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How Important is Technology Capital? Measurement and Theory Marek Kapicka∗ Department of Economics, UC Santa Barbara March 27, 2008, ver. 0.4.2 Abstract I construct the measures of technology capital and country openness, as introduced by McGrattan and Prescott (2007a), for the US economy and the rest of the world for 1976-2005. The key assumption behind the estimation is that the net rates of return on both tangible and technology capital are equalized within a country. The ratio of technology capital and tangible capital is estimated to be about one fourth for both the US economy and for the rest of the world. US economy is also found to be less open than the rest of the world, although the difference has been diminishing, especially before 1990. I use the estimates to show that the neoclassical growth model with technology capital successfully explains movements in foreign direct investment in the last thirty years. While the welfare losses from totally closing US economy are found to be only about 0.13% of consumption, the welfare gains from totally opening US economy are much larger: they are equal to 6.9% of consumption. ∗ Comments welcome at [email protected]. 1 1. INTRODUCTION Recently, McGrattan and Prescott (2007a) have extended the neoclassical growth model by introducing the concept of technology capital. The theoretical framework incorporates two seemingly incompatible features: technology capital is costlessly replicated at all locations at which a firm operates, but at the same time the aggregate production function exhibits constant returns to scale in relevant inputs and a standard general competitive analysis applies. Depending on country openness, technology capital can be also replicated abroad through foreign direct investment. The model thus offers a promising new mechanism through which (more or less open) economies interact. However, in order to develop sensible quantitative implications of the model, one needs to have estimates of two of the main ingredients of the model: the stock of technology capital, an the degree of openness of an economy. Both of them are directly unobservable in the data. In this paper I provide an estimation procedure that uncovers both from the data, and estimate them for the US economy and the rest of the world for the 1976-2005 period. I then use the estimates to evaluate the performance of a neoclassical growth model with technology capital. I also estimate the welfare gains from totally closing US economy and from opening US economy further. The estimation of the stock of technology capital and the degree of openness relies on two main ingredients. First, it requires an identifying assumption. I use the assumption that the net rates of return from investments to both technology capital and to the tangible capital are equalized within each country. This assumption is quite weak, as it is not required that the net rates of return are equalized across countries. The estimates are therefore consistent with a large set of models. For instance, models with any type of international trade frictions, or models with imperfect consumption 2 insurance within each country will be consistent with the estimates.1 The second ingredient in the estimation follows from the theory of aggregate production function. The theory implies that both tangible capital inputs and labor inputs of all firms within a given country are related to the country-wide inputs in the same proportion, which is a function of the stock of technology capital of all countries, and of country openness. The US technology capital is estimated to be 25% of the US tangible capital in 1976, and then slightly decreases to 23% in 2005. For the rest of the world, the ratio is about 2% lower than the US ratio. US economy is found to be less open than the rest of the world in the whole period. While the openness of the US economy increases over the whole period, the openness of the rest of the world decreases until about 1985, and increases after that. Although no immediate effect of NAFTA can be seen in the estimates, there is a gradual increase in the US openness between 1994 and 2000, which can possibly be attributed to NAFTA. Even then, the effect of NAFTA on US openness appears to be small. I find that the neoclassical growth model with technology capital successfully captures the movements in the foreign direct investment in the US and abroad. I compute the welfare gains from either totally closing or totally opening US economy. While the welfare losses from totally closing US economy are found to be very small (0.13% of consumption, in consumption equivalents), the welfare gains from totally opening US economy are large (6.9% of consumption, in consumption equivalents). This indicates that, despite the increase in openness after 1976, the US economy is still closer to being totally closed, rather than totally open. 1 The idea that theory can be used to obtain estimates of an unobserved quantity has been used frequently in a business cycle analysis, starting with the estimation of Solow residuals in the aggregate production function (Prescott 1986). For instance, Ambler and Paquet (1994) estimate the stock of physical capital and stochastic depreciation shocks, Burnside, Eichenbaum and Rebelo (1993) estimate the work effort, and Ingram, Kocherlakota and Savin (1997) estimate nonmarket hours worked. 