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International productivity and factor price comparisons
Journal of International Economics 87 (2012) 386–390
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Journal of International Economics journal homepage: www.elsevier.com/locate/jie
International productivity and factor price comparisons Kathryn G. Marshall ⁎ Orfalea College of Business, California Polytechnic State University, San Luis Obispo, CA 93407-0300, USA
a r t i c l e
i n f o
Article history: Received 4 August 2010 Received in revised form 29 December 2011 Accepted 9 January 2012 Available online 17 January 2012 JEL classification: F16 J24 J31 O15
a b s t r a c t Using OECD input–output tables for a diverse group of 33 countries in the year 2000 and estimates of each country's factor stocks, I compute factor payments for aggregate labor and capital with value-added data adjusted for self-employment by sector. Using a detailed technology matrix for the U.S., I compute factorspecific productivity measures in each country relative to the U.S., and show that these measures are strongly correlated with the pattern of wages and rental rates. I find that many low income countries with low labor productivity have relatively high capital productivity. I also find a distinctive pattern between factor productivity and factor payments depending on whether a country has a high or low wage-rental ratio compared to the U.S. I show these findings are consistent with the existence of sector-based differences in production technology and complementarities between factors. © 2012 Elsevier B.V. All rights reserved.
Keywords: Factor-specific productivity TFP differences Factor payments
Within a large and diverse group of open economies in the year 2000, average wages vary by a factor of twenty-fold and the rate of return to capital varies by almost four-fold. 1 Trefler (1993) gives a highly tractable and influential explanation for this evident failure of factor price equalization, demonstrating that factor-specific productivity variations can account for differences in factor payments. Due to limited data availability, Trefler was only able to impute factorspecific productivities from trade data using the standard assumptions of the Heckscher-Ohlin-Vanek (HOV) model of endowment-based trade. This paper measures factor-specific productivity directly from data on country endowments and production by sector, together with a detailed technology matrix for the United States. I show that differences in factor-specific productivity are strongly correlated with wages and rental rates, although I also find that many low income countries with low labor productivity have relatively high capital productivity and also have low wage–rental ratios compared to the United States.
To explain these findings I appeal to the well-established variations in total factor productivity (TFP) among nations, but I argue that these aggregate differences mask a range of variations across broad sectors such as agriculture, mining, and manufacturing.2 If sector-specific TFP in the modern capital-intensive sectors (i.e. mining, manufacturing) of low income countries is closer to that in high income countries when compared to the degree of convergence of laborintensive sectors (i.e. agriculture), these countries will tend to have a lower wage–rental ratio than high income countries. Imputed aggregate factor-specific productivities across all sectors will in turn be influenced by these differences in wage–rental ratios. Among newly industrializing countries today, a variety of forces contribute to more rapid productivity convergence in capital-intensive sectors. These forces include a policy bias towards modern industry, the concentrated role of foreign direct investment in some sectors such as manufacturing and mining, and the special challenges of improving agricultural practices in diverse ecological settings.3 Numerous recent studies, including Maskus and Nishioka (2009), Nishioka (forthcoming), Fadinger (2011), and Puzzelo (forthcoming)
⁎ Tel.: + 1 805 756 5305; fax: + 1 805 756 1473. E-mail address: [email protected]. 1 The sample includes 33 industrialized and newly industrializing economies that together account for 78% of world GDP in 2005 based on World Bank (2008) purchasing power parity measures. Measuring openness by the trade ratio, (exports + imports)/ GDP, the country with the lowest trade ratio (0.22) in the sample is the United States, and the median trade ratio is 0.72.
2 Hall and Jones (1999) and Parente and Prescott (2000) are among the best known studies of economy-wide differences in TFP. In a recent survey, Hsieh and Klenow (2010) note that differences in TFP account for between 50 and 70% of income differences among countries. 3 Lewis (2004), Duarte and Restuccia (2010), and McMillan and Rodrik (2011), among many others, document large differences in productivity by sector and the importance of structural transformation away from agriculture for income convergence; World Bank (2007) examines the wide range of agricultural productivity among nations at different levels of economic development.
1. Introduction
0022-1996/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jinteco.2012.01.003
K.G. Marshall / Journal of International Economics 87 (2012) 386–390
have taken advantage of detailed input–output data for a large sample of countries to evaluate the HOV model of international trade in light of international differences in technology. The original insights found in Trefler (1993, 1995) and Davis and Weinstein (2001) have been by now carefully scrutinized and extended. This study focuses more directly on understanding the sources of differences in factor payments. My estimates of factor-specific productivity generally conform to the results in Maskus and Nishioka (2009) and Fadinger (2011). Using a general equilibrium model with CES production technology, I demonstrate how these factor-specific productivity differences can be explained by uneven TFP convergence across sectors in each country when compared to the same sectors in the United States. I then corroborate this explanation with estimates of sectorspecific TFP measured relative to the United States across ten broad sectors designated as either labor or capital-intensive. 2. Measuring factor payments To measure factor payments across a wide range of countries in a uniform manner, I rely on OECD input–output tables available for 33 countries in or near the year 2000, which include value-added payments in the form of gross operating surplus (GOS), compensation of employees (COE), and indirect taxes on production reported in local currency units. I focus on only two factors: aggregate labor, measured by the total labor force, and the physical capital stock, measured by the perpetual inventory method. Conceptually, my measure of wages in a given country is simply payments to labor divided by the total labor force, and my measure of the rental rate of capital is likewise payments to capital divided by the capital stock. To convert to a common currency I use the purchasing power parity exchange rates published by the World Bank (2008) for the year 2005, adjusted to the relevant input–output year using domestic price deflators. The accuracy of this simple procedure to measure the stocks and returns to labor and capital has been drawn into question by Gollin (2002) and Caselli and Feyrer (2007). Gollin argues that COE is a biased measure of labor payments especially in low income countries where self-employment is significant. Caselli and Feyrer argue that a large share of payments to capital recorded as GOS in low income countries is in fact payments to the natural resource stock not captured in the standard estimate of the produced physical capital stock. I therefore adjust labor's share of value-added using selfemployment data following Bernanke and Gurkaynak (2001), although I am able to improve on their procedure for estimating mixed income – the combined labor and capital income of unincorporated producers – by taking into account the distribution of self-employment by broad sector. This is my preferred estimate of factor payments because it corrects for the disproportionate share of self-employed in the agricultural sector, and it is the foundation for the results presented here. However, as a robustness check I construct two alternative estimates of factor payments. First, I estimate the labor share based on aggregate selfemployment in the same manner as Bernanke and Gurkaynak (2001). Second, to address the objections raised by Caselli and Feyrer, I use the World Bank (2006) capital stock series that includes natural resource stocks estimated in U.S. dollars at market exchange rates for most countries in my sample, matched with OECD value-added payments converted to U.S. dollars using market exchange rates.4 The three different specifications of factor payments just described, including my preferred measure and two alternatives, are highly correlated. None of the statistical results presented here are significantly altered by using the two alternative measures. Based on my preferred measure, the U.S. wage rate is about $42,000 per 4 The appendix gives complete details on data construction, together with computed values and Fig. 1 replicated with the two other versions of factor payments and capital stock.
