than the increase in the endowment; and will cause the other sector to contract. A simple alternative to the specific factors model is the 3 × 2 model in which all three factors are intersectorally mobile and every good uses all three factors in production. Ruffin (1981) extends the ―friends and enemies‖ language of Jones and Scheinkman (1977), to include: factors i and k wi wi are friends if 0 and enemies if 0 . For the general m > n case, Ruffin uses zk zk Samuelson‘s reciprocity relationship, to show that friendship is reciprocal (i.e. if i is a friend to k, the k is a friend to i); and that every factor has a friend. For the 3-factor × 2-good case, Ruffin then shows that, without loss of generality, there is always an assignment of labels to factors such that, for I = {1,2,3} and J = {1,2}: a11 a31 a21 , a12 a32 a22 (10) Letting ζij denote the distributive share of factor i in sector j, i.e. (riaij )/pj, (8) follows from totally differentiating the zero profit condition for good j and solving in terms of proportional changes. See Jones (1965) or Jones and Scheinkman (1977). A more detailed presentation can be found in Silberberg and Suen, (2001, Section 18.3). 21 ~ 14 ~ and the weak inequalities can be replaced by strict inequalities if no two factors are used in the same proportions across sectors. In the case of strict inequalities, Ruffin refers to factors 1 and 3 as extreme factors, and 2 as the middle factor–as a result, in the case of strict inequalities, Ruffin refers to (24) as the factor extremity condition. Under this condition, Ruffin proves: Theorem: If there are three factors and two goods produced in a competitive, small open economy operating under constant returns to scale, an increase in the supply of an extreme factor will benefit the middle factor and hurt the other extreme factor. Thus, under the labeling convention of the factor extremity condition, factors 1 and 2 are enemies to each other and friends to 3, while factor 3 is a friend to both 1 and 2. One of the attractive features of this model is that the result depends only on factor-intensity ranking, and not at all on details of the substitution elasticities.22 For reasons that will be clearer following the discussion of the general m × n case, strong, general results on the link between endowments and outputs will not be forthcoming. Unlike the specific factors model, in the general 3 × 2 model, what emerges are a number of cases, where outcomes depend on delicate relations of factor intensities and relations of factor substitutability/complementarity (Jones and Easton, 1983; Thompson, 1985; 1987 section 2). Thompson and Clark (1983) apply this framework to US data, with y = {agriculture, manufacturing} and z = {skilled labor, unskilled labor, capital}, finding capital and skilled labor to be extreme factors, while unskilled labor is the middle factor. Thus, if current immigration in the US raises the endowment of unskilled labor, Ruffin‘s theorem implies that the wage of unskilled labor should fall and that of skilled labor rise, producing a change in the wage premium of the sort that was observed in the 1980s. Thompson and Clark (1990) extend this analysis to a 4 × 3 model–y = {agriculture, services, manufacturing} and z = {unskilled labor, semiskilled labor, skilled labor, and capital}–finding unskilled labor a friend to capital and skilled labor, and an enemy to semi-skilled labor. The magnitudes, in both cases, are such as to suggest that the only sizable effects will be that of unskilled labor on itself. These results seem loosely consistent with those we have already reported in both the labor and trade research frameworks.23 It should be noted that all of the implementations of the m > n model we have mentioned were of the form m = n + 1. One might reasonably wonder whether the results applied in this work are sensitive to this particular dimensional assumption. Jones (1985) shows that the answer is ―yes‖. 22 Of course, the substitution elasticities affect the magnitudes. Jones and Easton (1983) is an exceptionally useful development and exposition of this model, with a particular emphasis on the role of economywide elasticities and their conceptualization. Thompson (1983a; b) and Davies and Wooton (1992) develop the application of this model to migration in some detail. Clark and Thompson (1990) and Davies and Wooton also consider the effect of migration on the source country in this model. 23 Clark and Thompson (1986) carry out a similar analysis on Canadian data, but use 5 job categories and capital for a 6 × 5 model. In that case, all but highest skill category (L1: professional, technical, managerial, and administrative) bear the same relationship to capital and L1, and to each other: enemies to each other and friend to capital and skilled labor (i.e. L1). ~ 15 ~ Specifically, Jones notes that when m = n + 2 (or more) it is no longer possible to identify the qualitative effect of endowment change on factor wage from factor intensity. It is now necessary to have specific knowledge of factor substitutability as well.24 2.4. Factor Mobility in m-factor × n-good models For the general case of m factors used to produce n final goods, according to production functions which are linear homogeneous, strictly quasi-concave, and twice differentiable, we can represent the technology with the m × n matrix A = [aij] and the equilibrium by the system of full- employment and zero-profit conditions given in (1):25 Ay z Aw p Differentiating this system yields: s kI ik dwk aij dy j dzi , i I ; jJ aij dwi iI where we have used the fact that daij aij w wk kI for y da jJ j ij in the first equation; and w da iI (11) dp j , j J , i ij dwk , and sik : y j jJ aij w wk , to substitute 0, by cost minimization, in the second.26 In matrix form (26) is: S A dw dz A 0 dy dp . (12) Following Jones (1965), we can also write this framework in terms of proportional changes: ˆ zˆ w 0 yˆ pˆ , 24 (12) Jones then offers a useful result which rules out certain patterns of response of the wage vector to changes in the endowment vector, and which generalizes Ruffin‘s theorem, given above. 25 It should be clear that, since we are treating z and p as parametric, all of the results we will discuss below are derived only from technological conditions. For a closed economy, or for a large open economy, we also need to consider the role of tastes. When this is the case, we often make assumptions that render tastes essentially irrelevant to the analysis—e.g. identical homothetic preferences. However, we should not forget that preferences can interfere dramatically with otherwise standard results. For examples of these problems, see Deardorff (1986) on comparative advantage and Opp, Sonnenschein and Tombazos (2009) on the Rybczynski theorem. 26 Note that sik shows how economy-wide demand for factor i changes in response to an increase in wk. ~ 16 ~ where we let ij wi aij pj , ij y j aij zi ws , ik k ik z , and a ―hat‖ denotes proportional change. σ is i a matrix of economy-wide substitutions elasticities, with a negative diagonal and zero row sums. Furthermore, we also know that both θ and λ have unit row sums—that is, they are nonnegative, row-stochastic matrices. Thus, the entire matrix is row stochastic. S A K G , and its inverse B 1 : Now if we denote the first partitioned matrix, B : , the A 0 G L comparative statics in which we are primarily interested, dw/dz and dy/dz, are contained in:27,28 ˆ M dw K G dz w dy G L dp or yˆ Q N zˆ . R pˆ (13) The submatrix K gives us the effect of a change in the endowment vector on the wage vector (dw/dz). If m ≥ n, it can be shown that K is a symmetric, negative semi-definite matrix with rank m - n – to be denoted R(K) = m – n hereafter (Diewert and Woodland, 1977 appendix lemma 3; Takayama, 1982 theorem 7). Thus, when m = n (the ―even‖ case used extensively in the 27 It is important to note that B is nonsingular if, and only if, the rank of A, R(A), is n (Chang, 1979 lemma 1; Takayama, 1982 theorem 4). Since A is m × n, this means that B is singular if m < n (i.e. the number of produced commodities exceeds the number of factors). 28 It is useful to note that we can derive B-1 directly from an economy‘s GDP function. If we denote by Y(z) the set of outputs producible given the economy‘s technology sets and endowment, Y z y y j f j z , z j j 0; z j z; y 0 , jJ we can define the GDP function as: G p; z max p y y Y z . y Assuming G() is twice differentiable, denoting derivatives with subscripts, and using the derivative properties of the GDP function (Woodland, 1982, section 3.7), we have: Gzz G pz w w p Gzp z B 1. y y G pp z p That is, B-1 is the hessian matrix of the GDP function. From the assumption that the function is C2, and Young‘s theorem, we have the symmetry that underlies Samuelson‘s reciprocity conditions. From concavity in z we have that Gzz is negative semi-definite and symmetric, and from convexity in p we have that Gpp is positive semi-definite and symmetric. However, not surprisingly, those properties depend on dimensionality. For example, if n > m, Gpp will not be well defined. ~ 17 ~ literature), K is a zero matrix.29 So, in the even case, endowment change has no effect on factor prices. Again, Leamer (1995) calls this important result the factor-price insensitivity theorem. This is the one-country version of the more well-known, but empirically more dubious, factorprice equalization theorem. The maintained assumption of a common A matrix before and after an immigration shock seems much more empirically plausible than assumption that A matrices are common across countries.30 If m > n, the negative semi-definiteness of the K matrix implies that ∂wℓ/∂zℓ ≤ 0. That is, if the endowment of factor ℓ, z , rises, the return to zℓ cannot rise—factor-price insensitivity will not generally hold in this case. This is, of course, what our intuition tells us should be the effect of immigration on wages. Note, however, that it depends on the prima facie least plausible assumption about the relative dimensionality of endowments versus produced commodities. We return to this later, but it is worth noting that most empirical work seems to find support for a world in which there are many more commodities than factors and multiple cones of diversification (Bernstein and Weinstein, 2002).31 The empirically plausible case of n > m is tricky because in this case B is singular and, thus, cannot be inverted for comparative static purposes. The problem is that the production structure is indeterminate. However, at least for factor-price insensitivity, this is not so dire. First, as is often pointed out, if prices are parametrically given (the small country case), however many goods there are in the world, the small open economy will generally produce only n = m, with which we have already dealt (Samuelson, 1953/4 paragraph 9; Jones and Scheinkman, 1977 pg. 917). For the case of n > m in equilibrium, Chang (1979) develops an analysis by partitioning the A matrix into two matrices. We suppose that R(A) = r > 0 and rearrange the columns of A such we can partition A into two matrices such that A1 is m × r and R(A1) = r, and A2 which is m × (n – r). That is, A1 has a rank equal to the number of linearly independent columns in A so that R(A) = R(A1). Chang shows that if r = m, factor-price insensitivity holds (theorem 5).32 This makes sense, as before, the columns of the A1 matrix define a non-degenerate cone in m-dimensional factor-space. As in the m = n case, the endowment cannot change so much that the new endowment falls outside the initial cone of diversification, implying that some commodities cease production. Subject to that caveat, however, factor-price insensitivity continues to hold in the m < n case. Recall that the j‘th column of A gives the technique in use in sector j. Together, the optimal input vectors described by the columns define a cone in input space. When each of these vectors is unique, A has rank m = n, and the cone is non-degenerate. As long as the new endowment remains in the interior of that cone, i.e. m = n before and after a change in the endowment vector, such an endowment change will have no effect on factor prices as changes in output-mix will suffice to absorb the change. 30 Of course, in the one country case, this relies on an unchanged international price and unchanged set of goods in production. 31 The presence of multiple cones holds out the prospect that m = n is an empirically plausible maintained assumption from which to begin. Of course, in a sufficiently short period of time factors are specific to industries, the assumption of m > n becomes more reasonable. 32 Chang‘s analysis is actually in terms of factor-price equalization but, as we have already argued, the formal adjustment is literally rhetorical, while the empirical referent of FPI seems better grounded than that of FPE. 29 ~ 18 ~ For the effect of immigration on output, i.e. dy/dz, rather than the sub-matrix G in matrix equation (13), we will work with the proportional changes given in Q. The rows of Q show the effect on a given sector of an increase in each factor, while the columns show the effect of an increase in the endowment of a given factor on the output of every sector. When m = n, as long as the endowment change remains within the original cone of diversification and commodity prices are unchanged, factor-prices are unchanged, so there is no change in the technologies of production. In this case it can be shown that every column in Q has at least one negative element and one element greater than 1. That is, an increase in any given factor will cause some sector to increase output by proportionally more than the proportional increase in that factor, and cause some sector to contract. In terms of the rows, it can be proved that every row has at least one negative entry; however, even in the m = n case it cannot be proved that every row must have an entry greater than 1.33 That is, every sector has a factor whose increase will cause the sector to shrink, but need not have a factor that will cause it to expand by proportionally more than the endowment increases. This is a generalization of the Rybczynski theorem of the HOS model, which we will discuss in more detail below. 34 For the case of m > n, even with commodity prices constant, a change in the endowment vector (migration) can still affect factor prices which, in turn, will cause a change in the technologies in use (i.e. the aij(w)). For this case, then, while we can still show that every row of the Q matrix possesses at least one negative element, we cannot prove that it possesses an element greater than one.35 Furthermore, we cannot prove anything in general about the columns. Thus, while each sector has an enemy, we cannot prove that it has a friend; and we cannot prove that each factor is a friend to any sector or a friend to any sector. The literature on dimensional generalizations of the main theorems of trade models can be frustrating. There are a large number of such generalizations, all of which focus on different aspects of the original theorems.36 From the point of view of analyzing immigration flows, whether for framing evaluations of empirical work, as a basis for political economy modeling, or for thinking systematically about the effects of policy, the class of generalizations considered here seems to be the most useful. On the one hand, this is the clearest way to see and understand the factor price insensitivity theorem, which will be of considerable importance in understanding 33 Every row will, of course, have a positive element, but it need not exceed 1. If the sector to which the row refers is sufficiently small, ―unimportant enough‖, then the row must have an element greater than unity (Jones and Scheinkman, 1977, pp. 931-932). 34 In the language of Jones and Scheinkman, every factor is a natural friend to some sector and a natural enemy to some other sector; and every sector has a natural enemy and a qualified natural friend. 35 As in the even case, the problem here is the ―importance‖ of the sector. 36 The key elements of theorems like Rybczynski and Stolper-Samuelson are that the friend and enemy relations are: reciprocal (a factor is a friend to a sector if, and only if, the sector is a friend to the factor; and similarly for enemies); they are global (with respect to the values of the system‘s parameters); and they are characterized by magnification. Much of the early work on generalizing these theorems sought to find conditions on the technology, the A matrix, that retained all of these properties. For factor-price equalization, the goal was to find conditions that yielded a globally unique, technologically determined, relationship between commodity prices and factors prices. ~ 19 ~ empirical work; and, on the other hand, magnification plays an important role in welfare and political economy analysis. We have already asserted a presumption in terms of the m < n version of the model, but various specific versions, with stronger comparative static, results have been used so extensively that we will consider a number of these models in a bit more detail. We have spent considerable time on factor-price insensitivity in the standard HO environment, and related frameworks, because there seems to be quite a bit of misinterpretation. It is worth noting for future reference that the sole relevant difference between the basic frameworks in use by labor (m × 1) and trade economists (m × n) is dimensionality. First, dimensionality is not nearly so damaging of factor-price insensitivity as it is of factor-price equalization. The former is a one-economy comparative static result, while the second seeks to make a multi-country comparison, requiring both strong assumptions about internationally common technology and global univalence to make the comparisons. Second, contrary to some of the assertions by both trade and labor economists, it does not seem to us that the choice between m ≤ n and m > n, as interpretive frameworks, should rest on whether or not the framework generates income distribution effects from immigration.37 Given the very weak evidence in favor such income distribution effects, that we will discuss below, this seems doubtful in any event. But it seems that, on any but fairly short-term interpretations of the concepts of commodity and factor, there are massively more commodities than factors, and in this case the logic of factor-price insensitivity holds quite straightforwardly.38 Note that we are not arguing that factor-price insensitivity actually obtains, but that, within the parameters that are commonly agreed in the basic labor and trade theoretic traditions, m ≤ n seems a more plausible assumption, from which factor-price insensitivity follows. We should generally expect adjustment at the output-mix margin to play a considerable role in responding to factor immigration. If the mechanism breaks down, it must be as a result of deviations from those elements of the basic model that are shared between trade and labor economists, and not on dimensionality. Thus, we now turn to several plausible sources of such deviation. 2.5. Immigration in m × n Economies with Nontraded and Intermediate Goods The most obvious place to start looking for deviations from the model developed in the previous section is nontraded goods. It is at least arguable that a substantial portion of any economy, and any OECD economy in particular, is nontraded.39 We begin, as in the previous section with a brief discussion of the effect of nontraded goods on factor-price insensitivity in 37 Trade economists like Thompson and Wooton seem to make this argument as the entering wedge of a political economy argument, while labor economists make the argument to shore up the foundations of their estimating framework. 38 See Bernstein and Weinstein (2002) for a recent development of the dimensionality argument, and its implications for tests of directions of trade predictions. 39 It has been suggested, for example, that the following sectors be considered nontraded: government services; retail trade; wholesale trade; personal household services; restaurant services; health services; and construction. While government services should probably be netted out of any empirical analysis as a non-market sector, the remainder would be a sizable share of any economy. ~ 20 ~ general, and then consider several specific versions that have been applied to the analysis of immigration. In generalizing the analysis of factor-price insensitivity to the case of nontraded goods, there are at least two important considerations, both related to dimensionality. In the pure generalization of the comparative static analysis, we retain the assumption that factors are not immobile internationally and treat immigration as a comparative static increase in the endowment of some factor. In that case, we want to know whether the dimensionality of the wi model affects conclusions with respect to the sign of . However, when we turn to nontraded zk goods, it would seem to be incumbent upon us to be more explicit about factor mobility as well as good mobility. Here we will want to note some results that treat the appropriate generalization in terms of numbers of things (goods and factors) that are traded versus number of things that are not. Suppose that there are nT traded goods and nN nontraded goods, so n = nT + nN. We start by noting that as long as m ≤ nT the analysis of the previous section is essentially unchanged (Woodland, 1982; section 8.2.6.). That is, as long as there are at least as many traded goods as factors, factor-price insensitivity will continue to obtain, under the same restrictions, and for the same reason, as for the case without nontraded goods.40 Note the implication that, from factorprice insensitivity and cost minimization by nontraded good producers, nontraded commodity prices are determined by supply condition alone.41 As above, if m > nT endowment shocks will generally have an effect on wages, but this is not so much a consequence of nontraded goods as it is of the dimensionality of the model. Now suppose, instead, that there are mT traded factors and mN nontraded factors, so that m = mT + mN. Ethier and Svensson (1986 pg. 28) give as a condition for factor-price insensitivity that n + mT ≥ m.42 That is, the total number of international markets (for goods and internationally mobile factors) must be at least as great as the number of factors. Even reducing this condition to nT + mT ≥ m, it seems to us that this condition is likely to hold, but it also strikes us that this is a considerably more uncertain proposition than that n ≥ m. Thus, it is probably not surprising that a number of studies emphasize the role of non-traded goods. Before turning to a brief consideration of these, we again note that the essential thing here is not nontraded-ness, but dimensionality and market integration. 40 Deardorff and Courant (1990) raise the question of the effect of nontraded goods on the size of the cone of diversification, concluding that nontraded goods tend to reduce the size (though, of course, not the dimensionality) of the cone. In the context of factor-price insensitivity, this suggests that nontraded goods narrow the range of endowment shocks that are consistent with factor-price insensitivity, but does not undermine the basic logic. That is, as long as the same traded commodities are produced before and after the endowment shock, the ∂wi /∂zk will be zero. Factor-price insensitivity will hold. 41 This follows from Pj c j aij wi , j J , including the nontraded goods. Since the aij are functions of w, iI which is unchanged, cj is unchanged, and, thus, prices of nontraded goods are fixed. 42 Note that this condition can also be stated as n ≥ m - mT = mN, or when nT < n to nT ≥ mN. That is, the number of traded goods must be at least as large as the number of nontraded factors, which is the essential condition we have been noting throughout this section. ~ 21 ~ [Figure 5 about here] One approach to generating wage effects from endowment changes is to assume that m = n, but nN ≠ 0, ensuring that m > nT. Rivera-Batiz (1982) develops a 2-factor × 2-good model with one traded good and one nontraded good. The traded good price is locked in by the small country assumption, but the nontraded good price is determined by the interaction of supply and demand conditions in that market. Consider a setup like that in figure 5, with good 1 skilled-labor intensive and good-2 unskilled labor intensive, but now suppose that only good 1 is internationally traded. Once again, we suppose that there is an increase in unskilled labor. Following the logic of the Rybczynski theorem, as illustrated in figure 5, at fixed commodity prices, output of the traded good (1) will fall and output of the nontraded good will expand. Now, however, while the price of the traded good is fixed, the excess supply of the nontraded good at initial prices leads to a fall in its price. This will cause the unit value isoquant for good 2 to shift outward and a new factor-market equilibrium will be established at a lower wL and a higher wS. This dependence of factor-return on endowment makes this model a popular framework for the analysis of migration.43 It is useful to note, however, that if the world actually looks like figure 5, treating it like figure 1 for simulation purposes will produce an overestimate of the labor market effect because it will not be taking into account the adjustments in both demand and production that go into the determination of the final equilibrium here.44 Kuhn and Wooton (1991) develop an extension of this model to the 3-factor × 3-good case, with one non-traded good. Let good 1 be the exportable, good 3 the importable, and good 2 the nontraded good. Furthermore, we number factors so that, relative to the two traded good prices, good 1 uses factor 1 intensively, good 2 uses factor 2 intensively, and factor 3 is a middle factor. That is, we have the relationship given in (24). The analysis generates results that are very much like those of Ruffin (1981), referred to above: an increase in the endowment of any factor 43 Bond (1993a) presents an alternative approach, emphasizing cone conditions; Kondoh (1999) extends the RiveraBatiz analysis to consider demand effects based on duration of migrant stay; while Hatzipanayotou (1994) studies the interaction between various types of policy and immigration. This model has been used, in particular, to study welfare effects of migration in a two-country system, with a sending and a receiving country, e.g.: Krauss (1976); Rivera-Batiz (1983); and Rübel (1994). Interesting generalizations to higher dimensions can be found in Neary (1989) and Bond (1993b). 44 The magnitudes of the new factor wages will depend on both production and demand conditions, but the direction of the changes can be signed unambiguously. For example, in Jones‘ ζ-λ notation, Rivera-Batiz gives the effect on the return to L as: wˆ ST Lˆ SN Lˆ and wˆ L PˆN , D S D S where the ζij denote factor distributive shares and the λij are shares of the endowment of factor i in use in sector j; the hats denote proportional changes, ζS is the elasticity of substitution between goods 1 and 2 along the transformation curve, and ζD is the elasticity of substitution in consumption between good 1 and 2. Since, ζS and ζD are both positive, and the determinants │λ│ and │ζ│ have the same sign, and the traded good price is unchanged, these imply a fall in the real wage of L. The equivalent expressions for wS show a real increase. ~ 22 ~ reduces the return to that factor; the middle factor is a friend to both extreme factors; and both extreme factors are enemies to each other.45 The authors then use US data for 1960, 1970, 1980, and 1984 to construct the vectors z = {L,S,K} and y = {exports, imports, nontraded}, concluding that in nearly every case: skilled labor is the extreme factor in exports; unskilled labor is the extreme factor in imports; and capital is the middle factor (and used intensively in nontraded goods). Thus, given the model structure, the implication is that an increase in the endowment of unskilled labor, via immigration, will tend to reduce the wages of both types of labor and raise the return to capital. The fact that, at this level of aggregation, there is very little evidence of this pattern of effects, might suggest that the dimensionality assumption ensuring such effects are not a part of the world we observe. In closing this section we briefly note that neither the existence of intermediate goods nor of joint production undermines the general logic of factor-price insensitivity. This has been known since the pioneering analysis of McKenzie (1955).46 Thus, factor-price insensitivity is a surprisingly robust property of neoclassical/competitive trade models under a variety of assumptions about the production side of the model. 