3 The importance of foreign direct investment and openness for welfare has long been recognized by the economic literature.2 However, their quantitative importance has been addressed only recently. Most notably, Ramondo (2007) analyzes and estimates an Eaton and Kortum (2002) type model with technology diffusion across countries.3 While the source of welfare gains in her model is similar to this model, both approaches differ along several dimensions. First, the diffusion of technology in her model is exogenously given, rather than being endogenous like here. Thus, there is no interaction between the amount of technology diffusion in one country and openness of other countries. Second, her model is static, while this model is dynamic and one can analyze the transitional adjustment to a change in country openness. On the other hand, her model can be easily integrated with modern theories of international trade and one can jointly analyze gains from openness and gains from trade, as in Rodriguez-Clare (2007) and Ramondo and Rodriguez-Clare (2008). However, the main advantage of the approach in this paper is, in my view, that it is fully integrated with the neoclassical growth model. Therefore, all the available knowledge about the neoclassical growth model and its ability to match the data can be put to a new use. Next section introduces the technology capital. It also reviews the aggregation theory of McGrattan and Prescott, and highlights the elements of the aggregation that are important for the estimation that follows in Section 3. Section 4 describes the data used in the estimation, and provides the estimates. Section 5 then analyzes the neoclassical growth model with technology capital, evaluates its performance and provides results of the numerical simulations. Section 6 concludes. 2 See e.g. Horstmann and Markusen (1989) for an early analysis. See also Burstein and Monge-Naranjo (2006) where the gains from openness are derived from reallocation of managerial talent across countries, and quantitatively evaluated. 3 4 2. TECHNOLOGY CAPITAL There is I countries in the world. Country i has a population Ni . In each country there is a large number of locations where production can take place. The measure of locations is, without loss of generality, taken to be equal to Ni . In each location, at most one firm from each country can operate. All firms in country i, domestic and foreign, share the same total factor productivity Ai . There are two types of capital. Tangible capital is location and firm specific and depreciates at rate δK . Technology capital is firm specific but not location specific: investment in technology capital increases production abilities in all locations, both domestic and foreign, at which the firm operates. The technology capital depreciates at rate δM . The technology capital allows the firm to expand production by effectively multiplying number of plants that can be operated at each location. A domestic firm with M units of technology capital, k units of tangible capital and l units of labor produces in each location in country i ¶(1−φ) µ k α l (1−α) yi = Ai M ( ) ( ) , M M ¡ ¢(1−φ) = Ai M φ kα l(1−α) , α, φ ∈ (0, 1), since k and l is evenly spread over all plants at a given location. Similarly, it is efficient to spread all the available labor and tangible capital evenly across all locations. Therefore, the production of a domestic firm in country i that has technology capital M and uses K units of tangible capital and L units of labor in total is4 4 ¡ ¢(1−φ) Yii = Fii (Ni , M, K, L) = Ai (MNi )φ K α L(1−α) . In what follows, a subscript on a variable indicates the country where production takes place, while superscript indicates country of origin. 5 Production of firms from a foreign country is determined similarly but depends, in addition, on the openness of country i. The degree of openness is measured by a parameter ωi ∈ [0, 1] that determines the fraction of foreign technology capital that is permitted to enter the domestic country. A firm from country j 6= i produces a total output in country i given by ¡ ¢(1−φ) Yij = Fij (Ni , M, K, L) = Ai (ωi MNi )φ K α L(1−α) . As in McGrattan and Prescott, a country i is called totally open if ωi = 1 and totally closed if ωi = 0. The aggregate production function maximizes the output of a country i given the population Ni , aggregate capital and labor inputs Ki and Li , and aggregate stock of technology capital in all countries M = (M 1 , ...M I ) : Fi (Ni , M, Ki , Li ) = max j j X j Fi (Ni , M j , Kij , Lji ) {Ki ,Li } (1) j P j subject to the resource constraint on tangible capital j Ki ≤ Ki and on labor P