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Variety, Competition, and Population in Economic Growth: Theory and Empirics Alberto Bucci∗ Lorenzo Carbonari† Giovanni Trovato‡ September 14, 2016 Abstract By considering the average density of sectors in a country’s product space, measured by the Lafay’s net export flows-based specialization index, as an indicator of the degree of complexity of the same country’s production structure (Hausmann and Klinger [29]), this is the first paper that provides aggregate macroeconomic evidence on how, in the long-run, a diverse degree of production-complexity may affect in a differential way not only economic growth, but also the relation between economic growth, population growth and the monopolistic (intermediate) markup. On average, for the countries included in the sample, we find that, following an increase in the number of horizontally-differentiated (intermediate) inputs entering the aggregate production function, the specialization effect is greater than the corresponding complexity effect. In this case, the impact of population growth on economic growth is definitely negative, whereas the influence of the monopolistic markup on the same variable is negative. Keywords: Economic growth; Population growth; Variety-expansion; Specialization; Complexity; Product market competition. Jel codes: O3; O4; J1. ∗ Università di Milano, DEMM. E-mail address: [email protected] Università di Roma “Tor Vergata”& CEIS. E-mail address: [email protected]. ‡ Università di Roma “Tor Vergata”& CEIS. E-mail address: [email protected]. † 1 “The productivity-enhancing effects of horizontal innovations are not. . . obvious. . . For while having more products definitely opens up more possibilities for specialization, and of having instruments more closely matched with a variety of needs, it also makes life more complicated and creates greater chance of error. . . .” 1 Introduction Economic theory has long ago made clear that the degree of product market competition (PMC, henceforth) and the rate of population growth, by affecting, respectively, the path of future profits accruing to the successful innovator and the availability of researchers in an economy, have a strong impact on economic growth (i.e., the growth of per capita income). In order to analyze, both theoretically and empirically, how population growth and the extent of the monopolistic markups rewarding prospective innovators may affect economic growth, we employ a variant of the canonical semi-endogenous growth model by Jones [33], [34]. The main reason for using that framework resides in the fact that in two companion contributions Jones (1995a,b) has provided convincing evidence against two (the AK-type and the Research & Development, R&D-based, respectively) broad categories of fully endogenous growth models. In particular, the evidence against the first generation of R&D-based fully endogenous growth models (i.e., Romer [57]; Grossman and Helpman [27]; Aghion and Howitt [5]) is especially persuasive: these models predict that economic growth is proportional to the amount of resources invested in R&D (namely the number of researchers allocated to this activity), however in the last few decades R&D investments have increased remarkably in most of advanced countries, with the long-run growth rates of per capita output and total factor productivity of these countries not showing a comparable upward trend. In the light of this, the motivation of the present paper is twofold. The first objective is to re-examine the long-run relationship both between PMC and economic growth, and between population growth and economic growth. In our context, the relevance of reassessing these quite age-old problems/relations has to do with the fact that (and this is the main difference with the traditional semi-endogenous growth theory) we postulate that, following the introduction of new varieties of horizontally-differentiated intermediate inputs (i.e., following an improvement in the rate of technological change), a possible trade-off between productivity gains (due to more specialization) and productivity losses (due to more production-complexity) may emerge.1 More importantly, and related to the first one, the second objective of the present contribution is to reach some quantitative understanding of the magnitude of the production-complexity effect related to technological progress (namely, intermediate inputs proliferation), in comparison to the more standard specialization effect of variety-expansion. To have an immediate picture of the mechanisms involved in the framework we are going to describe in our paper, consider a typical R&D-based growth model à la Romer [57] and suppose, as in Jones [33], that there are diminishing technological opportunities in the sector -the R&D sector- that produces new ideas for new varieties of differentiated intermediates. Having diminishing technological opportunities means that an individual researcher becomes 1 In the canonical semi-endogenous growth model, the production-complexity effect is either non-existent at all or (at most) very much small, and as such totally negligible. 2 less and less productive as the number of existing ideas grows up, so that in the long run (i.e., along a balanced growth path - BGP - equilibrium) it is possible to keep on innovating at a constant pace only by allowing for a rise of the aggregate stock of researchers. In turn, if the stock of researchers is proportional to population size, expanding the number of researchers and, hence, the number of available ideas, will ultimately be possible only through an increase of population. Thus, a larger population generates two opposing effects in our setting: the first is negative and implies that the available aggregate GDP of the economy has to be split among a larger number of heads, which decreases per capita income over time, while the second is positive as a larger number of heads leads, as a consequence, to more ideas and therefore to a greater aggregate GDP. Our model suggests that, in line with the standard semi-endogenous growth theory, the positive effect on per capita income of a more sizeable population always prevails over the corresponding negative effect (so that the correlation between population and economic growth rates is unambiguously positive in the long-run) if and only if the productivity losses arising from more production-complexity due to varietyexpansion are extremely small and littler than the related productivity gains resulting from more specialization. In contrast, and this is a totally new result within the semi-endogenous branch of growth theory, when the (productivity) losses arising from production-complexity are extremely large, and larger than the corresponding (productivity) gains coming from specialization, then having more population (hence, more researchers, and ultimately more ideas) in the economy leads in the long-run to a lower per capita income growth rate.2 In this case, our model also suggests that it is possible to raise the economy’s growth rate through reducing, ceteris paribus, the incentives (instantaneous profits) to produce new ideas, which actually occurs by a reduction in the degree of monopoly power with which the potential innovators are rewarded. Finally, in the intermediate case where the productivity losses arising from production-complexity due to variety-expansion are sufficiently large, but still lower than (or equal to) the productivity gains resulting from specialization, we find that population growth has a negative impact while the monopolistic markup has a positive influence on economic growth (at most, both impacts are null). From the sketch of our theoretical model, it is immediate to infer that we do not aim here at capturing the mutual evolution of population growth, technological incentives, and per capita income along an economic and demographic transition toward a long-run equilibrium characterized by low fertility and mortality rates, high levels of R&D investments and persistent growth in per capita income.3 It is exactly for this reason that we use the simplest and 2 Thus, the model presented here accounts for the possibly negative long-run correlation between population and economic growth rates in R&D-based models through a mechanism which is completely different from the one recently suggested by Prettner [53]. Using a Romer [57]-Jones [34]’s setting, Prettner shows that an increase in population growth, while positively influencing aggregate human capital accumulation, decreases simultaneously schooling intensity (defined as the productivity of teachers times the public resources spent on educating each child). The fall of schooling intensity has, in turn, a negative impact on the future evolution of aggregate human capital. If the negative effect dominates, the resulting slowdown of aggregate human capital accumulation eventually reduces technological progress and, therefore, economic growth. In our model there is no human capital investment. 3 A comprehensive overview of the economic theories and consequences of the so-called demographic transition can be found in Galor [26] and Jones and Vollrath [38]. 