3. Core Empirical Results Based on Standard Models The preceding section considered two main comparative static questions: the effect of endowment changes on output; and the effect of endowment changes on factor wages. Perhaps not surprisingly, the second question has attracted by far the majority of systematic research with specific reference to the migration of labor. Nonetheless, there has been some research seeking to estimate Rybczynski effects. While most of this research did not specifically consider migration, because the causal factors are so closely related, following a review of the literature on labor market effects of immigration, this section turns to a brief discussion of empirical research on the Rybczynski theorem. In turning to the relevant empirical research, it is important to recall that the general analytical framework in (12), or (12), has two common interpretations as a way of organizing or interpreting empirical analysis. On the one hand, the referent of the analysis can be a single country (or some other discrete economic unit), observed before and after a comparative static shock. Alternatively, the referents can be two (or more) countries, differing only in the comparative static shock. We have already seen this distinction in the discussion of factor-price insensitivity versus factor-price equalization. There we noted that the auxiliary assumptions supporting empirical interpretation (specifically, identical technological opportunities before and after the shock) are more plausible across relatively short periods of time (for FPI) than across This result relies on a pair of ―normality‖ conditions–one a restriction on demand and the other on supply. See Woodland (1982; chapter 5) for an exceptionally clear development of these issues. Chang, Ethier, and Kemp (1980) is also very useful on the issue of joint production. Recently, there has been some discussion of the effect of joint production on the likelihood of factor-price equalization paralleling that discussed in note 65. See, in particular: Samuelson (1992); Jones (1992b); and Albert and Kohler (1995). 45 46 ~ 23 ~ countries (for FPE), and that this difference helps explain the greater skepticism as to the empirical content of FPE relative to that of FPI. In the next sub-section, we consider empirical work on the dw/dz comparative static. In the context of immigration, it makes sense to focus on the dw/dz comparative static in the national context, but it should be noted that testing for FPE is formally the same question. Then we turn briefly to empirical work on the dy/dz comparative static. In the one country case, for the HOS model, this is the usual interpretation of the Rybczynski theorem. However, the empirical literature has also considered cross-country analyses of the relationship between the endowment vector and the structure of output that is formally identical. 3.1. Empirics of Immigration and Wages In this section of the paper we discuss some of the major findings about immigration and labor markets that have been uncovered in recent research by labor economists. Our primary focus here is on the contribution of immigration to the growing inequality experienced in many OECD countries during the 1980s, and the implications of that experience for future policy. In this section we consider in some detail empirical research by labor economists on the link between immigration and labor market outcomes (primarily wages). Contemporary empirical research on the labor market effects of immigration has grown quite large since its development in the early 1980s. We will divide this research into 2 broad categories: production function based studies; and cross-sectional wage/unemployment. As we noted in the introduction, the most striking result from that research is how small the measurable effects are of what is a fairly sizable labor market shock. As we note in the preceding section, whether or not the implementation takes a structural form, the structure that drives both the econometric specification and the intuition for interpreting that analysis is generally a one-sector, perfectly competitive model. The labor economists‘ standard approach to wage inequality and income distribution is firmly rooted to an analysis of ―SDI‖ or ―supply, demand and institutions‖ (Freeman, 1993, pp. 444-449). To evaluate the labor market effects of immigration, identifying how the immigration of workers with differing skills affects the relative supply of labor can be viewed as necessary first step. In turn, the skill group characteristics of new immigrants are affected by the returns to skill as well as the distribution of earnings in both the source and host countries. Finally, labor market institutions are important because they affect the degree of wage inequality, the structure of wages and the labor market response to shocks. We place some of the latter considerations on the back burner for now and start by outlining a template competitive labor market model. In this section we sketch this framework in a bit more detail. Before proceeding with this discussion we comment briefly on what may be the best known gross distinction used to characterize this literature: area studies versus factor content studies (Borjas et al., 1997). The problem is that the label is misleading. We have already noted, in our discussion of figure 1, that virtually all labor theoretic frameworks apply a factor content based ~ 24 ~ approach–i.e. it is change in relative supply that generates the change in labor market outcomes. The issue is actually about level of analysis. That is: how large must the geographic unit (i.e. area) be such that observations on supplies and prices of various classes of labor are independent? As we shall see, there are good reasons for believing that geographic units like standard metropolitan statistical areas (SMSAs) or states are linked in ways that are inconsistent with cross-sectional observations being independent draws from some distribution, but it is not at all clear that the statistically optimal level of analysis is the nation. There is considerable evidence that national borders have economic effects, but, by the same token, there is also considerable evidence that quite local labor markets take significant periods of time to fully adjust to macro shocks.47 On balance, it is not clear to us that there is a good reason to prefer one level of analysis to another. Level of analysis is always an important research decision, but this does not strike us as an essential distinguishing aspect in this body of research. In addition to the issue of the appropriate level of analysis (local v. national), another essential research question is the manner in which the common theoretical framework structures the research. We can thus make another broad distinction between structural (or ―production function‖) methods and regression based methods. We start with the former for the case of local labor market data. 3.1.1. Production Function Based Methods The most direct implementation of the framework considered in the previous section, and the first to be developed in the current wave of research on the labor market effects of immigration, involves selecting a specific functional form for the production function given in equation (1), estimating that function on cross-sectional data, and testing hypotheses on the degree of substitutability or complementarity between inputs.48 In addition, elasticities of derived demand can then be used to carry out policy experiments—i.e. simulations. Recalling that our aggregate production function is y = f(z), z = {z1, ..., zm}, we seek to calculate the Hicksian partial elasticities of complementarity between any two of the inputs i and k as: ik f fik , i, k I , fi f k (14) 47 See Helliwell (1998) for a useful overview and extension of research on the economic effects of national borders. On local labor markets see Topel (1986), Blanchard and Katz (1992); and Bound and Holzer (2000). White and Mueser (1988) provide a very interesting discussion of the implications of level of analysis for studies of domestic migration. 48 Production functions can also be estimated using time series data, but in that case one must be concerned with technological change, certainly a concern in the apparently technologically dynamic 1980s. The equivalent assumption, that all regions within the same country have access to the same technology set seems considerably less demanding. ~ 25 ~ where we have used subscripts to denote partial derivatives. Following Hicks (1970; see also Sato and Koizumi, 1973), i and k are called q-complements if ςik > 0 and q-substitutes if ςik < 0.49 Because it is easier to interpret the quantity elasticities of inverse input demand, ik ln wi , ln zk (15) these are usually calculated using the relationship: ik ik k , (16) where, again, ζk is the distributive share of input k. In carrying out work of this sort, investigators must select a functional form that does not prejudice the conclusion from the start. In particular, we would like the data to determine the values of the elasticities defined in (14) and (16). Thus, the commonly used Cobb-Douglas and CES forms will be inappropriate for any input vector with more than two arguments. As a result, investigators have generally used one or another of the flexible functional forms.50 In addition to selecting a specific functional form, the other major choice in this body of research involves the definition of the input vector. Broadly speaking, there are two approaches here: one defines the input vector in terms of observable characteristics (e.g. gender, age, immigrant status, etc.); while the other seeks to identify production relevant characteristics (e.g. quantity of human capital). In the first paper using this approach, Jean Baldwin Grossman (1982) used crosssectional data for 1970 to estimate a translog function of native workers, first generation immigrants, second generation immigrants, and capital.51 She finds that both first and second 49 A pair of inputs (zi, zk) are q-complements if an increase in the endowment of k causes an increase in the wage of i; they are q-substitutes if the increase in zk produces a fall in wi. Hamermesh (1993) provides a clear discussion of these concepts. 50 A functional form is flexible if it can approximate any arbitrary, twice continuously differentiable function in the sense that its parameters can be chosen such that its value, gradient, and Hessian equal the corresponding magnitudes for the arbitrary function at a given point. Lau (1986) provides an excellent discussion of the issues that arise in choosing functional forms for empirical analysis. Chambers (1988, Chapter 5) is a somewhat more elementary discussion, with a strong emphasis on application. 51 T he translog function is: ln y ln f z 0 i ln zi 12 ik ln zi ln zk . iI iI kI our assumptions on the technology yield restrictions: βik = βki (Young‘s theorem); and iI ik iI i 1 and ik 0 (constant returns to scale). This yields a set of distributive share equations: kI i y i ik ln zk i , i I , zi kI ~ 26 ~ generation immigrants substitute for native labor, but that second generation immigrants are much closer substitutes for natives, and that new immigrants are closer substitutes for second generation immigrants than for natives. In addition, Grossman finds that capital is complementary with each type of labor, but that this complementarity is strongest with firstgeneration immigrants and weakest with natives. Grossman‘s analysis concludes with a policy simulation using the relationship in equation (16) to calculate own- and cross- elasticities to study the effect of a 10% increase in the number of legal immigrants in the labor force on a short-run equilibrium in which native wages are fixed (and thus adjustment occurs on the employment martin) and a long-run in which all wages are flexible. In the short-run, native employment falls by 0.8%, second generation wages fall by 0.06%, first-generation wages fall by 2.2%, and the return to capital rises by 0.2%. In the long-run, wages are flexible, so all markets clear: native wages fall by 1%, second generation immigrant wages fall by 0.8%, first-generation immigrant wages fall by 2.3%, and the return to capital rises by 4.2%.52 In an important series of papers, Borjas (1983; 1986b; a; 1987) uses a number of data sets from the 1980s to study different disaggregations of labor in the context of a generalized Leontief production function.53 Depending on the particular breakdown of labor (e.g. by gender, that can be estimated using Zellner‘s seemingly unrelated regression technique, to take the correlation among the νi into account, to generate values for the function‘s parameters. From these, one can calculate the Hicksian elasticities of complementarity, equation (15), as: ii ii i2 i i and ik ik i k . i k 52 In related studies, Bürgenmeier, Butare, and Favarger (1991) and estimate a translog function of immigrant labor, native labor, and capital using Swiss time series data from 1950-1986. In addition to finding qualitatively similar results on the pattern of complementarity between factors, the Swiss study finds evidence of a positive relationship between immigration and capital accumulation. Akbari and DeVoretz (1992) estimate a translog function on an industrial cross-section based on Canadian data for 1980. At the economy-wide level, the Canadian study finds no significant effect of immigrants–i.e. all Hicksian elasticities of complementarity between immigrants and natives are insignificantly different from zero. However, when the sample is restricted to labor intensive industries only, the Canadian study does find evidence of labor displacement as a result of immigration. 53 The generalized Leontief production function is defined as: y f z ik zi zk 2 , 1 iI kI where, as with the translog function, Young‘s theorem requires γik = γki, while concavity requires γik ≥0 for i ≠ k. As Borjas points out, the generalized Leontief production function leads to linear-in-parameters wage equations, rather than the linear share equations derived from the translog production function. Thus, Borjas estimates 1 z wi ik k , kI zi ~ 27 ~ 2 race, and immigration status), immigrants tend to be complements to some native labor and substitutes to others, though in all cases these effects are small–except for the effects of immigrants on other immigrants of the same type, for whom the effects can be sizeable and negative. Given Borjas‘ more recent position as a leading opponent of immigration and searcher for large effects, it may be worthwhile to quote his own summary of this, and other, work circa 1990: the methodological arsenal of modern econometrics cannot detect a single shred of evidence that immigrants have a sizable adverse impact on the earnings and employment opportunities of natives in the United States. (Borjas, 1990, pg. 81). In particular, Borjas fairly consistently finds that, while immigrants may be substitutes for white native born men, and thus increased immigration may have had a small negative effect on their labor market outcomes, immigrants are found to be complements to black native born men who, thus, may have gained from increased immigration. This approach is also used to examine the effects of legal Mexican immigration on labor market outcomes of Hispanic natives (King et al., 1986) and illegal Mexican immigration on a wide variety of labor groups (Bean et al., 1988) with essentially the same results: the first study finds evidence of complementarity, suggesting that Mexican immigration may have a positive effect on the wages of native born Hispanics; and the second study finds effects of legal immigration like those in Borjas, and finds that illegal immigration may have a small negative effect on white, non-Hispanic workers, but essentially no effect on native Hispanic workers. The production function approach receives its most sophisticated treatment to date in a series of papers by Michael Greenwood and Gary Hunt with a variety of colleagues. In Greenwood and Hunt (1995), the authors are interested in examining a variety of adjustment channels beyond change in wage. For input demands, they estimate a translog cost function on SMSA level data for 1970, and find immigrant labor to be a substitute for domestic labor.54 In addition, they estimate labor supply functions and aggregated output demand functions for the on individual level data, sorted by SMSA, usually with a variety of controls. Borjas estimates these labor demands using both OLS and a two-stage least squares procedure to control for endogeneity of labor supply, though the latter generally has little impact on the results. 54 The translog cost function is: ln C w; y i 0 ln wi ik ln wi ln wk ln y, iI iI kI with βik = βki, and the share equations are, from Shephard‘s lemma, i i 0 ik ln wk i , i I . kI The elements of the z vector are domestic labor, immigrant labor, and capital. ~ 28 ~ local markets. With these results they construct a large number of simulations permitting adjustment via flexibility in native labor supply (via both variable participation rates and internal migration) and changes in demand for final output, as well as adjustment along a given isoquant as in the previous studies. As with the previous studies, the wage, and now labor force participation, effects of immigration are uniformly small and, perhaps not surprisingly the magnitude of effects generally fall with the opening of additional channels of adjustment. The final output demand channel in particular seems to have a consistent effect of reducing the wage effects of immigration (or even making the effects on natives positive). These results can be seen to be closely related to our claim that, with multiple sectors the existence of adjustment at the output mix margin will generally lead to smaller effects. By the mid- and late-1980s, researchers working in applied production analysis had begun to recognize that standard flexible functional forms (including both the translog and generalized Leontief forms) could fail to satisfy concavity, but that flexibility may be destroyed if concavity is imposed globally (Diewert and Wales, 1987). Greenwood, Hunt, and Kohli (1996) begin their analysis by pointing out that virtually all of the studies we have reviewed to this point present results indicating the presence of failures of concavity, in addition they estimate CES, translog, and generalized Leontief cost functions on a common data set to illustrate violations. As a result, they conduct their analysis using the symmetric normalized quadratic form, developed by Diewert and Wales (1987), that permits curvature conditions to be imposed globally without endangering flexibility.55 The authors calculate the Hicksian elasticities of complementarity and find that native labor and immigrants are q-substitutes, while all other input pairs are q-complements. Thus, an increase in immigrants would lower the wage of native workers, and raise the wage of non-recent immigrants and capital, but these effects are quite small. For example, a 10% increase in the supply of recent immigrants would reduce the wage of native-born labor by 0.96%. The effect of this change on other recent immigrants, however, is quite large. Parasnis (2010) uses this form for the analysis of Australian data, reporting a complementary relationship between immigrant and native labor. The research that we have considered to this point focused on immigration status, among other things, as a production-relevant fact. Rivera-Batiz, Sechzer, and Gang (Rivera-Batiz and Sechzer, 1991; Gang and Rivera-Batiz, 1994), however, argue that there is no particular reason 55 The symmetric normalized quadratic functional form of the unit cost function is: c w 1 2 w w b w , w iI where βik = βki, and kI ik 0, βi ≥ 0 and iI i ik iI k I i i i k iI i i 1. Diewert and Wales (1987) provide a method for imposing global concavity and show that it does not undermine flexibility. The elements of the z vector in Greenwood, Hunt, and Kohli (1996) are native labor, recent immigrant labor, non-recent immigrant labor, and capital. ~ 29 ~ to believe that immigrant status, or race or gender, is directly production relevant. They prefer, instead, to assume that individuals with identical bundles of production relevant traits will receive the same wage. As a result their strategy involves estimating a translog production function of education, experience, and unskilled labor to derive the relevant Hicksian elasticities, and then using data on the skill composition of immigrants versus natives to derive distributional effects. Like Borjas and Bean et al., they use individual data sorted into local market areas to estimate, like Grossman, a translog production function, and then use equation (14) to get the Hicksian elasticities of complementarity, and (16) to get the relevant factor demand elasticities. In the first stage they find, for both US and European data, that own supply elasticities are negative, as expected, and that the cross-elasticities imply that unskilled labor, education, and skill are all complements for one another (i.e. ςik > 0 for i ≠ k). In addition, own elasticities are all estimated to be considerably larger than cross-elasticities. The authors then construct skill inventories of immigrant and native groups and use those, along with the estimated elasticities, to compute composite elasticities of complementarity that summarize this information. As with other work that we have reported, there are a variety of sign patterns, but ―the impact of all the immigrant groups on all the native-born groups are small in absolute magnitude‖ (Rivera-Batiz and Sechzer, 1991, pg. 106). The largest effect is that of Mexican immigrants on MexicanAmericans, where an increase in Mexican immigration of 10% will result in slightly less than an 1% fall in wages of Mexican-Americans (with a similar effect on native black labor). Similarly small results are found for the European case in Gang and Rivera-Batiz. Finally, Greenwood, Hunt, and Kohli (1997) mix the approaches of Grossman and Borjas with that of Rivera-Batiz by disaggregating native and immigrant labor into four skill categories each (based on earnings), as well as capital, and estimating a symmetric normalized quadratic cost function on a cross-section of SMSAs.56 Not surprisingly, given the number of factors, there is quite a variety of q-substitutability and -complementarity, but unskilled immigrants appear to be strong q-substitutes for low- and medium-skilled native labor, and q-complements for unskilled native labor. Once again, however, the authors are unable to find any evidence that unskilled immigration leads to large changes in the income distribution or in employment opportunities, with the exception of the effect on other unskilled immigrants. All of the preceding research considers essentially closed economies. A small number of papers develop analyses of immigration in the context of economies that are open to trade. For example, Wong (1988) works with an indirect trade utility function which is, itself, a function of 56 In a study of the impact of low-skilled migration from Mexico, Davies, Greenwood, Hunt, Kohli, and Tienda (1998) estimate a symmetric normalized quadratic production function in which the arguments are: low-skilled natives divided by gender and ethnicity (Mexican, non-Mexican); native high-skilled males and females (one category); foreign born, low-skilled Mexicans; foreign born, low-skilled non-Mexicans; and capital. As in the previous studies, the authors find that in both 1980 and 1990 immigrants has negative effects on the native born, but that these effects were small. The effects on other immigrants were found to be large. Furthermore, whatever might be the effects of trade and factor mobility within the US, the effects are larger in areas of high immigrant concentration. ~ 30 ~ the GNP function.57 This function is estimated, in translog form, on prices for home produced durable goods, home produced nondurable goods and services, and imported goods and services, and endowments of capital, land, and labor, for a number of years between 1948 and 1983. Foreign capital and labor are taken to be perfect substitutes for the domestic factors, so the comparative statics on the indirect utility function can be used to generate the relevant elasticities. These elasticities are all small. Kohli (1993; 1999; 2002) develops this sort of analysis in considerably greater detail. Specifically, using annual Swiss data from 1950-1986, Kohli (1999; 2002) estimates the translog cost function associated with the primal GNP function and a z vector containing capital, home labor, immigrant labor, and imports.58 Thus, where Wong treats home and immigrant labor as perfect substitutes, Kohli is able to test this relationship. In fact, Kohli finds that home and immigrant labor are both Allen-Uzawa and Hicks q- substitutes, though not perfect substitutes. Commodity imports and immigrant labor are found to be both Allen-Uzawa and Hicks q- complements.59 Once again, the magnitude of the estimated effect of immigration on native wages is negative, but quite small. However, Kohli simulates a short-run model in which the wage is downward inflexible, and finds the effect on home labor displacement to be large. Hijzen and Wright (2010) estimate a translog function with two types of domestic and immigrant labor, skilled and unskilled, along with capital and traded intermediates, and two types of output. Like a number of other production function based studies, Hijzen and Wright find that the largest effect of unskilled immigrants is on unskilled immigrants already in the labor force, and that is small. The impact on native unskilled workers is also negative, but even smaller. Skilled immigrants have little effect on the structure of factor payments at all. Overall, econometric research which explicitly exploits production theoretic structure, tends to find strong substitutability between immigrants and other immigrants of the same vintage and national origin and, otherwise, widely varying patterns of complementarity and substitutability between immigrants and natives (as measured by the Hicksian elasticity of complementarity). More importantly, the elasticities between immigrant and native labor are consistently small, and are smaller yet when other channels of adjustment than the wage are explicitly permitted in the analysis. That is, natives and immigrants are consistently found to be quite imperfect substitutes in production. 57 Letting p, z, and b be the parametric price vector, endowment vector, and trade balance, the indirect trade utility function is defined as: H p, z, b : max u y p y G p, z b V p; G p, z b , y where G() is a standard GNP function and V() is the indirect utility function of the representative consumer. 58 Kohli (1993) directly estimates a symmetric normalized quadratic GNP function on the same Swiss data. The results are broadly the same, increased immigration reduces home wage, but only weakly; and trade and immigration are found to be complements. 59 Interestingly, imports and capital are Allen-Uzawa substitutes, but Hicks q-complements. ~ 31 ~ 3.1.2. The Regression Based Approach to Estimating Wage Effects of Immigration60 While the production-theoretic framework directly implements the theory that forms the basis for much of the labor-theoretic research on the labor market effects of immigration, its requirements are demanding. To be set against the advantage of directly estimating cross elasticities of substitution is the reliance on functional form assumptions to identify the parameters of interest. As mentioned in the previous section, structural estimation of this sort invariably needs to tradeoff the requirements of functional form flexibility, or ease of estimation, and strict adherence to the restrictions implied by the theory. In addition, while human capital variables can relatively easily be accommodated in the production-theoretic framework, the incorporation of a wide range of standard control variables does not fit easily within this framework. Thus, as a result of the relative ease of application, greater similarity to existing techniques in labor econometrics and the desirability of including a richer set of controls, the majority of the research on the labor market effects of immigration has taken place within a regression framework. The latter approach generally involves reduced form regression analysis of the use of natural experiments to examine empirical regularities and determine ―causal‖ relationships. As above, we assume two types of labor, skilled (S) and unskilled (L), for simplicity.61 Within each skill class, domestic and immigrant labor is assumed to be equally productive. Other factors of production, such as physical capital, land and so on are left in the background by assuming a fixed price and applying a separability assumption. Following Altonji and Card (1991), we suppose that the economy produces one good according the production function Y = f(S, L).62 This good is consumed and is exchanged at fixed world prices for another consumption good.63 We will find it convenient to work with the total cost function: C wS , wL ; Y Yc wS , wL , (17) where c(•) is the unit cost function. We suppose that there are L unskilled workers and S skilled workers in the economy and define total labor force as Λ ≡ L + S. We define the per capita labor supply functions of skilled and unskilled workers, respectively, as: ls(ws) and lL(wL). Because, by Shephard‘s lemma, the c w , we can write the conditions for a local labor unit labor demand functions are ci w wi market equilibrium as: 60 There is a parallel literature applying regression analysis to unemployment. We focus on the wage results primarily because of the close link to the theory. We simply note here that the primary conclusions of this section– i.e. small to no effects, except on migrants of similar origin and vintage, and the least skilled native workers–holds as well for unemployment. 61 It should, however, be noted that this is not without loss of generality (Hamermesh, 1993, pp. 33-42). 62 As above, we take f() to be twice differentiable, linear homogeneous, and strictly quasi-concave. 63 As a result of the small country assumption, the foreign good will not enter our analysis explicitly, so we do not introduce any notation for it. The foreign good will be our numeraire. ~ 32 ~ SlS wS YcS w and LlL wL YcL w . (18) To focus on the impact of unskilled immigration, we will represent migration as an influx of unskilled workers into the economy. Let λL := L/Λ, the proportion of unskilled workers in the labor force. Totally differentiating (18), suppressing arguments, and using obvious notation, we have: Y Y L lLL dwL lL d L cLS dwS cLL dwL . 