A Note to Schooling in Development Accounting

ISSN 2042-2695 CEP Discussion Paper No 1102 December 2011 A Note on Schooling in Development Accounting Francesco Caselli and Antonio Ciccone Abstract How much would output increase if underdeveloped economies were to increase their levels of schooling? We contribute to the development accounting literature by describing a nonparametric upper bound on the increase in output that can be generated by more schooling. The advantage of our approach is that the upper bound is valid for any number of schooling levels with arbitrary patterns of substitution/complementarity. We also quantify the upper bound for all economies with the necessary data, compare our results with the standard development accounting approach, and provide an update on the results using the standard approach for a large sample of countries. Keywords: schooling; production; efficiency; human capital; development accounting; growth accounting JEL Classifications: I28; J24 This paper was produced as part of the Centre’s Macro Programme. The Centre for Economic Performance is financed by the Economic and Social Research Council. Acknowledgements We thank Marcelo Soto, Hyun Son, and very especially David Weil for useful comments. Francesco Caselli is a Programme Director at the Centre for Economic Performance and Professor of Economics, London School of Economics. Antonio Ciccone is ICREA Professor at the Universitat Pompeu Fabra. He is also Barcelona GSE Research Professor, and research associate of CREI. Published by Centre for Economic Performance London School of Economics and Political Science Houghton Street London WC2A 2AE All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means without the prior permission in writing of the publisher nor be issued to the public or circulated in any form other than that in which it is published. Requests for permission to reproduce any article or part of the Working Paper should be sent to the editor at the above address.  F. Caselli and A. Ciccone, submitted 2011 1 Introduction Low GDP per worker goes together with low schooling. For example, in the country with the lowest output per worker in 2005, half the adult population has no schooling at all and only 5% has a college degree (Barro and Lee, 2010). In the country with output per worker at the 10th percentile, 32% of the population has no schooling and less than 1% a college degree. In the country at the 25th percentile, the population shares without schooling and with a college degree are 22% and 1% respectively. On the other hand, in the US, the share of the population without schooling is less than 0.5% and 16% have a college degree. How much of the output gap between developing and rich countries can be accounted for by di¤erences in the quantity of schooling? A robust result in the development accounting literature, …rst established by Klenow and Rodriguez-Clare (1997) and Hall and Jones (1999), is that only a relatively small fraction of the output gap between developing and rich countries can be attributed to di¤erences in the quantity of schooling. This result is obtained assuming that workers with di¤erent levels of schooling are perfect substitutes in production (e.g. Klenow and Rodriguez-Clare, 1997; Hendricks, 2002). Perfect substitution among di¤erent schooling levels is necessary to explain the absence of large cross-country di¤erences in the return to schooling if technology di¤erences are assumed to be Hick-neutral. There is by now a consensus that di¤erences in technology across countries or over time are generally not Hicks-neutral and that perfect substitutability among di¤erent schooling levels is rejected by the empirical evidence, see Katz and Murphy (1992), Angrist (1995), Goldin and Katz (1998), Autor and Katz (1999), Krusell et al. (2000), Ciccone and Peri (2005), and Caselli and Coleman (2006) for example. Once the assumptions of perfect substitutability among schooling levels and Hicks-neutral technology di¤erences are discarded, can we still say something about the output gap between developing and rich countries attributable to schooling? Taking a parametric production function approach to the development accounting literature requires assuming that there are only two imperfectly substitutable skill types, that the elasticity of substitution between these skill types is the same in all countries, and that this elasticity of substitution is equal to the elasticity of substitution in countries where instrumental-variable estimates are available (e.g. Angrist, 1995; Ciccone and Peri, 2005). These assumptions are quite strong. For example, the evidence indicates that dividing the labor force in just two skill groups misses out on important margins of substitution (Autor et al., 2006; Goos and Manning, 2007). Once there are more than 3 skill types, 1 estimation of elasticities of substitution becomes notoriously di¢cult for two main reasons. First, there are multiple, non-nested ways of capturing patterns of substitutability/complementarity and this make it di¢cult to avoid misspeci…cation (e.g. Du¤y et al., 2004). Second, relative skill supplies and relative wages are jointly determined in equilibrium and estimation therefore requires instruments for relative supplies. It is already challenging to …nd convincing instruments for two skill types and we are not aware of instrumental-variables estimates when there are 3 or more imperfectly substitutable skills groups. We explore an alternative to the parametric production function approach and exploit that when aggregate production functions are weakly concave in inputs, assuming perfect substitutability among di¤erent schooling levels yields an upper bound on the increase in output that can be generated by more schooling. Hence, although the assumption of perfect substitutability among di¤erent schooling levels is rejected empirically, the assumption remains useful in that it yields an upper bound on the output increase through increased schooling no matter what the true pattern of substitutability/complementarity among schooling levels may be. This basic observation does not appear to have been made in the development accounting literature. It is worthwhile noting that the production functions used in the development accounting literature satisfy the assumption of weak concavity in inputs. Hence, our approach yields an upper bound on the increase one would obtain using the production functions in the literature. Moreover, the assumption of weakly concave aggregate production functions is fundamental for the development accounting approach as it is clear that without it, inferring marginal productivities from market prices cannot yield interesting insights into the factors accounting for di¤erences in economic development. The intuition for why the assumption of perfect substitutability yields an