3 most parsimonious possible setting (namely, a variant of the basic semi-endogenous growth model) in which population growth and the intermediate sector monopolistic markup are both regarded as exogenous variables, and focus on the relation between population change and economic growth and between markups and economic growth along a BGP.4 In theory, our model is able to account simultaneously (and eventually for different ranges of the parameter measuring the magnitude of the production-complexity effect) for a non-monotonic, non-uniform relationship not only between population growth and economic growth but also between the degree of the monopolistic markup and economic growth. This is the most important difference between our theoretical results and those of the basic semiendogenous growth model (Jones [33]) that, instead, does not allow any analysis of the long-run connection between PMC and economic growth. In the econometric part of the paper, we explicitly deal with this non-monotonicity using a Finite Mixture Model. Our estimates confirm that the most likely case found in the data is the one in which the proliferation of new horizontally-differentiated (intermediate) inputs to be assembled in the same aggregate production function generates a production-complexity effect that, while important in magnitude, is ultimately lower than the corresponding specialization effect, so that population growth produces a statistically significant and negative influence while the monopolistic markup has a statistically significant and positive impact on long-run per capita income growth. How do our results compare with those of the existing theoretical and empirical literatures on the two issues (the links between markups-economic growth, and between population growth-economic growth, respectively)? Although economists have been studying for a long time the effects of an increase in the intensity of PMC and in population growth on productivity growth, these questions still remain to a large extent unsettled. Unlike the traditional Schumpeterian [59] view, more recent theoretical research (both industrial organization- and macro- based5 ) finds mixed results in the correlation between product market competition and economic growth, and the existing empirical evidence confirms the non-monotonicity of this relation.6 In this regard, Aghion et al. [2] analyze a model of Schumpeterian growth with 4 In more detail, we do not illustrate here any new mechanism(s) able to command an economy’s take-off from a “stagnant-equilibrium steady state”into a self-sustaining “growth-equilibrium steady state”, during which the portion of full income eventually spent on R&D-investment-related activities (thus, economic growth) and population ageing ultimately rise, while fertility and mortality fall. Instead, using the simplest framework in which R&D activity plays a significant and explicit role, our goal is to show that the sign of the links between population and economic growth rates and between markups and economic growth, respectively, can ultimately be ascribed to the contrast of two different effects (specialization vs. production-complexity) that the introduction of new varieties of intermediate inputs, a proxy for the rate of technological progress, can yield. 5 An excellent review of these two branches of the literature on product market competition, incentives to innovate, and economic growth can be found in Aghion and Griffith [4]. In particular, the third chapter of their book extends the endogenous growth model from the first chapter. At the end of their analysis, the authors claim that, for some parameter values, the steady-state aggregate innovation intensity of their model is correlated in an inverted-U-shaped manner with the degree of competition. 6 While Nickell [52] and Blundell et al. [14]-[15], for instance, find that competitive pressures encourage innovation and, therefore, have a positive effect on productivity growth in a long-run perspective, other papers (notably, Aghion et al., 2005) show that the relationship between competition and growth is non-monotonic, i.e. inverted U-shaped, in the data. 4 step-by-step innovation and no leapfrogging.7 In their theoretical framework, each intermediate sector is assumed to be duopolistic with respect to production and research activities, and competition is proxied by the Lerner Index (or price-cost margin). In obtaining a nonmonotonic, empirically inverted-U relationship between product market competition and innovation/growth, they use UK panel-data on patents generated by matching the NBER patents database to accounting data (from Datastream) on firms listed on the London Stock Exchange.8 Our model is different from Aghion et al. [2]’s contribution because technical change takes the form of an expansion in the number of available varieties of intermediate inputs in our analysis and also because we are interested in analyzing the possible impacts of population change on economic growth. Similarly to the relationship between PMC, innovation and productivity growth, so far a complete agreement about the sign of the long-run correlation between population and economic growth rates has not emerged yet, both theoretically and empirically.9 While according to Kuznets ([43], p. 328): “. . . Population growth [. . . ] produces an absolutely larger number of geniuses, talented men, and generally gifted contributors to new knowledge whose native ability would be permitted to mature to effective levels when they join the labor force”, proponents of the view that population growth is detrimental to economic growth (Solow [61]; Coale and Hoover [21]; Barro [10]; and Mankiw et al. [48]) found their argument on the belief that an increase in population leads to a dilution of reproducible resources. More recently, a negative effect of population growth on economic growth is also found in the data by Li and Zhang [46] and Herzer et al. [31]. Finally, there are also strong arguments advocating that it is a better economic performance to cause an increased population growth rate. Blanchet [12] is among those who use this claim to explain the presence of an insignificant correlation between economic and population growth rates.10 Summing up, concerning the relation between population and economic growth rates, it seems that the main argument of the path-breaking paper by Kelley and Schmidt [40] still continues to hold today. Using both cross-section and time-series data, these two authors have indeed provided compelling evidence that the impact of population growth on per capita income growth has changed over time (it has been statistically not significant in the sixties and the seventies and statistically significant, large and negative in the eighties), 7 See also Aghion et al. [3] and Acemoglu and Akcigit [1] for comparable examples of Schumpeterian growthframeworks with step-by-step innovation. In particular, Aghion et al. [3], by developing an industry model, find that a firm’s response of innovation to increased competition is non-monotonic as it depends on how far it is from the world technology frontier. 8 Aghion et al. [2] explain theoretically such a relation through the interplay between two opposing effects, the “Escape-Competition”and the “Schumpeterian”effect, respectively. 9 See Sala-i-Martin et al. [58], who find in the data that the sign of the whole impact of population growth on economic growth is ambiguous. 10 Using a sample of 78 countries covering the period from 1965 to 1990, Williamson ([62], pp. 113-115) shows that there is no significant relationship between population and economic growth rates. This outcome is consistent with the “neutralist”position. However, he also shows that the result is sensitive to the empirical specification employed as, when the log of life-expectancy in 1960 and two further variables controlling for economic geography are added, population growth is shown to generate a positive and significant impact on GDP per capita growth, which would support the “optimist”position. 5 and varies with the level of economic development (it is generally negative in less developed countries and can be positive for some developed countries). Kelley and Schmidt [40] explain these results by the fact that the impact of population change on economic development may be drastically different in sign depending on which specific component of population growth is affected by a given demographic shock: an increase of population growth attained through a rise of fertility has a monotonically negative consequence on economic growth, whereas the same increase of population growth achieved through a decline of mortality has a monotonically positive influence on the growth rate of real per capita income. This has profound implications for the analysis, as it suggests that the composition of a simultaneous rise of fertility and decline of mortality, both leading to a higher population growth rate, is in theory an important explanation of the emergence of a non-monotonic, non-uniform relationship between population and economic growth rates. This work is especially related to Bucci [18] [19], Bucci and Raurich [20], Ferrarini and Scaramozzino [25], and Maggioni et al. [47]. Unlike Bucci [18], it is not an objective of this article to emphasize the growth effects of the so-called returns-to-specialization (Benassy [11]) and their role in shaping the link between population growth-economic growth and between markups-economic growth. Moreover, contrary to Bucci [18], we pay no attention here to how the type of agents’ intertemporal utility (whether Millian, Benthamite, or an intermediate case between the two) might ultimately affect the relationship between population and economic growth rates. Differently from Bucci [19], instead, we analyze here a semi-endogenous growth model without (intentional or unintentional) human capital accumulation with the objective of studying simultaneously, and within the same framework, the interactions between long-run economic growth, on the one side, and population growth and markups, on the other. In particular, the present paper formally demonstrates that having (exogenous or endogenous accumulation of aggregate) human capital within a semiendogenous-type growth framework is not essential in yielding the result of a non-uniform relation between population and economic growth rates. Unlike Bucci and Raurich [20], we do not aim at explaining the differential impact that in the long-run a given change in the population growth rate may have on economic growth through: (i) Either the nature (i.e., whether fully-endogenous or not) of the process of economic growth, (ii) Or the peculiar engine(s) driving economic growth (human capital, R&D, or both). After more than two centuries from Adam Smith [60]’s notable book, in which the specialization/division of labor was considered the key source of productivity growth, Kremer [42] has proposed another (the so-called “O-Ring”) complementary view of the process of economic development. This view is based on the observation that the number of tasks included in a given production process is the major determinant of its degree of complexity: more complex technologies are those incorporating more tasks and, then, more possibilities of errors. Another important conclusion of Kremer [42] is that when firms select among diverse technologies with different