1 L lSS dwS lS d L cSS dwS cSL dwL (19) Defining εi as the elasticity of the labor supply and εik as the elasticity of labor demand for skill group i with respect to wage k, the equations (19) may be rewritten as: 1 L S lS c c Y dwS lS d L SS S dwS SL S dwL wS wS wL l c c Y L S L dwL lL d L LS L dwS LL L dwL . wL wS wL (20) Letting hats (i.e. xˆ dx / x ) denote proportional changes, and using equation (20) to simplify, we have: 1 L S wˆ S d L SS wˆ S SL wˆ L L L wˆ L d L LS wˆ S LL wˆ L (21) The labor demand elasticities are governed by the usual Hicksian formula, i.e., for given wage changes ik k ik , (22) where ζk is the distributive share of labor type k, ζik is the partial elasticity of substitution between labor types i and k, and ξ is the elasticity of final output demand with respect to its relative price p.64 Comparative statics on equations (21) are straightforward. For instance, when the demand for skilled labor is independent of the wage paid to unskilled labor (i.e. εSL = 0), we have 64 Recall that we have taken the importable as our numeraire, so p = P/P*, where the star denotes a foreign magnitude. ~ 33 ~ wˆ S 1 d 0 1 L S SS L (23) Similarly, when the demand for unskilled labor is independent of the wage paid to skilled labor (i.e. εLS = 0), we have wˆ L 1 d L 0. L L SS (24) Equations (23) and (24) are immediately instructive. As suggested in the extensive literature on the LeChatelier-Samuelson principle, the long-run impact on wages is likely to be far smaller than the short-run impacts. Similarly, it is easy to see that if factor-price equalization causes these elasticities to approach infinity, there will be no wage effects.65 Equations (23) and (24) can be used directly to derive implications for the correlation between wages and shares of immigrants in a local labor market (see e.g. Altonji and Card, 1991). An alternative approach to evaluating the empirical relationship between skilled and unskilled wages is to assume an explicit functional form for the technology and use equation (18) to develop an estimating equation. For illustrative purposes, suppose that Y is produced from skilled and unskilled labor according the following CES function: 1 Y A S zS L zL , (25) where ζSL = (1 - ρ)-1 ≥ 0. The parameter A indexes factor-neutral total factor productivity; and the ηi index biased technical change that increases the ―effective‖ quantity of the relevant input. The cost function associated with this production function is (Varian, 1992, pg. 56): 1 wL 1 Y wS C wS , wL ; Y A S L 1 . (26) Using Shephard‘s lemma and taking the ratio of the unit labor demand functions, we obtain the relative demand for labor within a sector or location as: 1 cL wS , wL S 1 wL 1 . cS wS , wL L wS Local labor market equilibrium requires that 65 This conclusion is insensitive to the assumption that εSL = εLS = 0. ~ 34 ~ (27) 1 L lL wS , wL 1 w 1 S L , 1 L lS wS , wL L wS (28) where the left hand side is the ratio of the supplies of unskilled to skilled labor. Solving for relative wages and taking natural logarithms gives a regression specification: L lL wS , wL w ln L ln L 1 ln . 1 L lS wS , wL wS S (29) Equation (29) provides a general framework for understanding the determinants of relative wages. It should be kept in mind that the relative wage changes for different skill groups are for within local or regional labor markets. The link to outside markets comes from specifying how they respond to changing wages (i.e. the εi). Equation (29) can then be used to examine the determinants of relative wages across different (and fully separate) labor markets. Borjas et al. (1997) constitutes a prominent example of this type of approach. What they term the ‗aggregate factor proportions approach‘ involves regressing the ratio of skilled wages to unskilled wages in year t, on the relative labor supply of the two types of labor. Borjas et al. (1997) find that immigration affected certain groups of workers more so than others. Specifically, immigration may have been responsible for the decline in the earnings of unskilled native workers that occurred during the 1980s. Their paper has contributed to the view that, relative to the effects of growing international trade with less developed countries, immigration may have had a proportionately larger negative impact on the earnings of unskilled U.S. workers. A qualitatively similar approach is used to derive estimating equations for regional unemployment or wages. For example, Altonji and Card (1991) and LaLonde and Topel (1991) estimate wage equations taking the form: wj j X X j j , (30) where j indexes the local labor market, w is the logarithm of the wage for a particular skill group, X is a vector of control variables and, as above λ is the proportion of immigrants in the jth local labor market. In contrast to the above study by Borjas, et al. (1997), these studies find scant evidence that recent waves of immigration have disadvantaged U.S. workers. To eliminate region-specific fixed effects, due to ethnic enclave effects, for example (see Bartel, 1989), the first-differenced version of equation (30) can also be estimated. More generally, if the immigrant share in market j is correlated with unobservable variables only through a time-invariant individual fixed effect, then estimating fixed effects regressions may be appropriate (e.g. see Altonji and Card, 1991; Topel, 1994a; b). LaLonde and Topel (1991) estimate both equation (30) and its differenced version and find that the estimates of the effect of ~ 35 ~ immigration produced by the two methods are nearly identical, i.e., the wage effects are negligible. Unfortunately, fixed effects estimation is not a cure all for most sample selectivity and endogeneity problems. In the case of immigration and wages, the very nature of sorting on unobservable variables suggests that the migration decision of individuals may involve a process of learning about what is their correct state (i.e., industry, occupation, location, etc.). We discuss the endogeneity and sample selection further below in connection with the instrumental variables and natural experimental approaches to the study of the impact of immigration. Of course, the regression specifications based on either equation (29) or (30) are quite general. For instance, there have been many studies using the regression framework that have focused on the importance of the large increase in the relative supply of workers during the 1970s to the increasing wage inequality that occurred throughout the later 1980s and early 1990s. The increase in the U.S. workforce caused by the labor force entry of the baby boomers easily dwarfs the increase in the labor force caused by immigration. Welch (1979), Berger (1985), Murphy, Plant and Welch (1988) and Murphy and Welch (1991) are among the better-known U.S. studies here. A common finding of these studies is that changes in cohort size associated with the Baby Boom generation did not have a significant impact on cohort earnings. Overall, supply-side changes in the United States were very quickly discounted as a candidate explanation for the increased dispersion in the income distribution in the United States during the 1980s. Notwithstanding, the preceding findings on the effects of domestic labor supply shocks do not necessarily imply that all supply-side ―shocks‖ are unimportant. In the current context, some authors claim that immigration may have been responsible for the decline in the earnings of unskilled native workers that occurred during the 1980s. The immigration issue has been increasingly seen as one of ―distribution‖ rather than ―efficiency‖ (see Lalonde and Topel, 1997). Freeman (Freeman, 1998, pg. 110) argues that immigration may have had substantially larger effects on native unskilled workers than increased international trade with low-income countries, for instance. During the 1980s, a period during which wage inequality rapidly increased in the United States, immigration raised the supply of high school dropouts by approximately 25 percent, which far exceeds the increase in the ―implicit labor supply‖ of such workers attributable to trade. Furthermore, Borjas et al. (1992; 1997) conclude that the large increase in the number of unskilled immigrants explains about one third of the decline in the relative wage of high school dropouts during the 1980s. For the United States, wage inequality increased most in the West where the largest inflow of less-skilled immigrants was experienced (Topel, 1994a; b). In principle, changes in cohort quality can be analyzed in the same way as changes in cohort size. Borjas (1994a) considers the declining cohort quality of recent waves of immigrants to the United States to have been the result of the shift in U.S. immigration policy, specifically ~ 36 ~ the passage of the 1965 Immigration Act. However, his findings of decreasing cohort quality have recently been questioned by Butcher and DiNardo (2002) who focus on changes in the wage distribution through time. Using the methodology developed by DiNardo et al. (1996), they investigate the counterfactual of what the wage distribution would have looked like for new immigrants if they had faced the wage distributions from different eras. They find that earlier immigrants would have had wages much more similar to today‘s new arrivals, if they had faced the present day prices for their skills.66 Race and ethnicity, and not the changing education levels of the new immigrants, explain much of the change in comparative economic fortunes of recent immigrants once wage structure changes have been held constant. The point, as also stressed by LaLonde and Topel (1991), is that recent cohorts of immigrants will look as if they do worse, even if they have the same set of characteristics as earlier cohorts of immigrants, if the distribution of wages has become more dispersed and if the new immigrants lie near the lower tail of the income distribution. The use of regressions to uncover the wage effects of immigration by regressing immigrant shares and other controls on wages or relative wages poses many familiar problems. Among the more prominent concerns with multiple linear regression analysis is the omission of important right-hand side variables. Biased estimates result if relevant characteristics or controls are not included in the regression equation. Similarly, how do various characteristics that are included in a model specification interact with one another? More generally, empirical work usually forces researchers to assume an appropriate functional form in order to reduce the problem at hand to one of estimating the parameters of interest. For example, would a linear function involve a serious mis-specification loss? As the previous section revealed, there is a wide range of functional forms from which to choose and so the robustness of parameter estimates is invariably an issue that needs to be confronted. Variable (mis-)measurement and interpretation also pose problems. For instance, when does a migrant finally assimilate and become a native? The latter problem is particularly obvious one in those countries that are essentially composed of older generations of immigrants (e.g., Australia and the United States).67 More formally, there is the issue of weak separability (see Berndt and Christensen, 1974) of the various types of labor – not just of skilled versus unskilled labor, but also of native workers versus immigrant workers as well as first generation migrants versus second and later generations of migrants. 66 Carrasco, et al. (2008) apply the same methodology to Spanish data, also finding only small effects of immigration on wages. With similar implications, albeit from a different perspective, Friedberg and Hunt (1995) note that ―composition problems‖ make it difficult to ascertain the impact of immigration on wage inequality. For example, they argue that including the newly arrived waves of less-skilled migrants in inequality calculations is likely to bias the conclusion towards finding greater inequality in the United States. 67 Zimmermann (1995) reminds readers of the literature that the European research on immigration has more to do with the effects of possessing citizenship. Unlike the U.S. literature, which has tended to focus on the effects of newly-arrived immigrants on native workers as well as on earlier generations of immigrants, the European data do not distinguish individuals as foreign-born or not. ~ 37 ~ One of the most important difficulties in the empirical immigration and labor market effects literature is the likely possibility that labor supply functions are not independent of wages. The problem is reminiscent of the difficulties faced by the labor economists who attempted to uncover the effects of trade liberalization on relative wages (see Gaston and Nelson, 2000). Economic commonsense suggests that the immigrant labor force share is endogenous. To make the endogeneity issue transparent, consider a simple 2-equation model: wj j X X j j j w w j R R j j , (31) where X and R are (exogenous) scalars and all variables are expressed in deviations from their means. As before, j indexes a local labor market. The sign of the OLS bias is given by: plim OLS 2 w2 2X 2 2 . 2 X w X 1 w (32) It is not possible to argue a priori that the sign of the bias is either positive or negative. For illustration, supposse 2X 2 0 and that γw > 0 (i.e. higher relative wages are associated with higher relative supply). If the ―true‖ effect of a higher migrant share of unskilled workers is to depress unskilled wages, i.e. γλ < 0, then the bias is positive. That is, a failure to account for endogeneity will bias upward (i.e. toward zero) estimates of the impact of immigrants on wages. However, note that if we are estimating some variant of equation (31) that, strictly speaking, our focus is on wage inequality. Furthermore, in many of the early studies in this literature, λ is simply taken to be the share of migrant labor in market j. Under this interpretation, it is no longer obvious that γw > 0. Models of immigrant worker self-selection, based on the pioneering work of Roy (1951), are extremely illuminating here. Workers with high earnings potential are likely to migrate from a country with an egalitarian wage structure (where they cannot easily make high earnings), while workers with low earnings potential are especially likely to migrate from a country with great wage inequality. In terms of source country characteristics, equality of the income distribution encourages what is termed ―positive selection bias‖.68 Negative selection bias results when source countries have unequal income distributions and therefore migrants are likely to be the least skilled.69 Recent waves to the United States tend to have been increasingly drawn from the latter group (Borjas, 68 In fact, a point often overlooked is that host country labor market conditions are absolutely central to the migration decision. For example, Hanson and Spilimbergo (1999) found that attempted illegal immigration from Mexico is extremely sensitive to changes in real wages in Mexico. 69 Interestingly, increasingly negative self selection produces labor market outcomes in both the source and host countries similar to the picture of the effects of outsourcing on wage inequality painted by Feenstra and Hanson (Feenstra, 1996; Feenstra and Hanson, 1997). That is, if workers emigrating from Mexico are relatively high skilled from Mexico‘s viewpoint and unskilled from the United States‘ viewpoint, then wage inequality tends to rise in both countries. ~ 38 ~ 1994a). Immigrants are mobile, but they have tended to cluster in cities where their fellow countrymen reside. The clustering effects tend to dominate such economic incentives as differences in unemployment rates or welfare benefits across areas (Bartel, 1989; Bartel and Koch, 1991). The effects of clustering are borne by the gateway cities, while the geographic concentration tends to reduce economic progress and the rate of assimilation. Of importance for the present discussion is that, given that the primary adverse wage impact of new immigrants is upon previous generations of migrants, the clustering effect may imply γw < 0. If the effect of clustering is sufficiently strong, then it is possible that OLS estimates are biassed downwards, and not upwards.70 Friedberg‘s (2001) findings are consistent with this line of argument. She studies the impact of Russian migration on occupational wages in Israel and finds that IV estimates are higher than OLS estimates. That is, rather than immigrants choosing occupations based on them offering higher wages, she finds evidence of occupational immobility (so that γw < 0). That is, immigrants, irrespective of their skill levels are confined, initially at least, to lowpaying occupations. Hence, OLS estimates overstate the impact of immigrants on wages. Handling the endogeneity problem is the motivation for the use of the instrumental variables (IV) approach (e.g. Altonji and Card, 1991; Friedberg, 2001) and the quasiexperimental approach in the labor literature (e.g. Card, 1990; Hunt, 1992). Altonji and Card (1991) investigate the impact of immigrants on low-skilled native workers. They relate changes in the earnings and employment of low-skilled natives across cities to changes in the migrant population. As discussed, the problem is that the immigrant flows are likely to be correlated with current labor market conditions. Hence, Altonji and Card instrument the change in immigrants with the size of the immigrant enclave in an earlier period. They argue that the size of the immigrant enclave in the past is likely to affect immigrant flows but is not necessarily correlated with current demand shocks. In other words, the IV approach attempts to use only the variation in immigrant flows associated with variation in enclave ―pull‖ and not that associated with current demand shocks. Interestingly, Altonji and Card‘s estimate of γλ is one of the most negative. Notwithstanding, they conclude that immigrants and natives face little competition from one another. They find that there is some industry displacement from low-wage immigrant intensive industries; but still, the implied elasticities are small.71 Despite these mobility effects, the effects on employment and unemployment rates are virtually zero. Due to the substantial difficulties associated with choosing ―good‖ instruments (see e.g. Nelson and Startz, 1990; Bound et al., 1995), considerably more weight in this branch of the literature has been attached to the results of the quasi- or natural experiments. Natural Friedberg and Hunt (1995) make a related criticism of Goldin‘s (1994) findings. Using data for 1890 to 1923, Goldin found a significant negative correlation between the percentage of foreign-born residents and wages in U.S. cities. However, this may be a ‗composition‘ effect, i.e., if immigrants earn lower wages that natives, then even if immigrants have no effect on native wages, they tend to be clustered into cities with lower average wages. 71 Friedberg and Hunt (1995) note that Altonji and Card‘s ―large and negative‖ estimates imply that a 10 percent increase in the percentage of foreign-born in a local labor market implies a minuscule 0.86 percent reduction in wages. 70 ~ 39 ~ experiments occur when exogenous variation in independent (explanatory) variables (that determine ―treatment assignment‖) is created by either abrupt exogenous shocks to labor markets (Meyer, 1995). For example, natural experiments can arise due to institutional peculiarities (e.g., Vietnam-era draft lotteries) or due to exogenous policy changes that affect some groups but not other groups (e.g., changes in policies in some states but not others).72 In the latter case, Hanson and Spilimbergo (2001) examine how enforcement of the U.S.-Mexico border is affected by changes in illegal immigration. They find that the equilibrium level of border enforcement varies inversely with relative demand shocks (and consequently, demand for undocumented labor). In other words, the authorities relax border enforcement when the demand for undocumented workers is high. Natural experiments are most useful in situations in which econometric estimates are ordinarily biassed because of endogenous variables due to omitted variables or to sample selection. The basic approach involves a comparison of changes for ―treatment‖ and ―control‖ groups (i.e., differences-in-differences). This can be accomplished in a components of variance scheme (time effects, location effects, treatment group effects, interaction terms and so on) or by using an IV approach in which one instruments for the treatment dummy variable with the natural experiment indicator variables. In this sense, the IV and natural experimental approaches are qualitatively equivalent. With IV, legitimate instruments generate a natural experiment that assigns treatment in a manner independent of the unobserved covariates. The advantage is that the source of the identifying information is transparent. To illustrate the basic approach, consider the following example based on Meyer (1995). Suppose that we have: w js Ds js , (33) where wjs is the wage in local labor market j (e.g. city). The ―treatment‖ dummy is Ds, which may be thought of as measuring migration intensity above some critical threshold in market j. That is, if λj ≥ λ* then Ds = 1, and 0 otherwise. Also, an important assumption is that E(εjs│Ds = 0) = E(εjs│Ds = 1) or E(εjs│Ds) = 0. Equation (33) simply involves comparing wages in cities that have high migrant populations to those that do not. An unbiased estimate of β is obtained by differencing, i.e., b w1 w0 , (34) where overscores denote group means. Under typical assumptions, α would be consistently estimated as the group size goes to infinity. Of course, we could also simply estimate α from the regression equation (33). Note that the researcher needs strong evidence that the two types of labor markets would have been comparable, but for the arrival of foreign-born residents. Hamermesh (2000) argues that, unlike ―acts of God‖, treating changes in the legal environment as exogenous is rarely convincing. 72 ~ 40 ~ Occasionally, data are available for the time period before and after a ―treatment‖ (in our case, the treatment is an immigration shock) for a group that does not receive the treatment but experiences some or all of the other influences that affect the treatment group. At the very heart of the quasi-experimental approach to the immigration and labor market literature are the nonpolicy and non-institutional shocks that can be considered truly exogenous to existing labor market conditions in the destination country (e.g., Baby Boom, Black Death, Mariel Boatlift). That is, consider: w jst Ds Dt Dst jst , (35) where Dt can be thought of as a time period dummy, Ds is defined as above, and Dst = 1 if Dt = Ds = 1, and 0 otherwise. The key idea is that η summarises the way in which both treatment and non-treatment groups are influenced by time (e.g. such things as macroeconomic conditions and regional growth trends). The time-invariant difference in overall means between the groups is captured by β. Dst indicates membership of the experimental group after it receives the treatment and γ is the true causal effect of the treatment on the outcome for this group. Again, the key identifying assumption is that E(εjst│Dst) = 0. Note that γ would be 0 in the absence of the treatment (i.e. the immigration shock). An unbiased estimate of γ can be obtained by the differences-in-differences estimator, i.e.: g w11 w01 w10 w00 , (36) where the first subscript is t and the second is for treatment s. Without question, the most cited natural experimental paper is Card (1990) which examines the impact of the Mariel Boatlift on Miami‘s labor market. In his paper, the first bracketed term in equation (36) represents the difference in wages for black workers in Miami before and after the Boatlift.73 The second bracketed term is the wage difference for the same types of workers in a group of four comparison cities. The latter cites were chosen because they had relatively large populations of black and Hispanic workers and because they exhibited patterns of economic growth similar to those observed in Miami over the late 1970s and early 1980s. As is well known, despite the dramatic and sudden 7 percent increase in the size of Miami‘s work force, Card is unable to detect any adverse impact on the wages or unemployment of less-skilled workers.74 There are two notable quasi-experimental studies for Europe. Hunt (1992) examines the impact on wage differentials in France in 1968 of the influx of pied noirs from Algeria during the early 1960s; and Carrington and de Lima (1996) study the return of Portuguese colonialists 73 Card conducts a similar analysis for Hispanic workers, as well. Also, in addition to wages he uses the same methodology to examine whether the Boatlift had any effect on the unemployment rates of less-skilled workers. 74 This is an interesting and important finding, but Card‘s analysis does not tell us how the labor shock was absorbed. Interestingly, there is little support for Rybczynski effects (Lewis, 2008). Later work has suggested that demand effects (Saiz, 2003; Bodvarsson et al., 2008) and/or technological response (Lewis, 2008) may help. ~ 41 ~ from Africa and examine the wage effects across the provinces of Portugal. Consistent with Card‘s findings, these authors were unable to discern adverse wage effects for native workers. Recently, Lemnos and Portes (2008) use the labor market shock associated with the Eastern Enlargement of the EU to examine the effects on local labor markets, finding little evidence of wage effects. Similarly, Glitz (2006) uses the large migration associated with reunification of Germany to examine the labor market effects of migration. While he finds no evidence of wage effects, he does find that immigration increases unemployment. This is consistent with other findings, using different methods, that immigration in the context of labor market inflexibility can result in unemployment (e.g. Angrist and Kugler, 2003; D'Amuri et al., 2010). Finally, a pair of recent papers have used unexpected immigration shocks due to major hurricanes to examine the effect of migration shocks on local labor markets (Kugler and Yuksel, 2008; McIntosh, 2008). Both find statistically significant, but modest, effects of these shocks. Although subject to varying interpretations, the finding of small local labor market effects has been remarkably robust and in line with the findings from the econometric studies. LaLonde and Topel (1991) estimate the elasticities of complementarity between immigrants and natives and between new immigrants and older cohorts of immigrants and find both to be very small. Taken in conjunction with their analysis of wages and earnings changes in local labor markets, they conclude that the wage effects of immigration are ―quantitatively unimportant‖. Based on studies currently in print at the time that we are writing this paper, it appears to us, that such a conclusion is inevitable. One would expect that in the face of such a huge mountain of evidence that this would be the end of the story. Of course, even the briefest excursion through the recent literature reveals that the debate is far from having run its course. The attention of those intent on identifying large native labor market impacts of immigration has turned to explaining what the small statistical effect ―really means‖. One potential problem is the possibility that immigrants locate to areas where jobs are expanding anyway.75 Given the continuing significance of a small number of immigrant gateway cities (consistent with the major role played by networks in channeling immigration), it is not surprising that there is little evidence supporting this conjecture (Bartel, 1989; Bartel and Koch, 1991; Frey and Liaw, 1998; Gurak and Kritz, 2000). A potentially more serious problem is that the internal migration by natives offsets the increased supply of immigrants (Filer, 1992; Borjas, 1994a; Frey, 1995; Borjas, Freeman and Katz, 1997; Frey and Liaw, 1998; Hatton and Tani, 2005). Consider the case of the Mariel boatlift: natives that were considering moving to Miami might now foresee lower wages as a result of the increased labor force (or even decide to avoid Miami for racist or other social reasons); they will now try to identify a similar city as their new migration target; but those cities are likely to be 75 Once again, the issue is the econometric one of handling the possibility of endogeneity. If immigrants choose their destination locations or occupations based on wage growth and the growth of job opportunities, rather on wage levels, then controlling for the endogeneity problem appropriately requires the use of panel data. ~ 42 ~ precisely the cities used by Card as ideal untreated units (i.e. similar on all dimensions to Miami, but not receiving the immigrant shock). The new native immigrants to those cities will have a similar effect on the labor markets there to the effect of the Marielitos on the Miami labor market, thus biasing the analysis toward a finding of no effect. David Card (2001; See also Kritz and Gurak, 2001) examined precisely this effect and found that the inter-city migration decisions of natives and older immigrants are largely unaffected by inflows of new immigrants. Moreover, Card and DiNardo (2000) find no evidence of selective