j j Li ≤ Li . The maximization problem yields the aggregate production function that exhibits constant returns to scale in M, Ki and Li and is given by Fi (Ni , M, Ki , Li ) = Ai Niφ (M i + ωi X α(1−φ) (1−α)(1−φ) M j )φ Ki Li . (2) j6=i The solution to (1) requires that the factors of production, as well as the production 6 of all firms, are related to the country aggregates in the same proportions: where Yi = P j Yij = vij Yi , (3) Kij = vij Ki , (4) Lji = vij Li , (5) Yij is the total production of country i. The proportion factors {vij }i,j are given by vii = vij = Mi P M i + ωi M j (6) j6=i j Mi ωi M P , + ωi M j j 6= i. (7) j6=i Equation (4) shows that the proportion factor vij determines the amount of capital invested in country i by firms from country j, i.e. the foreign direct investment from country j to country j. Similarly, equation (3) shows that the same proportion factor determines the sales of foreign firms. As follows from (6) and (7), the proportion factor depends on the technology capital in all countries, as well as on the openness of the domestic country.5 Rates of Return It follows from the aggregation procedure that the capital output ratio is the same for all firms operating in country i. Hence the net rate of return from all investments 5 Equation (4) can be related to a similar equation (18) in Ramondo (2007). In her model, the fixed costs tij play a role similar to the role of country openness here, and the variable Γij plays a role similar to the stock of technology capital here. 7 in tangible capital in country i is equalized and is equal to riK = (1 − τip ) ¶ µ Yi α(1 − φ) − δK , Ki (8) where τip is the tax rate on profits in country i. The net rate of return from investment in technology capital riM is given by Yii + riM = φ P Yji j6=i Mi − δM . (9) 3. THE ESTIMATION PROCEDURE In this section I develop a procedure that estimates the stock of technology capital, and the degree of openness. I will assume that there are only two countries in the world, United States US and the rest of the world RW.6 The key identifying assumption is that the net rates of return on tangible and technology capital in all countries are equalized: M K M Assumption 1 rUKS = rUS and rRW = rRW . US , KURW Since the tangible capital stocks of both domestic and foreign firms KUS S , RW US KRW and KRW are all observed, one can use them to compute the proportion factors US RW , YRW , and vU S and vRW from equation (4).7 The production of domestic firms YUS US of foreign firms YURW S , YRW can be eliminated from the rate of return formula (9) 6 The rest of the world will occasionaly be called a country. US RW For the case of two countries the notation is simplified by writing vU S = vU S and vRW = vRW . RW US One then obtains vU S = 1 − vU S and vRW = 1 − vRW . 7 8 using equation (3): vUS YU S + (1 − vRW )YRW − δM , M US vRW YRW + (1 − vU S )YU S =φ − δM . M RW rUMS = φ M rRW (10) (11) Because the investment in technology capital is expensed rather than treated as an investment, country’s production Y is not equal to its Gross Domestic Product Ŷ . Rather, GDP is lower than the actual production: US ŶUS = YUS − XM , (12) RW , ŶRW = YRW − XM (13) US RW and XM is the investment in technology capital by US and RW firms. where XM Since the investment in technology capital is not observed in the data, YU S and YRW are not directly observed as well. Substituting the identities (12) and (13) for YUS and YRW in (10) and (11) and using Assumption 1, one can express the implied US stock of technology capital as follows: MtUS = φ US RW vU S,t (ŶUS,t + XM,t ) + (1 − vRW,t )(ŶRW,t + XM,t ) (1 − p τUS )(α(1 − ŶU S,t +X U S φ) KU S,tM,t , (14) − δK ) + δM Similarly, the stock of technology capital of the rest of the world satisfies: MtRW = φ RW US vRW,t (ŶRW,t + XM,t ) + (1 − vUS,t )(ŶU S,t + XM,t ) (1 − p τRW )(α(1 − ŶRW,t +X RW φ) KRW,tM,t . (15) − δK ) + δM US RW The investment in technology capital XM and XM can be recovered simultane- 9 ously with technology capital by using its law of motion: US US = XM,t + (1 − δM )MtUS Mt+1 RW RW = XM,t + (1 − δM )MtRW . Mt+1 (16) (17) Equations (14), (15), (16) and (17) form a system of first order difference equations in the technology capital MtU S and MtRW . Given some initial or terminal condition on technology capital, one can solve these difference equations for the time series of technology capital in both countries. After the stock of technology capital is computed, the equations (6) and (7) can be inverted to compute the openness parameters: 1 − vUS M U S , vU S M RW 1 − vRW M RW = . vRW M US ωUS = ωRW Note that there are alternative ways of estimating the stock of technology capiRW US RW tal. If firm level production YUS , YUS , YRW and YURW S is observed directly, then the proportion factors vU S and vRW can be computed from (3) rather than from (4). SimUS RW RW ilarly, if firm level employment LRW US , LU S , LRW and LU S is observed, vUS and vRW can be computed from (5). Although data availability may lead one to prefer one estimation procedure over the other, all three approaches are theoretically equivalent and should in principle yield the same results. 