tasks, in equilibrium they will choose by taking into account the amount of “capabilities”they own: firms endowed with more capabilities will decide to use technologies requiring a larger number of tasks. This may explain why in general “rich countries specialize in complicated products”(Kremer [42] , p. 563). The core implication of all this is that the proliferation of tasks/components/different inputs included in the same production process may ultimately yield opposing effects on long-run economic development and 6 growth, due to the differential role played simultaneously by specialization and productioncomplexity. In the model we are going to present in the next sections, the balance between positive (specialization) and negative (production-complexity) productivity-consequences related to an expansion in the number of varieties of (intermediate) inputs involved in a given production process is found to be important in affecting simultaneously the sign of the long-run correlations between population and economic growth, and between markups and economic growth. This is in line with the “O-Ring”theory of economic development, according to which for some countries (especially those using particularly “complicated”production processes) it may well be that the productivity-gains from more specialization are overcome by the associated productivity-losses due to a more complex production organization. More specifically, our paper shows that when this happens, we should observe (with respect to the opposing case) not only a different level of the growth rate of per capita income but also, and perhaps more importantly, a changing relation between economic growth, population growth and markups across countries. In order to (indirectly) measure production-complexity, some economists (Hausmann and Klinger [29]; Hidalgo et al. [32]; Hausmann and Hidalgo [28]) have developed a model that, by the use of trade-data, now consents to have a broad appraisal of that effect. The idea put forward by these economists is based on the notion of product space, which can be thought of as a forest, with sectors representing trees and countries being monkeys. A large distance between any two trees means that monkeys cannot easily jump from one to the other: in this case the sectors corresponding to those two trees are so different in terms of their patterns of specialization that, at a country-level, a revealed comparative advantage in one sector is not necessarily associated with a revealed comparative advantage in the other sector. By contrast, whenever two trees stay very close to each other, specialization in either of the two sectors typically leads the same country to specialize in the other, as well. At the same time, however, the degree to which sectors are close to each other (the so-called average product density) can also be viewed as a proxy for the degree of complexity of a country’s production structure in that an economy with a high average product density must possess all the necessary capabilities and technical competences to produce simultaneously within a thicker area of activities: in sum, the closer two sectors are to each other, the easier it is for a country to specialize in both of them, while simultaneously the more complicated (in terms of required competencies) it becomes for the same country to produce in both industries. By exploiting these ideas, and following the methodology illustrated by Lafay [44], Ferrarini and Scaramozzino [25] have used data on net trade flows to compute an average product density index for a cross-section of 89 countries over the period 1990-2009. For these countries, they separately estimate, through a panel data GLS model, the impact of a larger product density on the level and the growth rate of GDP per capita. For the whole sample, density has a positive and significant coefficient on the level of GDP per capita (countries occupying the denser areas of the product space have on average higher GDP per capita, with causality going from the former to the latter). However, when the sample is split by income levels, it is observed that density positively affects GDP per capita in middle/low income countries, while it dampens per capita income for the group of highincome countries. Concerning the growth regressions (that examine the relationship between product density and economic growth by including the initial level of GDP per capita as a 7 regressor), instead, the authors find that for the whole sample of countries the coefficient on density is still positive and significant. This result remains true when the sample is split by aggregated income groups (high vs. middle/low income countries). However, by considering six different geographical regions separately, it is observed that only for Europe and North America the coefficient on the density variable is significantly negative. All in all, in line with the “O-Ring”theory of economic development, the evidence presented by Ferrarini and Scaramozzino [25] supports very well the idea that, especially for advanced countries, it can be the case that the productivity-gains from more specialization are smaller than the associated productivity-losses due to increased complexity in production. Unlike Ferrarini and Scaramozzino [25], we focus solely on advanced (OECD) countries, employ a different econometric technique, and analyze how the balance between production-complexity and specialization (induced by input proliferation) contributes to affect not only the rate of economic growth, but also the joint long-run relation between population growth, economic growth, and markups. Finally, by using a sample of Turkish manufacturing firms between 2003 and 2008, Maggioni et al. [47] have recently studied the link between complexity and volatility at the firm-level. Their main conclusion is that firms producing more complex goods (i.e., goods requiring a wider set of diverse and exclusive capabilities, see Hausmann and Hidalgo [28]) enjoy higher output stability. Differently from Maggioni et al. [47], we employ here a macrolevel perspective and focus on the role of product/country complexity on aggregate economic growth, rather than firms’ output volatility. In this sense, we believe that our analysis does represent a nice complement to Maggioni et al. [47]’s contribution. This article is structured as follows. In section 2 we present the theoretical model with the objective of illustrating the differential impact that population growth and markups may have on long-run economic growth depending on the relative degree of production-complexity. In section 3, we perform our empirical analysis. In particular, in this section we present our econometric strategy, describe the employed dataset, discuss the econometric results, and provide robustness checks. As usual, the last section (section 4) summarizes, concludes and proposes new possible directions for future research. 2 The Model The model presented in this section is a version of Romer [57], with four relevant differences. The first concerns the shape of the aggregate technology: " #αm Z Nt 1 1−α 1/m Yt = LY t (xit ) di with 0 < α < 1 and m > 1 (1) Ntβ 0 This production function formalizes the idea (Aghion and Howitt, [6], Chap. 12, equation 12.4, p. 407) that: “. . . The productivity-enhancing effects of horizontal innovations are not . . . obvious. . . For while having more products definitely opens up more possibilities for specialization, and of having instruments more closely matched with a variety of needs, it also makes life more complicated and creates greater chance of error ...” 8 In equation (1), LY is the labor input employed in the production of the homogeneous final good Y , xi is the quantity of the i − th variety of differentiated capital goods/intermediate inputs, N is the existing number of these inputs, and m > 1 is a technological parameter that determines the elasticity of substitution between any generic pair of varieties of differentiated capital goods, equal to m/(m − 1). A decrease in m, by increasing the substitutability between durables, leads to tougher competition across capital-goods producers and to lower prices. Thus, m can be used as a (inverse) measure of the degree of competition in the intermediate product market. In a moment, we show that m is, indeed, the optimal markup on the production marginal cost in the durables sector (see equation (5)). As a whole, the aggregate production function (1) displays constant returns to scale to private and rival inputs (LY and xi ) and allows disentangling the measure of product market concentration (m) from the factor-shares in GDP (α and 1 − α).11 Depending on its magnitude, parameter β summarizes the different effects that innovation may have on GDP. In particular, when positive, β is meant to capture the detrimental effect on Y of having a larger number (N ) of intermediate-input varieties to be assembled in the same manufacturing process. This is the (production-) complexity effect. This effect contrasts with the traditional and positive specialization effect that is reflected by the upper bound of the integral within the square bracket of equation (1).12 As a matter of fact, under symmetry - i.e., xi = x > 0 ∀i ∈ [0, N ] - and with LY > 0 and N ∈ [0, ∞), equation (1) suggests that an increase in N may have either a positive (i.e., β < 1, the specialization gains are larger than the possible losses due to more complexity in production), or a negative ( i.e., β > 1, the specialization gains are smaller than the possible losses due to more complexity in production), or else no impact at all on ( i.e., β = 1, the specialization gains are exactly offset by the possible losses due to more complexity in production).13 Using equation (1), it is possible to compute the inverse demand function for the i − th intermediate: " pit = αL1−α Yt 1 Ntβ Z #αm−1 Nt (xit ) 0 1/m di 1 Ntβ 1−m xitm (2) The second difference with respect to Romer [57] is related to the technology for producing intermediates. We now postulate that monopolistically competitive firms have access to the same one-to-one technology employing solely labor as an input (as in Grossman and Helpman 11 Since final output is produced competitively under constant returns to scale to rival inputs, at equilibrium LY and xi are rewarded according to their marginal productivities. Hence, for given N , (1 − α) is the share of Y going to labor and α (the complement to one of the labor-share) is the share of total GDP going to intermediate inputs. 