upper bound on the increase in output generated by more schooling is easiest to explain in a model with two schooling levels, schooled and unschooled. In this case, an increase in the share of schooled workers has, in general, two types of e¤ects on output. The …rst e¤ect is that more schooling increases the share of more productive workers, which increases output. The second e¤ect is that more schooling raises the marginal productivity of unschooled workers and lowers the marginal productivity of schooled workers. When assuming perfect substitutability between schooling levels, one rules out the second e¤ect. This implies an overstatement of the output increase when the production function is weakly concave, because the increase in the marginal productivity of unschooled workers is more than o¤set by the decrease in the marginal productivity of schooled workers. The result that increases in marginal productiv2 ities produced by more schooling are more than o¤set by decreases in marginal productivities continues to hold for an arbitrary number of schooling types with any pattern of substitutability/complementarity as long as the production function is weakly concave. Hence, assuming perfect substitutability among di¤erent schooling levels yields an upper bound on the increase in output generated by more schooling. From the basic observation that assuming perfect substitutability among schooling levels yields an upper bound on output increases and with a few ancillary assumptions – mainly that physical capital adjusts to the change in schooling so as to keep the interest rate unchanged – we derive a formula that computes the upper bound using exclusively data on the structure of relative wages of workers with di¤erent schooling levels. We apply our upper-bound calculations to two data sets. In one data set of 9 countries we have detailed wage data for up to 10 schooling-attainment groups for various years between 1960 and 2005. In another data set of about 90 countries we use evidence on Mincerian returns to proxy for the structure of relative wages among the 7 attainment groups. Our calculations yield output gains from reaching a distribution of schooling attainment similar to the US that are sizeable as a proportion of initial output. However these gains are much smaller when measured as a proportion of the existing output gap with the US. This result is in line with the conclusions from development accounting (e.g. Klenow and Rodriguez-Clare, 1997; Hall and Jones, 1999; Caselli, 2005). This is not surprising as these studies assume that workers with di¤erent schooling attainment are perfect substitutes and therefore end up working with a formula that is very similar to our upper bound.1 The rest of the paper is organized as follows. Section 2 derives the upper bound. Section 3 shows the results from our calculations. Section 4 concludes. 2 Derivation of the Upper Bound Suppose that output Y is produced with physical capital K and workers with di¤erent levels of schooling attainment, Y = F (K; L0 ; L1 ; :::Lm ) (1) where Li denotes workers with schooling attainment i = 0; ::; m. The (country-speci…c) production function F is assumed to be increasing in 1 Our calculations are closest in spirit to Hall and Jones (1999), who conceive the development accounting question in terms of counterfactual output increases for a given change in schooling attainment. Other studies use mostly variance decompositions. Such decompositions are di¢cult once skill-biased technology and imperfect substitutability among skills are allowed for. 3 all arguments, subject to constant returns to scale, and weakly concave in inputs. Moreover, F is taken to be twice continuously di¤erentiable. The question we want to answer is: how much would output per worker in a country increase if workers were to have more schooling. Speci…cally, de…ne si as the share of the labor force with schooling attainment i, and s = [s0 ; s1 ::; si;::: sm ] as the vector collecting all the shares. We want to know the increase in output per worker if schooling were to change from the current schooling distribution s1 to a schooling distribution s2 with more weight on higher schooling attainment. For example, s1 could be the current distribution of schooling attainment in India and s2 the distribution in the US. Our problem is that we do not know the production function F . To start deriving an upper bound for the increase in output per worker that can be generated by additional schooling, denote physical capital per worker by k and note that constant returns to scale and weak concavity of the production function in (1) imply that changing inputs from (k 1 ; s1 ) to (k 2 ; s2 ) generates a change in output per worker y 2 y 1 that satis…es y 2 y 1 1 1 Fk (k ; s )(k 2 1 k )+ m X Fi (k 1 ; s1 )(s2i s1i ) (2) i=0 where Fk (k 1 ; s1 ) is the marginal product of physical capital given inputs (k 1 ; s1 ) and Fi (k 1 ; s1 ) is the marginal product of labor with schooling attainment i given inputs (k 1 ; s1 ): Hence, the linear expansion of the production function is an upper bound for the increase in output per worker generated by changing inputs from (k 1 ; s1 ) to (k 2 ; s2 ). We will be interested in percentage changes in output per worker and therefore divide both sides of (2) by y 1 , y2 y1 y1 Fk (k 1 ; s1 )k 1 y1 k2 k1 k1 + m X Fi (k 1 ; s1 ) i=0 y1 (s2i s1i ): (3) Assume now that factor markets are approximately competitive. Then (3) can be rewritten as ! m 2 1 1 X y2 y1 k k w 1 1 Pm i 1 1 (s2i s1i ) (4) + (1 ) y1 k1 i=0 wi si i=0 where 1 is the physical capital share in output and wi1 is the wage of workers with schooling attainment i given (k 1 ; s1 ).PSince schooling Pm inputs 1 shares must sum up to unity we have i=0 wi1 (s2i s1i ) = m w01 ) (s2i i=1 (wi 4 s1i ) and w1 = w01 + y2 y1 y1 1 Pm i=1 k2 (wi1 k1 k1 w01 ) s1i and, (4) becomes 1 0 m X w1 i 1 (s2i s1i ) C B w01 C B 1 B i=1 C: + (1 )B m C X 1 @ wi 1 A 1 s 1+ i w1 (5) 0 i=1 Hence, the increase in output per worker that can be generated by additional schooling and physical capital is below a bound that depends on the physical capital income share and the wage premia of di¤erent schooling groups relative to a schooling baseline. 2.1 Optimal Adjustment of Physical Capital In (5), we consider an arbitrary change in the physical capital intensity. As a result, the upper bound on the increase in output that can be generated by additional schooling may be o¤ because the change in physical capital considered is suboptimal given schooling attainment. We now derive an upper bound that allows physical capital to adjust optimally (in a sense to be made clear shortly) to the increase in schooling. To do so, we have to distinguish two scenarios. A …rst scenario where the production function is weakly separable in physical capital and schooling, and a second scenario where schooling and physical capital are not weakly separable. 