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person year and the U.S. rental rate to capital is about 12%. Eighteen countries have wage–rental ratios below that of the United States, ranging from 92% of the U.S. ratio (Spain) to 5% of the U.S. ratio (China). Only two countries in this group, Spain and Norway, have wages in the range of the wages among the 14 high wage–rental ratio countries. 5 In other words, countries with low wages do not typically have correspondingly low rental rates, suggesting that factor-specific productivity must account both for a wide range of factor payments and for differences between factors in the same country. 3. Measuring factor-specific differences in productivity The observed pattern in factor payments argues that productivity should vary between factors as well as across countries as proposed in Trefler (1993), who then imputed factor-specific productivities from trade data. Given the more extensive and conformable data on gross output by sector now available for a large group of countries, I am able to directly estimate factor-specific productivities in the following fashion. Following the notation of Trefler and Zhu (2010), let g = 1, …, G index goods, f = 1, …, K index factors, and c = 1, …, C index countries. Let Dc be the K by G technology matrix for country c; the (f, g) element of Dc is the amount of factor f whose services are used directly to produce one unit of good g in country c. Under the assumption of full employment, DcQc = Vc, where Qc is the G × 1 vector of country c's gross output and Vc is the K × 1 vector of country c's endowment. Denote a typical element of Vc by Vc(f), a typical element of Qc by Qc(g), and denote a reference country by subscript 0. I want to measure πfc, the factor-specific difference in productivity for factor f in country c relative to the reference country. Define the productivityadjusted endowment Vc* as the vector of factors that would be used by the reference country to produce country c's gross output. The factor-specific productivity measure is given by πfc ¼
V c ðf Þ ∑g D0 ðf ; g ÞQ c ðg Þ ¼ : V c ðf Þ ∑g Dc ðf ; g ÞQ c ðgÞ
ð1Þ
Let Πc be the f by f diagonal matrix of πfc. If factor-specific productivities do not vary between factors in the same country, Πc simplifies to πcI, where I is the f × f identify matrix. Under the strong assumptions of the Heckscher-Ohlin-Vanek (HOV) framework, including perfectly competitive goods and factor markets, no barriers to trade, and zero transport costs, common world prices will determine factor payments in each country. More precisely, P = AcTwc, where P is the G × 1 vector of world prices given in the reference country's currency units, Ac is the K × G matrix of direct and indirect factor inputs, and wc is the K × 1 factor payment vector for country c converted to the reference country's currency. Assuming factor-specific productivities capture all differences in technology so that D0 = ΠcDc, this in turn implies that wc = Πcw0. This framework leads to a simple comparison of factor payments to factor-specific productivities using the United States as the reference country. In the simple two factor case with labor and physical capital, each country's wage and rental rate relative to the U.S. should equal its respective factor-specific productivity relative to the U.S. 5 The complete list of 18 low wage-rental and 14 high wage-rental countries follows, with their GDP per capita and wage-rental ratio as a percent of the U.S. values noted parenthetically. Low wage-rental countries, ranked from lowest to highest GDP per capita relative to the U.S.: China (10, 5), Indonesia (11,8), Turkey (16, 10), Russia (21, 24), Brazil (21, 16), Poland (28, 27), Slovak Republic (30, 54), Hungary (33, 58), Czech Republic (41, 66), the Republic of Korea (47, 58), Portugal (50, 64), Greece (53, 49), New Zealand (55, 66), Taiwan (55, 47), Spain (64, 92), Finland (67, 74), Ireland (80, 41), Norway (1.06, 83). High wage-rental countries: Israel (57, 130), United Kingdom (69, 109), Italy (69, 107), Sweden (69, 126), France (70, 120), Japan (72, 153), German (74, 128), Belgium (75, 128), Australia (77, 99), Denmark (78, 115), Canada (80, 130), Austria (80, 107), Netherlands (81, 107), Switzerland (88, 168). I deemed Australia's wage-rental ratio sufficiently close to that of the U.S. to group with high wage-rental countries.
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K.G. Marshall / Journal of International Economics 87 (2012) 386–390
Following Trefler (1993), I present a visual representation of the estimated factor-specific productivities compared to factor payments for labor and capital in Fig. 1. I also replicate Trefler's regressions of country c's wage wLc and rental rate wKc on the productivity of labor πLc and capital πKc relative to the U.S. in logarithms. According to productivity-adjusted factor price equalization, the coefficient on the log of each productivity parameter should be equal to one. The results are as follows (standard errors are in parenthesis):
4. A sector-specific explanation for factor-specific differences in productivity
2
logðwLc Þ ¼ 3:68 þ 1:15 logðπLc Þ; R ¼ 0:97 ð0:03Þ ð0:04Þ 2
logðwKc Þ ¼ −2:18 þ 0:67 logðπKc Þ; R ¼ 0:46 ð0:05Þ
ð0:13Þ
The reverse regressions, which account for errors in the measurement of productivity, give a probability limit for the true coefficient on log(πLc) of [1.15, 1.19] and on log(πKc) of [0.67, 1.47]. Interpreted in light of Fig. 1, the coefficient on labor productivity reflects the clustering of low wage–rental countries below the diagonal line, and high wage–rental countries above the diagonal line. The reverse pattern occurs in the capital productivity prediction. Less evident in Fig. 1 is the statistically significant difference between labor and capital productivity in low wage–rental countries. A regression of the logarithm of πLc/πKc on a constant and a dummy variable set equal to 1 for the 14 high wage–rental countries gives the constant coefficient as −0.65, with a t-statistic equal to −4.24. The coefficient on the dummy variable is 0.75 with a t-statistic of 3.24 and the R 2 of the regression is equal to 0.26. A Wald test based on the null hypothesis that 1.20
Wage relative to USA
1.00 0.80 0.60 0.40 0.20 0.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
Labor productivity relative to USA 1.80 Turkey
Rental rate relative to USA
1.60
the sum of the two coefficients is equal to zero is not rejected, indicating that the logarithm of πLc/πKc is not statistically different from 0 for high wage–rental countries. On the whole, the results strongly corroborate Trefler's insight that factor-specific productivities are consistent with observed differences in factor payments, and point to a possible underlying explanation for the distinctive deviations from Trefler's (1993) model.