4. THE ESTIMATES I focus on the 1976-2005 time period. The data for real US tangible capital stock KUUSS are taken from the National Economic Accounts Fixed Assets Table. In the 10 benchmark estimates, the rest of the world definition includes OECD countries.8 RW Hence, KRW is is constructed as a sum of real capital stock for these countries, and the data are taken from the AMECO database. The data are converted into 1990 US dollars using Purchasing Power Parity. US The tangible capital stock of US firms abroad KRW is measured by the amount of US-owned private assets owned abroad from the International Investment Position of RW the United States. Similarly, the tangible capital stock of foreign firms in the US KUS is measured by foreign-owned private assets owned in the US from the International Investment Position of the United States. Current cost valuation is used for both assets. The real US Gross Domestic Product ŶU S is taken from the National Income and Product Accounts. To be consistent with the measure of US capital stock, US GDP is adjusted by imputing the flow of services from consumer durables and from government capital. The adjustment procedure is standard.9 The real Gross Domestic Product for the rest of the world ŶRW is constructed as a sum of real GDP for all the countries that are included in the definition of the rest of the world capital stock, and converted into 1990 US dollars using Purchasing Power Parity. The data are taken from the Groningen Growth and Development Center (GGDC) Total Economy database. The values of profit tax rate τUp S is taken to be equal to the ratio of total taxes on corporate income to corporate profits, and is taken from the National Income and p Product Accounts. The value of τRW is assumed to be equal to τUp S . The definition of the rest of the world is an important factor in the estimation. On one hand, one would like to take the rest of the world as large as possible. The cost of doing so is that by aggregating foreign countries into one, it is implicitly assumed 8 Czech Republic, Hungary, Slovak Republic and Poland are excluded because of limited data availability. 9 See Cooley and Prescott (1995). 11 that i) all the foreign countries included in the definition are totally open toward each other and ii) they have the same degree of openness toward USA. Especially the first assumption becomes increasingly unrealistic as the number of foreign countries included in the definition increases. Since foreign direct investment is mostly concentrated among OECD countries, I select only those countries in the benchmark estimation. However, I will also provide alternative estimates where the rest of the world includes a larger set of countries to see how the definition of the rest of the world affects the results. Benchmark Estimates I set the tangible capital share in GDP α to be equal to 0.326, and the depreciation rate of tangible capital δK to be equal to 5.6% annually. Both numbers are computed as an average over the 1976-2005 period. I follow McGrattan and Prescott (2007b) by setting the depreciation rate of technology capital to be 8% annually.10 The remaining parameter to be chosen is the degree of decreasing returns in each location φ. I set φ in such a way that the average ratio of investment in technology capital to the production of US economy is 7%, which is somewhat higher than the ratio of US. expenditures on R&D and advertisement to GDP. The resulting value of φ is 0.075. The terminal condition I use in solving the difference equations (14), (15), (16) and (17) is that the investment in technology capital in 2005 in both countries is the same as the investment in technology capital in 2004. Since this assumption is highly arbitrary, I will later experiment with alternative terminal conditions. Figure 1 plots the ratio of technology capital and tangible capital for both countries. The ratio of US technology capital and US tangible capital is approximately 0.25 initially, and then decreases to 0.23 in 2005. In the rest of the world, the ratio is 10 The argument why technology capital depreciates faster than the tangible capital is that it includes R&D investment, and BEA estimates that R&D investment depreciates at rate 15% annually. 