out-migration by natives in response to immigrant inflows at particular locations.76 However, Borjas (2006) responded to this challenge by developing a simple model illustrating the causal connection between migration and wages, which also provides a framework for structuring his empirical work. Using census data from 1960-2000, Borjas presents evidence consistent with a large effect of foreign migration on internal migration, and of the internal migration on estimates of the wage effect of foreign migration. In response, Peri and Sparber (2008) show that Borjas‘ results are an artifact of the way the variables are constructed for the analysis, while Peri (2007) extended Borjas‘ methodology for a focus on immigration to California—finding no native migration response, imperfect substitutability of migrants for natives and an average wage gain for native workers. Finally, while Cortes (2008) finds evidence of some offsetting native migration in her study of the effect of immigration on prices of non-traded goods and services in local markets, she concludes that this effect is not sufficient to arbitrage away the effect of migrants on prices. Furthermore, it remains a puzzle that regional economies should adjust so quickly to immigrant shocks, but so slowly to most other shocks studied by regional and labor economists. At this point, there is sufficient evidence on both sides of this question that one would have to have very tight priors indeed to assert a clear opinion one way or the other on this question. One possibility, suggested by factor-price insensitivity, is that adjustment occurs on the output margin rather than on the wage margin. That is, the composition of output may change in response to an endowment shock, in such a way that factor-prices are unchanged. The evidence on this is mixed: as we discuss in the next section, there is evidence of the sorts of Rybczynski effects needed to support this adjustment mechanism, as well as some (weak) direct evidence directly related to immigration shocks. Specifically, Hanson and Slaughter (2002) document the rapid growth in apparel, textiles, food products and other labor-intensive industries in California after the arrival of Mexican migrants. They focus on state-specific endowment shocks and statespecific wage responses. They show that the state output-mix changes broadly match state endowment changes and that variation in state unit factor requirements is consistent with factor price equalisation across states. States absorb regional endowment shocks through mechanisms other than changes in regional relative factor price changes. This is consistent with the findings of Blanchard and Katz (1992) which indicate that wages and income per capita converge for American states. However, Blanchard and Katz also find that employment performance 76 Earlier studies also found no evidence of such effects in the US (Wright et al., 1997) and Germany (Pischke and Velling, 1997). ~ 43 ~ diverges, i.e., shocks to employment grow and persist.77 Overall, this is consistent with the view that small local labor market effects may be consistent with somewhat larger aggregate labor market effects. Other work suggests that technological change, either exogenous (Gandal et al., 2004) or endogenous (Lewis, 2005; Card and Lewis, 2007; Lewis, 2008), is a more likely candidate than Rybczynski effects. The broad conclusion from the first large NBER project on immigration and trade was that immigration had a relatively smaller area impact than increased import penetration on native labor. Overall, the labor market was thought to easily adjust to migrant inflows, absorbing immigrants with little redistributive losses to natives (see Abowd and Freeman, 1991). This conclusion was largely, and somewhat surprisingly, reversed by the second NBER project (Borjas and Freeman, 1992). While the wage and employment effects for natives in local labor markets are small, it was argued that certain groups of workers have been adversely affected by immigration. The augmented factor supplies of less-skilled workers, due to either the effect of trade with low-income countries or from the immigration of workers from developing countries, were thought to have contributed to the poor outcomes of less-educated American workers during the 1980s and early 1990s. The finding that certain groups of workers may have been adversely affected by immigration is evident for some European studies as well. For example, Hofer and Huber (2003) find that immigration reduces wage growth and increases risk of unemployment in Austria. Similarly, De New and Zimmermann (1994) find that greater concentrations of foreign workers in German industries during the 1980s were associated with small wage gains for white-collar workers, but relatively large wage losses for blue-collar workers.78 Zimmermann (1995) attributes these findings to the greater labor market inflexibility, greater levels of unionization and low labor mobility in Europe in comparison to the United States.79 In the case of strong unions or wage inflexibility, the expectation is that immigration is associated with increases in native unemployment. In the case of labor immobility, equations (8) and (9) suggest that skilled wages increase and unskilled wages decrease when unskilled immigration increases. Similarly, 77 Decressin and Fatás (1995) have similar findings for the regions of Europe. However, they show that changes in labor force participation rates bear proportionately more of the burden of adjustment in response to labor market disturbances 78 Specifically, De New and Zimmermann find that their IV estimates were substantially more negative than their OLS estimates (in fact, 15 times larger). On one hand, this result may be seen as being consistent with Friedberg‘s (2001) occupational crowding finding for Israel, discussed above. On the other hand, at a more practical level there is evidence of some instability in the coefficients of the industry level variables in the IV model specification. De New and Zimmermann use industry dummies, industry growth rates and industry specific time trends as determinants of share of foreign workers by industry.) As the authors acknowledge, the issue of whether their instrumenting procedure has been able to fully control for the endogeneity of the foreign share of labor may have been insufficient. 79 Interestingly, Zimmermann (1995) notes that there has been little impact of immigration on unemployment rates for Germany (see also Winkelmann and Zimmermann, 1993; Pischke and Velling, 1997; Winter-Ebmer and Zweimüller, 1999a). Similar null results on immigration and unemployment have been found for Austria (WinterEbmer and Zweimüller, 1999a; b), Italy (Venturini and Villosio, 2006), Portugal (Carrington and deLima, 1996), the UK (Angrist and Kugler, 2003) and Australia Junankar et al. (1998). ~ 44 ~ Angrist and Kugler (Angrist and Kugler, 2003), while finding generally small effects for a sample of European countries, also find that labor market institutions can play a role in magnifying such effects. It should, however, be noted that the results for Europe, and other countries, are quite mixed. For instance, Pischke and Velling (1997) find that immigration had no adverse wage or unemployment effects in German local labor markets. Similarly, Winter-Ebmer and Zweimüller (1996; 1999a) using both OLS and IV estimation procedures find no detrimental immigration impact upon Austrian industry or regional wages. These methods have also yielded minimal wage effects for such countries as Italy (Gavosto et al., 1999), France (Jayet et al., 2001), Australia (Addison and Worswick, 2002), the United Kingdom (Dustmann et al., 2005), and the Netherlands, the UK and Norway (Zorlu and Hartog, 2005). In addition, we have already noted the small effects found using natural experiment methods for France (Hunt, 1992) and Portugal (Carrington and deLima, 1996). Taking all of the results using cross-sectional data together, whether based on production function or regression methods, the overwhelming conclusion is that immigration has, at most, small negative effects on wages and no effects at all on unemployment (see the meta-analytic study by Longhi et al., 2005). 3.1.3. ―Factor Proportions‖, Skill-Cells and National Data The approaches we have considered to this point, both production function and regression based, primarily identify labor market effects from variance across regions. We have just noted that internal migration of natives, and even of earlier waves of migrants, could interfere with inference in analyses based on local labor market data. As a response to this potential problem, Borjas has argued that analysis of the effect of migration on labor markets should proceed at the level of the national economy (Borjas, Freeman and Katz, 1992; 1997; Borjas, 2003; 2006). A first approach to this problem was taken by Borjas, Freeman and Katz (BFK 1992; 1997). The idea here was to use a standard, partial equilibrium framework to calculate the effect of a fixed increase in inelastically supplied labor implied by empirical immigration. Specifically, BFK follow Katz and Murphy (1992) in focusing on the effect of a change in the supply of one factor relative to another on the relative wages of those factors. Factors are taken to be inelastically supplied while the relative demand for labor is smoothly downward sloping. If every factor i‘s supply is made up of a domestic component and an immigrant component (i.e. zi = Ni + Mi), and if we let the ratio of domestic to immigrant labor be mi = Ni/Mi we can rewrite the aggregate supply of factor i as zi = Ni(1 + mi). Then, using a framework like that in (25)-(29), with all labor aggregated into either skilled (S) or unskilled (U), one can calculate the effect of a change in relative supplies on relative wages as: 1 mS w 1 ln L ln . SL wS 1 mU ~ 45 ~ (37) where the change is taken between fixed dates.80 BFK also follow Katz and Murphy in constructing two pairs of aggregate labor terms: {high school dropouts, high school grads}and {high school equivalent, college equivalent}, and apply the Katz/Murphy estimates of ζSL to make the calculations of the effect of immigration on relative wages.81 BFK conclude that the immigration-induced change in the relative supply of high school dropouts accounted for about 44% of the total decline in their relative wage. The work in this method goes mostly into constructing the aggregates. As equation (37) suggests, the actual calculation is quite simple. However, this is also the problem with this method. As DiNardo notes in his comment on BFK: As to the aggregate proportions approach, I am reluctant to conclude that it provides a more reliable [than spatial correlation] way of predicting the impact of immigration on relative wages. The authors' simulations are based on the assumption that the principal mechanism by which immigration affects wages is shifting labor supply along a demand curve. Maybe this is correct; however, the approach provides no independent testable pre- dictions. It can only be confirmed by the extent to which it is in accord with a priori beliefs about the size and directions of the effects. (DiNardo, 1997, pg. 75) In addition, by focusing on a one sector model, all adjustment to immigration is forced through the wage margin. As our discussion of the relevant general equilibrium theory suggests, this virtually guarantees overestimates of wage effects. Thus, it is probably not surprising that the impact of these papers was short lived. Responding to DiNardo‘s critique, while retaining the national-level empirical focus, involves finding an alternative to regions as a source of variation as a basis for estimating effects. One alternative that has been applied in other branches of empirical labor economics is to exploit variance across similar, but imperfectly substitutable, cohorts of workers (Freeman, 1976; 1979; Welch, 1979; Katz and Murphy, 1992; Card and Lemieux, 2001). The key to identifying the effect of immigrants on wages is the assumption that the individuals in the ―skill cells‖ are perfect substitutes for one another, but are imperfect substitutes across cells. In this case, is seems perfectly plausible to assume that individuals cannot switch cells in response to differentials in wages. As with research based on spatial correlations, there are both regressionbased and production function-based variants on the skill cell approach. The standard reference for both of these is Borjas (2003; see also Borjas and Katz, 2007). The first step in applying this approach is to construct the skill cells. Since the goal is to exploit variance in immigrant presence across skill cells to identify the effect of immigration on wages, In addition to the BFK papers, and Borjas‘ (1999a, pp. 1751-1759) survey, detailed discussions of this method can be found in Johnson (1980; 1998). 81 It is interesting to note that BFK were interested in evaluating the effects of both trade and immigration on relative wages. Their estimate of the effect of trade on labor supply applied input-output methods to identify the implicit imports and exports of labor via trade. At the time, immigration had not generally been considered in the set of major factors taken to explain the rapid rise of the skill premium in the 1980s (i.e. technological change, trade, shifts in product demand, and erosion of institutions supporting higher wages (e.g. unions and minimum wages). As a result, BFKs conclusion that immigration played a major role in accounting for the change in the skill premium was all the more striking. 80 ~ 46 ~ the key here is to aggregate up from individual data to skill cells such that individuals in a given cell are perfect substitutes for one another and individuals in difference cells are imperfect substitutes. Borjas aggregates on age cohort (―experience‖) and education. That is, Borjas assumes that workers (whether native or immigrant) with the same level of schooling and experience are perfect substitutes, but that workers with the same level of schooling, but different experience are imperfect substitutes (similarly for same experience but different schooling). For this strategy to work, we must be confident that the definitions of the cells are such that workers in different cells really are imperfect substitutes and that workers in the same cell really are perfect substitutes.82 For his analysis, Borjas works with four education groups i {high school dropouts, high school grads, some college, college grads} and 8 labor market experience groups j {5 year bands for workers with 1-40 years of experience}—for a total of 32 age/experience cells. Since he uses data from five US censuses t = {1960, 1970, 1980, 1990, 2000}, this gives Borjas a dataset of 160 ijt observations on male workers. For each of these cells, he calculates the share of immigrants in total (male) workers in a given cell: pijt M ijt / zijt . Using these data, Borjas estimates the following reduced form regression: ijt pijt si x j t si x j si t x j t ijt , (38) Both of these turn out to be tricky. Borjas (2003, pp. 1344-1347) provides evidence that ―(for given education) immigrants and natives with similar levels of experience are closer substitutes than immigrants and natives who differ in experience‖ (pg 1344). However, Card (2009, section III B) argues that ―workers with less than a high school education are perfect substitutes for those with a high school education‖ (pg. 2, our emphasis). Given that Borjas treats these as two, of four, distinct categories, if Card is correct this implies a serious misspecification on the part of Borjas. Ottaviano and Peri (2008) provide evidence that this is, in fact, the case. The issue of whether or not immigrants and natives are perfect substitutes is considerably more fraught, and a matter of ongoing dispute in this literature. The argument for treating any worker with the same labor marketrelevant attributes (i.e. education and experience) as identical to any other worker is strong on a priori grounds. Anti-discrimination law even tries to mandate this as an outcome when gender or race is the discriminating factor. Not surprisingly, aggregating workers (characterized by many forms of heterogeneity) into age/experience cells is a standard approach in labor economics (e.g. Katz and Murphy, 1992; Card and Lemieux, 2001). This has certainly been a common strategy in research on the labor market effects of immigration in virtually every sort of method: factor proportions (Borjas, Freeman and Katz, 1992; 1997), production function (Gang and Rivera-Batiz, 1994; Suen, 2000), regression analysis of local labor markets (Card, 2001; 2005), and, of course, the regression analysis of skill cells in national labor markets (Borjas, 2003; 2006). In addition, Cortes (2008) finds evidence of imperfect substitutability in her study of the effect of immigration on prices of final goods in local markets. Note from this list that, given the range of outcomes reported in these papers, that the perfect substitutes assumption alone cannot account for findings of large or small effects. Nonetheless, it is also the case that production function-based studies consistently find that immigrants and natives are imperfect substitutes. While most of these studies consider only aggregate factors {domestic labor, immigrant labor}, Greenwood, Hunt and Kohli (1997) do consider an input vector that distinguishes both native/immigrant and skill level distinctions. The result is the same: immigrants are not found to be perfect substitutes for native workers. In addition to the classic paper by Chiswick, Chiswick and Miller (1985), which develops in detail reasons we might expect immigrants and natives to be imperfect substitutes, a recent paper by Peri and Sparber (2009) develops an interesting model of task specialization and careful empirical analysis supporting the same presumption in favor of imperfect substitutability. Given that Ottaviano and Peri (Ottaviano and Peri, 2006; Peri, 2007; Ottaviano and Peri, 2008) have made this a central element of their critique of his empirical results, it is not surprising that Borjas (Borjas et al., 2008) has responded strongly on just this issue. 82 ~ 47 ~ where ijt denotes a labor market outcome (log annual earnings, log weekly earnings, fraction of time worked), si, xj, and πt are education, experience and time fixed effects. This structure involves indentifying the effects of immigration from variance within education/experience cells over time. Using the estimate of ζijt, Borjas calculates the elasticity of the wage wrt to the ratio ln wijt . For his basic specification, of immigrants to natives in a given cell as: 2 mijt 1 mijt Borjas calculates this elasticity to be -0.40—i.e. an increase of immigrants in cell ijt by 10% is estimated to cause a 4% fall in weekly earnings. The effect on annual earnings is estimated to be -6.4% and on labor supply -3.7%. As Borjas notes, these estimates are on the high side of previous estimates found in non-immigration studies (Juhn et al., 1991), and much higher than in other immigration studies. In addition to this reduced form approach, Borjas also considers a more structural approach based on estimation of a production functions defined on labor defined in skill/experience terms. Unlike the production function approach based on spatial variation and a limited set of labor types (often just {native, immigrant} or native/immigrant crossed with racial categories), Borjas has a large number of schooling/experience types and a relatively small number of annual observations, so he requires a technology that has a relatively small number of parameters that must be estimated. For this purpose, he uses a nested CES function.83 Specifically, Borjas assumes a top-level aggregator that produces GDP as a function of capital and labor Yt Kt Kt Lt Lt 1 , KL 1 1, Kt Lt 1. KL (39) 83 The basic approach applied in this work is to assume a nested CES structure (Sato, 1967; Bowles, 1970; Chung, 1994 Chapter 11). This involves a top-level aggregator that gives output at time t as: 1 Yt f z t it zit , iI where the δit > 0 are technical efficiency parameters; ρ is a parameter related to the elasticity of substitution between aggregate factors, ζ, as ρ = (1 – ζ)/ζ and -∞ < ρ < 1. However, unlike the standard CES function, the nested CES function nests some lower level aggregates: 1 zit lti zlti , lSi where Si is the set of types of input i, and α is related to the constant elasticity of substitution between these types, δ, as above. For example, in labor applications i might denote an education category (e.g. high school dropouts) and the elements of Si might be experience (proxied by age category). As we shall see, there is no need to stop at two levels. A general treatment of multiply nested CES functions is given in Perroni and Rutherford (1995). ~ 48 ~ Aggregate labor at time t (Lt) is itself a CES aggregate of workers with varying schooling and labor market experience. This is constructed by first aggregating workers with the differing experience, but the same level of education into an education-based aggregate (Lit); and then aggregating those lower level aggregates across education groups into aggregate labor (Lt). Thus, the input to the top-level aggregator is: 1 1 Lt it Lit , E 1, it 1, E iI iI (40) where ζE is the elasticity of substitution between the education aggregates. The lowest level aggregator aggregates workers with different levels of experience into iso-education level aggregates: Lit ij Lijt jJ 1 , X 1 1, ij 1, X jJ (41) where ζX is the elasticity of substitution between experience classes within an education group. Using the condition that the wage equals the marginal product for skill group ijt (taking the sole good, GDP, as numeraire so value marginal product is equal to marginal product), Borjas solves for the wage as: ln wijt ln Lt 1 ln Yt ln Lt ln it ln Lit (42) ln ij 1 Lijt . Borjas follows Card and Lemieux (2001) in estimating the elasticities using fixed effects regressions to recover the relevant elasticities. Thus, to recover ζX, Borjas estimates: ln wijt t it ij 1 ln Lijt , X (43) where the first line of the RHS of equation (42) is represented by the time fixed effect (δt), the second line is represented by an interaction between the education and time fixed effects, and δij = ln αij is an interaction between education and experience fixed effects. From equation (41) we can use the estimates of αij and ζX to calculate the Lit. Next, from the second level of the production function, for the average wage paid to a worker in education group i at time t, we estimate: ln wit t ln it ~ 49 ~ 1 ln Lit . E (44) Borjas uses education group-specific time trends to approximate the ζit and the number of immigrants in each skill group as an instrument for the size of each skill group. Borjas then applies the same methods as those applied in analyzing production functions using regional data (see section 3.1.1) to simulate the effects of immigration shocks on wages. Using this framework, Borjas calculates that US immigration in the 1980s and 1990s resulted in a 9% reduction in the wages of high school dropouts and a 4.9% reduction in the wages of college graduates. These are the two education categories with the highest shares of immigrants. For high school graduates wages fell by 2.6% and workers with some college were only minimally affected. Borjas‘ (2003) estimates of the effect of immigration are the largest not associated with an explicitly adversary purpose. There have been a number of applications of the methods from this paper, and none have produced estimates of equivalent magnitude. 84 The most explicitly critical work is contained in a pair of papers by Ottaviano and Peri (OP, 2006; 2008).85 The core of OP‘s criticism is an argument that three of Borjas‘ simplifying assumptions—high school dropouts and high school grads are imperfect substitutes, natives and migrants are perfect substitutes, and capital is a fixed endowment—end up biasing his results toward finding larger negative effects of immigration. OP work with the structural approach developed in Borjas, but they extend the approach to embed, and test for, two versus four skill groups and perfect versus imperfect substitutability of immigrants and native. To deal with the potential perfect substitutability between types of skilled and types of unskilled labor, instead of equation (40), OP consider an aggregate of two types of labor--LH (skilled) and LL (unskilled): 84 In addition to the papers by Ottaviano and Peri (2006; 2008) that we discuss here, other papers include, Suen (2000), Manacorda, Manning and Wadsworth (2006), Peri (Peri and Sparber, 2008; Peri, 2009), D‘Amuri, Ottaviano and Peri (2010), Felbermayr, Geis and Kohler (2010), and Raphael and Smolensky (2009a; b) all of which adopt structural approaches based on nested CES production functions of differentiated labor, while Bonin (2005) and Cohen-Goldner and Paserman (2004) pursue the econometric approach. These papers work with data from Hong Kong, the UK, California, Germany, Germany, the US, Germany, and Israel, respectively. All of these papers find negative effects of immigration on the lowest education cell, but none find that these effects are large. Another group of papers apply the same method of working at the national level on skill cells, but define those cells in terms of occupation rather than education. As with education/experience, the idea here is that people are not able to change occupation readily in response to shocks. This permits identification of the labor market effects of immigration if immigrants are distributed unevenly across occupations and over time. Camarota (1997) and Card (2001) both focus on occupation, but identify effects from variance across regions in a single year. Friedberg (2001) looks at the unexpected shock to the Israeli labor market of Russian immigrants 1990-1994 identifying effects from occupation level data (using Russian occupations as an instrument) and finds essentially no effect on Israeli wages. Orrenius and Zavodny (2007) use data on occupation and region over time to estimate the effects of immigration and find statistically significant, but small effects. It should be noted that Borjas has produced other papers showing essentially perfect substitutability and large effects (Aydemir and Borjas, 2007; Borjas et al., 2009). 85 The key paper here is OP (2008). OP (2006), which emphasized imperfect substitutability between natives and migrants and capital adjustment, whose results were criticized by Borjas, Grogger and Hanson (2008) for sensitivity to the way they constructed their four schooling aggregates. In response, OP (2008) show: first, that the problem is less the construction of the variables than the use of so many dummy variables that results in insignificant results; and, second, argue that the four education groups should be tested against the more standard two groups applied in empirical labor economics outside the economics of immigration. Thus, while the results of this paper seem unlikely to be the last word on this topic, at this point it does seem to be fair to conclude that the Borjas (2003) results will continue to be seen as extreme. ~ 50 ~ 1 1 Lt H LHt L LLt , HL 1, it 1, HL iI (45) where ζHL is the elasticity of substitution between high and low skilled labor and each of the Lit (i {H,L}) is itself an aggregate of two sub-types: LHt is a CES aggregate of college dropouts and college grads; and LLt a CES aggregate of high school dropouts and high school grads. This specification nests the four skill-group structure (i.e. equation (40)) and can be used to test the Borjas specification against the more standard specification. To deal with the assumption that migrants and natives might be imperfect substitutes, they develop a fourth aggregate that produces the Lijt that are the inputs of equation (41) from home and native workers with education level i and experience level j in time t: Lijt Hijt H ijt Fijt Fijt 1 , 1 1, Hijt Fijt 1, (46) where ζκ is the elasticity of substitution between home and foreign born labor. Finally, OP introduce an explicit model of sluggish capital adjustment rooted in earlier work in empirical work on economic growth. The empirical implementation results in two broad results: first, while high school dropouts/high school grads and college dropouts/college grads are very good (essentially perfect) substitutes for one another, their aggregates are very imperfect substitutes; and second, immigrants and natives are imperfect substitutes for one another. That is, OP produce strong evidence that a model using two education groups and distinguishing between natives and immigrants dominates the Borjas model. In addition, OP develop a framework in which, assuming international capital mobility or capital accumulation, capital adjusts to immigration shocks to maintain a constant real return to capital and a constant capital-output ratio. Under these two adjustments to Borjas‘ structural model, OP calculate that immigration has had a small negative effect on high school dropouts, positive effects on other groups and a positive aggregate effect on the average wage of US workers overall.86 Overall, then, the broad conclusion from all four approaches—regional v. skill based observations by structural v. reduced form methods—to estimating/calculating the effect of immigrants on native labor market performance come to the same conclusion: at worst, immigration has small negative effects on native wages and employment prospects, with the largest negative effects falling on previous waves of immigrants with the same labor market traits. There is some evidence that, consistent with a loose interpretation of Samuelson‘s LeChatelier principle, the negative effects are more severe in the short-than in the long-run. For an area of research that is often seen as riven by deep debates between rival schools, this level of overall agreement seems surprising. 