Ireland
1.40 1.20 1.00 0.80 0.60 0.40
Among low income countries, labor-intensive sectors such as agriculture often lag in productivity growth in spite of their importance for employment due to a complex set of factors. 6 To capture this type of sector-based difference in productivity I use a general equilibrium model of production with a constant elasticity of substitution (CES) technology, assuming the elasticity of substitution σ between capital and labor is the same across countries and sectors. Considered first in the absence of international trade, the standard cost minimization exercise allows a comparison of direct input coefficients between the reference country 0 and country c in terms of total factor productivity θgc and autarkic prices pgc indexed by sector and country, and nominal factor payments Wfc in local currency units indexed by factor and country: D0 ðf ; g Þ ¼ Dc ðf ; g Þ
θgc θg0
!1−σ
W fc pgc
!σ
pg0 Wf 0
!σ ð2Þ
Eq. (2) shows that differences in factor usage in a given sector across countries depend both on the relative TFP and on the relative real wages expressed in terms of the output price in each sector. 7 Let c represent a country with a low capital to labor endowment relative to the reference country, and consider the simple two good case with a labor-intensive good (representing agriculture) and a capital intensive good (representing manufacturing). In the absence of TFP differences across sectors, the relative price of the labor intensive good would tend to be lower in the capital-scarce country (assuming similar demand conditions in both countries). When sector-specific differences in TFP are introduced such that the labor-intensive sector is relatively backward in the capital-scarce country, the laborintensive good may be relatively more expensive in that country. Hence a move to costless free trade where goods' prices are equalized at the market exchange rate would also likely imply that the capitalscarce country specializes in the manufactured product and imports food, while the reverse occurs in the labor-scarce reference country. Although this simple result does have some ring of truth to it, insofar as the United States is a major food exporter and many capital-scarce countries like China export manufactured goods and import food, it is clearly at odds with the presence of large agricultural sectors in most low wage countries and does not address the complex pattern of trade in different types manufactured goods. A more liberal interpretation follows that of Davis and Weinstein (2001) who assume each sector consists of a range of traded and non-traded goods, and that trade costs introduce price differences even in traded goods. This heterogeneous world is most easily captured empirically by using a purchasing power parity exchange rate ecppp which expresses local currency units of country c per international dollar, so that ecppppgc = pg0 for all goods. Eq. (2) can then be expressed in
0.20 0.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Capital productivity relative to USA High wage-rental countries
Low wage-rental countries
Fig. 1. Factor payments and factor productivity.
1.80
6 Within this sample of countries, the share of agricultural employment in total employment averages 17% in the 17 low wage-rental countries (excluding Taiwan, which does not report sector employment to the ILO), compared to less than 4% in the 14 high wage rental countries. 7 Woodland (1982), page 383, shows how Eq. (2) can be derived from the CES unit cost function using Shephard's lemma.
K.G. Marshall / Journal of International Economics 87 (2012) 386–390
terms of the factor payments measured in international dollars, denoted by w:
D0 ðf ; g Þ ¼
θgc θg0
!1−σ
wfc wf 0
!σ Dc ðf ; g Þ
ð3Þ
In the special Cobb-Douglas case where σ = 1, the expression (θgc/θg0) 1 − σ disappears from the right-hand side so that factorspecific productivities will be industry-neutral. In the general equilibrium setting, sector-specific differences in TFP will determine the differences in factor payments. A country with relatively low TFP in the labor-intensive sector will have a low wage–rental rate, reflected in a low factor-specific productivity measure for labor and a high factor-specific productivity measure for capital. The Cobb-Douglas assumption of unitary substitutability between capital and labor does not explain the distinctive clustering pattern above and below the diagonal lines pictured in Fig. 1, but this pattern can be explained by the existence of complementarities between capital and labor when the elasticity of substitution between factors is less than 1. To show this I can use Eq. (3) to rewrite the measure of factor-specific productivity given in Eq. (1) as:
πfc ¼
wfc wfo
!σ " !1−σ # G X θgc ϖfgc θg0 g¼1
ð4Þ
Dc ðf ; g ÞQ c ðg Þ gives the share of country c's factor f ∑g Dc ðf ; g ÞQ c ðg Þ G P ϖfgc ¼ 1. This important used in the production of good g, and where ϖfgc ¼
g¼1
result shows that when σ ≠ 1, the factor-specific productivity does not equal the wage relative to the reference country, but is instead a function of the wage and a sectoral TFP adjustment. In particular, when σ is less than 1 and θgc/θg0 > θic/θi0 for all i ≠ g where g is the capital-intensive sector, Eq. (4) indicates that πLc > wLc/wL0 and πKc b wKc/wK0. If θgc/θg0 b θic/θi0 for all i ≠ g, the direction of the two productivity, payment inequalities will be reversed. 8 This explanation for factor-specific productivity differences argues for a re-evaluation of the data presented in Fig. 1. The clustering of low wage–rental countries below the diagonal line in the top axes and above the diagonal line in the bottom axes suggests that the capital-intensive sector in these countries is closer to the productivity frontier set by the United States than is the labor-intensive sector. If factor-specific productivity differences were instead inherent in the factors themselves, there would be no obvious explanation for the dispersion of countries across the diagonal line beyond random measurement error. To evaluate the clustering pattern more carefully, I use a simple statistical test based on a two-way contingency table which categorizes countries by wage–rental rate relative to the United States and whether πLc/πKc − wLc/wKc is greater than or less than 0. Based on the null hypothesis that the sign of πLc/πKc − wLc/wKc does not depend on whether a country is a high or a low wage–rental country, the resulting chi-squared statistic with one degree of freedom is equal to 18.7, rejecting the null hypothesis at a significance level of 0.001. I also note that the magnitude of the differences between factorspecific productivity and factor payments is not trivial. Among the low wage–rental countries, wages relative to the U.S. are on average 23% below πL. For these countries, πL averages only about 50% of the labor productivity in the U.S. On the other hand, their rental rate is about 13% above πK, and πK is about 80% of that in the U.S. The relative
8 The claims in the last two sentences are not trivial to prove. In the on-line appendix I show that they are true for the case of two factors, two sectors, and an interior solution for factor prices in all countries.