12 In equation (1) we observe that if β < 0, then there is no (production-) complexity-effect, since this parameter would amplify the positive effect of specialization emerging from the upper bound of the integral inside the square bracket. A fortiori, this is also true when β = 0 (again, in this case we would end up with the sole, traditional specialization-effect in the square bracket). Therefore, in order to model explicitly a (production-) complexity-effect arising from an increase of N some positive β is needed. 13 We do not make any ad hoc assumption on the sign and the magnitude of β. 9 [17] Chap. 3):14 ∀i ∈ [0, N ] xit = lit N ∈ [0, ∞) (3) where li is the amount of labor required in the production of the i−th durable, whose output is xi . Thus, the marginal cost of production is the wage. For given Nt , equation (2) implies that the total amount of labor employed in the intermediate sector at time t, LIt , is given by: Nt Z Z Nt lit di = LIt xit di = (4) 0 0 Under the assumption that there exists no strategic interaction across intermediate firms, maximization of the generic i − th firm’s instantaneous profit leads to the traditional markup rule:15 ∀i ∈ [0; Nt ] pit = mwIt = mwt = pt (5) This expression says that the price is the same for all intermediate goods i and equal to a constant markup (m) on the marginal production cost (wt ). In this model all labor (L) is employed to produce, respectively, consumption goods (LY ), durables (LI ), and ideas (LN ). Since it is assumed to be perfectly mobile, at equilibrium all labor will be rewarded according to the same wage rate, i.e., wY t = wIt = wN t ≡ wt . The hypothesis of symmetry (i.e., xi and pi equal across i) leads to: xit = xt = πit = α m−1 m LY t Nt 1−α LIt Nt LIt Nt α ∀i ∈ [0; Nt ] α[m(1−β)−1] Nt (4’) ∀i ∈ [0; Nt ] = πt (6) The third difference with respect to Romer [57] is related to the aggregate R&D technology: 1 Ṅt = LλN t Ntφ with N (0) > 0, χ > 0, 0 < λ ≤ 1, φ < 1 (7) χ where χ is a technological parameter, Nt is the number of ideas already invented and LN t is the labor input employed in research. The fourth and last difference we introduce in this model with respect to Romer [57] is that population grows at a positive, constant L˙t and exogenous rate, L ≡ n > 0.16 Equation (7) stems from the criticism of strong scale t effect one may find in the first-generation of Schumpeterian growth models (see Jones [34], 14 We show that our results would not change if physical capital (as opposed to labor) is assumed to be the only input into the production of intermediate goods (as in Romer [57]). A formal proof can be obtained from the authors upon request. » –αm−1 RN 15 More precisely, we assume that each of these firms is so small that it takes 1β 0 t (xit )1/m di as given, Nt hence: ∂ ∂xit » 1 Ntβ –αm−1 Nt (xit )1/m di =0 Z 0 16 We simplify further the analysis by assuming that the aggregate labor-force equals the total population. Under this assumption per capita and per-worker variables do coincide. 10 equation (6), p. 765; Jones [37], equation (16), p. 1074). In equation (7), the parameters λ and φ denote, respectively, the returns to the labor input employed in research and the intertemporal spillover coming from the accumulated stock of (disembodied) knowledge. When φ < 1, higher values of N imply that the same amount of R&D resources (research labor) generates a lower growth rate of ideas, i.e., there exist diminishing technological opportunities. The presence of diminishing technological opportunities is key to the removal of the strong scale effect in the first-generation of Schumpeterian growth models: since individual researchers become less and less productive as the level of disembodied knowledge (N ) increases, it is possible to maintain a constant rate of innovation only by increasing the number of researchers. This, in turn, is possible solely if the economy’s population grows at a positive rate. Because the R&D sector is competitive, there is free entry into this market: wN t = where Z VN t = ∞ πτ e − Rτ t 1 Ntφ VN t χ L1−λ Nt r(s)ds dτ (8) with τ > t (9) t In equations (8) and (9), VN t is the market value of the generic i − th blueprint, π is the instantaneous profit of the i − th intermediate firm, r denotes the real rate of return on households’ asset holdings (to be introduced in a moment) and wN t is the wage rate going to one unit of research labor-input. 2.1 Households The number of infinitely lived households of this economy is constant and normalized to one. Hence, the size of population/labor-force coincides with the size of the single dynastic family (L). The representative household uses savings (forgone consumption) to accumulate assets, taking the form of ownership claims on firms. Thus, Ȧt = (rt At + wt Lt ) − Ct with A(0) > 0 (10) In equation (10), A, C and L denote, respectively, household’s asset holdings, consumption and labor-input, w is the real wage and r is the real rate of return on A.17 According to this equation, household’s investment in assets (the left hand side) equals household’s savings (the right hand side). In turn, household’s savings are equal to the difference between household’s income (the sum of interest income, rA, and labor income, wL) and household’s consumption (C). Given the above expression, the law of motion of per capita assets is: ȧt = (rt − n)at + wt − ct with a(0) > 0 (11) C with a ≡ A L and c ≡ L representing per capita asset holdings and per capita consumption, respectively. With a constant inter-temporal elasticity of substitution (CIES) instantaneous utility function, the objective of the household is to maximize, under the usual budget constraint, the discounted utility of per capita consumption of all its members: 17 Notice that, in this economy, all labor is employed and at equilibrium obtains the same wage, w. 11 Z max {ct ,at }t=+∞ t=0 U +∞ c1−θ −1 t 1−θ ≡ 0 s.t. ! e−(ρ−n)t dt (12) (11) a(0) given with θ > 0 and ρ > n > 0. In equation (12) we have normalized population at time 0 to one, L(0) = 1. The representative dynastic family chooses the optimal path of per capita t=+∞ consumption {ct , at }t=0 , taking the interest rate rt and the wage rate wt as given. The assumption that ρ > n > 0 ensures that U is bounded away from infinity if c remains constant over time. The solution to this problem gives the usual Ramsey-Keynes rule: γc ≡ 2.2 ċt 1 = (rt − ρ) ct θ (13) The labor market and the BGP equilibrium Since labor is fully employed and distributed across production of consumption goods, production of intermediates and invention of new ideas, at equilibrium the following equalities must hold: LY t + LN t + LIt = Lt wY t = wN t = wIt = wt ∀t ≥ 0 (14) (15) Equation (14) says that at equilibrium total supply (the right hand side) and total demand (the left hand side) of labor must be equal. In the model, labor is a homogeneous factorinput, i.e., it can be employed interchangeably in the three sectors of the economy. Thus, labor will continue to move across these sectors until wage equalization is attained (equation (15)). Moreover, in equilibrium, aggregate household’s asset holdings (A) must equalize the aggregate value of firms: At = Nt VN t (16) where VN t is given by equation (9) and satisfies the no-arbitrage condition: V̇N t = rt VN t − πt (17) In the model, the i-th idea allows the i-th intermediate firm to produce the i-th variety of durables. This explains why in equation (16) total assets (A) equal the number of profitmaking intermediate firms (N ) times the market value (VN ) of each of them (equal, in turn, to the market value of the corresponding idea). On the other hand, the no-arbitrage condition suggests that the return on the value of the i-th intermediate firm rt VN t must equal the sum of the instantaneous monopoly profit accruing to the i-th intermediate input producer (π) and the capital gain/loss matured on VN t during the small time interval dt (i.e., V̇N t ). We can now move to a formal definition and characterization of the balanced growth path (BGP) of this model. Definition 1. A BGP equilibrium in this economy is an equilibrium-path along which: 12 (i) all variables depending on time grow at constant (possibly positive) exponential rates; (ii) the sectoral shares of labor employment (sj = Ljt Lt , with j = Y, I, N ) are constant. The following results do hold in the BGP equilibrium (algebraic details are in the online appendix, not intended for publication, where we also compute the BGP allocation of labor across the final output, intermediate and research sectors and check for the respect of the transversality condition): Ṅt ≡ γN = Ψn Nt ẏt ċt ȧt γy ≡ = γc ≡ = γa ≡ = ΦΨn yt ct at r = θΦΨn + ρ (18) (19) (20) where: Φ ≡ α [m(1 − β) − 1] R 0 and Ψ≡ λ 1−φ >0 Equation (18) gives the BGP equilibrium growth rate of the economy’s number of intermediate input varieties (N ). According to equation (19), real income (y), consumption (c) and asset holdings (a), all expressed in per capita terms, grow at the same constant rate in the BGP equilibrium. Equation (20) gives the BGP value of the real rate of return on asset holdings (r). It is evident from these equations that, for any ρ > n > 0, θ > 0 and Ψ > 0, ρ . γN is always positive whereas r is positive as long as Φ is sufficiently large, i.e., Φ > − θΨn Instead, for the common BGP growth rate of the economy (19) to be positive, Φ needs to be strictly greater than zero, which implies that we would restrict our analysis to the case where 0 < β < m−1 m < 1. In other words, our theory suggests that along a BGP the economy’s growth rate can be positive only if the production-complexity effect (as summarized by β) is sufficiently low and smaller than the corresponding specialization effect. This is compatible with the basic semi-endogenous growth model (see Jones [33]), where (intermediate-)input proliferation yields no production-complexity effect at all. However, since the main objective of the present paper is to study the macroeconomic (growth) effects of intermediate inputvariety proliferation, in what follows we do not limit ourselves to the very restrictive case in which 0 < β < m−1 m < 1. Instead, we present the results of our model in their more general form without imposing any ex-ante restriction on the magnitude of parameter β.18 These results are summarized in the following proposition. Proposition 1. Along the BGP we observe that: 1. Sign(γy ) = Sign(Φ); ∂γ 2. Sign ∂ny = Sign(Φ); 3. Real per capita income growth is equal to zero in the absence of any population change (i.e., when n = 0); 18 As a matter of fact, in our regressions we deal with negative per capita GDP growth rates, as well (see table 3). 