86 Peri (2007) refines the OP approach by developing a creative instrumental variable approach to the estimation of the relevant elasticities—i.e. he uses immigration by skill in the rest of the US as an instrument for the supply driven part of immigration to California—and applies it to California. The results are consistent with those in OP. ~ 51 ~ 3.2. Empirical links between endowment changes and output changes As with the previous sub-section, the most direct approach to evaluating the Rybczynski theorem is a small group of papers that directly exploits the model structure, extending the production theoretic approach to the simultaneous existence of trade in goods and factors. Following original work by Burgess (1974), empirical trade economists have exploited duality theory to estimate comparative static effects of trade by treating trade as a direct argument in a GNP function.87 The marriage of this approach to trade modeling to the production theoretic modeling of immigration seems obvious, but has only rarely been done. As we noted above, Kohli (1993; 1999; 2002) develops this sort of analysis in considerable detail. With particular reference to the Rybczynski relations, using Swiss data, most of Kohli‘s work analyzes a single output economy and can‘t really speak to Rybczynski effect. However, the economy in Kohli (2002) has two final outputs (exports and domestically consumed goods), and here there is evidence that immigration is associated with increased production of the domestic good, but not the exportable. Hijzen and Wright (2010) explicitly evaluate Rybczynski effects in a production theoretic framework with two final outputs (high and low skill-intensive) and 6 factors (high and low skilled domestic and foreign workers, capital and imports) for UK data from 1975-1996.88 Loosely consistent with the Rybczynski theorem, Hijzen and Wright find a (small) positive effect of immigration on output quantities. Taken together with evidence of a (small) negative effect on own wages, it seems sensible to interpret the overall results as suggesting that economies adjust to an immigration shock on both the wage and output margins. Additional evidence on Rybczynski-like effects in a trade theoretic mode is found in the literature (often seeking to ―test‖ HO theory) examining the empirical link between endowments and production structures.89 The most straightforward approach exploits the fact that, under HOV assumptions (in particular, common, constant returns to scale technologies and costless trade) and assuming m = n, there is a linear relationship between outputs and endowments. From the full employment conditions in 1, and letting A-1 ≡ B = [bji], we can write: y kj b ji zik , (47) iI where k denotes a country. This expression can be used as the basis for empirical evaluation of the ―Rybczynski‖ relations. A widely cited paper exploiting this approach is Harrigan (1995) 87 The underlying idea is to treat trade as an input to final GNP under the argument that virtually all goods in trade must be processed further for final sale. See Kohli (1991) for an excellent development of the theory, econometrics, and results from this research. 88 While the Rybczynski elasticities‖ are perfectly well-defined in this analysis, the 6 = m > n = 2 structure renders their interpretation in terms of the Rybczynski theorem is problematic. The same stricture applies as well to the interpretation of the results in Kohli (2002). 89 Two survey papers are particularly worth consulting on the issues we briefly discuss in this paragraph: Maskus (1991), in addition to presenting original results we discuss below, provides an excellent discussion of data issues that arise in research on factor content models of trade; and Harrigan (2002, section 3) provides detailed discussion of theoretical and methodological issues in evaluating the link between endowments and output. ~ 52 ~ constructs an analysis with 4 factors (capital, skilled and unskilled labor, and land) and 10 manufacturing sectors. Harrigan finds a statistically significant relationship between endowments and outputs, but also finds large within sample prediction error. Ultimately he concludes (pg. 41) that ―there is more to the international location of production than can be explained by the free trade/factor proportions model used here‖. Kim (1999) applies this same method (with 7 inputs and 20 manufacturing sectors) to the case of US states for the years 1880, 1900, 1967, and 1987. This analysis found regional endowments explaining a large share of regional differences in output patterns. For Kim, the alternative was local spillovers and agglomeration, for which he found little evidence. Several papers using this approach are specifically concerned with the possibility of technological differences between countries. Dollar, Wolff and Baumol (1988), Maskus (1991) and Davis and Weinstein (2001, section III A) apply this method to data sets with two inputs (K and L) and many sectors (13 in DWB, 28 in Maskus, and 34 in Davis and Weinstein). Endowments play a major role, but, contrary to the standard model, technology differences between countries appear to be significant (and quite large). In work explicitly focused on both Rybczynski effects and technological difference, Harrigan (1997) estimates a translog GDP function with 7 manufacturing sectors and 6 factors (arable land, 2 types of capital, and 3 types of labor), for 10 industrial countries over the years 1970-1988. Importantly, technology in sectors is permitted to vary across countries and time in Hicks neutral fashion. The results are consistent with significant effects of endowments on sectoral outputs. Redding and Vera-Martin (2006) apply a similar method to the analysis of European regions, again finding evidence that endowments help predict to production structure. The work discussed in the previous paragraph interprets technological difference as a function of differing degrees of technological progress across countries (and, possibly, sectors). An alternative, and complementary, approach sees technological difference as a function of selecting technologies from common sets (i.e. isoquants) in the face of differing prices. Thus, where the work discussed in the previous paragraph presumes (and seeks to test for) factor-price equalization, the work considered in this paragraph permits factor-prices to differ across countries. That is, there may be multiple cones of diversification. An early effort to indentify production structure in the context of multiple cones is Brecher and Choudhri (1993). The authors develop a number of tests, applied to production data for the US and Canada, seeking to identify the presence and sources of non-factor price equalization. The conclusion of this analysis is that endowment differences matter in accounting for production structure, but that account must be taken of interindustry differences in factor prices seen as a function of imperfect factor mobility. Schott (2003) marks a substantial advance in its attempt to develop direct tests of multi-cone production that might be obscured by aggregation of different industries within standard industrial classifications. In this paper, Schott first demonstrates that 3-digit industrial aggregates almost surely contain industries that are heterogeneous in inputs, then constructs aggregates of industries that may be more heterogeneous for specific countries, and then estimates a model with multiple cones. While there are some problems in both the construction of the industry aggregates and interpretation of the results (Harrigan, 2002, pp. 97-99), Schott is ~ 53 ~ quite convincing that specialization of production structures in distinct cones plays an important role in accounting for patterns of production.90 Related to this work, and explicitly about immigration, is a pair of important papers by Hanson and Slaughter (2002) and Gandal, Hanson, and Slaughter (2004), the first dealing with the US the second with Israel. These papers are based on a clever accounting decomposition that seeks to identify the contributions of output-mix change and technological change in adjusting to endowment shocks.91 In the US case, Hanson and Slaughter present results consistent with productivity-adjusted factor-price equalization across states and, further, present evidence suggesting that states have absorbed changes in labor endowments primarily via skill-biased technological change which is common across all states and, secondarily, via changes in output mix. That there should be evidence of output-mix adjustment in a period of rapid and substantial technological change strikes us as important. However, such evidence does not exist in the Israel case, where Gandal, Hanson, and Slaughter find that global changes in technology were (more than) sufficient to absorb the huge, relatively skilled influx of immigrants from Russia. In addition to the finding that output-mix adjustment was playing a role, there are two important implications of this work for the discussion to follow. First, there is some suggestion that, at least among relatively developed economies, the assumption of a common technology across countries may be less of a distortion that assuming a common technology across a finite period of time (at least during a technologically dynamic period). Second, while appropriately constructed comparative static analysis will identify important forces operating at the level of the economy as a whole, dynamic forces that are not incorporated in the analysis might well overwhelm the static forces.92 On the other hand, since these forces are both less well understood and less controllable, their relevance for policy analysis is very unclear. We offer the following quotation from as a summary of the work discussed in this section: ―The study does not provide evidence that the Heckscher-Ohlin-Vanek framework can be blithely and blindly applied to international data. However, it does validate the use of the underlying general equilibrium structure as an excellent description of national data‖ (Davis, Weinstein, Bradford and Shimpo, 1997, pg. 422). This is certainly good news, since for the purposes of evaluating the effect of immigration, it is the national effects that are relevant. Thus, to repeat the claim 90 For other empirical work on multi-cone models, see: Leamer (1987) and Xiang (2007). An unpublished paper by Harrigan and Zakrajšek (2000) using an extension of the methods from Harrigan (1997), does not find evidence supporting multiple cones. On the subject of the endowment-output link, and the ways results vary in moving from inter-regional to international environments, see: Davis, Weinstein, Bradford, and Shimpo (1997); Davis and Weinstein (1999); and Bernstein and Weinstein (2002). One of the key results in the work of Davis, et al. and Bernstein and Weinstein is that the HOV production model performs quite well once one accounts for the indeterminacy that results from m < n, and non-factor price equalization. 91 Lewis (2003) and Card and Lewis (2007) also develop a useful decomposition to analyze the role of adjustment on the output margin in absorbing immigrant shocks. Card and Lewis conclude that ―most of the inflows appear to be absorbed by city-specific–within-industry increases in use of unskilled labor‖ (pg. 219). 92 In addition to technological change, we would also consider factor accumulation to be a dynamic force of considerable significance. It should probably be noted, as Hanson and Slaughter do, that capital accumulation may be playing a large role as well. ~ 54 ~ from above, while there is certainly an effect of immigration on wages, part of the explanation for the very small magnitude of that effect is adjustment on the output margin.93 3.3. Increasing Returns, Agglomeration, and Immigration To this point, we have stressed the fundamental theoretical consistency of the frameworks in use by trade and labor economists. As we have noted, both rely on assumptions of perfect mobility within the relevant geographic market, perfect competition within all markets, constant returns to scale in production, et cetera. The only essential difference between the two is dimensionality, and here we have argued for a presumption that the number of goods is at least as large as the number of factors of production. Under this assumption, we have seen that factor-price insensitivity generally obtains. As we shall see, this seems broadly consistent with the overwhelming majority of studies which find, at most, small wage/employment effects. At a minimum, something other than wage adjustment is going on—it might be adjustment on the output margin (as implied by factor-price insensitivity), or endogenous technological adjustment (as suggested by Ethan Lewis), or something else, but there just is not much evidence of major adjustment on the wage margin. This said, the apparent existence of quite distinct local economies is problematic for either approach. Even within the state of California, we can observe quite distinct production structures between a northern economy characterized by high tech industry supporting a high wage structure and a southern economy in which low tech industry supports a low wage structure.94 If local labor markets are somehow segmented, this multi cone structure is an equilibrium. However, the existence of free trade and free factor mobility between northern and southern California would seem to be completely inconsistent with an account of this sort. This leads us to the question of whether some form of geographic model supports the endogenous determination of multiple local cones. Bernard and Jensen (2000) note that although the United States as a whole experienced increasing wage inequality, that this fact disguised very different patterns of wage inequality at the state level. In fact, some states experiencing sharp declines in inequality. They argue that this fact argues against the view of a well-oiled, highly-integrated U.S. economy – at least in the short- to medium-terms. In response to employment shocks, Blanchard and Katz (1992) found that labor markets were integrated after a period of 10 years. Interstate migration does indeed act to smooth shocks, but it only does so very slowly. Wage adjustments were also extremely sluggish, with some effects often lingering beyond 10 years. In other words, shocks to regions are not rapidly transmitted to other regions. This suggests that even the most carefully crafted research, e.g., such as Borjas‘, which divides workers into industry, occupation, education, 93 Of course, this is not the whole story. As we have already seen, much of the work explaining this effect must be some combination of the imperfect substitutability between natives and immigrants, and capital accumulation emphasized by Ottaviano and Peri (2006; 2008), and the technological response emphasized by Lewis (2005; 2008). 94 Similar structures certainly exist in other countries—northern and southern England is another example. ~ 55 ~ experience, race and sex may be biased because it does not also distinguish between locations – or separate labor markets. There are at least two further implications of this research. Firstly, the measured effects on local labor markets are genuinely indicative of the small adverse impact that new immigrants have on native workers and second, that the skating rink hypothesis, in which each new foreign unskilled worker forces a native off the ice (i.e., to migrate to another region), is dubious. In more recent work, Bernard et al. (Bernard et al., 2008; Bernard et al., 2009) show that relative wages vary across regions in the United States and the United Kingdom. They also show that the type of industry varies with the skill wage premium and that skill-abundant regions exhibit lower skill premia than skill-scarce regions. Hence, firms adjust production across and within regions in response to relative wage differences. In a Heckscher-Ohlin model with multiple cones of diversification one implication is that different regions with different skill endowments have different relative wages. In equilibrium, regions abundant in skilled workers offer lower skill premia. This finding is at seemingly at odds with economic geography models that have skill abundance and skill premia being positively related as a result of agglomeration externalities. The existence of multiple cones suggests that economic activity, as well as factors of production, tend to agglomerate. Courant and Deardorff (1992) show that when factors are immobile, regions specialise in the good that uses most intensively its abundant factor. In turn, the ―lumpiness‖ of factor endowments can constitute a basis for trade. The point of course is that regions within countries may often differ more than they do with comparable regions overseas. The lumpiness can be sustained by lower prices for non-tradeable goods or by locational amenities, such as nice weather. In the latter case, real wages wouldn‘t equalise, although sunshine-adjusted real wages would. Hence, there would be no FPE. In a similar vein, Quah (1996) finds that regional per capita income varies more strongly with what happens in neighbouring locations than with other regions of the same country. Likewise, Overman and Puga (2002) show the existence of regional unemployment clusters in the EU which often span national borders. These neighbourhood effects are important, regardless of whether the neighbours happen to be domestic or foreign. They argue that the clustering reflects the agglomeration effects of economic integration. Interestingly, the polarisation into high unemployment regions and low unemployment regions cannot be being driven by migration because intra-regional migration has been falling in Western Europe.95 Hanson (2001) provides a very nice review of empirical work on the new economic geography models and describes how increasing returns to scale is one of the main reasons why industries spatially agglomerate. Increasing returns to scale or agglomeration effects can be internal or 95 The EU seems to differ from the United States, where local unemployment significantly influences the migration decisions of the unemployed. On the other hand, local unemployment has little influence on employed individuals in the United States. See Greenwood (1997). ~ 56 ~ external to firms. In the former case, transport costs give agents an incentive to locate close to one another. In the latter case, costs per unit decreases as the industry size increases. This can occur because a larger market lowers cost of key inputs. For example, highly specialised service industries or firms can profitably service a large number of firms in a cluster, but would not be able to do so in isolation. There could also be labor market pooling benefits, where labor is attracted to the opportunities in the cluster. This lowers costs for firms as well. Last, but not least, there may be knowledge spillovers due to the informal and formal diffusion of knowledge afforded by larger clusters. This implies an improved quality and productivity of factor inputs. In fact, individual wages increase in the presence of more-educated workers in the local labor force, which is consistent with localised human-capital externalities. An occasional finding in individual wage regressions is that a measure of average human capital is significant and positive (e.g. Dickens and Katz, 1987). Wages are also known to be higher in urban areas and areas with large consumer markets (Hanson, 2001). However, it is unclear whether agglomeration has wage benefits for workers. For example, de Blasio and di Addario (2002) finds that industrial agglomeration affects employment probabilities, but affects neither wages nor wage premia. Such a finding suggests a moderation of the forces that lead to agglomeration as agglomeration may be partly sustained by workers migrating to higher wage areas. Worker immobility and equilibrium wage differences that are not eliminated by migration will actually act as a dispersion force (see Krugman, 1991; Ottaviano and Puga, 1998; Puga, 1999; Neary, 2001). [Figure 6 about here] When regions are skilled labor-abundant, they are attractive to skill-intensive industries. This is illustrated in Figure 6, which is taken from Bernard et al. (2003). Unit-value Leontief isoquants for three industries are shown. Endowments of skilled (z1) and unskilled (z2) workers for regions A and B are also shown. There are two cones of diversification. The relative wage of skilled workers is easily seen to be lower in B, which is relatively skill-abundant. Obviously, the production structure will also differ in regions A and B. The authors reject absolute FPE and, unlike Hanson and Slaughter (2002), relative or productivity-adjusted FPE for both the United States and for the United Kingdom. They argue that this is due to the presence of multiple cones of diversification and not to region-industry technology differences, agglomeration or increasing returns to scale. Factor immobility, of at least one of the factors, prevents regional factor prices (and endowments) from converging to a common value across the country. Once again, regions exhibit systematic differences in production structure.96 Thus, one of their other major findings is that firms reallocate production 96 Kim (1999) finds that factor supplies can account for a large share of the cross-sectional output variation across U.S. states. ~ 57 ~ facilities that best match their factor needs, i.e., using their words, ―industries move towards workers more readily than workers move towards industries” Bernard et al. (2003, pg. 14).97 4. Global Effects of International Migration To this point we have looked at the issue of migration primarily from the perspective of a single, immigrant-receiving country. We now turn to three issues which are fundamentally about the international equilibrium: comparative advantage and the pattern of trade; the relationship between trade and factor mobility; and the brain drain. 4.1. International Equilibrium and Comparative Advantage with (Some) Mobile Factors The simplest model of international equilibrium with migration is the MacDougall-Kemp model we discussed briefly above. Recall that, in this model, each country produces one good with two (or many) factors of production. Equilibrium is determined by equalization of returns to the internationally mobile factor. This is a useful model for a basic analysis of the allocation of the mobile factor between countries, migration pressure as a function of immigration policy, optimal immigration policy, income distribution, and welfare; but, because there is no trade in goods, comparative advantage cannot be analyzed. As explained by Ethier (1986c), immigration has an interesting effect on comparative advantage in the Ricardian model. Free migration equalizes wages, but in the Ricardian model this means that absolute advantage will determine the location of production (rather than comparative cost differences). If either country has an absolute advantage in the production of both goods, the technologically disadvantaged country will simply empty out. In the intermediate case, in which each country has an absolute advantage in the production of one of the goods, the world economy functions like a single Ricardian economy, so relative commodity prices are determined by the technology (i.e. taste plays no role).98 Tastes do, however, play a role in the determination of the pattern of factor labor flows between the two countries. Specifically, if world demand is such that, at the technologically determined prices, the demand for the good produced in , say, the Home country exceeds the capacity of the initial Home labor endowment to produce that good, migration will flow from Foreign to Home. Factor mobility in the basic HOS model is also quite straightforward. The classic paper here is by Mundell (1957), who retained the full set of HOS assumptions and proved a converse to Samuelson‘s (1948; 1953/4) factor-price equalization theorem. As we discuss in the next section, under HOS assumptions, factor mobility is at least a partial substitute for commodity 97 Hanson (2001) argues that available evidence in the economic geography literature favours demand-driven agglomeration in which firms are attracted to densely concentrated regions and large potential local markets (Krugman, 1991); rather than in which workers benefit from being close to other workers (as in Black and Henderson, 1999). 98 Jones (1980) develops an interesting analysis with nationally fixed factors and globally ―footloose‖ factors in which comparative and absolute advantage both play a role. ~ 58 ~ mobility. One way of seeing this is that free trade without factor mobility can produce the same equilibrium (in the sense of final prices and allocations) as free factor mobility without trade. The key here is that the endowments of the two countries must fall in the same factor-price equalization region (Travis, 1964, Chapter 1; Dixit and Norman, 1980, pp. 110-125). Where specialization can interfere with complete equalization of factor-prices, if one of the factors in mobile as well, there must be complete equalization of factor prices. In the absence of trade, mobility of one factor will move the national economies toward the integrated equilibrium, and to it if the initial endowments are sufficiently similar. Furthermore, the directions of trade and migration are predictable based on initial endowments and knowledge of the common technologies. As we noted in sections 2.4 and 2.5, the m n HO model can be generalized to the case of international factor mobility. An important series of papers uses duality methods, primarily the properties of the GNP function, to develop such generalizations.99 The first step was taken by Svensson (1984), who develops a two-country, m n model of trade with international factor mobility. As in Dixit and Woodland (Dixit and Woodland, 1982), the analysis proceeds by considering identical countries, so under HO assumptions there is no trade in goods or factors, then considering the effect of a marginal change in endowments on equilibrium trade in goods and factors.100 Within this framework, and using a ―controversial identification of Rybczynski effects with generalized factor intensities‖ (pg. 375), the presence of factor trade weakens the relationship between commodity trade and factor endowments.101 Of course, there is a relationship of the usual kind between factor use and trade, but factor use is endogenous, so the usual causal inference in the standard HO model is not available. We will return to the nature of the link between commodity trade and factor trade in more detail in the next section. Ethier and Svensson (1986) develop the analysis beyond the case of marginal changes in the neighborhood of an autarkic equilibrium and consider the full range of standard comparative statics on the m n model (e.g. factor-price equalization, Samuelson reciprocity, StolperSamuelson, Rybczynski, Heckscher-Ohlin). Most of these comparative statics survive the introduction of international factor mobility as long as, in the notation of section 2.5, n + mT ≥ m. That is, the number of internationally traded goods and factors is at least as large as the number of factors. Of relevance here is that Ethier and Svensson are able to deliver a fairly strong These papers build on Dixit and Woodland‘s (1982) analysis of the link between factor endowments and trade volumes in an m n HO model. Also very useful are papers by Neary (1985) and Falvey and Kreickemeier (2005) who apply these duality methods to the case of international trade and factor mobility in a world with one large and one small economy. 100 Ohyama (1989) pursues essentially the same strategy. 101 As Svensson (1984, footnote 6) notes, ―factor intensity‖ is an ambiguous concept in general models. The problem with the ―generalized factor intensities‖ used in this paper is that they are defined by the effect of the factor on output—i.e. where ∂2G/∂pi∂zj = ∂yi/∂zj > 0, sector i is said to be intensive in the use of factor j. But to use this definition of intensity to discuss Rybczynski effects seems tautological. 