389
wage among high wage-rental countries does not differ statistically from πL although their rental rate is about is about 12% belowπK. 9 This paper shows that a simple general equilibrium model of trade together with uneven productivity convergence by sector can generate the distinctive pattern of factor-specific productivities and factor payments presented in Fig. 1. In the presence of complementarities between capital and labor and uneven development, Eq. (4) gives a variant of productivity-adjusted factor price equalization that both predicts the observed wide range of wages and rents among open countries and explains the underlying cause of these differences. 4.1. Further empirical evaluation of sector-specific TFP differences between countries I have argued that a specific pattern of cross-country variations in TFP between labor and capital intensive sectors can explain the relation of measured factor-specific productivities to factor payments. By making a number of strong assumptions, I can compute the widely-used multilateral productivity index following Caves et al. (1982) for fourteen broad sectors in each of 32 countries, measuring productivity in each sector relative to the same U.S sector. 10 First, I construct a 14 sector by 2 factor estimate of Dc to match the availability of self-employment data by sector. I allocate capital to each sector by assuming the economy-wide rental rate is equalized between sectors, and I allocate labor in a similar way, adjusting for differences in skills by measuring labor use in each sector as the payments to labor in that sector divided by the economy-wide average wage. In this general equilibrium framework, a country with relatively higher TFP in capital-intensive industries will have a lower relative wage–rental ratio. 11 Fig. 2 compares each country's wage–rental ratio relative to the U.S. to that country's ratio of TFP in capitalintensive sectors compared to labor-intensive sectors also measured relative to the US. 12 Recognizing the data limitations involved in accurately estimating TFP, Fig. 2 indicates that sector-specific variations in productivity can readily explain the range of wage-rental ratios observed among these 33 open economies. 5. Conclusion Most of the international variations in factor payments can be explained by variations in factor-specific productivity. One explanation for factor-specific productivity differences is underlying sector-specific variations in TFP, which can in turn explain the pattern of high capital productivity and low labor productivity common among countries with a low wage-rental ratio. Complementarities between labor and capital can also explain why wages tend to be lower than labor 9 These percentages represent the mean of the log of each factor productivity relative to factor payment × 100; in order of presentation the t-statistic for each mean is 6.12**, − 2.04**, 0.89, 3.37** (** indicates significantly different from 0 for a onetailed t-distribution at 5% significance). While I do not attempt to estimate σ given the relatively small sample size, I show in the appendix that these results are consistent with a model simulation using my TFP estimates and σ in the range of 0.6 to 0.8. This result is in line with Fadinger (2011), who estimates σ to be about 0.8. The particular direction of the bias is also evidence that σ b 1 since in the case where σ > 1 I show in the appendix that the direction of the bias would be reversed. 10 I follow Harrigan (1997), who gives a particularly clear discussion of this index and uses it to estimates TFP across manufacturing sectors in several industrialized countries. Like Harrigan, I am actually estimating a value-added index which assumes that capital and labor is separable from other inputs. Since this index is transitive, the choice of reference country would not fundamentally alter the data presented in Fig. 2. 11 This is shown mathematically by Eqs. A.1 and A.2 in the on-line appendix. 12 It is common in the empirical trade literature to identify wholly non-traded sectors such as public services, whose relative price level may be misstated even by the PPP exchange rate, in turn distorting the measure of TFP. Based on the input–output data, I identify 4 of the 14 sectors with virtually no trade (ISIC sectors F, construction, L, public administration, M, education, and N, health services) and drop them from this analysis. Further details on the categorization between capital and labor intensive sectors are given in Appendix Table 5.
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K.G. Marshall / Journal of International Economics 87 (2012) 386–390
1.0 0.5
-0.1
Log (wage rental ratio)
-0.2
0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5
Log( average TFP of capital intensive sectors/ average TFP of labor intensive sectors) High wage-rental countries
Low wage-rental countries
Fig. 2. The log difference in wage–rental ratio (relative to U.S.) as a function of uneven development measured by the log difference of average TFP in capital-intensive sectors compared to labor-intensive sectors. Capital intensive sectors comprise ISIC Rev. 3 sectors C, mining, D, manufacturing, E, utilities, and I–J, various modern business services. Labor-intensive sectors comprise A and B, agriculture and forestry, G, H, and O–P, various labor-intensive services. TFP in each industry is relative to the same U.S. industry.
productivity and rental rates higher than capital productivity among low wage-rental countries, while the reverse tends to holds true for high wage-rental countries. Economy-wide TFP comparisons, while useful and easily measured, may obscure the more complex pattern of uneven development and its ramifications for international differences in factor payments among open economies. Role of funding source Partial funding was provided by the Orfalea College of Business Summer Research Grant, 2008. No stipulations on research content were imposed by the funding source. Acknowledgments I would like to thank the editor, Daniel Trefler, for invaluable suggestions that greatly improved this paper. I would also like to thank an anonymous referee for helpful comments. Appendix A. Supplementary material Supplementary data to this article can be found online at doi:10. 1016/j.jinteco.2012.01.003. References Bernanke, B., Gurkaynak, R.S., 2001. Is growth exogenous? Taking Mankiw, Romer and Weil seriously. In: Bernanke, B.S., Rogoff, K. (Eds.), NBER Macroeconomics Annual 2001. MIT Press, Cambridge, pp. 11–72. Caselli, F., Feyrer, F., 2007. The marginal product of capital. Quarterly Journal of Economics 122, 535–568. Caves, D.W., Christensen, L.R., Diewert, W.E., 1982. Multilateral comparisons of output, input, and productivity using superlative index numbers. The Economic Journal 92, 73–86.