13 4. Sign ∂γy ∂m depends on whether β is greater, smaller, or else equal to one. Proof. The proof of the first part of the proposition is immediate when one takes into account that in the model Ψ > 0 and n > 0. To prove the second part of the proposition, notice that: ∂γy ∂n = ΨΦ. To prove the third result, we observe that in equation (19) γy = 0 if n = 0. The same equation (19) also implies that: Ψn [α(1 − β)] > 0 if β < 1 ∂γy ≡ Ψn [α(1 − β)] = 0 if β = 1 ∂m Ψn [α(1 − β)] < 0 if β > 1 Using the definition of Φ and equation (19), we also obtain that: - if 0 < β < - if β = - if m−1 m m−1 m , m−1 m , then: Φ > 0, γy > 0, then: Φ = 0, γy = 0, ∂γy ∂n < β < 1, then: Φ < 0, γy < 0, - if β = 1, then: Φ < 0, γy < 0, - if β > 1, then: Φ < 0, γy < 0, ∂γy ∂n ∂γy ∂n ∂γy ∂n > 0 and = 0 and ∂γy ∂n ∂γy ∂m < 0 and < 0 and < 0 and ∂γy ∂m ∂γy ∂m ∂γy ∂m > 0; = 0; ∂γy ∂m > 0; = 0; < 0. Specifically, proposition 1 tells us that the impact of the intermediate sector markup on real per capita growth crucially depends on the sign of (1 − β). If β < 1, the specialization gains obtained from an expansion in input variety are larger than the possible losses due to more ∂γ complexity in production and ∂my > 0. If β > 1 , the specialization gains are smaller than ∂γ the possible losses due to more complexity in production and ∂my < 0. Finally, when β = 1, the specialization gains are exactly offset by the possible losses due to more complexity ∂γ in production and ∂my = 0. Therefore, a decrease in m, by increasing the elasticity of substitution across intermediate inputs and, hence, the toughness of competition in this industry, can imply a lower, or a higher, or else no effect at all on per capita income growth (PMC and economic growth are ambiguously correlated in sign in the model). Although the result that in the absence of demographic change (n = 0) growth in real per capita incomes is equal to zero is a distinctive characteristic of basic semi-endogenous growth models (Jones [34]), our setting also includes other features that cannot be found in canonical semi-endogenous growth theory. The most important of these features is that, unlike Jones [34] (p. 767, equation (8)) where γN = γy = Ψn, in our model the relation between γN and γy is mediated by Φ ≡ α [m(1 − β) − 1]. Thus, while in Jones [34] (p.780, equation (A1)) β = 0, and hence Φ ≡ α(m − 1) > 0, in our model Φ can also be negative. This occurs, for any given m > 1, when β is sufficiently large, β > (m − 1)/m ∈ (0, 1), i.e., if the (production-) complexity effect related to an increase in N is strong enough, which can ultimately lead to negative growth rates of per capita income when the innovation activity expands. Moreover, since n affects positively γN (as in Jones, [34]), an increase in the rate of population growth can also imply (when Φ < 0, or with a complexity effect particularly strong) a negative impact on per capita income growth. Our model differs from Jones [34] also because in equation (19) the growth rate of the economy depends not only on the growth rate of population (n) and the parameters φ, λ and β, but also (among others) on m. This specific difference with respect to Jones [34] 14 can be ascribed to the fact that in our model we have: (i) postulated that intermediate firms produce with labor (rather than forgone consumption) and, more importantly, (ii) disentangled the intermediate firms’ gross markup of price over the marginal production cost from the factor-input shares in GDP. It can be easily demonstrated (see on-line Appendix B) that, using the Jones’ assumptions, our model can exactly reproduce the BGP growth rate of the Jones’ economy. 3 Quantitative analysis From the theoretical analysis developed in the previous section, three main testable predictions emerge. Case I When the possible losses due to more complexity in production are extremely small, and lower than the specialization gains from innovation (i.e., an expansion in input-variety), then per capita real GDP growth rate is positively correlated to the population change and the intermediate sector markup, i.e., ∂γy ∂γy ∂n > 0 and ∂m > 0. Case II When the possible losses due to more complexity in production are moderately large, but still lower or, at most, equal to the specialization gains from innovation (i.e., an expansion in input-variety), then per capita real GDP growth rate is negatively correlated to the population change and positively ∂γ ∂γ correlated to the intermediate sector markup, i.e., ∂ny ≤ 0 and ∂my ≥ 0. Case III When the possible losses due to more complexity in production are very big, and definitely larger than the specialization gains from innovation (i.e., an expansion in input-variety), then per capita real GDP growth rate is negatively correlated to the population change and the intermediate sector markup, ∂γ ∂γ i.e., ∂ny < 0 and ∂my < 0. The three testable predictions obtained from our theory and listed above are summarized by table 1. The rest of the paper confronts these predictions with the data. In particular, how the magnitude of β (in our setting a measure of the production-complexity effect due to intermediate inputs proliferation) may affect the interaction between population growth and economic growth, and between markups and economic growth, respectively. In doing this, we abstract λ . Since this term must be positive, this choice entails, at most, an attenuation from Ψ ≡ 1−φ bias in our estimates. As we will see later on, our empirical results corroborate the theoretical predictions and document, at least for a group of countries, a positive role for population change in economic development.19 We proceed now by discussing the econometric strategy, then we illustrate the dataset and the main findings of our contribution. 19 This result substantially departs from the existing literature on the topic, which finds general lack of correlation between population and real per capita growth rates (see Herzer et al. [31] and Li and Zhang [46] and Kelley and Schmidt [40] among others). 15 Table 1: Summary of the theoretical predictions >0 ∂γy ∂m >0 m−1 m ∂γy ∂n =0 ∂γy ∂m =0 <β<1 ∂γy ∂n <0 ∂γy ∂m >0 0<β< Case II β= Case II 3.1 ∂γy ∂n Case I m−1 m m−1 m Case II β=1 ∂γy ∂n <0 ∂γy ∂m =0 Case III β>1 ∂γy ∂n <0 ∂γy ∂m <0 Econometric strategy In this section, we estimate different models that are consistent with our theory. The econometric approach we follow allows to test the behavior of per capita GDP growth dynamics, under the assumption that unobserved heterogeneity affects parameters estimation. In particular, we employ a finite mixture model (FMM), relaxing the hypothesis of IID residuals (see Aitkin [7] and Alfò et al. [8], among others), and allowing for correlated random terms.20 In such a model, the random component captures the impact of unobserved country-specific variables, limiting the effects of the omitted variable bias. It is worth noticing that FMM allows also to deal with the unobserved heterogeneity due to the non-monotonic, non-uniform relationship between regressors and response, as predicted by our theory. According to the Generalized Linear Models framework (see McCullagh and Nelder [49]), the empirical counterpart of equation (19) can be written as: T E(γit |nit , mit ) = ω0i + mT i ω1i + ni ω2i (21) where γi,t is the per capita GDP growth rate, mT i is the vector measuring the product between intermediate sector markup and population change, nT i is the vector of the population growth 21 The parameters ω1i and ω2i capture the country-specific rates, for country i at time t. unobserved factors that affect per capita GDP growth, through population change and its interaction with intermediate sector markup. Finally, ω0i captures the unobserved countryspecific factors related with other variables not included in the model. Equation (21) entails a data generation process for per capita GDP growth that can be 20 Assuming that some of the fundamental covariates were not included into the model specification, and that their joint effects can be accounted by adding latent variables to the linear predictor, it is possible to relax the assumption of IID residuals (Aitkin [7], McLachlan and Peel [51]). 21 In this section, the subscript y on the per capita GDP growth rate γ is omitted for notational simplicity. 