99 ~ 59 ~ quantity version of the Heckscher-Ohlin theorem, though were not able to deliver much in the way of a price version. Beginning with important papers by Kemp (1966) and Jones (1967), the focus of much of the literature on trade and migration in general equilibrium shifted to models in which countries differ in their technologies. Ruffin (1984) refers to the HOS model with mobile capital under international differences in technology as the Kemp-Jones model. Jones argued that, with technological differences, there was a presumption that international factor mobility would lead to specialization of at least one economy: ―If capital is mobile between countries, whether or not impeded by a tax, complete specialization is apt to occur in at least one of the countries, regardless of the similarities or differences in technical knowledge as between the two countries‖ (Jones, 1967, pg. 2). This will certainly be the case if one country has a technological advantage in one sector. In that case, as stressed by Jones and Ruffin (1975) and Ferguson (1978), the model will have a strongly Ricardian flavor with technological difference determining the pattern of international flows.102 However, if there is a reversal of comparative costs, there will be some factor-price ratio at which both countries are unspecialized and there will be a range of feasible outputs over which the allocation of production between the countries is indeterminate (i.e. there is a ―flat‖ on the world production frontier, see: Inada and Kemp, 1969; Chipman, 1971; Ethier and Ross, 1971; Uekawa, 1972).103 Markusen and Svensson (1985) seek to extend this analysis to the m n case. They follow Dixit and Woodland (1982) and Svensson (1984) in beginning with identical countries and, where the previous papers consider the effect of a marginal change in endowments, considering the effect of a marginal change in technology on one of the countries. Not surprisingly, it is difficult to derive much in the way of general results in this model. However, assuming a specific form of product-augmenting technical change, Ethier and Svensson are able to show that factor mobility strengthens the relationship between trade and endowments in the no factor mobility case; and are able to show that countries will import factors that are used intensively in the sectors with technological advantage. As in the Kemp-Jones case, international factor mobility pushes countries to specialize more strongly and induces a Ricardian element in the model. The authors also consider factor-augmenting technological differences between countries, but the results are less clear cut. As Jones (1970) and Ruffin (1984) stress that the parallel is less than perfect if one country‘s technological advantage is identical in both sectors. In this case, in the mobile factor version, the country with superior technology will export the good whose production uses the mobile factor intensively, while in the Ricardian model with factor mobility, there will be no trade (i.e. autarky prices between the countries will be the same if one country‘s technology is uniformly superior in both sectors). 103 Of these, a particularly important result is Chipman‘s (1971, theorem 2) substitution theorem, which provides conditions under which non-specialization (and a flat on the world production frontier) are to be expected. The logic of this result is exposited in Ethier and Ross (1971) and Jones and Ruffin (1975), and extended and examined in greater detail in Uekawa (1972), Ferguson (1978), Woodland (1983), Brecher and Feenstra (1983), Inoue (1986), and Tawada (1989). In addition to providing a particularly clear exposition of Chipman‘s analysis, Ethier and Ross (1971) develop a dynamic analysis that qualifies the Chipman et al. analysis. 102 ~ 60 ~ A different generalization involves introducing transaction costs into an otherwise standard HOS model so that with trade in goods alone factor prices are not equalized, which creates a new basis for international factor mobility with trade in goods. Norman and Venables (1995) develop this analysis and derive the pattern of trade in goods and factors endogenously (see also Tombazos et al., 2005 for related work). Not surprisingly, the interactions between commodity and factor trade can be quite complicated. An alternative way of avoiding specialization is to work with a multisector specific factors model with an internationally mobile specific factor. With the specific factors model, we must first decide whether the globally mobile factor is intersectorally mobile or specific to one of the sectors. This would seem to be tricky on a priori grounds. Suppose, as is often the case, that we are interested in unskilled labor mobility, and that we denote its factor payment w. Does it make more sense to think of this as an undifferentiated factor that is used in all sectors (e.g. field hands, janitors, construction workers) or, recalling that we are working with a relatively low dimensional model of the economy as a whole, do we think of unskilled labor as being specific to some broadly construed sector (labor intensive agriculture, unskilled services, or some composite of such sectors) with a factor like capital as the mobile factor? I don‘t think there is a good answer to this question. If we presume, as in the HOS case, that preferences are identical and homothetic and technologies are identical and linearly homogeneous across countries, the analysis of comparative advantage is straightforward in either case. If the internationally mobile factor is used in both sectors, the presence of specific factors in both sectors under standard technologies implies that equilibrium will involve positive use of the internationally (and intersectorally) mobile factor in both countries. But this means that w = w* (i.e. unskilled labor moves until the wage is equalized) and both countries produce both goods in equilibrium. However, this implies that the payments to the other factors must be equalized as well. With identical, homothetic preferences and equalization of goods prices by trade in goods, both countries indirectly consume factors in the same proportions, so each country will export the product that uses the specific factor with which it is abundantly endowed. Suppose, instead, that unskilled labor is specific to a single sector and that the intersectorally mobile factor is not internationally mobile.104 Now there are two possibilities: mobility does not equalize wages and so all unskilled labor ends up in the country with the higher wage; or mobility equalizes the unskilled wage between countries. In the first case, the country of immigration produces both goods but exports the good using the internationally mobile specific factor, while the country emigration specializes in the production of (and thus exports) the other good. In the second case, unskilled wages are equalized by migration with positive allocations of unskilled labor to both countries. In this case, both countries produce both goods and, as in 104 While there is no particular reason that this model should not be used to analyze migration, as a matter of fact, it has not been much used for this purpose. However, especially since Caves (1971), the mobile specific factor model has been seen as a simple, natural general equilibrium framework of the analysis of foreign direct investment (Amano, 1977; Burgess, 1978; Falvey, 1979; Jones and Dei, 1983; Jones, 1989; Neary, 1995). ~ 61 ~ the previous case, all factor-prices are equalized. As in the previous case, comparative advantage will be determined by the relative endowments of the immobile factors. 4.2. Are Factor Mobility and Commodity Mobility Complements or Substitutes? An issue of theoretical, empirical and policy interest is the degree to which trade and migration are substitutes or complements. As a policy matter, it is often argued that countries have a choice between admitting goods and admitting people. During the NAFTA debates, proponents of NAFTA often argued that the US could reduce immigration pressure by increasing its trade with Mexico.105 Similar arguments have been made about the EU‘s eastern enlargement (e.g. in Layard et al., 1992). The default position for most people seems to be that trade should be expected to substitute for immigration. The logic is clear enough, and derives directly from the HOS model: commodities are simply bundles of factors of production, so trade along HOS comparative advantage lines should cause factor prices to become more similar, reducing pressure for migration. 4.2.1. Complements and Substitutes in Theory --Figure 7 about here-Robert Mundell‘s (1957) classic develops precisely this logic. In the context of a standard 2factor 2-good 2-country HOS model, Mundell proves a converse to Samuelson‘s (1949) factor-price equalization theorem. Samuelson showed that, under the full set of HOS assumptions and as long as both countries remained unspecialized after the opening of trade, free trade between countries that differ only in their endowments of productive factors, in addition to equalizing commodity prices, must equalize the real prices of factors even though they are not internationally mobile. Furthermore, even if one country specializes before factor-prices are completely equalized, commodity trade must cause factor-prices to move toward equalization. The key to understanding this result is that, in the HOS model, there is a one-to-one, technologically determined, relationship between relative commodity prices and relative factor prices. Figure 7 is a diagram of the sort Samuelson used to illustrate this fact (Samuelson, 1949, pg. 188).106 As Mundell argued, under the same conditions (in particular, non-specialization) that guaranteed factor-price equalization, if a wedge is driven between commodity prices (say, by a tariff) but factor-mobility is permitted, that factor mobility will support the same allocations as in the free trade equilibrium. Not surprisingly, the same diagram illustrates this fact: start from an equilibrium where countries are in autarky, so that they are at different points on the p-ω schedule; now permit factor mobility so that factor-prices are equalized; it must be the case that See, as one among many examples, the New York Times article (18 February 2007) called ―NAFTA Should Have Stopped Illegal Migration, Right?‖ 106 Note that we have drawn the figure under the assumption that good 1 is capital intensive. Thus, if p = P2/P1 and ω = w/r, we know from the Stolper-Samuelson theorem that the technologically determined relationship between these two variables is positively sloped. 105 ~ 62 ~ commodity prices are equalized. Furthermore, given the assumptions on technology and demand, this must be the same relative commodity price and relative factor-price as in the free trade case.107 Thus, as the public logic maintains, in this case trade and immigration are substitutes. However, it turns out that most movements away from the strict HOS framework open the door to complementarity (or, at least, greater complexity) in the relationship between commodity trade and factor trade. It is probably worthwhile to follow Wong (1986, appendix 1) in being clear on just what we will mean by ―substitutes‖ and ―complements‖. As Wong argues, we can focus on the relationship between: physical movement of commodities and factors; commodity and factor prices as a function of such movements; and final allocations under commodity or factor movements.108 Wong also emphasizes that each of these is made up of two comparisons: the effect of commodity trade on immigration flows, prices and allocations; and the effect of immigration on commodity trade, prices and allocations. We follow Wong in referring to: 1) Quantity substitutes: if an increase in the volume of trade reduces the volume of migration (trade substitutes for migration); and if an increase in the volume of migration reduces trade in commodities (migration substitutes for trade). If the relationship is symmetric, we will say that trade and migration are quantity equivalent. If an increase in the volume of one increases the volume of the other, we will say they are quantity complements. 2) Price substitutes: if an increase in the volume of trade reduces the difference in factor-prices between countries (trade substitutes for migration); and if an increase in the volume of migration reduces the difference in prices between countries (migration substitutes for trade). If the relationship is symmetric, we will say that trade and migration are price equivalent. If an increase in the volume of one causes the prices of the other to move further apart between countries, we will say they are price complements. 3) Allocation equivalence: if trade is sufficient to reproduce the integrated equilibrium; and if migration is sufficient to reproduce the integrated equilibrium.109 If trade and An early, and important, criticism of Mundell‘s analysis argued that, if tariffs generate the wedge between commodity prices, and the payment for the imported factor must be repatriated to the factor‘s Home country, a wedge will remain driving the economy to specialization and non-equalization (Rakowski, 1970; Flatters, 1972). It is worth making two comments here: first, the factor-mobility remains a substitute, just not a perfect substitute; and second, to the extent that immigrants primarily consume where they work (and under the maintained assumption of identical, homothetic preferences across countries), this criticism is less relevant for the case of immigration. 108 Wong refers to the last in terms of ―efficiency‖, while Ethier (1996, pg. 52) refers to ―equilibrium substitutability‖. Both refer to the same fact--equilibria in which allocations of commodities to households are identical. Such equilibria are obviously welfare equivalent. We prefer to refer to the fundamental fact (allocations) rather than consequences of that fact. 109 The integrated equilibrium is the equilibrium of the single global economy in which all factors and goods are perfectly and costlessly mobile—i.e. before Samuelson‘s angel (Samuelson, 1949, pg. 194) divides the world into separate countries. This integrated equilibrium has proved a highly useful baseline. For more details on its construction and examples of its use, see: Travis (1964, Chapter 1); Dixit and Norman (1980, pp. 110-125); and 107 ~ 63 ~ migration are individually allocation equivalent, we say following Purvis (1972) and Wong (1986) that trade and migration are allocation substitutes. If both are required to reproduce the integrated equilibrium, they are allocation complements. With these definitions in hand, it is easy to see that in the HOS model trade and migration quantity equivalent, price equivalent, and allocation equivalent. If both countries produce both goods in all equilibria (i.e. under free commodity trade, free trade in factors, and free mobility of both) these equivalences are perfect. The existence of a technologically determined, one-to-one relationship between commodity prices and factor prices (as in figure 7) is an essentially 2 2 phenomenon.110 However, as long as there are at least as many final commodities as factors, it is once again the case that, if country endowments are relatively similar (as defined by sharing the same cone of diversification), trade and migration are price, quantity and allocation equivalent (McKenzie, 1955; Rodriguez, 1975; Neary, 1985; Falvey and Kreickemeier, 2005).111 The situation becomes harder to interpret in a world that involves some mobile factors as well as mobile goods (e.g. Svensson, 1984; Ethier and Svensson, 1986). When we consider substitutability of commodity for factor trade, under any of the definitions, are we interested in mobility of the previously immobile factors (as in all of the previous analyses discussed in this section), or are we interested in the already mobile factors. Denoting the set of mobile factors by k and the immobile factors by l, Svensson says that mobile factor i is cooperative with immobile factor j if ki / l j 0, where the tilde denotes the amount of mobile factor i in use, and competitive if the inequality is reversed, both of which are possible. Svensson focuses on trade in the mobile factors (k) and finds that whether mobility of k and trade in goods are (quantity) substitutes or complements depends on whether l and k are cooperative (substitutes) or competitive (complements). --Figure 8 About here-Now let us return to the 2-factor 2-good model and retain all of the HOS assumptions except we suppose countries have identical initial endowments and that one country (―Home‖) has a Hicks neutral superior technology in the production of good 1. In terms of the technological relationship between factors and commodity prices in figure 7, if this is the only change relative to the economy represented there, the Home country will be represented by a curve that lies Helpman and Krugman (1985, Chapter 1). In general, and abstracting from tricky issues of second-best (i.e. in the context of other distortions considered in this literature), the integrated equilibrium should be the weakly most efficient of the three candidate equilibria (free trade only, free migration only, integrated equilibrium). 110 Global univalence, the generalization of the no factor intensity reversal condition which underwrites the one-toone mapping between the commodity price vector and the factor price vector, is not generally a property of higher dimensional versions of the Heckscher-Ohlin model. A detailed technical development can be found in Nikaido (1968, Chapter 7). Very clear short presentations can be found in Ethier (1984, pp. 150-151) and Woodland (1982). Parthasarathy (1983) and Campbell (1993) present many attempts to carry this sort of analysis further 111 As Deardorff points out, inference in the m n case is affected by both demand conditions (1986) and dimensionality (Deardorff, 1994). ~ 64 ~ uniformly below that of the Foreign country (which is represented by the original curve).112 Figure 8 reflects this change. Now suppose that free trade results in the equalization of commodity prices at pw. Note that national factor prices are different. Specifically, as drawn, the return to labor in Home exceeds the return to labor in Foreign. In this trading environment the Home country exports L-intensive good 1. If we now permit migration, labor will flow to the Home country, increasing its comparative advantage in standard Rybczynski fashion and, thus, increasing trade. So factor mobility is both price and quantity complementary to free trade in goods. Now suppose, instead, that free migration is permitted following the technical change. L will move until real wages are equalized. If both countries continue to produce both goods, the factor-price ratio (ω) will be equalized but commodity prices will move apart. If trade is now permitted, there will be increased production of each country‘s comparative advantage good, which should result in increased migration. Thus trade is price and quantity complementary to migration.113 It is easy to see that the migration only and trade only equilibria involve very different commodity and factor prices. Thus, neither alone moves the economy to the integrated equilibrium. Rather, that requires both to be fully mobile, so trade and migration are allocation complements as well. Markusen and Svensson (1985) show that a dimensional generalization of the above case is available. Specifically, if the countries differ only in terms of productaugmenting technological differences, they show that trade and factor mobility are quantity complements.114 Markusen (1983) and Ethier (1996) consider a variety of other sources of comparative advantage, including taxes, economies of scale, imperfect competition (monopoly, oligopoly, and monopolistic competition), and factor market distortions. Ethier summarizes these additional cases as follows: There is a strong presumption that intra-industry trade and trade due to aggregative economies of scale or to international differences in the degree of imperfect competition are strongly complementary to migration. There is also a strong presumption that inter-industry trade due to disaggregative economies of scale or to monopolistic competition relates to migration in the same ways as does comparative advantage trade. (Ethier, 1996, pg. 65) Taking all of this together, it seems clear that theory alone does little to underwrite any strong presumption of a complementary or substitutive relationship between trade and migration. However, it is interesting to note that research on the foundations of comparative advantage over 112 If, instead, we assume that the Foreign country has a Hicks neutral superiority in the other sector, the schedule representing its relationship between commodity prices and factor prices would shift uniformly up relative to the original schedule. 113 Wong (1986, proposition 3) shows that, while it holds in the case presented above, the two-way relationship is actually somewhat more complicated. Specifically, whether or not labor mobility is a quantity substitute for trade depends on whether the good experiencing technical change in an importable or an exportable; and whether or not trade is a quantity substitute for labor mobility depends on 114 Markusen and Svensson (1985) show that general results on factor mobility with technological differences in high dimensions are not available. Even in the case of commodity augmenting technology differences, the result is derived, following Dixit and Woodland (1982) and Svensson (1984), only for infinitesimal differences under the assumption of m > n. ~ 65 ~ the last couple of decades has stressed precisely the factors that imply a presumption of complementarity (i.e. technological differences and monopolistic competition as a foundation for intra-industry trade). This leads us to the empirical evidence on the relationship between trade and immigration. 4.2.2. Empirical Research on Complements and Substitutes All of the theoretical work we have discussed to this point considers the question of whether trade and migration (or capital flows) are substitutes or complements in terms of factor arbitrage. That is, the source of any relationship is taken to be the way factors respond to differences in wages (or rentals) between countries. Early empirical work on this question was motivated in precisely this fashion. Early work by Horiba and Kirkpatrick (1983) looked at interregional trade and migration between regions (South and non-South) in the US in the 1960s. This paper looked at quantity flows of people (considering heterogeneity of labor) between regions and (using standard input-output techniques) the flows of labor embodied in trade. Under the maintained assumption of an m n HO-type economy, Horiba and Kirkpatrick predict that labor should flow from a region relatively well-endowed with labor to regions relatively poorly endowed with labor; and, in standard HOV fashion (see Chapter by Bernhofen in this Handbook), embodied trade in factors should follow the same pattern. For our purposes, the key finding was that both of these predictions were borne out.115 In addition, there was some evidence of a tendency toward factor-price equalization. These results would seem to be broadly consistent with a substitutive relationship between trade and labor mobility. In a recent paper, Horiba (2008) carried out the same analysis on more recent data (from the 1970s and 1980s) and confirmed his earlier finding. These results are closely related to a growing body of trade research, discussed above, whose results suggest that the HO model, under various plausible extensions of the model (e.g. the presence of trading costs or Hicks neutral international differences in technology) and generalization of the Rybczynski theorem, does a reasonably 115 Thus, as Horiba (2008) notes, the regions endowments become more similar over time, but this convergence is slow. Collins, O‘Rourke and Williamson (1999) ask a similar set of questions using historical data for the ―Atlantic Economy‖ in the period 1870-1936. They also look at whether quantities of trade and migration are positively or negatively correlated. If there is a positive correlation, they take that as evidence of complementarity; if they are negatively correlated, they take that as evidence of substitutability; and if there is no correlation, they call that a ―neutral‖ result. As the formal analytics in Horiba and Kirkpatrick and Horiba suggest, it is far from clear that these correlations relate to the underlying issue of complementarity in any obvious way. Interpreting the panel analysis is similarly problematic. In any event, the overwhelming number of cases are characterized by ―neutral‖ results. In a methodologically related paper, Gaisford (1995) revisits the Leontief paradox under the assumption that capital is mobile. Gaisford applies the Ethier and Svensson (1986) model to rederive HOV results for the case with capital mobility and finds that the US is revealed capital intensive in terms of direct and indirect export of capital relative to labor. ~ 66 ~ good job of accounting for production patterns, and research on growth which fails to find a link between migration and convergence.116 A more direct approach to evaluating the relationship between trade and migration involves introducing migration into a theoretically well-grounded model of international trade. One approach that has been applied a number of times involves estimating a maximum value function consistent with competitive models and evaluating the relationship implied. We have already seen this methodology applied to the question of the relationship between immigration and wages (section 3.2.1 above). An early paper by Wong (1988) estimated an indirect trade utility function, for an economy with three final goods and three factors of production, for US annual data from 1948-1973, estimating elasticities that allowed him to evaluate the effects of migration on trade. This function is estimated, in translog form, on prices for home produced durable goods, home produced nondurable goods and services, and imported goods and services, and endowments of capital, land, and labor, for a number of years between 1948 and 1983. Wong finds that trade is a quantity complement to immigration. Ulrich Kohli is the scholar that is probably most associated with the development and application of these methods to international trade and migration. In his approach, trade is treated as an intermediate input to the production of GDP.117 It is straightforward to treat immigrant labor in a similar fashion.118 In this framework, using Swiss data for 1950-1986, Kohli finds that non-resident labor and imports are complements in the quantity sense (Kohli, 1993; 1999). In a more recent paper, Kohli (2002) explicitly considers domestic output and exports as outputs in a joint revenue function and, once again, finds immigration and imports to be quantity complements, but essentially no relationship between immigration and exports. Hijzen and Wright (2010) apply the Kohli (1993; 1999) methodology of treating imports and immigrants as intermediate inputs to final output using UK data for the period 1975-1996. In an important extension, Hijzen and Wright divide immigrants (and the endowments of domestic labor) into skilled and unskilled labor—thus, production involves capital, domestic skilled labor, domestic unskilled labor, immigrant skilled labor, immigrant unskilled labor, and imports. In addition, because they want to permit output adjustment, Hijzen and Wright consider two outputs—skill-intensive and unskilled-intensive outputs. The results here are interesting: skilled immigrants are quantity complements with trade; but unskilled workers are, if anything (i.e. the result is statistically insignificant), quantity substitutes.119 116 For the lack of a relationship between migration and convergence, see Barro and Sala-i-Martin (1991) and related work by Kim (1998) suggesting an important role for industrial structure, as well as technological change, in accounting for convergence. 117 For a text treatment of Kohli‘s approach to trade modeling, see Kohli (1991). 118 It is probably worth noting that Kohli‘s work deals with ―non-resident workers‖ (i.e. guest-workers) not ―immigrants‖ in the sense that most of the empirical work considered here analyzes. 119 As the authors suggest, this seems prima facie plausible—i.e. an increase in the factor used intensively in the exportables sector should, via Rybczynski effects, increase production of exportables and thus trade; while an increase in the factor used intensively in importables should increase Home production of importables, thus reducing ~ 67 ~ To this point we have considered empirics explicitly motivated by the theoretical frameworks presented in section 4.2.1. In all of this work, migration (factor mobility more generally) is an arbitrage activity. Trade costs, especially such essentially social cost reducing phenomena as networks, play no role. However, the great majority of empirical research addressing the relationship between trade and migration has taken place in the context of a gravity model, where migration and/or trade enter as a factor that affects costs. Thus, while the empirical issue of whether trade and migration are substitutes or complements can be addressed, the theoretical motivation ends up being rather different. Most of this research treats aggregate exports or imports between a pair of countries as the dependent variable and immigration as a dependent variable. In most of these papers, this is seen as reflecting either a direct increase in the demand for goods from the immigrants‘ home countries; or a reduction in information costs (in either direction) resulting in increased trade. 5. Migration as People Moving: Social Structures, Institutions and Political Economy The research we have reviewed to this point treats migration as an instance of factor arbitrage, where the relationship between trade and immigration emerges from the general equilibrium. For this analysis, there was no essential difference between capital and labor: both generate income for households and can be used to produce outputs under given production functions. To the extent that there is any difference, it is not uncommon to treat the income from internationally mobile capital as consumed in its Home country, while the income from mobile labor is consumed in the Host country.120 This is an extremely useful simplification for many analytical purposes; however, it is also the case that, in many ways, capital and labor are fundamentally different things. In the words of the Swiss writer Max Frisch commenting on guest worker programs: ―We wanted workers, we got people‖. Capital, by contrast, is fundamentally separable from its human owners.121 Thus, in addition to differences in the skill mix (and possibly taste differences) of migrants relative to natives, immigrants also carry cultural differences that might affect their willingness to cooperate with natives in unions (and vice versa). Perceptions of social/citizenship difference might affect the legitimacy of state transfer programs or participation in reciprocal arrangements natives in the labor market. These perceptions of difference even go to economically important social values like fairness. Sociologists and political scientists have dealt, seriously and at length, with many of these issues. trade. However, it is tricky to know how to evaluate positive immigration of both labor factors (though the UK may well be a net exporter of capital). 