2.1.1 Weak Separability between Physical Capital and Schooling Assume that the production function for output can be written as Y = F (K; G(L0 ; L1 ; :::Lm )) (6) with F and G characterized by constant returns to scale and weak concavity. This formulation implies that the marginal rate of substitution in production between workers with di¤erent schooling is independent of the physical capital intensity. While this separability assumption is not innocuous, it is weaker than the assumption made in most of the development accounting literature.2 We also assume that as the schooling distribution changes from the original schooling distribution s1 to a schooling distribution s2 ; physical capital adjusts to leave the marginal product of capital unchanged, 2 Which assumes that F in (6) is Cobb-Douglas, often based on Gollin’s (2002) …nding that the physical capital income share does not appear to vary systematically with the level of economic development. 5 M P K 2 = M P K 1 : This could be because physical capital is mobile internationally or because of physical capital accumulation in a closed economy.3 With these two assumptions we can develop an upper bound for the increase in output per worker that can be generated by additional schooling, that depends on the wage premia of di¤erent schooling groups only. To see this, note that separability of the production function implies y2 y1 k2 1 y1 k1 k1 1 + (1 ) G(s2 ) G(s1 ) G(s1 ) : (7) The assumption that physical capital adjusts to leave the marginal product unchanged implies that F1 (k 1 =G(s1 ); 1) = F1 (k 2 =G(s2 ); 1) and therefore k 2 =G(s2 ) = k 1 =G(s1 ): Substituting in (7), y2 y1 y1 G(s2 ) G(s1 ) : G(s1 ) (8) Weak concavity and constant returns to scale of G respectively, Pm Pimply, m 2 1 1 2 1 1 G(s ) G(s ) si ) and G(s ) = i=0 Gi (s1 )s1i , where i=0 Gi (s )(si Gi denotes the derivative with respect to schooling level i: Combined with (7), this yields y 2 y y1 1 m X Gi (s 1 )(s2i s1i ) i=0 m X = Gi (s1 )s1i m X wi1 w01 1 (s2i s1i ) i=1 1+ m X (9) wi1 w01 1 s1i i=1 i=0 where the equality makes use of the fact that separability of the production function and competitive factor markets imply F2 (k 1 ; G(s1 ))Gi (s1 ) wi1 Gi (s1 ) = = : G0 (s1 ) F2 (k 1 ; G(s1 ))G0 (s1 ) w01 (10) Hence, assuming weak separability between physical capital and schooling, the increase in output per worker that can be generated by additional schooling is below a bound that depends on the wage premia of di¤erent schooling groups relative to a schooling baseline. 3 See Caselli and Feyrer (2007) for evidence that the marginal product of capital is not systematically related to the level of economic development. 6 2.1.2 Non-Separability between Physical Capital and Schooling Since Griliches (1969) and Fallon and Layard (1975), it has been argued that physical capital displays stronger complementaries with highskilled than low-skilled workers (see also Krusell et al., 2000; Caselli and Coleman 2002, 2006; and Du¤y et al. 2004). In this case, schooling may generate additional productivity gains through the complementarity with physical capital. We therefore extend our analysis to allow for capital-skill complementarities and derive the corresponding upper bound for the increase in output per worker that can be generated by additional schooling. To allow for capital-skill complementarities, suppose that the production function is Y = F (Q [U (L0 ; ::; L 1 ); H(L ; ::; Lm )] ; G [K; H(L ; ::; Lm )]) (11) where F; Q; U; and H are characterized by constant returns to scale and weak concavity, and G by constant returns to scale and G12 < 0 to ensure capital-skill complementarities. This production function encompasses the functional forms by Fallon and Layard (1975), Krusell et al.(2000), Caselli and Coleman (2002, 2006), and Goldin and Katz (1998) for example (who assume that F; G are constant-elasticity-of-substitution functions, that Q(U; H) = U , and that U; H are linear functions).4 The main advantage of our approach is that we do not need to specify functional forms and substitution parameters, which is notoriously di¢cult (e.g. Du¤y et al., 2004). To develop an upper bound for the increase in output per worker that can be generated by increased schooling in the presence of capital-skill complementarities, we need an additional assumption compared to the scenario with weak separability between physical capital and schooling. The assumption is that the change in the schooling distribution from s1 to s2 does not strictly lower the skill ratio H=U , that is, H(s12 ) ; U (s11 ) H(s22 ) U (s21 ) (12) where s1 = [s0 ; :::; s 1 ] collects the shares of workers with schooling levels strictly below and s2 = [s ; :::; sm ] collects the shares of workers with schooling levels equal or higher than (we continue to use the superscript 1 to denote the original schooling shares and the superscript 4 Du¤y et al. (2004) argue that a special case of the formulation in (11) …ts the empirical evidence better than alternative formulations for capital-skill complementarities used in the literature. 7 2 for the counterfactual schooling distribution). For example, this assumption will be satis…ed if the counterfactual schooling distribution has lower shares of workers with schooling attainment i < and higher shares of workers with schooling attainment i . If U; H are linear function as in Fallon and Layard (1975), Krusell et al.(2000), Caselli and Coleman (2002, 2006), and Goldin and Katz (1998), the assumption in (12) is testable as it is equivalent to X1 w1 i w01 (s2i m X w1 s1i ) i w1 (s2i s1i ) i= i=0 X1 wi1 w01 , m X w1 (13) i 1 s w1 i s1i i= i=0 where we used that competitive factor markets and (11) imply wi1 =w01 = F1 Q1 Ui =F1 Q1 U0 = Ui =U0 for i < and wi1 =w1 = (F1 Q2 + F2 G2 ) Hi = (F1 Q2 + F2 G2 ) H = Hi =H for i . It can now be shown that the optimal physical capital adjustment implies k2 k1 k1 H(s22 ) H(s12 ) : H(s12 ) (14) To see this, note that the marginal product of capital implied by (11) is h i1 0 G H(sk 2 ) ; 1 k i A G1 M P K = F2 @1; h ;1 : (15) U (s1 ) H(s ) 2 Q H(s2 ) ; 1 Hence, holding k=H constant, an increase in H=U either lowers the marginal product of capital or leaves it unchanged. As a result, k=H must fall or remain constant to leave the marginal product of physical capital unchanged, which implies (14). Using steps that are similar to those in the derivation of (9) we obtain X1 w1 i w01 U (s21 ) U (s11 ) U (s11 ) (s2i i=0 X1 w1 i 1 s w01 i i=0 8 s1i ) ; (16) where we used wi1 =w01 = (F1 Q1 Ui )=(F1 Q1 U0 ) = Hi =H for i < ; and m X w1 i k 2 k 1 H(s22 ) H(s12 ) H(s12 ) k1 w1 (s2i s1i ) i= ; m X w1 (17) i 1 s w1 i i= where we used wi1 =w1 = (F1 Q2 Hi + F2 G2 Hi ) = (F1 Q2 H + F2 G2 H ) = Hi =H for i and (14). These last two inequalities combined with (11) imply y 2 y y1 1 0 X1 w1 i (s2 B w01 i B 1 