Davis, D.R., Weinstein, D.E., 2001. An account of global factor trade. American Economic Review 9, 1423–1453. Duarte, M., Restuccia, D., 2010. The role of the structural transformation in aggregate productivity. Quarterly Journal of Economics 125, 129–173. Fadinger, H., 2011. Productivity differences in an interdependent world. Journal of International Economics 84, 221–232. Gollin, D., 2002. Getting income shares right. Journal of Political Economy 110, 458–474. Hall, R., Jones, C., 1999. Why do some countries produce so much more output per worker than others? Quarterly Journal of Economics 83–116 (Feb.). Harrigan, J., 1997. Technology, factor supplies, and international specialization: estimating the neoclassical model. The American Economic Review 87, 475–494. Hsieh, C., Klenow, P., 2010. Development accounting. American Economic Journal: Macroeconomics 2, 207–223 (2010). Lewis, W., 2004. The Power of Productivity. University of Chicago Press, Chicago. Maskus, K., Nishioka, S., 2009. Development-related biases in factor productivities and the HOV model of trade. Canadian Journal of Economics 42, 519–553. McMillan, M., Rodrik, D., 2011. Globalization, structural change, and productivity growth. NBER Working Paper No. w17143. Nishioka, S., forthcoming. Production Techniques and Factor Content of Trade. Journal of International Economics. doi:10.1016/j.jinteco.2011.11.010. Parente, S.L., Prescott, E.C., 2000. Barriers to Riches. MIT Press. Puzzello, L., forthcoming. A Proportionality Assumption and Measurement Biases in the Factor Content of Trade. Journal of International Economics. doi:10.1016/j.jinteco. 2011.11.009. Trefler, D., 1993. International factor price differences: Leontief was right. Journal of Political Economy 101, 961–987. Trefler, D., 1995. The case of the missing trade and other mysteries. American Economic Review 85, 1029–1046. Trefler, D., Zhu, S., 2010. The structure of factor content predictions. Journal of International Economics 82, 195–207. Woodland, A.D., 1982. International Trade and Resource Allocation. (North-Holland, Amsterdam). World Bank, 2006. Where is the Wealth of Nations. World Bank, Washington, DC. World Bank, 2007. World Development Report 2008: Agriculture for Development. World Bank, Washington, DC. World Bank, 2008. Global Purchasing Power Parities and Real Expenditures: 2005 International Comparison Project Program. The World Bank, Washington, DC.
Contents lists available at SciVerse ScienceDirect
Journal of International Economics journal homepage: www.elsevier.com/locate/jie
International productivity and factor price comparisons Kathryn G. Marshall ⁎ Orfalea College of Business, California Polytechnic State University, San Luis Obispo, CA 93407-0300, USA
a r t i c l e
i n f o
Article history: Received 4 August 2010 Received in revised form 29 December 2011 Accepted 9 January 2012 Available online 17 January 2012 JEL classification: F16 J24 J31 O15
a b s t r a c t Using OECD input–output tables for a diverse group of 33 countries in the year 2000 and estimates of each country's factor stocks, I compute factor payments for aggregate labor and capital with value-added data adjusted for self-employment by sector. Using a detailed technology matrix for the U.S., I compute factorspecific productivity measures in each country relative to the U.S., and show that these measures are strongly correlated with the pattern of wages and rental rates. I find that many low income countries with low labor productivity have relatively high capital productivity. I also find a distinctive pattern between factor productivity and factor payments depending on whether a country has a high or low wage-rental ratio compared to the U.S. I show these findings are consistent with the existence of sector-based differences in production technology and complementarities between factors. © 2012 Elsevier B.V. All rights reserved.
Keywords: Factor-specific productivity TFP differences Factor payments
Within a large and diverse group of open economies in the year 2000, average wages vary by a factor of twenty-fold and the rate of return to capital varies by almost four-fold. 1 Trefler (1993) gives a highly tractable and influential explanation for this evident failure of factor price equalization, demonstrating that factor-specific productivity variations can account for differences in factor payments. Due to limited data availability, Trefler was only able to impute factorspecific productivities from trade data using the standard assumptions of the Heckscher-Ohlin-Vanek (HOV) model of endowment-based trade. This paper measures factor-specific productivity directly from data on country endowments and production by sector, together with a detailed technology matrix for the United States. I show that differences in factor-specific productivity are strongly correlated with wages and rental rates, although I also find that many low income countries with low labor productivity have relatively high capital productivity and also have low wage–rental ratios compared to the United States.
To explain these findings I appeal to the well-established variations in total factor productivity (TFP) among nations, but I argue that these aggregate differences mask a range of variations across broad sectors such as agriculture, mining, and manufacturing.2 If sector-specific TFP in the modern capital-intensive sectors (i.e. mining, manufacturing) of low income countries is closer to that in high income countries when compared to the degree of convergence of laborintensive sectors (i.e. agriculture), these countries will tend to have a lower wage–rental ratio than high income countries. Imputed aggregate factor-specific productivities across all sectors will in turn be influenced by these differences in wage–rental ratios. Among newly industrializing countries today, a variety of forces contribute to more rapid productivity convergence in capital-intensive sectors. These forces include a policy bias towards modern industry, the concentrated role of foreign direct investment in some sectors such as manufacturing and mining, and the special challenges of improving agricultural practices in diverse ecological settings.3 Numerous recent studies, including Maskus and Nishioka (2009), Nishioka (forthcoming), Fadinger (2011), and Puzzelo (forthcoming)
⁎ Tel.: + 1 805 756 5305; fax: + 1 805 756 1473. E-mail address: [email protected]. 1 The sample includes 33 industrialized and newly industrializing economies that together account for 78% of world GDP in 2005 based on World Bank (2008) purchasing power parity measures. Measuring openness by the trade ratio, (exports + imports)/ GDP, the country with the lowest trade ratio (0.22) in the sample is the United States, and the median trade ratio is 0.72.
2 Hall and Jones (1999) and Parente and Prescott (2000) are among the best known studies of economy-wide differences in TFP. In a recent survey, Hsieh and Klenow (2010) note that differences in TFP account for between 50 and 70% of income differences among countries. 3 Lewis (2004), Duarte and Restuccia (2010), and McMillan and Rodrik (2011), among many others, document large differences in productivity by sector and the importance of structural transformation away from agriculture for income convergence; World Bank (2007) examines the wide range of agricultural productivity among nations at different levels of economic development.