16 affected by some hidden factors, underlying the relationship between mit and nit . Conditionally to the regression parameters η i = [ω0i , ω1i , ω2i , σi2 ]T , the probability density function of γit is given by: fγi = f (γit |η i ) = T Y ( t=1 ) 1 2 p exp − 2 (γit − ω0i − ω1i mit − ω2i nit ) 2σi 2πσi2 1 (22) We assume that parameters in η i can be empirically described by random variables, with unspecified probability function, and cluster-specific variances σi . In this way, equation (22) takes explicitly into account the between countries random terms correlation. The nonparametric maximum likelihood estimator (NPMLE) of the distribution is discrete (Laird [45], Heckman and Singer [30]), with at a finite number of locations and masses. This implies that the country-specific latent variables are modeled as measures of the difference between country i-th’s covariates and their sample mean. We assume that γit is a conditionally independent realization of the potential per capita GDP growth, given the set of random factors, which varies over countries and accounts for both individual variation and dependence among country-specific rates of growth. Let now ui denote the set the country-specific unobservable factors that affect mit and nit , T T i.e., ui = [uT ω0 , uω1 , uω2 ]. Treating the latent effects as nuisance parameters, and integrating them out, we obtain the following likelihood function: L (·) = n Z Y i=1 U fγi dG(η) (23) where U is the support for the latent variables space G(u), i.e., U is the discrete probability measure on the space η i , with k = 1, . . . , K support points, each of them with probability PK πk = π1 , . . . , πK with k=1 πk = 1. McLachlan and Peel [51] stress that the mixture reduces to a simple homogenous regression when U degenerates in a single support point with probability πk = 1. By introducing an undefined random distribution of parameters, this specification allows to estimate unbiased coefficients for population growth and its interaction with intermediate sector murk-up, conditional to the effects of additional unobserved environmental variables. Our goal is to find the best discretization of the conditional log likelihood, given the data generating process of the response variable (Dempster et al. [22], McLachlan and Krishnan [50], among others). Equation (23) can be approximated by the sum of finite number (K) locations: L (·) = (K I Y X i=1 ) f (γi |mi , ni , uk )πk = (K I Y X i=1 k=1 ) [fik πk ] (24) k=1 where f (γi |mi , ni , uk ) = fik denotes the response distribution in the k-th component of the finite mixture. Locations uk and corresponding masses πk (prior probabilities) represent unknown parameters while the optimal number of cluster K is estimated via penalized 17 likelihood criteria. This implies that: n n K K XX ∂ log[L (η)] ∂` (η) X X ∂ log fik πk fik ∂ log fik = = = wik K P ∂η ∂η ∂η ∂η i=1 k=1 i=1 k=1 πk fik (25) k=1 where wik represents the posterior probability that the i − th unit comes from the k − th component of the mixture. The corresponding likelihood equations are weighted sums of those of an ordinary log-linear regression model, with weights wik . Solving these equations for a given set of weights, and updating the weights from the current parameter estimates, we define an Expectation Maximization (EM) algorithm (see, for instance, McLachlan and Peel [51], and Alfò et al. [8] for the computation of EM in growth contest). 3.2 The data In this section, we provide a description of our data and discuss the procedures adopted to merge information from different sources in a single dataset. First, we get data on real per capita GDP growth, population growth and exchange rate (to convert all the monetary values in constant PPP US$) from the Penn Table database.22 Second, in order to construct a measure for the markup in the intermediate sector, we use the EUKLEMS database, which collects data on output, productivity, employment (skilled and unskilled), physical capital at industry level, for all European Union member states and for five of the high developed countries (US, Japan, Korea, Canada and Australia) from 1970 to 2007.23 At the lowest level of aggregation, data are collected for 72 industries according to the European NACE revision 1 classification. We proxy the intermediate sector with the sum of the following industries: basic metals and fabricated metal; electrical and optical equipment; electricity; gas and water supply; machinery; other non-metallic mineral; rubber and plastics; textiles; textile; leather and footwear; transport and storage; transport equipment; wood and cork. We then compute the markup index for the intermediate sector, of country i at time t, as follows: Gross Outputit mit = (26) Total Labor Costsit + Total Capital Costsit In our regressions, m is an index set equal to 1 in the base year 1995. Third, the variable “research-labor”has been identified through an aggregate measure of investment in research activity: we use the Gross Domestic Expenditure in R&D, converted in constant PPP US$, as in Bottasso et al. [16].24 22 Time span: 1970-2007, 2005 as reference year. PWT 8.0 Alan Heston, Robert Summers and Bettina Aten, Penn World Table Version 8.0, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania. For more information on the Penn Table database the interested reader can refer to the following web page: https:http://www.rug.nl/research/ggdc/data/pwt/. 23 For more information on the EUKLEMS database the interested reader can refer to the following web page: http://www.euklems.net/. 24 The primary source of these data is EUROSTAT. In the case of missing data, Bottassio et al. [16] collect information either from the OECD-STAN database or, for some countries, from EUROSTAT on Business Ex- 18 Fourth, the “number of ideas already invented”, i.e., a country stock of knowledge, has been measured through the patent applications to the European Patent Office, collected by EUROSTAT.25 In the robustness checks, we use the number of citation weighted patents filed in each year at the USPTO. Finally, in order to identify a country’s underlying complexity in production, we use alternative indexes, i.e. the Network Trade Index and density measures, based on Lafay index and Balassa index, provided by Ferrarini and Scaramozzino [25]. Our final dataset consists of a sample that includes 23 OECD countries (Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Japan, The Netherlands, Poland, Portugal, Slovak, Slovenia, Spain, Sweden, United Kingdom and USA), with a time span ranging from 1970 to 2007. Table 2 presents summary statistics. Table 3 shows that all countries in the sample experienced a positive average real GDP per capita growth rate, along the period under observation. Since we are dealing with OECD countries, this is not surprising. At the same time, the same table also shows that the same countries (with the only exception of Ireland and Slovenia) have experienced over time some negative annual real GDP per capita growth rates, as well. 3.3 Results Tables 4 provides the estimation results for equation (21), using the annual real GDP per capita growth rate as a dependent variable. Columns (1) and (2) report OLS fixed effects and Feasible GLS estimates, respectively. In the OLS fixed effects model, inference is biased because of the residuals non-normality (i.e., the Shapiro-Wilk test rejects the normality hypothesis with a value 0.988 and a p-value=0.000). The FGLS model allows for heterogeneous variance in the residuals and takes into account the possible correlation between the covariates. In both models, the marginal effects of population change and its interaction with the intermediate sector markup on per capita GDP growth are consistent with our second theoretical prediction. This suggests that, on average, for the countries in the sample, the specialisation effect is greater than the complexity effect. Columns (3), (4), and (5) report the Finite Mixture Model (FMM) estimates, where we relax the assumption of global normality of the residuals. Using the AIC, we identify three clusters of countries, i.e., K = 3 in equations (24) and (25), listed along with summary statistics for n and m in tables 6-8. The Shapiro-Wilk normality test on the residuals had p-value=0.056 in cluster 1, 0.241 in cluster 2, and 0.830 in cluster 3. FMM parameter estimation provides the same results of the previous models, with respect to the second cluster of countries. Results of models (1), (2) and (4) are consistent with the second prediction of our theoretical model. In particular, the location k = 2 of the Finite Mixture Model identifies a cluster penditure on R&D. The authors notice that “only in the case of Sweden, Norway and New Zealand the amount of missing data was substantial and we had to rely on linear interpolation: for this reason, as a robustness check we have also performed our analysis after excluding these countries”.The full dataset is available at the following web page: http://qed.econ.queensu.ca/jae/2015-v30.2/bottasso-castagnetti-conti/bcc-data.zip. 25 Data are available at the web page: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=pat_ ep_nic&lang=en. 19 of countries for which the potentially large losses due to the complexity in production are lower than the specialization gains arising from innovation (see table 7). Table 7 shows that those countries are characterized by higher (average) population growth and intermediate sector markup and a lower (average) GDP growth (7.185 annual percentage points against 8.098 and 9.272). Results from the Finite Mixture Model (3) indicate also that exists a group of countries, those of locations k = 1 and k = 3, whose sources of growth dynamics are not captured by our theoretical model (see tables 6 and 8). Finally, parameter estimation for countries in cluster 3 provides not significant results, even though the signs of the effects of population change and intermediate sector markup on economic growth in this cluster are compatible with the third prediction of our theoretical model. It is wise noticing that, in our regression, we consider only three random components (i.e., the intercept, population growth and its interaction with the intermediate sector markup). The set of unobserved differences between countries is, however, potentially larger and multidimensional. Our approach, then, has the limit of representing a multi-dimensional phenomenon on a reduced dimensional scale. This is proven by the fact that the variance of the latent effects is high in all clusters (see table 4). To examine whether the increase in production complexity influences the cluster membership, we estimate the following multinomial logit model: P r{Cluster = 1, 2, 3} = log πic πiC = %0C + %1C ntiC + %2C R&DC (27) PC where: πic is the probability that the country i belongs to cluster c, with c πic = 1, for each country i; %0C is the intercept; nti is our proxy for complexity in production; R&D is the expenditure on Research & Development activities, in percentage of GDP.26 The second cluster (FMM, k=2) is the reference group for the odds. Results are reported in table 9. In line with our theory, our estimates show that an increase of complexity in production (here captured by an increase of nti) increases the odds for cluster 3 (FMM, k=3) - where ∂γy /∂n < 0 - while reduces that for cluster 1 (FMM, k=1) - where ∂γy /∂n > 0. This implies that, ceteris paribus, the higher the degree of complexity of a country’s production structure, the lower probability that population growth acts as an engine for real per capita GDP growth. Notice finally that, surprisingly, the R&D variable does not play any significant role in the cluster membership probability. 