12 USA Rest of the World 0.25 0.2 0.15 1975 1980 1985 1990 year 1995 2000 2005 Fig. 1. Ratio of Technology Capital and Tangible Capital about 2% lower in all periods. US investment in technology capital is found to be highly procyclical (at annual frequency), and less volatile than investment in tangible capital. Figure 2 plots the openness parameters ωU S and ωRW . Overall, the magnitude of the openness parameters shows that both the US economy and the rest of the world are rather closed than open. The fraction of foreign technology capital permitted in any of the two countries never exceeds 6%. The rest of the world is more open than USA throughout the whole period, despite the fact that the difference in openness between both economies has been diminishing. While the US economy has increased its openness more or less steadily throughout the whole period (from 0.0054 to 0.0283), the openness of the rest of the world has been declining until about 1985. The degree of openness of the US economy is uncorrelated with US production, although it is 13 positively correlated with US GDP. 0.06 0.05 0.04 0.03 0.02 0.01 USA Rest of the World 0 1975 1980 1985 1990 year 1995 2000 2005 Fig. 2. Openness Parameters Interestingly, there is no spike in the degree of openness of the US economy in or immediately after 1994 when NAFTA came into effect. This may be so because NAFTA investment restrictions have been lifted only gradually. This is consistent with the estimates: before 1994 the degree of openness was constant for several years, but started to increase gradually after 1994. But even in that case the effect of NAFTA on openness appears to be small, at least compared to the secular trends in openness. The US production has been growing on average at 2.98% per year which is slightly lower than the growth rate of GDP. The total factor productivity has been growing at a rate of 0.88% per year. In contrast, the average growth rate of the total factor 14 productivity one would incorrectly measure by ignoring technology capital has been growing at a rate of 1.03% per year. Thus, the contribution of the total factor productivity, why still of first order importance, is somewhat diminished if one properly accounts for the technology capital. Alternative Estimates To examine the robustness of the results, I have considered alternative assumptions about i) the definition of the rest of the world, ii) the way proportion factors vUS and vRW were computed, iii) the average ratio of investment to technology capital and production, and iv) the terminal condition that was used in solving the difference equations (14), (15), (16) and (17). Definition of the Rest of the World I have redefined the rest of the world to include a larger number of foreign countries for which all data were available.11 I use the World Bank estimates of Nehru and Dhareshwar (1993) for capital stock data12 , and the GGDC Total Economy database for GDP data. Figure 3 shows that, while the alternative estimates of the US technology capital to tangible capital stock ratio are almost identical to the benchmark estimates, the estimates for the rest of the world are now higher by about 1%.13 The alternative estimates of the openness parameters are plotted in Figure 4. The openness parameters for the US economy are slightly lower, but the time profile is practically the same as before. For the rest of the world, the estimates are almost the same as before. Thus, the effect of the definition of the rest of the world is rather small. 11 The following countries were added: Argentina, Bolivia, Brazil, Chile, China, Colombia, Costa Rica, Cyprus, Dominican Republic, Ecuador, Guatemala, Jamaica, Malta, Peru, Singapore, Taiwan, Uruguay and Venezuela. 12 Since the World Bank time series end in 1990, I extend the series by assuming that capital-output ratio in 1991-2005 is the same as capital-output ratio in 1990. 13 Naturally, since the stock of tangible capital in the rest of the world is now higher (by about 25% on average), the stock of technology capital in the rest of the world is also higher. 15 0.28 0.27 US, benchmark RW, benchmark US, alt RW definition RW, alt RW definition US, alt proportion factor RW, alt proportion factor 0.26 0.25 0.24 0.23 0.22 0.21 0.2 1975 1980 1985 1990 year 1995 2000 2005 Fig. 3. Ratio of Technology Capital and Tangible Capital, Alternative Estimates Computation of Proportion Factors As mentioned previously, if one observes the production of domestic and foreign firms separately, then the proportion factors vU S and vRW can be computed from equation (3) rather than from (4). The production of domestic and foreign firms is not observed directly in the data, but one can infer it from the data on Foreign Direct Investment Income, which is available in the U.S. International Transactions Accounts. The production of US firms abroad is related to the Foreign Direct Investment Income F DIU S : The foreign direct investUS S US ment income of US firms from abroad equals dividends YRW − WRW LURW − IRW plus 16 0.09 0.08 0.07 US, benchmark RW, benchmark US, alt RW definition RW, alt RW definition US, alt proportion factor RW, alt proportion factor US, alt investment ratio RW, alt investment ratio 0.06 0.05 0.04 0.03 0.02 0.01 0 1975 1980 1985 1990 year 1995 2000 2005 Fig. 4. Openness Parameters, Alternative Estimates US US reinvested earnings IRW − δK KRW , or p US US )(YRW − WRW LUS F DIU S = (1 − τUS RW − δK KRW ) p US US )[(φ + α(1 − φ))YRW − δK KRW ], = (1 − τUS (18) S by using where the second equality follows from elimination of labor income WRW LURW the first order condition in labor demand. Similarly, the production of firms from the rest of the world in the US can be obtained from their Foreign Direct Investment Income F DIRW : p RW )[(φ + α(1 − φ))YURW F DIRW = (1 − τRW S − δK KUS ]. 