1. Introduction
0022-1996/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jinteco.2012.01.003
K.G. Marshall / Journal of International Economics 87 (2012) 386–390
have taken advantage of detailed input–output data for a large sample of countries to evaluate the HOV model of international trade in light of international differences in technology. The original insights found in Trefler (1993, 1995) and Davis and Weinstein (2001) have been by now carefully scrutinized and extended. This study focuses more directly on understanding the sources of differences in factor payments. My estimates of factor-specific productivity generally conform to the results in Maskus and Nishioka (2009) and Fadinger (2011). Using a general equilibrium model with CES production technology, I demonstrate how these factor-specific productivity differences can be explained by uneven TFP convergence across sectors in each country when compared to the same sectors in the United States. I then corroborate this explanation with estimates of sectorspecific TFP measured relative to the United States across ten broad sectors designated as either labor or capital-intensive. 2. Measuring factor payments To measure factor payments across a wide range of countries in a uniform manner, I rely on OECD input–output tables available for 33 countries in or near the year 2000, which include value-added payments in the form of gross operating surplus (GOS), compensation of employees (COE), and indirect taxes on production reported in local currency units. I focus on only two factors: aggregate labor, measured by the total labor force, and the physical capital stock, measured by the perpetual inventory method. Conceptually, my measure of wages in a given country is simply payments to labor divided by the total labor force, and my measure of the rental rate of capital is likewise payments to capital divided by the capital stock. To convert to a common currency I use the purchasing power parity exchange rates published by the World Bank (2008) for the year 2005, adjusted to the relevant input–output year using domestic price deflators. The accuracy of this simple procedure to measure the stocks and returns to labor and capital has been drawn into question by Gollin (2002) and Caselli and Feyrer (2007). Gollin argues that COE is a biased measure of labor payments especially in low income countries where self-employment is significant. Caselli and Feyrer argue that a large share of payments to capital recorded as GOS in low income countries is in fact payments to the natural resource stock not captured in the standard estimate of the produced physical capital stock. I therefore adjust labor's share of value-added using selfemployment data following Bernanke and Gurkaynak (2001), although I am able to improve on their procedure for estimating mixed income – the combined labor and capital income of unincorporated producers – by taking into account the distribution of self-employment by broad sector. This is my preferred estimate of factor payments because it corrects for the disproportionate share of self-employed in the agricultural sector, and it is the foundation for the results presented here. However, as a robustness check I construct two alternative estimates of factor payments. First, I estimate the labor share based on aggregate selfemployment in the same manner as Bernanke and Gurkaynak (2001). Second, to address the objections raised by Caselli and Feyrer, I use the World Bank (2006) capital stock series that includes natural resource stocks estimated in U.S. dollars at market exchange rates for most countries in my sample, matched with OECD value-added payments converted to U.S. dollars using market exchange rates.4 The three different specifications of factor payments just described, including my preferred measure and two alternatives, are highly correlated. None of the statistical results presented here are significantly altered by using the two alternative measures. Based on my preferred measure, the U.S. wage rate is about $42,000 per 4 The appendix gives complete details on data construction, together with computed values and Fig. 1 replicated with the two other versions of factor payments and capital stock.
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person year and the U.S. rental rate to capital is about 12%. Eighteen countries have wage–rental ratios below that of the United States, ranging from 92% of the U.S. ratio (Spain) to 5% of the U.S. ratio (China). Only two countries in this group, Spain and Norway, have wages in the range of the wages among the 14 high wage–rental ratio countries. 5 In other words, countries with low wages do not typically have correspondingly low rental rates, suggesting that factor-specific productivity must account both for a wide range of factor payments and for differences between factors in the same country. 3. Measuring factor-specific differences in productivity The observed pattern in factor payments argues that productivity should vary between factors as well as across countries as proposed in Trefler (1993), who then imputed factor-specific productivities from trade data. Given the more extensive and conformable data on gross output by sector now available for a large group of countries, I am able to directly estimate factor-specific productivities in the following fashion. Following the notation of Trefler and Zhu (2010), let g = 1, …, G index goods, f = 1, …, K index factors, and c = 1, …, C index countries. Let Dc be the K by G technology matrix for country c; the (f, g) element of Dc is the amount of factor f whose services are used directly to produce one unit of good g in country c. Under the assumption of full employment, DcQc = Vc, where Qc is the G × 1 vector of country c's gross output and Vc is the K × 1 vector of country c's endowment. Denote a typical element of Vc by Vc(f), a typical element of Qc by Qc(g), and denote a reference country by subscript 0. I want to measure πfc, the factor-specific difference in productivity for factor f in country c relative to the reference country. Define the productivityadjusted endowment Vc* as the vector of factors that would be used by the reference country to produce country c's gross output. The factor-specific productivity measure is given by πfc ¼
V c ðf Þ ∑g D0 ðf ; g ÞQ c ðg Þ ¼ : V c ðf Þ ∑g Dc ðf ; g ÞQ c ðgÞ
ð1Þ
Let Πc be the f by f diagonal matrix of πfc. If factor-specific productivities do not vary between factors in the same country, Πc simplifies to πcI, where I is the f × f identify matrix. Under the strong assumptions of the Heckscher-Ohlin-Vanek (HOV) framework, including perfectly competitive goods and factor markets, no barriers to trade, and zero transport costs, common world prices will determine factor payments in each country. More precisely, P = AcTwc, where P is the G × 1 vector of world prices given in the reference country's currency units, Ac is the K × G matrix of direct and indirect factor inputs, and wc is the K × 1 factor payment vector for country c converted to the reference country's currency. Assuming factor-specific productivities capture all differences in technology so that D0 = ΠcDc, this in turn implies that wc = Πcw0. This framework leads to a simple comparison of factor payments to factor-specific productivities using the United States as the reference country. In the simple two factor case with labor and physical capital, each country's wage and rental rate relative to the U.S. should equal its respective factor-specific productivity relative to the U.S. 5 The complete list of 18 low wage-rental and 14 high wage-rental countries follows, with their GDP per capita and wage-rental ratio as a percent of the U.S. values noted parenthetically. Low wage-rental countries, ranked from lowest to highest GDP per capita relative to the U.S.: China (10, 5), Indonesia (11,8), Turkey (16, 10), Russia (21, 24), Brazil (21, 16), Poland (28, 27), Slovak Republic (30, 54), Hungary (33, 58), Czech Republic (41, 66), the Republic of Korea (47, 58), Portugal (50, 64), Greece (53, 49), New Zealand (55, 66), Taiwan (55, 47), Spain (64, 92), Finland (67, 74), Ireland (80, 41), Norway (1.06, 83). High wage-rental countries: Israel (57, 130), United Kingdom (69, 109), Italy (69, 107), Sweden (69, 126), France (70, 120), Japan (72, 153), German (74, 128), Belgium (75, 128), Australia (77, 99), Denmark (78, 115), Canada (80, 130), Austria (80, 107), Netherlands (81, 107), Switzerland (88, 168). I deemed Australia's wage-rental ratio sufficiently close to that of the U.S. to group with high wage-rental countries.