26 As in Ferrarini and Scaramozzino [25], we employ the Network Trade Index (nti) as a measure of the intensity of trade among countries participating in the international production networks (see also Ferrarini [24]). The net index is defined as follows: t t Xijk − Mijk (28) nettijk = t t Xijk + Mijk t t where Xijk is country i’s exports of product k to country j, in year t and Mijk is country i’s imports of product k from country j. By construction, the nti ∈ [−1, 1]. A nti index equal to 1 indicates pure exports (and the highest comparative advantage); a nti index equal to -1 indicates pure imports (and the highest comparative disadvantage); finally, a nti index equal to 0 indicates balanced trade. 20 3.4 Robustness checks In order to check the robustness of our results to different model specifications, in this section we briefly present all the alternatives we have estimated and compare the results with the baseline specification presented in the previous section.27 First of all, we run our regressions using the 5-year average real GDP growth rate as dependent variable. This has been done with the objective of getting rid of possible shortrun business-cycle effects. Estimation results are provided in table 5. In this case, parameters estimation through OLS Fixed Effects and Feasible GLS is in line with that presented in the previous section and the AIC suggests four groups for the Finite Mixed Model. The main difference with the previous results is that we can now identify a group of countries (namely, Hungary, Ireland and Poland), which have actually the highest (average) per capita GDP growth rate along the period under observation, that experience a positive impact both of population change and the intermediate sector markup on economic growth, as predicted by the first testable implication of our theoretical model.28 We control also for other measures of GDP. As mentioned at the top of tables 4 and 5, our dependent variable, i.e. the (annual and the 5-year average) real GDP growth rate, has been computed using the expenditure-side real GDP at chained PPP (rgdpe ), provided by the Penn World Tables 8.0. Alternatively, we employ the rate of change of the real GDP using national-accounts growth rates (rgdpna ) and the GDP per capita growth provided by the World Bank. Although some modifications occur in the composition of the clusters, our results do not change significantly. We run our regressions also using different measures of intermediate sector markup. As usual, when dealing with index numbers, results can be dependent on the base year. Since we are examining long-run changes, we use an alternative base year, the 1985. We don’t find any significant change in our estimates. Finally, we estimate the multinomial logit model using the (logarithm of 5-year average of the) country product density, according to the Lafay product space definition, to proxy for complexity in production. The average density provides a measure of how fungible a country’s capabilities are in terms of adjustment to complex production structures.29 Even in this case, we do not obtain any significant change in our estimates. 4 Concluding remarks This paper has re-assessed how the changing degree of production complexity (i.e., the number of horizontally-differentiated intermediate inputs entering the same aggregate production function of a country) can ultimately affect not only the long-run growth rate of per capita 27 As our results are robust to the alternative specifications used, for the sake of brevity we do not present and discuss in detail all the parameter estimates. However, they are available upon request from the authors. 28 Ireland is included by Durlauf et al. [23] (pag. 566, table 2) in the group of “fifteen growth miracles”. 29 Ferrarini and Scaramozzino [25] compute the density index for sector j in country i as a weighted average of the trade specialization indicators, where the weights are the proximities of sector j with all the other sectors. Then the average density of country i is obtained as an average of the density indexes across all sectors of the country. 21 income, but also the relation between the latter variable, population growth, and the degree of product market competition (PMC). Building upon Romer [57] and Jones [33] we have developed a variant of the basic, well-known semi-endogenous growth model capable of explaining why we may observe (as suggested by the already available empirical evidence) a non-uniform correlation between population growth/economic growth and between economic growth/markups. The theoretical explanation offered by our model is based on the idea that introducing new varieties of intermediate inputs generates a tension between productivity-gains due to more specialization and productivity-losses due to the presence of a more complex production process. The composition of these two differential effects of technological progress represents in the model the basis for the occurrence of a potentially non-monotonic correlation between population growth/economic growth and between PMC/economic growth. The empirical analysis presented in the second part of the paper suggests that a different degree of production complexity yields in the long-run a different growth rate of per capita income and, more importantly, a diverse impact of, respectively, population growth and PMC on economic growth. In particular, using the annual real GDP per capita growth rate as a dependent variable, OLS and FGLS models show the specialization effect of (intermediate)input-proliferation is larger than the corresponding production-complexity effect, so that the marginal effects of population change and the intermediate sector markup on per capita GDP growth are consistent with the second theoretical prediction of our model (negative impact of population growth, and positive influence of markups on economic growth). Once the unobserved heterogeneity has been taken into account (via FMM), it is possible to identify the countries for which these results hold (Canada, France, Netherlands, Slovenia, Spain, UK, and US). These countries are characterized, with respect to the rest of the sample, by the highest (average) population growth rate and the lowest (average) level of markups and per capita GDP growth. The use of the 5-year average real per capita GDP growth rate as dependent variable confirms our previous results. The only difference is that in this case our empirical model identifies a new cluster of countries (Hungary, Ireland, and Poland) in which the marginal effects of population change and the intermediate sector markup on per capita GDP growth are both positive, consistently with the first theoretical prediction of our model. This fact, together with the observation that these three countries have enjoyed the highest (average) GDP per capita growth rate along the period under observation, induces us to believe that in these economies population growth and R&D incentives (in the form of greater instantaneous monopolistic profits/markups accrued to the successful innovators) can ultimately act as a powerful source of long-run productivity growth. References [1] Acemoglu, D., and Akcigit, U., 2012, Intellectual property rights policy, competition and innovation, Journal of the European Economic Association, 10(1), 1-42. [2] Aghion, P., Bloom, N., Blundell, R., Griffith, R., and Howitt, P., 2005, Competition and Innovation: An Inverted-U Relationship, Quarterly Journal of Economics, 120 (2), 701-728. 22 [3] Aghion, P., Blundell, R., Griffith, R., Howitt, P, and Prantl, S., 2009, The effects of entry on incumbent innovation and productivity, Review of Economics and Statistics, 91(1), 20-32. [4] Aghion, P., and Griffith, R., 2005, Competition and Growth: Reconciling Theory and Evidence, Cambridge, MA: MIT Press. [5] Aghion, P., Howitt, P., 1992, A Model of Growth through Creative Destruction, Econometrica, 60(2), 323-351. [6] Aghion, P., and P. Howitt, 1998, Endogenous Growth Theory, Cambridge, MA: The MIT Press. [7] Aitkin, M.A., 1997, Contribution to the discussion paper by S. Richardson and P.J. Green, Journal of The Royal Statistical Society, B, 59, pp. 764-768. [8] Alfò, M., Trovato, G., and Waldmann, R.G., 2008 Testing for country heterogeneity in growth models using a finite mixture approach, Journal of applied econometrics, 23, 487-514. [9] Aitkin, M.A., and Rocci, R., 2005, A general maximum likelihood analysis of measurement error in generalized linear models, Statistics and Computing,12, pp. 163-174. [10] Barro, R.J., 1991, Economic Growth in a Cross Section of Countries, Quarterly Journal of Economics, 106(2), 407-443. [11] Benassy, J.-P., 1998, Is there always too little research in endogenous growth with expanding product variety?, European Economic Review, 42(1), 61-69. [12] Blanchet, D., 1988, A Stochastic Version of the Malthusian Trap Model: Consequences for the Empirical Relationship between Economic Growth and Population Growth in LDC’s, Mathematical Population Studies, 1(1), 79-99. [13] Bloom, D., Sachs, J., 1998, Geography, demography, and economic growth in Africa. Mimeo, Harvard. Institute for International Development [14] Blundell, R., Griffith, R., and J. van Reenen, 1995, Dynamic Count Data Models of Technological Innovation, Economic Journal, 105, 333-344. [15] Blundell, R., Griffith, R., and J. van Reenen,1999, Market Share, Market Value and Innovation in a Panel of British Manufacturing Firms, Review of Economic Studies, 66(3), 529-554. [16] Bottasso, A., Castagnetti, C., and Conti, M.,2015, R&D, Innovation and Knowledge Spillovers: A Reappraisal of Bottazzi and Peri (2007) in the Presence of Cross-Sectional Dependence, Journal of Applied Econometrics, vol. 30, pp. 350-352. [17] Grossman, G, and Helpman, H., 1991, Innovation and Growth in the Global Economy. MIT Press, Cambridge, MA. [18] Bucci, A., 2013, Returns to Specialization, Competition, Population, and Growth, Journal of Economic Dynamics and Control, 37(10), 2023-2040. [19] Bucci, A., 2015, Product Proliferation, Population, and Economic Growth, Journal of Human Capital, 9(2), 170-197. 