17 (19) US Inverting the equations (18) and (19) yields the estimates of YRW and YURW S . While using the income data to compute the proportion factors is theoretically equivalent to using the capital stock data, there are reasons why it may be inferior in practice. In particular, as argued by Prescott and McGrattan (2007b), the foreign direct investment income includes return on investment on intangible location specific capital. In contrast, no such problems affect the data on tangible capital stock. Using capital stock data to compute the proportion factors is therefore a better alternative. Nevertheless, it is interesting to obtain the alternative estimates to see how they differ from the benchmark ones. Figure 3 shows that the estimates of the technology capital to tangible capital ratio are very close to the benchmark estimates for the US economy, and about 1% lower for the rest of the world. The alternative estimates of the openness parameters are shown in Figure 4. They are substantially more volatile than the benchmark estimates, presumably because of the fluctuations in the return from investments in intangible capital. They are slightly higher on average for the rest of the world, but have about the same magnitude for the US economy. Overall, despite the problems in using income data to compute the proportion factors, the alternative estimates confirm the results that were obtained in the benchmark estimation. Ratio of Investment to Technology Capital and Production I have experimented with alternative values for the average ratio of investment in technology capital and production. I have increased this ratio to be 9% rather than 7%. As a result, the ratio of technology capital and tangible capital has increased by about 7% for both US economy and for the rest of the world. The change in country openness was negligible. The results were similar when the ratio has been 5% rather than 7%: the technology and tangible capital stock ratio has decreased by about 7%, while the openness parameters were almost unchanged. 18 Terminal Condition I have also experimented with several sensible alternatives. First, I have assumed that the ratio of investment in technology capital to output in 2005 is equal to its long run average of 7%. Second, I have assumed that the investment in technology capital in 2005 is 20% higher (lower) than the investment in 2004. In all cases, the effects on the aggregate estimates of capital stock and openness parameters were negligible. 5. THEORY I will now use the estimates of technology capital and country openness to evaluate the performance of a neoclassical growth model with technology capital. I will also estimate the welfare loss from totally closing US economy in 1976, welfare gain from totally opening US economy in 1976, and welfare gains from NAFTA. The agents in country i ∈ {US, RW } evaluate sequences of consumption according to the following utility function: ³ ´1−θ Cit ∞ X Nit 1 t ( ) Nit , 1 + ρ 1 − θ t=0 θ > 0, where ρ is the discount rate, Nit is the population in country i and (20) Cit Nit is consumption per person in country i. Agents face a tax rate on profits (net of depreciation) τitP . The proceeds from taxation are rebated back as a lump sum transfer. The budget constraint is i = Wit Nit + (1 − τitP )RitK Kit + τitP δK Kit + RitM Mti Cit + Ki,t+1 + Mt+1 + (1 − δK )Kit + (1 − δM )Mti + Tit + NXit , (21) where Wit is the wage rate, RitK and RitM are the gross rates of return on tangible and 19 technology capital, Tit is lump sum transfer, and NXit is net export.14 Each agent supplies one unit of labor inelastically, and so the aggregate labor supply in country i is Nit . The production of country i is thus given by (2) with L = N, i.e. by 1−α(1−φ) Yit = Ait Nit α(1−φ) (Mti + ωit Mt−i )φ Kit . Consumption, tangible capital and technology capital are all required to be nonnegative. Moreover, it is not possible to convert technology capital back to consumption goods and so the investment in technology capital is required to be nonnegative as well. i The competitive equilibrium consists of allocations {Cit , Yit , Ki,t+1 , Mt+1 , NXit } and prices {Wit , RitK , RitM } such that, given the initial capital stocks Ki0 , M0i and the exogenous sequences {Nit , Ait , ωit , τitP }, i) households in each country maximize (20) subject to (21) taking prices as given, ii) prices are given by Wit = (1 − α)(1 − φ) NYitit , Y−it Yit RitK = α(1 − φ) K and RitM = φ M i +ωYit M −i + φω−it M −i +ω it t it t t i −it Mt , iii) the government budget is balanced each period, and iv) markets clear. Properties of Equilibrium Balanced Growth Path It is assumed that the total factor productivity Ait and population Nit fluctuate in a finite number of initial periods and grow at a constant rate γ and η afterwards. Similarly, the tax rate on profits τitP and the openness parameter wit is assumed to be constant after a finite number of periods. The economy then converges to a balanced growth path where consumption per person per person 14 Yit , Nit technology capital per person Net export satisfies N Xit + N X−it = 0. 