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Following Trefler (1993), I present a visual representation of the estimated factor-specific productivities compared to factor payments for labor and capital in Fig. 1. I also replicate Trefler's regressions of country c's wage wLc and rental rate wKc on the productivity of labor πLc and capital πKc relative to the U.S. in logarithms. According to productivity-adjusted factor price equalization, the coefficient on the log of each productivity parameter should be equal to one. The results are as follows (standard errors are in parenthesis):
4. A sector-specific explanation for factor-specific differences in productivity
2
logðwLc Þ ¼ 3:68 þ 1:15 logðπLc Þ; R ¼ 0:97 ð0:03Þ ð0:04Þ 2
logðwKc Þ ¼ −2:18 þ 0:67 logðπKc Þ; R ¼ 0:46 ð0:05Þ
ð0:13Þ
The reverse regressions, which account for errors in the measurement of productivity, give a probability limit for the true coefficient on log(πLc) of [1.15, 1.19] and on log(πKc) of [0.67, 1.47]. Interpreted in light of Fig. 1, the coefficient on labor productivity reflects the clustering of low wage–rental countries below the diagonal line, and high wage–rental countries above the diagonal line. The reverse pattern occurs in the capital productivity prediction. Less evident in Fig. 1 is the statistically significant difference between labor and capital productivity in low wage–rental countries. A regression of the logarithm of πLc/πKc on a constant and a dummy variable set equal to 1 for the 14 high wage–rental countries gives the constant coefficient as −0.65, with a t-statistic equal to −4.24. The coefficient on the dummy variable is 0.75 with a t-statistic of 3.24 and the R 2 of the regression is equal to 0.26. A Wald test based on the null hypothesis that 1.20
Wage relative to USA
1.00 0.80 0.60 0.40 0.20 0.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
Labor productivity relative to USA 1.80 Turkey
Rental rate relative to USA
1.60
the sum of the two coefficients is equal to zero is not rejected, indicating that the logarithm of πLc/πKc is not statistically different from 0 for high wage–rental countries. On the whole, the results strongly corroborate Trefler's insight that factor-specific productivities are consistent with observed differences in factor payments, and point to a possible underlying explanation for the distinctive deviations from Trefler's (1993) model.
Ireland
1.40 1.20 1.00 0.80 0.60 0.40
Among low income countries, labor-intensive sectors such as agriculture often lag in productivity growth in spite of their importance for employment due to a complex set of factors. 6 To capture this type of sector-based difference in productivity I use a general equilibrium model of production with a constant elasticity of substitution (CES) technology, assuming the elasticity of substitution σ between capital and labor is the same across countries and sectors. Considered first in the absence of international trade, the standard cost minimization exercise allows a comparison of direct input coefficients between the reference country 0 and country c in terms of total factor productivity θgc and autarkic prices pgc indexed by sector and country, and nominal factor payments Wfc in local currency units indexed by factor and country: D0 ðf ; g Þ ¼ Dc ðf ; g Þ
θgc θg0
!1−σ
W fc pgc
!σ
pg0 Wf 0
!σ ð2Þ
Eq. (2) shows that differences in factor usage in a given sector across countries depend both on the relative TFP and on the relative real wages expressed in terms of the output price in each sector. 7 Let c represent a country with a low capital to labor endowment relative to the reference country, and consider the simple two good case with a labor-intensive good (representing agriculture) and a capital intensive good (representing manufacturing). In the absence of TFP differences across sectors, the relative price of the labor intensive good would tend to be lower in the capital-scarce country (assuming similar demand conditions in both countries). When sector-specific differences in TFP are introduced such that the labor-intensive sector is relatively backward in the capital-scarce country, the laborintensive good may be relatively more expensive in that country. Hence a move to costless free trade where goods' prices are equalized at the market exchange rate would also likely imply that the capitalscarce country specializes in the manufactured product and imports food, while the reverse occurs in the labor-scarce reference country. Although this simple result does have some ring of truth to it, insofar as the United States is a major food exporter and many capital-scarce countries like China export manufactured goods and import food, it is clearly at odds with the presence of large agricultural sectors in most low wage countries and does not address the complex pattern of trade in different types manufactured goods. A more liberal interpretation follows that of Davis and Weinstein (2001) who assume each sector consists of a range of traded and non-traded goods, and that trade costs introduce price differences even in traded goods. This heterogeneous world is most easily captured empirically by using a purchasing power parity exchange rate ecppp which expresses local currency units of country c per international dollar, so that ecppppgc = pg0 for all goods. Eq. (2) can then be expressed in
0.20 0.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Capital productivity relative to USA High wage-rental countries
Low wage-rental countries
Fig. 1. Factor payments and factor productivity.
1.80
6 Within this sample of countries, the share of agricultural employment in total employment averages 17% in the 17 low wage-rental countries (excluding Taiwan, which does not report sector employment to the ILO), compared to less than 4% in the 14 high wage rental countries. 7 Woodland (1982), page 383, shows how Eq. (2) can be derived from the CES unit cost function using Shephard's lemma.
K.G. Marshall / Journal of International Economics 87 (2012) 386–390
terms of the factor payments measured in international dollars, denoted by w:
D0 ðf ; g Þ ¼
θgc θg0
!1−σ
wfc wf 0
!σ Dc ðf ; g Þ
ð3Þ
In the special Cobb-Douglas case where σ = 1, the expression (θgc/θg0) 1 − σ disappears from the right-hand side so that factorspecific productivities will be industry-neutral. In the general equilibrium setting, sector-specific differences in TFP will determine the differences in factor payments. A country with relatively low TFP in the labor-intensive sector will have a low wage–rental rate, reflected in a low factor-specific productivity measure for labor and a high factor-specific productivity measure for capital. The Cobb-Douglas assumption of unitary substitutability between capital and labor does not explain the distinctive clustering pattern above and below the diagonal lines pictured in Fig. 1, but this pattern can be explained by the existence of complementarities between capital and labor when the elasticity of substitution between factors is less than 1. To show this I can use Eq. (3) to rewrite the measure of factor-specific productivity given in Eq. (1) as:
πfc ¼
wfc wfo
!σ " !1−σ # G X θgc ϖfgc θg0 g¼1
ð4Þ
Dc ðf ; g ÞQ c ðg Þ gives the share of country c's factor f ∑g Dc ðf ; g ÞQ c ðg Þ G P ϖfgc ¼ 1. This important used in the production of good g, and where ϖfgc ¼
g¼1
result shows that when σ ≠ 1, the factor-specific productivity does not equal the wage relative to the reference country, but is instead a function of the wage and a sectoral TFP adjustment. In particular, when σ is less than 1 and θgc/θg0 > θic/θi0 for all i ≠ g where g is the capital-intensive sector, Eq. (4) indicates that πLc > wLc/wL0 and πKc b wKc/wK0. If θgc/θg0 b θic/θi0 for all i ≠ g, the direction of the two productivity, payment inequalities will be reversed. 8 This explanation for factor-specific productivity differences argues for a re-evaluation of the data presented in Fig. 1. The clustering of low wage–rental countries below the diagonal line in the top axes and above the diagonal line in the bottom axes suggests that the capital-intensive sector in these countries is closer to the productivity frontier set by the United States than is the labor-intensive sector. If factor-specific productivity differences were instead inherent in the factors themselves, there would be no obvious explanation for the dispersion of countries across the diagonal line beyond random measurement error. To evaluate the clustering pattern more carefully, I use a simple statistical test based on a two-way contingency table which categorizes countries by wage–rental rate relative to the United States and whether πLc/πKc − wLc/wKc is greater than or less than 0. Based on the null hypothesis that the sign of πLc/πKc − wLc/wKc does not depend on whether a country is a high or a low wage–rental country, the resulting chi-squared statistic with one degree of freedom is equal to 18.7, rejecting the null hypothesis at a significance level of 0.001. I also note that the magnitude of the differences between factorspecific productivity and factor payments is not trivial. Among the low wage–rental countries, wages relative to the U.S. are on average 23% below πL. For these countries, πL averages only about 50% of the labor productivity in the U.S. On the other hand, their rental rate is about 13% above πK, and πK is about 80% of that in the U.S. The relative
8 The claims in the last two sentences are not trivial to prove. In the on-line appendix I show that they are true for the case of two factors, two sectors, and an interior solution for factor prices in all countries.