B i=0 B X1 w1 @ i 1 s1i ) C C C + (1 C A 1 s w01 i i=0 0 m X w1 i (s2i B w1 B 1 B i= )B m X @ wi1 1 s1i ) C C C ; (18) C A 1 s w1 i i= where 1 is the share of workers with schooling levels i < in aggregate income. Hence, with capital-skill complementarities, the increase in output per worker that can be generated by additional schooling is below a bound that depends on the income share of workers with schooling levels i < and the wage premia of di¤erent schooling groups relative to two schooling baselines (attainment 0 and attainment ). To get some intuition on the di¤erence between the upper bound in (9) and in (18), note that the upper bound in (18) would be identical to the upper bound in (9) if, instead of 1 , we were to use the share of workers with schooling levels i < in aggregate wage income. Hence, as the share of workers with low schooling in aggregate wage income is greater than their share in aggregate income, (18) puts less weight on workers with low schooling and more weight on workers with more schooling than (9) (except if there is no physical capital). This is because of the stronger complementarity of better-schooled workers with physical capital.5 Because obtaining estimates of 1 is beyond the scope of the present paper in the rest of the paper we focus on the upper bound in (9) rather than in (18). The main di¢culty in estimating 1 is de…ning threshold schooling : If was college attainment, the upper bound could be quite large because developing countries have very low college shares and the increase in college workers would be weighted by the physical capital income share plus the college-worker income share (rather than the much smaller college-worker income share only). If is secondary school, the di¤erence with our calculations would be small. 5 9 2.2 The Upper Bound with a Constant Marginal Return to Schooling The upper bound on the increase in output per worker that can be generated by additional schooling in (9) becomes especially simple when the wage structure entails a constant return to each additional year of schooling, (wi wi 1 )=wi 1 = . This assumption is often made in development accounting, because for many countries the only data on the return to schooling available is the return to schooling estimated using Mincerian wage regressions (which implicitly assume (wi wi 1 )=wi 1 = ). In this case the upper bound for the case of weak separability between schooling and physical capital in (9) becomes m X ((1 + )xi 1)(s2i s1i ) 2 1 y y i=1 : (19) m 1 X y 1+ ((1 + )xi 1)si i=1 where xi is years of schooling corresponding to schooling attainment i (schooling attainment 0 is assumed to entail zero years of schooling). The upper-bound calculation using (19) is closely related to analogous calculations in the development accounting literature. In development accounting, a country’s human capital is typically calculated as (1 + )S (20) where S is average years of schooling and the average marginal return to schooling is calibrated o¤ evidence on Mincerian coe¢cients.6 For example, several authors use = 0:10, where 0:10 is a “typical” estimate of the Mincerian return. One di¤erence with our approach is therefore that typical development accounting calculations identify a country’s schooling capital with the schooling capital of the average worker, while our upper-bound calculation uses the (more theoretically grounded) average of the schooling capital of all workers. The di¤erence, as already mentioned, is Jensen’s inequality.7 Another di¤erence is that we use country-speci…c Mincerian returns instead of a common value (or function) for all countries. 6 More accurately, human capital is usually calculated as exp( S), but the two expressions are approximately equivalent and the one in the text is more in keeping with our previous notation. 7 To see the relation more explicitly, for small , (1 + )xi is approximately linear and the right-hand side of (19) can be written in terms of average years of schooling Xm Xm S= xi si , as we do not miss much by assuming that (1+ )xi si (1+ )S i=1 i=o (ignoring Jensen’s inequality). As a result, if the Mincerian return to schooling is small, the upper bound on the increase in output per worker that can be generated 10 2.3 Link to Development Accounting and Graphical Intuition At this point it is worthwhile discussing the relationship between our analysis of schooling’s potential contribution to output per worker differences across countries and the analysis in development accounting. Following Klenow and Rodriguez-Clare (1996), development accounting usually assesses the role of schooling for output per worker under the assumption that workers with di¤erent schooling are perfect substitutes in production. This assumption has been made because it is necessary to explain the absence of large cross-country di¤erences in the return to schooling when technology is Hick-neutral (e.g. Klenow and Rodriguez-Clare, 1996; Hendricks, 2002). But there is now a consensus that di¤erences in technology across countries or over time are generally not Hicks-neutral and that perfect substitutability among di¤erent schooling levels is rejected by the empirical evidence, see Katz and Murphy (1992), Angrist (1995), Goldin and Katz (1998), Autor and Katz (1999), Krusell et al. (2000), Ciccone and Peri (2005), Caselli and Coleman (2006). Moreover, the elasticity of substitution between more and less educated workers found in this literature is rather low (between 1.3 and 2, see Ciccone and Peri, 2005 for a summary). Hence, the assumption of perfect substitutability among di¤erent schooling levels often made in development accounting should be discarded. But this does not mean that the …ndings in the development accounting literature have to be discarded also. To understand why note that the right-hand side of (9) – our upper bound on the increase in output per worker generated by more schooling – is exactly equal to the output increase one would have obtained under the assumption that di¤erent schooling levels are perfect substitutes in production, G(L0 ; L1 ; :::; Lm ) = a0 L0 + a1 L1 + ::: + am Lm : Hence, although rejected empirically, the assumption of perfect substitutability among di¤erent schooling levels remains useful in that it yields an upper bound on the output increase that can be generated by more schooling. To develop an intuition for these results, consider the case of just two by more schooling depends on the Mincerian return and average schooling only y2 y1 y1 2 1 (1 + )S (1 + )S : (1 + )S 1 Another approximation of the right-hand side of (19) for small that is useful for relating our upper bound to the development accounting literature is (S 2 S 1 )= 1 + S 1 . 