20 Mti , Nit Cit , Nit output and tangible capital per person Kit Nit all grow at a common rate g, given by 1 g = [(1 + γ)(1 + η)φ ] (1−α)(1−φ) − 1. Equality of Rates of Return Depending on whether the nonnegativity constraints on investment in technology capital bind, three possibilities can arise in any given period. In the first case, investment in technology capital is strictly positive in both countries. The net rates of return from all investments are then equalized: K M RitM − δ M = RitK − δ K = R−it − δ K = R−it − δM . In the second case, investment in technology capital is zero in country i but strictly positive in country −i. Then the net rates of return from investments in tangible capital and from investment in technology capital in country i are still equalized, and they are greater than the net rate of return from investment in technology capital in country −i: K M RitM − δ M = RitK − δ K = R−it − δ K > R−it − δM . In the third case, both investments in technology capital are zero. Then the net rates of return from investment in technology capital is smaller in both countries: K M − δ K > R−it − δM . RitM − δ M < RitK − δ K = R−it The Results In the benchmark scenario, the openness parameters are assumed to be equal to the estimated values in the first thirty periods (corresponding to years 1976-2005) and constant after that. The tax rates on profits are equal to their values used in the estimation for the first thirty period and are constant after that as well. The model 21 total factor productivity equals the Solow Residual. The common long run growth rate of total factor productivity γ is taken to be the average growth rate of US total factor productivity in the 1976-2005 time period. Finally, the country population is equal to the US and rest of the world population in the first thirty years, and grows at a rate equal to the the average growth rate of US population after that. The discount rate ρ is chosen in such a way that the net rate of return in steady state equals 4.29%, which is the average net rate of return in the US economy between 1976-2005. The coefficient of relative risk aversion θ is set equal to one. The remaining parameters φ, α, δ M , δ K are the same as the ones used in the estimation. Figure 5 plots the (detrended) US production in the data and in the model. It shows that the model is able to replicate the fluctuations in US output. Figure 6 shows that the same can be said about fluctuations in both US investments abroad and foreign investments in the US. The model successfully captures the decline in US investments abroad until about 1985 and its rise thereafter. Both the initial decline and subsequent rise can be explained by changes in the openness of the rest of the world towards USA.15 Although the model is successful in explaining movements in foreign direct investment, it is not very successful in explaining movements in US net exports. US net exports in the data are negative and small. US net exports predicted by the model are negative and large. The inability to explain net exports is not surprising since the model assumes that there are no trade frictions between both countries. 15 It is worth noting that, to some extent, the success of the model is to be expected because the openness parameters and technology capital stocks were estimated using one of the equilibrium condition of the model, namely the equality of the net rates of return within country. Naturally, the model provides more restrictions which determine its success in explaining the data. 22 5000 4900 1990 USD, detrended 4800 4700 4600 4500 4400 data benchmark model 4300 1975 1980 1985 1990 year 1995 2000 2005 Fig. 5. US Output Gains from Current US Openness The welfare loss from forever totally closing US economy in 1976 turns out to be very small: they are equal to 0.13% of consumption (in consumption equivalents). When both US economy and the rest of the world are totally closed in 1976, the welfare losses are larger, but still small: they are equal to 0.36% of consumption. Figure 7 illustrates the results by plotting US production in all three cases. Assuming that all the changes in US openness after 1994 are associated with NAFTA, one can compute the implications of not joining NAFTA. The welfare costs of not joining NAFTA are naturally even smaller than the welfare costs of totally closing US economy, and are equal to 0.03% of consumption. There is, however, a significant effect on the quantity of foreign direct investment in the US. About a third 23 800 700 1990 USD, detrended 600 500 400 300 200 Foreign Investment in US, data Foreign Investment in US, model US Investment Abroad, data US Investment Abroad, model 100 0 1975 1980 1985 1990 year 1995 2000 2005 Fig. 6. Foreign Direct Investment of foreign direct investment after 1994 can be attributed to