120 The reality, of course, is more complex—target earning immigrants intend to return home with most of their income for investment in the Home country and nearly all immigrants repatriate at least some income; similarly, many small capitalists follow their capital to the countries in which they invest. Nonetheless, this simple distinction is useful and sufficiently close to the reality to underlie basic factor arbitrage models. Under conditions of identical and homothetic preferences, even this difference is essentially irrelevant. 121 Human capital is, of course, inseparable from humans. That is why, legally and socially, immigration of human capital is treated as labor, not as capital. It is also worth noting that research on foreign direct investment, since Hymer‘s (1960/1976) famous MIT dissertation, has tended to emphasize firm-theoretic factors rather than capital arbitrage. An important early paper introducing firms into general equilibrium models is Ethier (1986d). Current work follows Antras (2003) in drawing on contract theoretic models. ~ 68 ~ In this survey we will focus on those elements that emerge directly in the analysis of international trade, or apply trade theoretic methods. Specifically, we will focus on three issues that deal with social institutions, broadly construed (networks, illegality, and welfare states); and then turn to a brief discussion of political economy issues. 5.1. The Social Structure of Migration: Networks, Migration and Trade As tables 1 and 2 above show, emigration and immigration are far from uniformly distributed across the globe. This heterogeneity becomes even more pronounced as one takes account of individual-level variation (e.g. by age, gender, education, etc.). Accounting for this heterogeneity in aggregate patterns has been a very active area of research for a long time, and that activity continues to this day. For economists, the essential starting point for such analysis is the notion that emigration emerges from a utility maximizing choice. That is, immigrants compare the benefits of staying in their home country to the benefits (net of costs) of moving to some new country. Because this decision involves comparison of returns to various choices that occur in time, it is convenient to conceive of the choice as one of investment in human capital (e.g. Sjaastad, 1962). In making such a comparison, a potential emigrant compares the origin country wage to that in alternative destination countries. For each destination country, the potential emigrant must deduct the costs of migrating to that country. Since all of this must be done in expectation, one might also want include a measure of the likelihood of finding a job (e.g. a comparison of unemployment rates). An important advance in the theoretical and empirical analysis of immigration flows was Borjas‘ (1987) adaptation of Roy‘s (1951) model of occupational selection to the case of selection among emigrant destinations. While Borjas was primarily interested in identifying the causes and consequences of differences in immigrant ―quality‖ across source countries to the US, he also argues that the same analytical framework predicts emigration pattern across those source countries. Taking per capita GDP as a proxy for wages and distance as a proxy for costs, one can represent the Roy-Borjas selection model, loosely speaking, by a gravity model.122 Gravity modeling of migration generally takes the form: mijt Gijt ijt ijt , (48) Where mitj is the value of migration from origin country i to destination country j; Gijt is a matrix of standard gravity variables (e.g. origin and destination GDP, distance, and other ―migration 122 Immigration, and related issues of inter-regional travel, has been a focus of research using the gravity model for virtually as long as the gravity model has been applied (e.g. Ravenstein, 1885; 1889; Zipf, 1946). For useful surveys tracing gravity modeling of migration back to the 19th century, see: Carrothers (1956) and Greenwood and Hunt (2003). The majority of this work focuses on inter-regional/intra-national migration, but the results are quite consistent with that which focuses on international migration. For surveys of this work, see Greenwood (1975; 1997) for the case of developed countries, and Lucas (1993) for less developed countries. In addition to Sjaastad and Borjas, early attempts to derive a gravity model from utility maximizing fundamentals include Ginsberg (1972) and Smith (1975; 1976). For a general overview of gravity modeling, with a primary focus on international trade see Bergstrand and Egger‘s Chapter X in this volume. ~ 69 ~ cost‖ variables), λijt is a matrix of fixed effects, and ε is an error term. Among the papers motivating a gravity-based analysis by reference to Sjaastad and Roy-Borjas are: Karemera, Oguledo, and Davis (2000); Pedersen, Pytlikova and Smith (2006); Gallardo-Sejas, et al. (2006); Clark, Hatton and Williamson (2007); and Lewer and Van den Berg (2008). 123 More recently, in addition to Borjas (1987) a number of papers have sought to make the link between the RoyBorjas model and the gravity framework more explicit, e.g.: Dahl (2002); Mayda (2008a); Grogger and Hanson (2008); and Ortega and Peri (2009). All of these papers consistently find destination GDP positively and distance negatively associated with migration flows. Unexpectedly, origin GDP (which should be negatively associated with migration and about the same magnitude as origin GDP) is generally not significantly different from zero, and even sometimes of the wrong sign.124 In addition to such standard gravity variables, immigration policy variables in the destination country have been found to have a significant effect (Bertocchi and Strozzi, 2008; Mayda, 2008a; Letouzé et al., 2009; Ortega and Peri, 2009). We note, for later reference, that a small number of papers introduce some trade variable into the migration gravity model (Molle and van Mourik, 1988; Gallardo-Sejas, Pareja, Llorca-Vivero and Martinez-Serrano, 2006; Letouzé, Purser, Rodríguez and Cummins, 2009). In all cases, the trade variable is positive and, usually, significant. Stories about immigration, whether contemporary or historical, journalistic, academic, or fictional, have long stressed the role of social relations as an essential element in the decision to engage in migratory behavior. Migrants are linked to both their home and host countries by networks that provide information, resources, and comfort, all in a variety of forms (Hugo, 1981; Boyd, 1989; Gurak and Caces, 1992; Portes and Sensenbrenner, 1993). Where economists have tended to analyze immigration as reflecting optimization by individuals (Sjaastad, 1962; Borjas, 1987) or households (Mincer, 1978; Stark and Levhari, 1982; Katz and Stark, 1986), sociologists/demographers have been very successful building network models of the immigration decision. 125 More recently, as economists have developed increasingly 123 The empirical success of gravity models of migration has led to their extensive use in policy research as a predictor of migration pressure. For example, a substantial body of policy research was interested in predicting migration flows to the European Union as a result of the various enlargements (e.g. Molle and van Mourik, 1988; Alvarez-Plata et al., 2003; Brücker and Siliverstovs, 2006). 124 In the gravity literature on migration, destination GDP is a ―pull factor‖ and origin GDP is a ―push factor‖. In the theory, since what matters to the potential migrant is income net of costs, the ultimate comparison is [(wD – wO) – C] where the w‘s are wages in origin and destination and C is the cost of migration from O to D. It should be clear that the effects of the first two terms enter this analysis symmetrically. Thus the asymmetry in the results is a puzzle. Among attempts to account for this anomaly are: poverty constraints in the context of large fixed migration costs and imperfect credit markets (Lopez and Schiff, 1998; Yang, 2008); age heterogeneity in response to destination restrictions (Hunt, 2006); formal restrictions operating under political economy constraints (Mayda, 2008a); and inappropriate specification of the econometric form estimated (Grogger and Hanson, 2008). 125 Beginning with the modern classic Return to Aztlan (Massey et al., 1987), Douglas Massey and his colleagues have developed an impressive body of research focusing on these networks between Mexico and the United States (see e.g. Massey, 1990; Alarcón, 1992; Massey and Espinosa, 1997; Massey et al., 1998; Phillips and Massey, 2000; Palloni et al., 2001; Durand and Massey, 2004; Fussell and Massey, 2004; Massey, 2008). In addition to the massive literature on Mexican migration to the US, the importance of networks to the migration decision have been found for many other cases as well—e.g. Japanese (Jedlicka, 1979);Italians (Moretti, 1999); Germans (Bauer and ~ 70 ~ sophisticated models of networks, these considerations have increasingly been built into migration analysis.126 Empirical work seeking to explain migration patterns now commonly includes variables intended to capture network effects—usually some measure of stock of immigrants from a given home country in a given host country. The key here is not that networks substitute for rational choice of destinations by migrants, but that networks affect the costs of migrating to one market versus another. Just as networks play a fundamental role in getting migrants from one country to another, and helping determine the allocation of migrants from home to host countries, networks also play a fundamental role in organizing the social and economic life of migrants once they arrive in a given host country.127 Of particular interest for us is the way that networks affect the relationship between migration and trade. Broadly speaking, networks of migrants might affect international trade by responding to two sources of transaction costs: uncertainty/incomplete information; and asymmetric information/opportunism. With respect to the first, the idea is that trade in some commodities requires search, and that the cost of such search varies systematically across countries. Especially for the case of specialized/differentiated goods, the lack of a deep, well-developed arms-length market can require costly search. When this search must occur across international borders, especially between countries with very different social and/or political structures, those costs can be quite high (Rauch, 1999; Rauch and Casella, 2003; Portes and Rey, 2005). In this situation, migrants can act as ―weak ties‖ in Granovetter‘s (Granovetter, 1973; 1983; 2005) sense of providing an information bridge between two dense networks (in this case, suppliers in the home market and demanders in the host market). That is, because migrants possess economic, cultural, and institutional knowledge about both the home and the host markets, they are able to mediate economic exchange between those markets, thus increasing trade above what it would be in the absence of such migration. In this case, migrants engage in market creation. Because such information problems are expected to be more severe for differentiated products, we would expect to find strong positive effects for trade in such products, especially between countries with very different economic, cultural, and political Zimmermann, 1997; Wegge, 1998); Hong Kong Chinese (Wong and Salaff, 1998); Indians (Banerjee, 1983; Poros, 2002; Harvey, 2008);Turks (Böcker, 1994; 1995); and Central and Eastern Europeans (Dahinden, 2005; Haug, 2005; 2008; Elrick and Ciobanu, 2009). For general treatments of sociological theory and methods of network analysis, see: Marsden and Lin (1982); Wellman and Berkowitz (1988); and Wasserman and Faust (1994). Of particular interest to economists is the work of Harrison White (1992; 2002) and Ronald Burt (1992; 2000). 126 Although early work by economists recognized the role of networks (e.g. Nelson, 1959; Rees, 1966), economists generally came late to the analysis of networks, in general and with specific reference to migration. However, networks are now an active area of research in economic theory and empirics. For excellent text treatments see: Goyal (2009) and Jackson (2008). For examples of theoretical analyses of network effects in migration see: Carrington, Detragiache, and Vishwanath (1996);Helmenstein and Yergorov (2000), Moretto and Vergalli (2008); Teteryatnikova (2008), and Moenius, Rauch and Trindade (2007). 127 The concerns of social capital theory overlap very strongly with those of network theory. Research on the social capital generated by groups in general goes back at least to the foundational work of Loury (1977; 1981), Bourdieu (1986; Bourdieu and Wacquant, 1992) and Coleman (1990). The application to immigrant communities has a long pedigree in sociology. In economics, a number of recent papers have stressed the role of networks/social capital among immigrants. In particular, see the work of Borjas (Borjas and Bronars, 1991; Borjas and Trejo, 1991; Borjas, 1992; 1993; 1994b; 1995; 1998), and Lazear (Lazear, 1999; 2000). ~ 71 ~ environments. In some sense, once such a bridge has been constructed, the need for additional migrants might well be expected to decline. Unlike transactions costs that emerge through simple lack of knowledge, those related to asymmetric information, imperfect enforcement of contracts, and opportunism create a more fundamental role for networks.128 In an environment characterized by these problems, the opportunity for mutually beneficial trades may be foregone (Anderson and Young, 2006). In the limit, these problems can cause the collapse of markets. This, in turn, creates an opportunity for non-market (or ―market replacing‖) institutions; which, of course, is the opening wedge for Williamson‘s (Williamson, 1975; 1985; 1996) Nobel prize winning development of transaction cost economics. However, independently of transaction cost economics‘ emphasis on the role of asymmetric information and opportunistic behavior in understanding the creation and operation of firms; anthropologists, sociologists and historians used essentially the same factors in explaining the role of ethnic networks and disasporas in the organization of trade across political jurisdictions or, more generally, in the absence of effective protection of contractual/property rights (Polanyi, 1957; Geertz, 1963; Polanyi, 1968; Cohen, 1969; 1971; Bonacich, 1973; Geertz, 1978; Curtin, 1984). More recently the analytical structures of transaction cost economics (Landa, 1981; 1994) and game theory (Greif, 1989; 1991; 1993; 1997; Dixit, 2003a; b; 2004; 2009) have provided more formal frameworks for examining these relationship-based trade links. The basic idea here is that ties of trust, and social capital more generally, built up among coethnics in the migration process can substitute for imperfect contract enforcement (whether a function of incomplete contracts or lack of effective judicial systems). The enforcement mechanism in this case is exclusion from the social and economic benefits of the community/network.129 As with the case of transaction costs deriving from informational problems, where migrants engage in market creation, we would expect contracting problems to be most severe in the case of goods for which a deep, arms-length market does not exist. However, unlike that case, where we might expect the need for a weak-link to decline once the information bridge has been built; as long as the contracting problem remains in a given market, the need for the contract enforcement role of the network will remain in place. Furthermore, to the extent that the role of the ethnic community declines with successive generations, we might even expect a need for continuing flows of migrants to support that role. 128 As Rauch (2001) points out, effective networks need not be immigrant or ethnic networks. Any group of people that share information and are related by bonds of trust, the violation of which are costly to members of the network, can serve at least a well. However, immigrant/ethnic networks have served this purpose historically and, unlike ―old school tie‖ networks, they are relatively easily identifiable at the aggregate level. 129 While economists tend to stress exclusion from economic benefits (e.g. Greif, 1993), one of the reasons that ethnic communities play such an important role here (rather than simply repeated interaction of more-or-less randomly generated networks) is the broader role of social solidarity. This social solidarity is often linked to distinctiveness relative to the native community induced via common language and religion, as well as ghettoization and endogamy. Thus to be excluded from the community implies substantially higher costs than simple exclusion from trading networks. Epstein and Gang (2006) develop an interesting analysis of the tension between the benefits of the social network and those of assimilation in the context of a model of international trade. ~ 72 ~ Before turning to a discussion of the empirical work on the role of immigrant networks in reducing trade costs, we should note that, in addition to the role of networks, the most straightforward way that immigrant differences might affect trade patterns runs through preferences—immigrants may have a preference for their own goods that they bring with them when they emigrate.130 Not only does this have a direct effect on demand for the immigrantpreferred goods, but we would also expect that demonstration effects would increase the demand for these goods among natives as well. Given that non-immigrants from a given country (i.e. natives and immigrants from other countries) will generally dramatically outnumber immigrants from a given country, we might expect the indirect effect to be larger than the direct effect. It is conventional in the empirical literature to assert that taste effects should affect only imports, and among imports only consumer goods. While this may be a plausible approximation, it is surely the case that information gleaned by immigrants from consuming in the host country can be transferred to the home country in a variety of ways. Thus, the common inference in the gravity literature that a positive estimated effect of immigrant stock on imports is evidence of a preference effect, while a positive effect on exports is evidence of network effects, seems less than strong. By contrast, the presumption that the preference effect should be seen in consumer goods seems quite well founded. In either case, when evaluating the link between immigration and trade, we surely need to account for the effect of differences in preferences between immigrants and natives. Empirical work suggesting the presence of large border effects (McCallum, 1995; Helliwell, 1998) and missing trade (Trefler, 1995) has spurred extensive research on the role of trade (i.e. transaction) costs as a source of these findings (Anderson, 2004; Anderson and VanWincoop, 2004), and networks as a response to these costs (Rauch, 2001; Combes et al., 2003). A standard tool for evaluating the effects of such trade costs is the gravity model (see the Chapter in this Handbook by Bergstrand and Egger for an extensive discussion of the use of gravity model in trade modeling). Analysis using gravity models has provided strong support for the notion that social and political differences, and poor enforcement of contractual rights, act as barriers to trade.131 We are particularly interested here in the evidence of the role of immigrant networks in alleviating these transaction costs. Gravity modeling of trade, with the variables extended to include a migration variable, takes the form 130 Most of the theoretical research on the complements v. substitutes questions abstracts from taste differences by assuming globally common, homothetic preferences. Once we permit either systematically different preferences or heterogeneity/monopolistic competition, the analysis becomes more complex. In the HOS world, the obvious assumption is that natives have a strong preference for their exportable commodity (thus immigrants carry a stronger preference for the exports of their home country, increasing the host country‘s demand for imports from the immigrant‘s home); but this pattern of preferences can yield the Opp, Sonnenschein, Tombazos (2009) ―reverse Rybczynski‖ effect. Similarly, once we enter the world of country-specific varieties of goods, we are in a world where results are sensitive to details of market structure (Ethier, 1996). 131 For cultural differences, gravity models have used: language (Boisso and Ferrantino, 1997; Hutchinson, 2002; 2005); and broad measures of cultural difference (Guiso et al., 2009). A number of papers have used measures of rule of law and other institutions to get at the costs associated with poor enforcement of contracts (Anderson and Marcouiller, 2002; de Groot et al., 2004; Berkowitz et al., 2006; Turrini and van Ypersele, 2006; Nunn, 2007; Ranjan and Lee, 2007; Leeson, 2008; Li and Samsell, 2009). ~ 73 ~ xijt mijt Gijt ijt ijt , (49) Where xitj is the value of dyadic trade (exports or imports) between partner country i and reference country j at time t, Gijt is a matrix of standard gravity variables (e.g. reference and target country GDP, distance, and other ―trade cost‖ variables), λijt is a matrix of fixed effects, and ε is an error term.132 The parameter of interest in this work is α. Since these models are commonly estimated in logs, this can be interpreted as estimates of the elasticity of trade volume with respect to immigration.133 The seminal paper here is Gould‘s (1994) study of the effect of immigrants on trade between the US and 47 trading partners that were also sources of US immigrants, for the years 1970-1986. In addition to estimating a gravity model, extended to include stocks of immigrants from the foreign country residing in the US, for bilateral aggregate imports and exports; Gould also estimated separate regressions for imports and exports of producer and consumer goods. With respect to aggregate imports and exports, Gould found immigrants increased trade (though at lower levels than much of the later literature); and, somewhat unusually given later results, found a larger effect on exports than on imports. The usual inference from this pattern is that preference effects explain the difference between the import effect and the export effect (since the network effects are apparently taken to be symmetric). Thus, this is taken as evidence against a significant role for preference effects. When the analysis was done on consumer and producer goods separately, Gould found the effect on consumer goods was larger for both imports and exports. Gould‘s presumption was that consumer goods are more differentiated than producer goods, and took this as evidence of network effects.134 132 Most of these papers have a single reference country, which is the host country for the immigrants from various home countries. As we note below, in most papers the reference country is the US. 133 Starting with Wagner, Head and Ries (2002), a number of papers have contained tables reporting estimates of these elasticities in previously published papers. However, given the range of specifications, countries analyzed, years, and estimation techniques, the value of such an exercise is less than clear. Since, in all of these tables, each paper is represented by a single pair of elasticities (one for exports, one for imports), the goal of the authors of the tables is usually to pick the most ―comparable‖ specifications; but, since the point of many of the papers is precisely different specifications, this seems an odd choice. On the other hand, reporting elasticities from widely different specification and estimation techniques would make little sense. 134 There are two somewhat unusual elements of Gould‘s framework. The first is the use of a specific functional form for the effect of immigrants on transaction costs which is decreasing at a decreasing rate (also used by Mundra, 2005). While this permits him to estimate the point at which the positive effect of immigrants on trade begins to decline, it is also apparently responsible for the sizable difference between Gould‘s results and those of other work with otherwise similar specifications. In the event, Gould finds that the effect of immigrants on exports is exhausted at a quite small level (12,016 immigrants), while the effect on imports is exhausted at a substantially larger level (370,879 immigrants). The second peculiarity, which a small number of other papers apply, is the use of average length of stay for a given country‘s immigrants—in both a linear and a quadratic term. As in the other papers that use these variables, the effects tend to be small. This is especially the case for the quadratic term, with the result that most papers end up excluding both of these variables, or including only the linear term. More problematically, it is not clear what this variable is really supposed to measure in terms of networks and information. In neither the market creation case nor the market replacement case, as long as the networks are in place, is there any reason why average length of stay should matter. ~ 74 ~ Building on Gould‘s original work, a sizable literature of gravity-based estimates of the effect of migration on trade has developed. The single most studied reference country is the US (Dunlevy and Hutchinson, 1999; Hutchinson and Dunlevy, 2001; Co et al., 2004; Herander and Saavedra, 2005; Mundra, 2005; Dunlevy, 2006; Millimet and Osang, 2007; White, 2007b; Bandyopadhyay et al., 2008; Tadesse and White, 2008; White and Tadesse, 2008b; a; Jansen and Piermartini, 2009; White, 2009; Tadesse and White, 2010); but there are also analyses featuring Canada (Helliwell, 1997; Head and Ries, 1998; Ching and Chen, 2000; Wagner, Head and Ries, 2002; Jiang, 2007; Partridge and Furtan, 2008); the UK (Girma and Yu, 2002; Ghatak et al., 2009); Switzerland (Kandogan, 2009; Tai, 2009); Germany (Bruder, 2004); Denmark (White, 2007a); France (Briant et al., 2009); Spain (Blanes-Cristóbal 2004; 2005; 2008); Greece (Piperakis et al., 2003); Italy (Murat and Pistoresi, 2009); the EU 15 (Parsons, 2005); Australia (White and Tadesse, 2007); New Zealand (Bryant et al., 2004); and Malaysia (Hong and Santhapparaj, 2006).135 Very broadly, and with very few exceptions, these papers consistently find significant positive effects of immigration on trade—whether measured as imports or exports. Furthermore, of the papers that report results for both imports and exports, it was about twice as common to find the estimated effect of immigration on imports greater than that on exports. Again, this is taken as evidence that preference effects and network effects are both operating. There are a few closely related papers that should be mentioned in this context. The first is Rauch and Trindade‘s (Rauch and Trindade, 2002) important paper on the role of Chinese communities in trade. Rather than looking at the effect of immigration from a home country on the trade of a host country, Rauch and Trindade ask if the stock of Chinese in each country affects trade in a dyad. Chinese communities are well-known in the ethnographic and business literatures as actively involved in trade (e.g. Landa, 1994; Weidenbaum and Hughes, 1996; Liu, 2000; 2001). Thus, Rauch and Trindade‘s interest in the presence of Chinese immigrant communities in explaining trade in a gravity framework makes a lot of sense. In addition, the authors use Rauch‘s (1999) distinction between standardized goods (goods with reference prices), goods traded on organized exchange, and differentiated goods, finding that the effects of Chinese communities on the latter two categories are economically and statistically more significant than on standardized goods. Given the other controls, the authors take this as evidence that Chinese communities provide both market making and market replacing services to the countries in which they reside. A second related paper is Combes, Lafourcade and Mayer‘s (2005) analysis of the effect of migration between French départements on trade between those départements. While the analysis uses strictly domestic data, the issues of theoretical and empirical implementation are identical to the international case. This paper is particularly notable for the care it takes in developing both a theoretical framework and its explication of the empirical framework. This paper develops data and analysis considering both immigration networks and networks of firms, ultimately finding both to be economically and statistically significant. As with Gould, the effect of immigrant networks is greater on exports than it is on imports. Millimet and Osang (2007) examine the relationship between intranational trade and intranational migration for the case of the US, though this paper is primarily interested in analyzing the border effect. As in Combes, Lafourcade and Mayer, Millimet and Osang‘s results strongly support a positive relationship between trade and migration. Another paper using sub-national data on trade and immigration is Helliwell‘s (1997) analysis of intra-provincial, intra-state and international (US-Canadian) trade and migration. Like Millimet and Osang, Helliwell‘s main interest is in the border effect, but he also finds strong evidence of a positive link between trade and migration. Finally, a paper by Blanes- Cristóbal and Martin-Montaner (Blanes-Cristóbal and Martín-Montaner, 2006) examine the effect of migration on intra-industry trade. Given the usual interpretation of intra-industry trade in terms of monopolistic competition, this seems a natural development of Rauch‘s (Rauch, 1999) analysis of differentiated products. While this paper does not apply gravity methods, the results are broadly consistent with the results of those papers that do. That is, at least for Spain, immigration is strongly, positively associated with intraindustry trade. 