11 labor types, skilled and unskilled, and no capital, Y = G(LU ; LH ) (21) where G is taken to be subject to constant returns to scale and weakly concave. Suppose we observe the economy when the share of skilled labor in total employment is s1 and want to assess the increase in output per worker generated by increasing the skilled-worker share to s2 : The implied increase in output per worker can be written as y(s2 ) y(s1 ) = G(1 s2 ; s2 ) G(1 s1 ; s1 ) Z s2 @G(1 s; s) ds = @s s1 Z s2 [G2 (1 s; s) G2 (1 s; s)] ds: = (22) s1 Weak concavity of G implies that G2 (1 s; s) G1 (1 s; s) is either ‡at or downward sloping in s: Hence, (22) implies that y(s2 ) y(s1 ) [G2 (1 s1 ; s1 ) G1 (1 s1 ; s1 )] (s2 s1 ) : Moreover, when factor markets are perfectly competitive, the di¤erence between the observed skilled 1 and unskilled wage in the economy wH wU1 is equal to G2 (1 s1 ; s1 ) 1 1 2 1 1 G1 (1 s ; s ). As a result, y(s ) y(s ) wU1 ) (s2 s1 ). As (wH 1 (wH wU1 ) (s2 s1 ) is also the output increase one would have obtained under the assumption that the two skill types are perfect substitutes, it follows that our upper bound is equal to the increase in output assuming perfect substitutability between skill types. Figure 1 illustrates this calculation graphically.8 The increase in output is the pink area. The upper bound is the pink plus blue area. The …gure also illustrates that the di¤erence between our upper bound and the true output gain is larger – making our upper bound less tight – the larger the increase in schooling considered.9 It is worth noting that while weak concavity of the production function implies that the increase in output generated by more schooling is always smaller than the output increase predicted assuming perfect substitutability among schooling levels, it also implies that the decrease in output generated by a fall in schooling is always greater than the decrease predicted under the assumption of perfect substitutability. Hence, our approach is not useful for developing an upper bound on the decrease in output that would be generated by a decrease in schooling. 8 We thank David Weil for suggesting this …gure. Our implementation of the upper bound below considers US schooling levels as the arrival value. As a result, the increase in schooling considered is large for many developing countries and our upper bound could be substantial larger than the true output gain. 9 12 3 Estimating the Upper Bounds We now estimate the maximum increase in output that could be generated by increasing schooling to US levels. We …rst do this for a subsample of countries and years for which we have data allowing us to perform the calculation in equation (9). For these countries we can also compare the results obtained using (9) with those using (19), which assume a constant return to extra schooling. These comparisons put in perspective the reliability of the estimates that are possible for larger samples, where only Mincerian returns are available. We also report such calculations for a large cross-section of countries in 1990. 3.1 Using Group-Speci…c Wages We implement the upper bound calculation in equation (9) for 9 countries for which we are able to estimate wages by education attainment level using national censa data from the international IPUMS (Minnesota Population Center, 2011). The countries are Brazil, Colombia, Jamaica, India, Mexico, Panama, Puerto Rico, South Africa, and Venezuela, with data for multiple years between 1960 and 2007 for most countries. The details vary somewhat from country to country as (i) schooling attainment is reported in varying degrees of detail across countries; (ii) the concept of income varies across countries; and (iii) the control variables available also vary across countries. See Appendix Tables 1-3 for a summary of the micro data (e.g. income concepts; number of attainment levels; control variables available; number of observations). These data allow us to estimate attainment-speci…c returns to schooling and implement (9) using the observed country-year speci…c distribution of educational attainments and the US distribution of educational attainment in the corresponding year as the arrival value. It is worthwhile noting that in implementing (9) – and also (19) below – we estimate and apply returns to schooling that vary both across countries and over time. Given our setup, the most immediate interpretation of the variation in returns to schooling would be that there is imperfect substitutability between workers with di¤erent schooling attainments and that the supply of di¤erent schooling attainments varies over time and across countries. It is exacly the presence of imperfect substitutability among di¤erent schooling levels that motivates our upper-bound approach. Another reason why returns to schooling might vary could be that there are di¤erences in technology. Our upper-bound approach does not require us to put structure on such (possibly attainment-speci…c) technology di¤erences. Of course, our upper bound would be inaccurate if technology changes in response to changes in schooling. To the extent 13 that this is an objection, it applies to all the development-accounting literature. For example, the Hall-Jones calculation would be inaccurate if total factor productivity increases in response to an increase in human capital. However, our interpretation of the spirit of development accounting is precisely to ask about the role of inputs holding technology constant.10 The results of implementing the upper-bound calculation in (9) for each country-year are presented (in bold face) in Table 1. For this group of countries applying the upper-bound calculation leads to conclusions that vary signi…cantly both across countries and over time. The largest computed upper-bound gain is for Brazil in 1970, which is of the order of 150%. This result largely re‡ects the huge gap in schooling between the US and Brazil in that year (average years of schooling in Brazil was less than 4 in 1970). The smallest upper bound is for Puerto Rico in 2005, which is essentially zero, re‡ecting the fact that this country had high education attainment by that year (average years of schooling is almost 13). The average is 0.59. A di¤erent metric is the fraction of the overall output gap with the US that reaching US attainment levels can cover. This calculation is also reported in Table 1 (characters in normal type). As a proportion of the output gap, the largest upper-bound gain is for Brazil in 1980 (57%), while the smallest is again for Puerto Rico in 2005 (virtually zero). On average, at the upper bound attaining the US education distribution allows countries to cover 21% of their output gap with the US. The shortcoming of the results in Table 1 is that they refer to a quite likely unrepresentative sample. For this reason, we now ask whether using the approach in equation (19) leads to an acceptable approximation of (9). As we show in the next section, data to implement (19) is readily available for a much larger (and arguably representative) sample of countries, so if (19) o¤ers an acceptable approximation to (9) we can be more con…dent on results from larger samples. To implement (19), we …rst use our micro data to estimate Mincerian returns for each country-year. This is done with an OLS regression using the same control variables employed to estimate the attainment-speci…c returns to schooling above.11 See Appendix Table 2 for point estimates and standard errors of Mincerian returns for each country-year. Once we have the Mincerian return we can apply equation (19) to assess the 10 Another possible source of di¤erences in schooling returns across countries is sampling variation. However our estimates of both attainment speci…c and Mincerian returns are extremely precise, so we think this explanation is unlikely. 