NAFTA. These results reinforce the view that the US economy still appears to be very much closed: not much has been gained from the current level of openness and not much would be lost from closing them completely. Next subsection investigates whether there are potential gains from opening the US economy further. Gains from Opening US Economy Further If the US economy opens totally, it is no longer efficient to invest in technology capital in the US. Rather, the US economy imports all its technology capital from abroad. The steady state gain in terms of output is 9.35%. The gain in measured productivity is even larger: it is about 12% in all periods. The welfare gain from 24 4900 4800 1990 USD, detrended 4700 4600 4500 4400 Benchmark US totally closed US and RW totally closed 4300 1975 1980 1985 1990 year 1995 2000 2005 Fig. 7. US Output, Alternative Openness Assumptions totally opening US economy turn out to be large as well: It is equal to 6.91% of consumption. Figure 7 illustrates the gains in terms of US production.16 The fact that there is no investment in US technology capital allows for an immediate increase in consumption in both countries. At the same time, total openness of US economy increases the rate of return on investment in technology capital in the rest of the world. In response, rest of the world increases its investment in technology capital. Increases in foreign technology capital is more significant than decreases in US technology capital and so consumption grows faster over the transition. 16 The magnitudes of both welfare losses from totally closing and welfare gains of US economy from totally opening are similar to the ones reported by Ramondo (2007) where the welfare losses from closing US economy are 0.00% and the welfare gains from opening are 8%. See her Table 9, case II. 25 6. CONCLUSIONS This paper has two goals. First, it estimates the stock of technology capital, country openness in the US and in the rest of the world. Second, using the estimates, it evaluates the performance of a neoclassical growth model with technology capital, and quantifies the gains from country openness. I identify the time series of technology capital and country openness by assuming that the net rates of return on both types of capital are equalized within each country. I estimate that the technology capital is about one fourth of the stock of tangible capital stock for both the US economy and for the rest of the world. The openness of US economy has been increasing over time, but is smaller than the openness in the rest of the world. These estimates are found to be robust to alternative assumptions about the definition of the rest of the world, the way proportion factors are computed, average size of the investment in technology capital and the terminal condition on investment in technology capital. I find that the neoclassical growth model with technology capital performs well in explaining the movements in output and foreign direct investment between 1976 and 2005. I also find that the losses from totally closing both economies are small. On the other hand, the gains from opening US economy totally are much larger. Several assumptions are likely critical in the estimation of country openness, technology capital stock, and the welfare gains from opening an economy. First, the estimation procedure relies on an assumption that the rest of the world countries are mutually totally open. While this assumption seems to be the only alternative if one wants to restrict attention to a tractable two country model, it may result in estimating an implausibly large stock of the world technology capital. If this is the case, the actual welfare gain from totally opening US economy may be smaller than the one computed in this paper. 26 But how sensitive are the estimates and the welfare calculations to this assumption? This question is not easy to answer in the current two country framework, because a relaxation of this assumption will simultaneously change the estimates of the technology capital stock, country openness, as well as the theoretical predictions of the model. Clearly, a multicountry model is needed to find out how important this assumption is. Another reason why the estimates of welfare gains from opening the economy further might be too large is that total openness may be impossible to achieve. The implicit assumption in the welfare calculation is that the degree of openness is related to government policies and one thus computes the welfare gains from moving toward the best government policy. But maybe no government policy can achieve total openness because there are other limitations on the flow of foreign direct investment like physical distance (see the evidence in Ramondo (2007)). If that is the case, one should really compare the current degree of openness with a degree of openness that is achievable by the best government policy. Estimation of the upper bound on country openness is left for future research. 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