23 [20] Bucci, A., and X. Raurich, 2016, Population and Economic Growth under Different Growth Engines, German Economic Review, in press (doi: 10.1111/geer.12092). [21] Coale, A.J., and E.M. Hoover, 1958, Population Growth and Economic Development in Low-Income Countries. Princeton: Princeton University Press. [22] Dempster, A.P. , Laird, N.M., and Rubin, D.A., 1977, Maximum Likelihood Estimation from Incomplete Data via the EM Algorithm (With Discussion), Journal of Royal Statistical Society, B 39, pp. 1-38. [23] Durlauf, S.N., Johnson, P. A., and Temple, J.R.W., 2005, Growth econometrics, in P. Aghion and S. N. Durlauf (eds.) Handbook of Economic Growth, Volume 1A, NorthHolland: Amsterdam, 2005, pp. 555-677. [24] Ferrarini, B., 2013, Vertical trade maps Asian Economic Journal, vol. 27 (2), pp. 105123. [25] Ferrarini, B., and Scaramozzino, P., 2016, Complexity, Specialization and Growth, Structural Change and Economic Dynamics, vol. 37, pp. 52-61. [26] Galor, O., 2011, Unified Growth Theory. Princeton: Princeton University Press. [27] Grossman, G.M., and E. Helpman, 1991, Innovation and Growth in the Global Economy. Cambridge, MA: MIT Press. [28] Hausmann, R., and C.A. Hidalgo, 2009, The Building Blocks of Economic Complexity, Proceedings of the National Academy of Sciences of the United States of America, 106(26), 10570-10575. [29] Hausmann, R., and B. Klinger, 2006, Structural Transformation and Patterns of Comparative Advantage in the Product Space, Working Paper No. 128, Harvard University: Center for International Development. [30] Heckman, J., and Singer, B., 1984, A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data, Econometrica, vol. 52(2) , pp. 271-320. [31] Herzer, D., Strulik, H., Vollmer, S., 2012. The long-run determinants of fertility: one century of demographic change 1900-1999, Journal of Economic Growth, vol. 17 (4), pp. 357-385. [32] Hidalgo, C.A., B. Klinger, A.L. Barabasi, and R. Hausmann (2007), The Product Space Conditions the Development of Nations, Science, 317(5837): 482-487. [33] Jones, C.I., 1995, Time Series Tests of Endogenous Growth Models, Quarterly Journal of Economics, 110(2), 495-525. [34] Jones, C.I., 1995, R&D-based Models of Economic Growth, Journal of Political Economy, vol. 103, pp. 759-84. [35] Jones, C.I., 1999, Growth: With or Without Scale Effects?, American Economic Review, vol. 89, pp. 139-44. [36] Jones, C.I., 2003, Population and Ideas: A Theory of Endogenous Growth. In Aghion, P., Frydman, R., Stiglitz, J., Woodford, M. (Eds.), Knowledge, Information, and Expectations in Modern Macroeconomics: In Honor of Edmund S. Phelps. Princeton: Princeton University Press, 498-521. 24 [37] Jones, C.I, 2005, Growth and Ideas, In Handbook of Economic Growth, edited by P. Aghion and S.N. Durlauf. Amsterdam: Elsevier-North Holland, Chap. 16: 1063-1111. [38] Jones, C.I., and Vollrath, D., 2013, Introduction to Economic Growth. New York: W.W. Norton &Company, Third Edition. [39] Jones, C.I., and Williams, J.C., 2000, Too Much of a Good Thing? The Economics of Investment in R&D, Journal of Economic Growth, vol. 5, pp. 65-85. [40] Kelley, A., Schmidt, R., 1995, Aggregate population and economic growth correlations: The role of the components of demographic change, Demography, vol. 32, pp. 543-555. [41] Kelley, A., Schmidt, R., 2001, Economic and demographic change: a synthesis of models, findings, and perspectives, N. Birdsall, A.C. Kelley, S. Sinding (Eds.), Population Matters: Demographic Change, Economic Growth, and Poverty in the Developing World, Oxford University Press, New York (2001), pp. 67-105. [42] Kremer, M., 1993, The O-Ring Theory of Economic Development, Quarterly Journal of Economics, 108(3), 551-575. [43] Kuznets, S., 1960, Population Change and Aggregate Output. In Universities-National Bureau Committee for Economic Research (Special Conference Series, No. 11), Demographic and Economic Change in Developed Countries. Princeton: Princeton University Press, 324-340. [44] Lafay, G., 1992, The Measurement of Revealed Comparative Advantage. In Dagenais, M.G., Muet, P.A. (Eds.), International Trade Modelling. London: Chapman & Hall. [45] Laird, N., 1978, Nonparametric Maximum Likelihood Estimation of a Mixing Distribution, Journal of the American Statistical Association, vol. 73, pp. 805-811. [46] Li, H., Zhang, J., 2007. Do high birth rates hamper economic growth? Review of Economics and Statistics, vol. 89, pp. 110-117. [47] Maggioni, D., Lo Turco, A., and Gallegati, M.,2016, Does Product Complexity Matter for Firms’ Output Volatility?, Journal of Development Economics, vol. 121, pp. 94-109. [48] Mankiw, N.G., Romer, D., and D.N. Weil (1992), A Contribution to the Empirics of Economic Growth, Quarterly Journal of Economics, 107(2), 407-437. [49] McCullagh, P., Nelder, J.A., 1989, Generalized Linear Models, Second Edition. Chapman & Hall, London. [50] McLachlan, G., and Krishnan, T., 1997, The EM Algorithm and Extensions, John Wiley & Sons Inc. [51] McLachlan, G., and Peel, D., 2000, Finite Mixture Models, John Wiley & Sons Inc. [52] Nickell, S.J., 1996, Competition and Corporate Performance, Journal of Political Economy, 104(4), 724-746. [53] Prettner, K., 2014, The non-monotonous impact of population growth on economic prosperity, Economics Letters, 124(1), 93-95. [54] Rabe-Hesketh, S., Pickles, A., and Skrondal, A. 2003, Correcting for covariate measurement error in logistic regression using nonparametric maximum likelihood estimation, Statistical Modelling, 3, pp. 215-232. 25 [55] Rabe-Hesketh, S., Skrondal, A., and Pickles, A. 2003, Maximum likelihood estimation of generalized linear models with covariate measurement error, The Stata Journal, 3, pp. 386-411. [56] Rabe-Hesketh, S., Skrondal, A., and Pickles, A. 2004, Generalized multilevel structural equation modeling, Psychometrika, 69, 167-190. [57] Romer, P.M., 1990, Endogenous Technological Change, Journal of Political Economy, University of Chicago Press, vol. 98(5), pp. 71-102. [58] Sala-i-Martin, X., G. Doppelhofer, and R.I. Miller, 2004, Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach, American Economic Review, 94(4), 813-835. [59] Schumpeter, J.A., 1942. Capitalism, Socialism and Democracy. New York: Harper and Row. [60] Smith, A., 1776, The Wealth of Nations. London: W. Strahan and T. Cadell. [61] Solow, R.M.,1956, A contribution to the theory of economic growth, Quarterly Journal of Economics, 70(1), 65-94. [62] Williamson, J.G., 2003, Demographic change, economic growth, and inequality. In Birdsall, N., Kelley, A.C., Sinding, S.W. (Eds.), Population Matters: Demographic Change, Economic Growth, and Poverty in the Developing World. New York: Oxford University Press, Paperback Edition, 106-136. 26 Figure 1: Empirical cumulative functions 27 28 intermediate sector markup index (1995=1) population growth rate (pop) real per worker GDP growth rate based on expenditure-side real GDP at chained PPP (rgdpe ) real per worker GDP growth rate based on national-accounts growth rates (rgdpna ) real per capita GDP growth rate R&D expenditure (% GDP) Net Trade Index m n γy γc R&D nti γy/na Description Variable PWT 8.0 World Bank Ferrarini and Scaramozzino [25] PWT 8.0 EUKLEMS PWT 8.0 PWT 8.0 Source Table 2: Summary statistics 660 484 335 660 660 660 660 Obs. 0.027 1.769 4.539 2.064 1.277 0.507 2.309 Mean 0.030 0.747 3.312 1.830 0.727 0.460 2.628 Std. Dev. -0.100 0.390 0.741 -9.830 0.152 -0.269 -11.912 Min 0.125 3.913 14.500 9.850 5.597 2.018 10.610 Max Table 3: Descriptive statistic on annual GDP per capita growth rate Country Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Ireland Italy Japan Netherlands Poland Portugal Slovak Republic Slovenia Spain Sweden United Kingdom United States Min Mean Max -4.713 -2.704 -4.568 -1.872 -2.510 -3.349 -3.644 -5.023 -3.790 -4.564 -1.134 0.595 -5.239 -2.822 -4.025 -0.451 -11.912 -0.129 0.531 -3.804 -3.911 -5.907 -2.144 1.636 2.138 2.086 1.369 2.637 1.766 2.653 2.015 2.188 2.500 2.707 3.743 2.380 2.593 1.892 4.567 2.531 3.836 2.591 2.688 2.484 2.395 1.566 7.308 5.614 6.742 3.849 6.052 5.573 7.467 6.085 8.123 7.380 9.883 7.424 7.525 8.782 6.395 9.406 9.944 10.610 6.168 7.800 7.220 7.160 3.661 29 Table 4: Results I, country level data (1) OLSFE (2) FGLS (3) FMMk=1 (4) FMMk=2 (5) FMMk=3 Dependent variable: annual real per capita GDP growth rate(rgdpe ) m∗n n 0.819*** -1.079* 0.672*** -1.348*** -1.752*** 5.022*** 1.564*** -2.424*** -0.008 -0.744 constant σk 2.347*** 2.443*** 1.507*** 2.173 2.374*** 2.040 2.967*** 2.986 ∂γy ∂n -0.071* -1.041*** 2.936*** -0.579*** -0.760 ∂γy ∂m 0.374*** 0.307*** -0.414*** 1.062*** 647 2.109 106 2.050 225 γy obs. 647 Significance levels:* : 10% **: 5% *** 1%. Colors: case I, case II, case III. 30 -0.005 2.592 316 Table 5: Results II, country level data (1) OLSFE (2) FGLS (3) FMMk=1 (4) FMMk=2 (5) FMMk=3 (6) FMMk=4 Dependent variable: 5-years real per capita GDP growth rate(rgdpe ) m∗n n 0.083** -0.113** 0.058*** -0.157** 1.098*** -1.300*** 0.223** -0.353** -0.294* 0.599*** -0.028 0.102* constant σk 0.316*** 0.335*** 0.752*** 0.178 0.323** 0.178 0.219*** 0.178 0.375*** 0.178 ∂γy ∂n –0.077* -0.132*** 0.675*** -0.065** 0.281** -0.133 ∂γy ∂m 0.120** 0.085* 0.396*** 0.124** -0.083** -0.017 597 5.608 44 2.957 130 2.77 293 3.004 130 γy obs. 597 Significance levels:* : 10% **: 5% *** 1%. Colors: case I, case II, case III. Table 6: FFM, cluster 1 (k=1) Country n m Austria Denmark Germany 0.288 0.281 0.146 1.215 1.415 0.931 mean std. dev. 0.238 0.080 1.187 0.243 Note: Model with the annual real GDP growth rate as dependent variable. 31 Table 7: FFM, cluster 2 (k=2) Country n m Canada France Netherlands Slovenia Spain United Kingdom United States 1.135 0.550 0.644 0.198 0.750 0.244 1.008 0.934 1.483 1.398 1.072 1.380 0.914 0.952 mean std. dev. 0.647 0.354 1.162 0.249 Note: Model with the annual real GDP growth rate as dependent variable. Table 8: FFM, cluster 3 (k=3) Country n m Australia Belgium Czech Republic Finland Greece Hungary Ireland Italy Japan Poland Portugal Slovak Republic Sweden 1.369 0.235 -0.007 0.374 0.587 -0.226 0.966 0.296 0.502 -0.047 0.554 0.110 0.361 1.401 1.394 1.362 0.941 2.158 1.929 0.935 0.846 0.912 3.213 1.196 3.404 1.282 mean std. dev. 0.390 0.429 1.613 0.846 Note: Model with the annual real GDP growth rate as dependent variable. 32 Table 9: Multinomial Logit Model for cluster membership Cluster 1 nti R&D constant % s.e. -0.121∗∗∗ 0.051 0.185 0.357 -0.027 0.746∗∗∗ Cluster 3 nti R&D constant % s.e. 0.124∗∗∗ 0.239 -1.869∗∗∗ 0.048 0.250 0.508 Significance levels : ∗ : 10% 33 ∗∗ : 5% ∗ ∗ ∗ : 1%