11 The empirical labor literature …nds that OLS estimates of Mincerian returns to schooling are often close to causal estimates, see Card (1999). 14 upper-bound output gains of increasing the supply of schooling (assuming that technology remains unchanged). The results are reported, as a fraction of the results using (9), in the …rst row of Table 2 (bold type). This exercise reveals di¤erences between the calculations in (9) and (19). On average, the calculation that imposes a constant proportional wage gain yields only 77% of the calculation that uses attainment-speci…c returns to schooling. Therefore, the …rst message from this comparison is that, on average, basing the calculation on Mincerian coe¢cients leads to a signi…cant underestimate of the upper bound output increase associated with attainment gains. However, there is enormous heterogeneity in the gap between the two estimates, and in fact the results from (19) are not uniformly below those from (9). Almost one third of the estimates based on (19) are larger. The signi…cant average di¤erence in estimates and the great variation in this di¤erence strongly suggest that whenever possible it would be advisable to use detailed data on the wage structure rather than a single Mincerian return coe¢cient. It is interesting to note that the ratio of (19) to (9) is virtually uncorrelated with per-worker GDP. To put it di¤erently, while estimates based on (19) are clearly imprecise, the error relative to (9) is not systematically related to per-worker output. Hence, one may conclude that – provided the appropriate allowance is made for the average gap between (19) and (9) – some broad conclusions using (19) are still possible. We can also compare the results of our approach in (9) to the calculation combining average years of schooling with a single Mincerian return in (20). The results are reported in the second rows of Table 2. On average, the results are extremely close to those using (19), suggesting that ignoring Jensen’s inequality is not a major source of error in the calculations. However, the variation around this average is substantial. 3.2 Using Mincerian Returns Only The kind of detailed data on the distribution of wages that is required to implement our "full" calculation in equation (9) is not often available. However, there are estimates of the Mincerian return to schooling for many countries and years. For such countries, it is possible to implement the approximation in (19). We begin by choosing 1990 as the reference year. For Mincerian returns we use a collection of published estimates assembled by Caselli (2010). This starts from previous collections, most recently by Bils and Klenow (2003), and adds additional observations from other countries and other periods. Only very few of the estimates apply exactly to the year 1990, so for each country we pick the estimate prior and closest to 1990. In total, there are approximately 90 countries with an estimate of 15 the Mincerian return prior to 1990. Country-speci…c Mincerian returns and their date are shown in Appendix Table 3. For schooling attainment, we use the latest installment of the Barro and Lee data set (Barro and Lee, 2010), which breaks the labor force down into 7 attainment groups, no education, some primary school, primary school completed, some secondary school, secondary school completed, some college, and college completed. These are observed in 1990 for all countries. For the reference country, we again take the US.12 Figure 2 shows the results of implementing (19) on our sample of 90 countries. For each country, we plot the upper bound on the right side of (19) against real output per worker in PPP in 1995 (from the Penn World Tables). Not surprisingly, poorer countries experience larger upper-bound increases in output when bringing their educational attainment in line with US levels. The detailed country-by-country numbers are reported in Appendix Table 3. Table 3 shows summary statistics from implementing (19) on our sample of 90 countries. In general, compared to their starting point, several countries have seemingly large upper bound increases in output associated with attaining US schooling levels (and the physical capital that goes with them). The largest upper bound is 3.66, meaning that output almost quadruples. At the 90th percentile of output gain, output roughly doubles, and at the 75th percentile there is still a sizable increase by three quarters. The median increase is roughly by 45%. The average country has an upper bound increase of 60%. Figure 3 plots the estimated upper bounds obtained using (19) as a percentage of the initial output gap with the US.13 Clearly the upperbound output gains for the poorest countries in the sample are small as a fraction of the gap with the US. For the poorest country the upperbound output gain is less than 1% of the gap with the US. For the country with the 10th percentile level of output per worker the upperbound gain covers about 5% of the output gap. At the 75th percentile of the output per worker distribution it is about 7%, and at the median it is around 20%. The average upper-bound closing of the gap is 74%, but this is driven by some very large outliers. In Table 4 we also report summary statistics on the di¤erence between the upper bound measure obtained using (19) and the upper bound obtained using (20). While the di¤erence is typically not huge, 12 To implement (19) we also need the average years of schooling of each of the attainment groups. This is also avaiable in the Barro and Lee data set. 13 For the purpose of this …gure the sample has been trimmed at an income level of $60,000 because the four countries above this level had very large values that visually dominated the picture. 