135 ~ 75 ~ In addition to aggregate imports and exports, a number of papers also estimated separate regressions for various categories of commodities: consumer and producer goods (Gould, 1994; Blanes-Cristóbal 2004; Herander and Saavedra, 2005; Mundra, 2005; Blanes-Cristóbal 2008; Kandogan, 2009); Rauch‘s (1999; Rauch and Trindade, 2002) categories (White, 2007a; White and Tadesse, 2007; Briant, Combes and Lafourcade, 2009); intra-industry trade and interindustry trade (Blanes-Cristóbal 2005); manufactured and non-manufactured goods (BlanesCristóbal 2005; White and Tadesse, 2007); cultural and non-cultural goods (Tadesse and White, 2008; White and Tadesse, 2008b; Tadesse and White, 2010); and various product-specific disaggregations (Dunlevy and Hutchinson, 1999; Hutchinson and Dunlevy, 2001; Jiang, 2007; Kandogan, 2009; Tai, 2009). These papers attempt to identify the category of commodity that is most likely to be characterized by product differentiation and, thus, information problems, e.g.: consumer goods; differentiated good & products traded on an organized exchange; intra-industry trade; manufactured goods; and cultural goods. The hypothesis is that these goods will be traded less, so immigrants will improve their tradability more. In addition, goods are differentiated by category of trading partner: by common colonial past (Girma and Yu, 2002; Blanes-Cristóbal 2004; 2008); goods differentiated by per capita income of the exporter (Co, Euzent and Martin, 2004; White, 2007b; 2009); by whether the trading partner is an old or new market (Murat and Pistoresi, 2009); or by cultural similarity (proxied by language in many papers). Commodities from more ―foreign‖ trading partners should be traded less and, thus, immigrants should improve their tradability more. While these variables might be tapping the need for either market creation or market replacement, papers that use variables measuring (Dunlevy, 2006) corruption or institutional quality (Briant, Combes and Lafourcade, 2009) are directly related to the market replacing role of immigration. In both cases, the usual strategy is either to estimate separate regressions across category and compare coefficients, or to interact a dummy for the category with the immigrant stock measure. Across categories and specifications, the results are broadly consistent with the expected outcomes.136 That is, more differentiated goods and more foreign countries tend to be associated with greater trade creation from immigration. Again, this is taken as consistent with one of the information stories (market creating or market replacing) and providing less support for the preference effect of immigration. A number of papers have taken advantage of the existence of trade and migration data collected at subnational levels: Canadian provinces (Helliwell, 1997; Wagner, Head and Ries, 2002; Partridge and Furtan, 2008); French départements (Combes, Lafourcade and Mayer, 2005; Briant, Combes and Lafourcade, 2009); and U.S. states (Bardhan and Guhathakurta, 2004; Co, Euzent and Martin, 2004; Dunlevy, 2006; Millimet and Osang, 2007; Bandyopadhyay, Coughlin and Wall, 2008; Tadesse and White, 2008; White, 2009; Tadesse and White, 2010). The first 136 One really distinctive approach should be mentioned. In a currently unpublished paper, Jiang (2007) argues that the presence of fixed trade costs (associated with what we have called the market creation role immigration) can be identified from their effect on the extensive margin of trade, while the variable costs (associated with what we have called the market replacing role of immigration) will affect both margins. Using Canadian data, for 1988-2004, Jiang finds that migrants primarily affect the extensive margin and, thus, the fixed costs. ~ 76 ~ benefit of using sub-national data is that it permits the analysis to focus on more specifically defined geographic regions, thus achieving greater precision in estimation. A related benefit is that analysts can control for national level common determinants of trade and migration using country-level fixed effects, but still retaining sub-national level variation for identifying the effect of migrants. A particularly interesting paper in this group is Herander and Saavedra‘s (2005), which attempts to identify the relative effects of both state- and national-level migrant stocks. Consistent with the motivation for all of these papers, Herander and Saavedra find strong evidence that the local effects are larger than the national effects. This suggests that, whether they are mainly market creating or market replacing, network links are about proximity. Herander and Saavedra also test for whether size of previous immigrant stock reduces the effect of current immigrants on trade flows. Consistent with Gould‘s result, these authors find that previous immigrant stock does reduce the effect of current immigrants. Given the discussion above (i.e. that market creating networks should experience such a decline, while market substituting links do not), this would appear to be strong evidence in favor of the relatively greater importance of market creation. To summarize: there is strong and consistent support for immigration having a positive effect on trade; that link appears to be stronger for commodities whose trade is likely to involve informational problems; and that link appears to be stronger for trade with countries that are different from the reference country on a number of dimensions; and that link appears to be stronger when the partner country is characterized by institutional problems.137 This would seem to be strong evidence for the network story. However, since these analyses are never carried out in the context of a structural analysis that permits an evaluation of the relative price effects that drive the general equilibrium analysis standard in the trade theoretic accounts, these results neither permit comparison with the trade theoretic claims, nor do they speak directly (or unambiguously) to the issues of whether trade and migration are substitutes or complements. 5.2. Political structuring of migration: Community, Illegality and Welfare State Effort The previous section focused on the social aspect of the act of migration itself. This issue naturally emphasizes social relations within the community of migrants. In this section, by contrast, we focus on the social relations between the community of immigrants and that of natives. We briefly note three specific aspects of this relationship: the ―foreignness‖ of immigrants affects natives‘ sense of who they are as a community; the act of fixing legal limits on the number of immigrants below the free migration level creates a need to spend real resources to enforce those limits and creates a class of illegal immigrants; and the presence of a redistributive welfare state in all major immigrant host countries creates yet another margin on which immigration might affect native welfare. Given their potential impact on native welfare, like effects on relative wages and unemployment, each of these forms the basis of political 137 Corruption and low institutional quality would, presumably, also be a problem for the reference country. There is essentially no evidence of this side of the link given that virtually all of the reference countries are characterized by globally quite high institutional quality. ~ 77 ~ mobilization on the immigration question. This section comments briefly on the direct analysis of these issues, the next section briefly discusses political economic analyses of immigration. Immigrants generally differ on a number of dimensions from natives. Most economic research focuses on economically relevant differences (i.e. individual factor endowments--usually taken to be some measure of skill). However, even the most cursory reading of the history or immigration should make it clear that other dimensions of difference can also matter a great deal (Jones, 1992a; Reimers, 1998). Similarly, the emergence of radical right parties in Europe has been strongly associated with anti-immigrant politics that can only very partially be explained by economic effects of that immigration (Kitschelt and McGann, 1995; Marcus, 1995; Betz, 1998; Beirich and Woods, 2000; Betz, 2001). ―Foreigners‖ make a particularly attractive target for more-or-less unfocussed anger in the context of general economic difficulties. Thus, while it is surely true that attitudes toward immigrants are affected by understandings of labor market effects, recent research suggests that these effects are dwarfed by social concerns (Citrin et al., 1997; Dustmann and Preston, 2007; Card et al., 2009). Card, Dustmann and Preston (2009) refer to these social concerns as ―compositional amenities‖. Given the overall conclusion of empirical research on labor market effects of migration, and the increasingly heated public politics of immigration, the centrality of such compositional amenities should not surprise us. Illegality is also directly related to the ―foreignness‖ of immigrants. Virtually all of the economic analysis we have reviewed to this point proceeds under the assumption that governments can fix immigrant flows perfectly—this is as true of trade theoretic analyses as it is of labor economic research that treats immigrants as inelastically supplied to the labor market. Governments certainly do attempt to fix the level of immigration flows, but (unless such policies are perfectly effective) the act of trying to fix quantities in a world with dramatic differences in the returns to work creates a large inducement to migrate and, as a consequence, creates the status of illegal immigrant. This, in turn, requires governments to spend real resources in an attempt to regulate immigration. Not surprisingly, there is a large literature on illegal immigration in both demography and economics dealing with such issues as the choice between legal and illegal migration, counting the number of illegal immigrants, the labor market effects of illegality, and the effectiveness of various policies to restrict illegal migration.138 Much rarer are attempts to embed analyses of illegal immigration in standard general equilibrium models. An important first effort in this direction was made by Wilfred Ethier (1986a; b).139 Ethier develops a one-sector model with legal and illegal immigration to analyze how border and internal enforcement affect national income and income distribution (among skilled and unskilled native workers), as well as the fiscal consequences of such policy.140 138 Hanson (2006) is an excellent guide to the main issues, with a specific focus on the Mexican case. Although we do not cover the issue in this survey, Ethier (1985) also produced an interesting analysis of temporary migration in which immigrants respond to an economy characterized by stochastic shocks. 140 Bond and Chen (1987) and Djajic (1997) extend Ethier‘s analysis to the case of a two-sector economy—Bond and Chen permit international capital mobility, while Djajic considers a long-run when skill distribution of workers 139 ~ 78 ~ All industrial countries (the major host countries for migration) maintain more-or-less extensive welfare states that provide some combination of income support (―citizen wage‖) and direct provision of goods (―decommodification‖, e.g. housing, health care, education). These policies were created, and are generally justified, as a right of citizenship—i.e. a necessary component of a good community. Some such justification is necessary since welfare state provision is inherently redistributive. The level of such provision is controversial even in the context of a relatively homogeneous community, but it is dramatically more controversial in the face of large immigration flows. Part of the difficulty stems from the rights of non-citizens, or ―foreigners‖ (on some politically relevant dimension) even if a citizen, to these community goods. This is an extension of the ―compositional amenity‖ issue that we have already commented on.141 The literature on the fiscal effects of immigrants focuses on the fact that immigrants have implications for both the expenditure and revenue sides of the welfare state. If, as much of the theoretical literature presumes, immigrants are younger, poorer, and have more children than natives, their pattern of consumption of services and contribution to the welfare state will differ from those of natives. In particular, the usual presumption is that welfare states in most relatively wealthy countries involve net transfers from natives to immigrants. This presumption is undermined, to some extent, by two factors: the actual pattern of immigration; and the valuation of lifetime effects. Most countries are not characterized simply by a large shock of young, poor immigrants. The US, for example, is characterized by U-shaped immigration (i.e. most of the immigration is in the two tails of a distribution defined by skills). Studies that attempt to evaluate the current fiscal effect of immigrants deal with this problem explicitly (Rothman and Espenshade, 1992; Borsch-Supan, 1994; Espenshade and Huber, 1998; Lee and Miller, 1998; MaCurdy et al., 1998; Nannestad, 2007). The overall result of these studies is that immigrants receive net transfers from natives via the welfare system.142 However, a complete evaluation of these effects requires a dynamic, general equilibrium perspective that evaluates the long-term fiscal effects of immigration. The effects identified in these studies tend to be smaller and less certain, but the qualitative pattern is more-or-less the same (Auerbach and Oreopoulos, 1999; 2000; Storesletten, 2000; 2003). 5.3. The Peculiar Political Economy of Immigration responds endogenously to immigration. Bucci and Tenorio (1996) use Ethier‘s model to examine the fiscal effects in more detail. Yoshida and Woodland (2005) collects a number of the authors‘ articles that extend Ethier-type models in a number of these directions. Carter sticks with the one sector model, but considers labor market distortions created by efficiency wages (Carter, 1999) and segmented labor markets (Carter, 2005). 141 There is a large philosophical literature on citizenship and immigration that is quite relevant to welfare analysis, but is beyond the scope of this review. 142 It is important to note that, controlling for observable characteristics, immigrants rate of use of the welfare state is not higher than that of natives. Rather, immigrants, relative to natives, have traits that involve greater current transfers—i.e. they are young, poor, and have relatively more children than citizens. A different issue is whether immigrants are attracted to locations as a result of generosity of welfare systems. This is the ―welfare magnet‖ hypothesis. The link between welfare provision and immigration is a mainstay of open economy public finance theory (e.g. Wildasin, 1991; 1994; Brueckner, 2000; Myers and Papageorgiou, 2000). The empirical results here are quite mixed, clustering around finding of no effect to small positive effects (Barrett and McCarthy, 2008). ~ 79 ~ Political economy research generally proceeds relative to some "good" policy outcome, deviations from which are explained by 'political economy' forces. For economists, this 'good' outcome is the welfare optimum; for political scientists, it is the democratic optimum. The, usual villain, for both, is ‗special interests‘ (though early pluralist theory saw lobbying as a way of conveying information about preference intensity rather than distorting outcomes from the democratic optimum). For the case of immigration, what these optima are is so fraught that most work leaves them implicit.143 While nothing like as extensive as research on the political economy of trade, there is a very lively literature on the political economy of immigration. Much, perhaps most, of the recent work has focused on identifying the preferences of citizens, a small amount has sought to model equilibrium outcomes as a function of factor-price effects, and a larger sub-literature has focused on the political economic link between immigration and welfare state provision. We comment briefly on each of these. It should be clear from the work surveyed in section 2 that it is a straightforward task to derive the effects of immigration on relative wages. Under otherwise standard assumptions, the essential assumption for generating certain redistributive effects is that the number of factors of production should exceed the number of sectors. Among others, this will be the case in onesector models with many types of labor and in specific-factor models (Bilal et al., 2003). Since factor market effects play a large role in political economy modeling, it is not surprising that a substantial amount of effort has gone into finding evidence of such effects. The current approach to doing this is to use individual responses in public opinion polls on questions relating to immigration policy along with information on individual skill endowments to ―test‖ for consistency between model predictions and individual evaluations. For this purpose, endowments are usually considered as more- and less-skilled labor, and measured by education. In this approach, it is common to find that individual preferences on immigration policy are determined, at least in part, by endowment (Scheve and Slaughter, 2001; Mayda, 2006; O'Rourke and Sinnott, 2006). While this seems sensible, there are at least two problems: first, if the findings of research on the labor market effect of immigration are correct (i.e. that the labor market effects are small to zero, even on unskilled natives), it is not clear what we should make of the results from opinion polls; and, second, it seems likely that, in addition to its relationship to labor market status, education is related to things like cosmopolitanism that affect tolerance, or to training in economics that predisposes people to more Liberal attitudes on globalization in general and immigration in particular (Hainmueller and Hiscox, 2007). As the previous section noted, another channel via which immigration affects native economic interests is the welfare state/fiscal redistribution channel. Recent research on individual attitudes that seeks to take such considerations into account is characterized by mixed results. For example Facchini and Mayda (2009) find that, while both labor market and redistributive effects are significant, the latter are stronger; but Hainmueller and Hiscox (forthcoming) find that neither if these channels are 143 For economists this is a bit easier since every model has a welfare optimum. However, since the usefulness of this optimum (usually some version of free mobility) is highly contested, we still tend to steer away from explicit discussion. See Greenaway and Nelson (2005) for more on this. ~ 80 ~ unambiguously supported. Finally, as we noted above, while labor market effects (to the extent that they can be effectively identified with education-based endowments) and redistributive effects surely matter, there is evidence that compositional amenities/social interaction effects may be even more important (Citrin, Green, Muste and Wong, 1997; Dustmann and Preston, 2007; Card, Dustmann and Preston, 2009).144 While the findings of research on both labor market effects and citizen attitudes are such as to lead us to doubt that such effects are the primary causal factor in determining immigration policy, there is still a significant literature seeking to analyze immigration policy in precisely this way. As in the literature on the political economy of international trade, there are two broad classes of political institution that are considered in solving for political economic equilibrium: referendum models; and lobbying models. It is probably most useful to think of the single issue referendum model as a reduced form for considering the general effect of public preferences on immigration policy.145 Black‘s (1948) median voter theorem, combined with the auxiliary assumptions that the immigration issue is one-dimensional (e.g. size of quota) and the preferences identified by factor ownership are single-peaked over that dimension, yields a simple prediction about the link between preferences and political outcomes (e.g. Benhabib, 1996; Flores, 1997; de Melo et al., 2001).146 A small number of studies have attempted to frame accounts of contemporary immigration policy outcomes in these terms (de Melo, Miguet and Muller, 2004; Facchini and Mayda, 2008; Miguet, 2008). In addition, Goldin (1994) and Timmer and Williamson (1998) frame accounts of late-19th early 20th Century U.S. immigration policy in these same terms. It is also possible to rationalize policy via lobbying models (Amegashi, 2004; Facchini and Willmann, 2005; Schwellnus, 2008), and systematic empirical work is presented suggesting consistency between immigration policy outcomes and the predictions of these models (Facchini and Mayda, 2008; Facchini et al., 2008). The Facchini and Mayda (2008) paper is particularly interesting in its presentation of both referendum and lobbying model and an attempt to provide a link between these two modes of policy determination. A fundamental problem with the lobbying models is that, unlike lobbying on 144 This last point is related to the question of whether negative attitudes are causally linked to proximity to large numbers of immigrants. The results on this question are mixed: Scheve and Slaughter (2001) find no evidence of such links, while Gang, Rivera-Batiz and Yun (2002) and Hanson, Scheve and Slaughter (Hanson et al., 2007) do find such effects. 145 Unlike international trade, immigration policy is quite often an issue of general public political discourse. Furthermore, genuine referenda on the issue have occurred: 1994‘s proposition 187 in California (Calavita, 1996; Tolbert and Hero, 1996; MacDonald and Cain, 1997; Alvarez and Butterfield, 2000; Lee et al., 2001); while in Switzerland immigration was a continuing issue in electoral politics in the 1990s (de Melo et al., 2004; Miguet, 2008). While deMelo et al. and Miguet argue that Swiss electoral politics and outcomes are consistent, broadly speaking, with factor market-based preferences, the research on proposition 187 tends to argue that labor market effects are strongly dominated by broader social attitudes. 146 While it is probably easiest to conceive of immigration policy in terms of number of migrants, as our brief discussion of enforcement issues suggests, there is a parallel political economy dealing with illegal immigrants. Standard theoretical political economy models have been developed (Hillman and Weiss, 1999; Nelson and Xu, 2001) to analyze enforcement activity, and empirical analyses suggest a role for political economic forces in determining those policies (Shughart et al., 1986; Dávila et al., 1999; Hanson and Spilimbergo, 2001). ~ 81 ~ trade policy, the actual patterns of lobbying are not particularly consistent with the predictions of the model. While there certainly are influential economic interests involved in lobbying (e.g. western agricultural interests), these groups do not reflect the broad, economy-wide interests implied by claims about national level labor market effects. Instead, national level groups tend to be religious and environmental (Gimpel and Edwards, 1999). Ultimately, for all the convenience in linking the material conditions of the economy to political outcomes, the empirical weakness of the core relationship between immigration and labor market outcomes renders the claims of this line of research deeply problematic.147 The presence of a redistributive welfare state can change both the welfare optimum and individual political economic calculation (Wildasin, 1994; Wellisch and Wildasin, 1996; Wellisch and Walz, 1998; Gatsios et al., 1999; Razin and Sadka, 2001; Razin et al., 2005). The basic question addressed by this body of research is clear: does admitting immigrants (especially poor immigrants) lead to a reduction in welfare state effort? The overwhelming majority of papers on this topic use some version of a referendum as the political economic mechanism, and assume that immigrants receive immediate access to full welfare state benefits. In addition, most work on this topic also assumes that immigrants receive immediate access to the franchise. Given the well-known problems with spatial voting models in higher dimensions, these models all rely on relatively special assumptions about sequencing of votes on issues and admission. Partly as a result of such structure, and partly given the mix of static and dynamic structures, the theoretical models yield a large range of results (Cukierman et al., 1994; Mazza and van Winden, 1996; Scholten and Thum, 1996; Flores, 1997; Cremer and Pestieau, 1998; Haupt and Peters, 1998; Michel et al., 1998; Razin and Sadka, 1999; 2001; Kemnitz, 2002; Razin et al., 2002; Hansen, 2003; Haupt and Peters, 2003; Dolmas and Huffman, 2004; Leers et al., 2004; Thum, 2004; Mayr, 2007; Facchini and Mayda, 2008). What little systematic empirical research exists on this topic tends to find that increased immigration from relatively poor countries is associated with lower public support for the welfare state and lower welfare state effort (Razin, Sadka and Swagel, 2002; Hanson, Scheve and Slaughter, 2007; Facchini and Mayda, 2008; Eger, 2010).148 Unlike the case of trade, it turns out to be considerably more difficult to rationalize immigration policy in terms of straightforward models that run from factor ownership to preferences over policy to policy outcomes. It seems an unavoidable conclusion that the social fact of immigrant differences from the native community plays a major role in the determination of individual attitudes and the politics of immigration. We have already commented several times on the role of these compositional externalities on preferences. We close this section by taking note of an interesting research program developed by John Roemer and colleagues that seeks to explicitly build these considerations into formal political economy models (Roemer and Van der Straeten, 147 Gaston and Nelson (2000) and Greenaway and Nelson (2005) develop this argument at greater length. This is consistent with the fact that the standard result in closed economy models of redistribution that greater inequality should be associated with a bigger/more redistributive state (Meltzer and Richard, 1981) is consistently and decisively rejected in virtually every attempt to evaluate the model (Harms and Zink, 2003; Alesina and Glaeser, 2004). 148 ~ 82 ~ 2005; Lee and Roemer, 2006; Lee et al., 2006; Roemer and Van der Straeten, 2006; Roemer et al., 2007). This is hardly the last word on the political economy of immigration policy, but it is does suggest a promising avenue for both theoretical and empirical research in the future. One way of teasing out the distinctive elements of immigration policy is via explicit comparison to trade policy (Greenaway and Nelson, 2006; Hatton and Williamson, 2007; Mayda, 2008b; Greenaway and Nelson, 2010). 6. Conclusions When it comes to the impact of immigration, trade theory under the empirically most plausible assumptions yields a fairly tight prior on an essentially zero labor market impact. As for the empirical literature, it is widely agreed that there are non-trivial negative effects on migrants of the same origin and vintage, and, perhaps not quite so widely held, agreement that the small, and shrinking, group of native high school dropouts experience statistically significant, but economically modest, negative consequences from contemporary immigration. Otherwise, evidence of negative effects is largely absent. In fact, aggregate welfare effects seem likely to be positive. To the extent that there is a dispute in the immigration case, it revolves around the framework to be used for evaluating the results of the empirical work. The main substantive difference between labor and trade economists relates to the dimensionality of the model used to evaluate the results - with labor economists preferring an m-factor × 1-final good model and trade economists preferring an m × n good model (with a modal preference for the 2 × 2 model). As long as m 2 and n 2, output-mix adjustment will play a role in adjusting to an immigration shock, and the failure to account for that role will produce over-estimates of the wage (or unemployment) effects of any given shock. Furthermore, we have also argued for the fundamental plausibility of the m-factor n-good model on essentially a priori grounds. If this argument is accepted, there is some presumption that output-mix adjustment fully absorbs the immigration shock and that factor price insensitivity holds. 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