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wage among high wage-rental countries does not differ statistically from πL although their rental rate is about is about 12% belowπK. 9 This paper shows that a simple general equilibrium model of trade together with uneven productivity convergence by sector can generate the distinctive pattern of factor-specific productivities and factor payments presented in Fig. 1. In the presence of complementarities between capital and labor and uneven development, Eq. (4) gives a variant of productivity-adjusted factor price equalization that both predicts the observed wide range of wages and rents among open countries and explains the underlying cause of these differences. 4.1. Further empirical evaluation of sector-specific TFP differences between countries I have argued that a specific pattern of cross-country variations in TFP between labor and capital intensive sectors can explain the relation of measured factor-specific productivities to factor payments. By making a number of strong assumptions, I can compute the widely-used multilateral productivity index following Caves et al. (1982) for fourteen broad sectors in each of 32 countries, measuring productivity in each sector relative to the same U.S sector. 10 First, I construct a 14 sector by 2 factor estimate of Dc to match the availability of self-employment data by sector. I allocate capital to each sector by assuming the economy-wide rental rate is equalized between sectors, and I allocate labor in a similar way, adjusting for differences in skills by measuring labor use in each sector as the payments to labor in that sector divided by the economy-wide average wage. In this general equilibrium framework, a country with relatively higher TFP in capital-intensive industries will have a lower relative wage–rental ratio. 11 Fig. 2 compares each country's wage–rental ratio relative to the U.S. to that country's ratio of TFP in capitalintensive sectors compared to labor-intensive sectors also measured relative to the US. 12 Recognizing the data limitations involved in accurately estimating TFP, Fig. 2 indicates that sector-specific variations in productivity can readily explain the range of wage-rental ratios observed among these 33 open economies. 5. Conclusion Most of the international variations in factor payments can be explained by variations in factor-specific productivity. One explanation for factor-specific productivity differences is underlying sector-specific variations in TFP, which can in turn explain the pattern of high capital productivity and low labor productivity common among countries with a low wage-rental ratio. Complementarities between labor and capital can also explain why wages tend to be lower than labor 9 These percentages represent the mean of the log of each factor productivity relative to factor payment × 100; in order of presentation the t-statistic for each mean is 6.12**, − 2.04**, 0.89, 3.37** (** indicates significantly different from 0 for a onetailed t-distribution at 5% significance). While I do not attempt to estimate σ given the relatively small sample size, I show in the appendix that these results are consistent with a model simulation using my TFP estimates and σ in the range of 0.6 to 0.8. This result is in line with Fadinger (2011), who estimates σ to be about 0.8. The particular direction of the bias is also evidence that σ b 1 since in the case where σ > 1 I show in the appendix that the direction of the bias would be reversed. 10 I follow Harrigan (1997), who gives a particularly clear discussion of this index and uses it to estimates TFP across manufacturing sectors in several industrialized countries. Like Harrigan, I am actually estimating a value-added index which assumes that capital and labor is separable from other inputs. Since this index is transitive, the choice of reference country would not fundamentally alter the data presented in Fig. 2. 11 This is shown mathematically by Eqs. A.1 and A.2 in the on-line appendix. 12 It is common in the empirical trade literature to identify wholly non-traded sectors such as public services, whose relative price level may be misstated even by the PPP exchange rate, in turn distorting the measure of TFP. Based on the input–output data, I identify 4 of the 14 sectors with virtually no trade (ISIC sectors F, construction, L, public administration, M, education, and N, health services) and drop them from this analysis. Further details on the categorization between capital and labor intensive sectors are given in Appendix Table 5.
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1.0 0.5
-0.1
Log (wage rental ratio)
-0.2
0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5
Log( average TFP of capital intensive sectors/ average TFP of labor intensive sectors) High wage-rental countries
Low wage-rental countries
Fig. 2. The log difference in wage–rental ratio (relative to U.S.) as a function of uneven development measured by the log difference of average TFP in capital-intensive sectors compared to labor-intensive sectors. Capital intensive sectors comprise ISIC Rev. 3 sectors C, mining, D, manufacturing, E, utilities, and I–J, various modern business services. Labor-intensive sectors comprise A and B, agriculture and forestry, G, H, and O–P, various labor-intensive services. TFP in each industry is relative to the same U.S. industry.
productivity and rental rates higher than capital productivity among low wage-rental countries, while the reverse tends to holds true for high wage-rental countries. Economy-wide TFP comparisons, while useful and easily measured, may obscure the more complex pattern of uneven development and its ramifications for international differences in factor payments among open economies. Role of funding source Partial funding was provided by the Orfalea College of Business Summer Research Grant, 2008. No stipulations on research content were imposed by the funding source. Acknowledgments I would like to thank the editor, Daniel Trefler, for invaluable suggestions that greatly improved this paper. I would also like to thank an anonymous referee for helpful comments. Appendix A. Supplementary material Supplementary data to this article can be found online at doi:10. 1016/j.jinteco.2012.01.003. References Bernanke, B., Gurkaynak, R.S., 2001. Is growth exogenous? Taking Mankiw, Romer and Weil seriously. In: Bernanke, B.S., Rogoff, K. (Eds.), NBER Macroeconomics Annual 2001. MIT Press, Cambridge, pp. 11–72. Caselli, F., Feyrer, F., 2007. The marginal product of capital. Quarterly Journal of Economics 122, 535–568. Caves, D.W., Christensen, L.R., Diewert, W.E., 1982. Multilateral comparisons of output, input, and productivity using superlative index numbers. The Economic Journal 92, 73–86.
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