16 the measure based on (20) tends to be larger than our theory-based calculation. Since the latter is an upper bound, we can conclude that the calculation in (20) overstates the gains from achieving the attainment levels of the US. 4 Conclusion How much of the output gap with rich countries can developing countries close by increasing their quantity of schooling? Our approach has been to look at the best-case scenario: an upper bound for the increase in output that can be achieved by more schooling. The advantage of our approach is that the upper bound is valid for an arbitrary number of schooling levels with arbitrary patterns of substitution/complementarity. Application of our upper-bound calculations to two di¤erent data sets yields output gains from reaching a distribution of schooling attainment similar to the US that are sizeable as a proportion of initial output. However these gains are much smaller when measured as a proportion of the existing output gap with the US. This result is in line with the conclusions from the development accounting literature, which is not surprising as many development accounting studies assume that workers with di¤erent schooling attainment are perfect substitutes and therefore end up employing a formula that is very similar to our upper bound. REFERENCES Angrist, Joshua, 1995. "The Economic Returns to Schooling in the West Bank and Gaza Strip." American Economic Review, 85, pp. 10651087: Autor, David, and Lawrence Katz, 1999. "Changes in the Wage Structure and Earnings Inequality." In Orley Ashenfelter and David Card, Handbook of Labor Economics, Amsterdam: Elsevier. Autor, David H., Lawrence F. Katz and Melissa S. Kearney, 2006. “The Polarization of the U.S. Labor Market,” American Economic Review Papers and Proceedings, 96(2), pp. 189-194. Barro, Robert and Lee, Jong-Wha, 2010. "A New Data Set of Educational Attainment in the World, 1950-2010." National Bureau of Economic Research Working Paper #15902, Cambridge, MA. Data downloadable at: http://www.barrolee.com/ Bils, Mark and Pete Klenow, 2000. “Does Schooling Cause Growth?” American Economic Review, 90(2), pp. 1160-1183. Card, David, 1999. "The Causal E¤ect of Education on Earnings." In Orley Ashenfelter and David Card, Handbook of Labor Economics, Amsterdam: Elsevier. 17 Caselli, Francesco and Coleman, John Wilbur II, 2002. "The U.S. Technology Frontier." American Economic Review Papers and Proceedings, 92(2), pp. 148-152. Caselli, Francesco and Coleman, John Wilbur II, 2006. "The World Technology Frontier." American Economic Review, 96(3), pp. 499-522. Caselli, Francesco, and James Feyrer, 2007. "The Marginal Product of Capital." Quarterly Journal of Economics, 122(2), pp. 535-568. Caselli, Francesco, 2010. Di¤erences in Technology across Time and Space. 2010 CREI Lectures, Powerpoint Presentation. Ciccone, Antonio, and Giovanni Peri, 2005. "Long-Run Substitutability Between More and Less Educated Workers: Evidence from US States 1950-1990."Review of Economics and Statistics, 87(4), pp. 652-663. Du¤y, John, Chris Papageorgiou, and Fidel Perez-Sebastian, 2004. "Capital-Skill Complementarity? Evidence from a Panel of Countries." Review of Economics and Statistics, 86(1), pp. 327-344. Fallon, Peter R., and Richard G. Layard, 1971. "Capital-Skill Complementarity, Income Distribution, and Output Accounting." Journal of Political Economy, 83(2), pp. 279-302. Goldin, Caudia, and Lawrence Katz, 1998. "The Origins of TechnologySkill Complementarity." Quarterly Journal of Economics, 113(3), pp. 693-732. Gollin, Douglas, 2002. "Getting Income Shares Right." Journal of Political Economy, 110(2), pp. 458-474. Goos, Maarten, and Alan Manning, 2007. "Lousy and Lovely Jobs: The Rising Polarization of Work in Britain." Review of Economics and Statistics, 89, pp. 118-133. Griliches, Zvi, 1969. "Capital-Skill Complementarity." Review of Economics and Statistics, 51(1), pp. 465-468. Hall, Robert and Charles Jones, 1999. "Why Do Some Countries Produce So Much More Output Per Worker Than Others?" Quarterly Journal of Economics, 114(1), pp. 83-116. Hendricks, Lutz, 2002. "How Important is Human Capital for Development? Evidence from Immigrant Earnings." American Economic Review 92(3), pp. 198-219. Katz, Lawrence, and Kevin Murphy, 1992. "Changes in Relative Wages 1963–1987: Supply and Demand Factors." Quarterly Journal of Economics, 107(2), pp. 35-78. Klenow, Peter, and Andres Rodriguez-Claire, 1997. "The Neoclassical Revival in Growth Economics: Has It Gone Too Far?". In NBER Macroeconomic Annual. Cambridge MA: MIT Press. Krusell, Per, Lee Ohanian, Victor Rios-Rull, and Gianluca Violante, 2002. "Capital-Skill Complementarity and Inequality: A Macroeco18 nomic Analysis." Econometrica 68(4), pp. 1029-1053. McFadden, Daniel, Peter Diamond, and Miguel Rodriguez, 1978. "Measurement of the Elasticity of Factor Substitution and the Bias of Technical Change." In Melvyn Fuss and Daniel McFadden, Production Economics: A Dual Approach to Theory and Applications, Amsterdam: Elsevier. Minnesota Population Center. Integrated Public Use Microdata Series, International (IPUMS), 2011. Version 6.1 [Machine-Readable Database.]. Minneapolis: University of Minnesota. Data downloadable at: http://www.international.ipums.org 19 Figure 1: Change in Output from Change in Schooling Observed MP / Wage Skilled Marginal Product/ Wage of Unskilled Labor Marginal Product/ Wage of Skilled Labor MP Skilled MP Unskilled Share of Unskilled labor Observed MP/ Wage Unskilled Share of Skilled labor Note: Output increase when share of skilled labor grows from s1 to s2. Pink area: correct calculation; pink plus blue area: upper bound calculation. Figure 2: Upper bound income increase when moving to US attainment 4 3.5 3 2.5 2 1.5 1 0.5 0 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 Figure 3: Upper bound income gain as percent of output per worker gap with US 3 2.5 2 1.5 1 0.5 0 0 10000 20000 30000 40000 50000 60000 70000 Table 1 1960 Brazil 1970 1980 1.576 1.201 1990 1.020 0.441 0.567 0.304 0.224 0.620 0.242 0.469 India Puerto Rico 0.209 0.076 0.908 0.945 0.769 0.792 0.053 0.056 0.047 0.054 0.135 0.543 1.238 0.916 0.439 0.543 0.524 0.411 0.169 0.187 0.769 0.06 0.201 0.434 0.408 0.331 0.255 0.088 0.109 0.072 0.055 0.202 0.108 0.045 -0.003 -0.012 0.209 0.111 0.061 ‐0.006 ‐0.019 0.708 0.609 0.129 0.130 0.745 South Africa Venezuela 2005 0.159 Jamaica Panama 2000 0.901 0.901 Colombia Mexico 1995 0.140 0.757 0.604 0.403 0.860 0.568 0.353 0.132 0.235 Note: upper bound changes in income from moving to US education distribution. Figures in bold type are percent income increases, based on equation (19) [i.e. Use attainment-specific returns to education] Figures in normal type are percent income increases as share of overall income gap with US. 1970 figure refers to 1971 for Venezuela and 1973 for Colombia; 1980 figure refers to 1981 for Venezuela, 1982 for Jamaica, and 1983 for India; 1990 figure refers to 1987 for India and 1991 for Brazil and Jamaica; 1995 figure refers to 1993 for India and 1996 for South Africa; 2000 figure refers to 1999 for India and 2001 for Jamaica, South Africa, and Venezuela; 2005 figure refers to 2004 for India and 2007 for South Africa Table 2 1960 Brazil Colombia 1970 1980 0.828 0.816 0.839 0.873 0.749 0.821 1.269 1.255 0.954 1.100 0.983 1.055 0.978 1.231 0.992 1.369 1995 2000 0.657 0.773 2005 0.439 0.431 0.907 0.866 0.842 India 1.042 1.017 1.000 1.137 1.195 1.109 0.886 Mexico 1.049 1.105 1.311 1.024 0.934 0.984 1.017 Panama 1.065 1.202 1.278 0.996 1.023 -1.748 0.134 Puerto Rico 1.237 1.285 -4.333 -0.479 0.711 0.612 0.694 South Africa 0.861 0.739 0.855 0.693 0.917 1.112 0.283 Venezuela 0.612 0.958 1.172 0.283 Note: alternative measures of upper bound changes in income from moving to US education distribution, as percent of baseline measure. Figures in bold type assume constant returns to each additional year of schooling [based on equation (19)]; Figures in nornal type assume constant returns and assign to all workers the average years of schooling 1970 figure refers to 1971 for Venezuela and 1973 for Colombia; 1980 figure refers to 1981 for Venezuela, 1982 for Jamaica, and 1983 for India; 1990 figure refers to 1987 for India and 1991 for Brazil and Jamaica; 1995 figure refers to 1993 for India and 1996 for South Africa; 2000 figure refers to 1999 for India and 2001 for Jamaica, South Africa, and Venezuela; 2005 figure refers to 2004 for India and 2007 for South Africa Jamaica 1.052 1.092 0.915 1.037 1990 0.743 0.880 Table 3 mean max 90th percentile 75th percentile % Output gain using (19) 0.61 3.66 1.20 0.68 % Output gain using (20) 0.80 7.59 1.48 0.82 Note: upper bound on income changes in a large cross‐section, assuming constant returns to extra schooling median 0.45 0.54 Brazil Appendix Table 1: Description of Individual‐Level Data Income concept used in the analysis : total income per hour worked for 1980, 1991, 2000; total income for 1970. Other income concepts available: earned income per hour worked for 1980, 1991, 2000 (yield nearly identical results as income concept used for 1991 and 2000 but a significantly negative return to schooling in 1980). Control variables used in the analysis: age, age squared, gender, marital status, age*marital status, gender*marital status, dummies for region (state) of birth, dummies for region (state) of residence, dummy for urban area, dummy for foreign born, dummies for religion, dummies for race (except 1970). Educational attainment levels: 8 Colombia Income concept used in the analysis: total income for 1973. Other income concepts available: none. Control variables used in the analysis: age, age squared, gender, marital status, age*marital status, gender*marital status, dummies for region (state) of birth, dummies for region (municipality) of residence, dummy for urban area, dummy for foreign born. Educational attainment levels: 9 Income concept used in the analysis: wage income for 1983, 1987, 1993, 1999, India 2004. Other income concepts available: none. Control variables used in the analysis: age, age squared, gender, marital status, age*marital status, gender*marital status, dummies for region (state) of residence, dummy for urban area, dummies for religion. Educational attainment levels: 8 Jamaica Income concept used in the analysis: wage income for 1982, 1991, 2001. Other income concepts available: none. Control variables used in the analysis: age, age squared, gender, marital status, age*marital status, gender*marital status, dummies for region (parish) of birth, dummies for region (parish) of residence, dummy for foreign born, dummies for religion, dummies for race. Educational attainment levels: 7 Income concept used in the analysis: earned income per hour worked for 1990, Mexico 1995, 2000; earned income for 1960; total income for 1970. Other income concepts available: total income per hour for 1995, 2000. Control variables used in the analysis: age, age squared, gender, marital status, age*marital status, gender*marital status, dummies for region (state) of birth, dummies for region (state) of residence, dummy for urban area, dummy for foreign born, dummies for religion (except 1995). Educational attainment levels: 10 Note: Point estimates of the Mincerian regressions and the number of observations available are summarized in Appendix Tables 2 and 3. For more details on the variables see https://international.ipums.org/international/. Panama Puerto Rico South Africa Appendix Table 1: Continued Income concept used in the analysis: wage income per hour worked for 1990, 2000; wage income for 1970; total income per hour worked for 1980. Other income concepts available: earned income per hour worked for 1990, 2000; total income per hour worked for 1990 (yield nearly identical results as income concept used). Control variables used in the analysis: age, age squared, gender, marital status, age*marital status, gender*marital status, dummies for region (state) of birth (except 1990), dummies for region (district) of residence, dummy for urban area (except 1990), dummy for foreign born (except 1980). Educational attainment levels: 8 Income concept used in the analysis: wage income per hour worked for 1970, 1980, 1990, 2000, 2005. Other income concepts available: total income per hour worked for 1970, 1980, 1990, 2000, 2005; earned income per hour worked for 1990, 2000, 2005 (yield nearly identical results as income concept used. Control variables used in the analysis: age, age squared, gender, marital status, age*marital status, gender*marital status, dummies for region (metropolitan area) of residence, dummy for foreign born, dummies for race (only 2000, 2005). Educational attainment levels: 8 Income concept used in the analysis: total income per hour worked for 1996, 2007; total income for 2001. Other income concepts available: none. Control variables used in the analysis: age, age squared, gender, marital status, age*marital status, gender*marital status, dummies for region (province) of birth (except 1996), dummies for region (municipality) of residence, dummy for foreign born, dummies for religion (except 2007), dummies for race. Educational attainment levels: 6 Venezuela Income concept used in the analysis: earned income per hour worked for 1971, 1981, 2001; earned income for 1990. Other income concepts available: total income per hour worked 2001 (yields a Mincerian return to schooling of 13.7% as compared to 4.4% using earned income). Control variables used in the analysis: age, age squared, gender, marital status, age*marital status, gender*marital status, dummies for region (state) of birth, dummies for region (province) of residence, dummy for foreign born. Educational attainment levels: 10 Note: point estimates of the Mincerian regressions and the number of observations available are summarized in Appendix Tables 2 and 3. For more details on the variables see https://international.ipums.org/international/. 1960 Brazil Colombia India Jamaica Mexico Panama Puerto Rico South Africa Venezuela 1970 0,124 (0,00005) 0,0889 (0,0005) 0,123 (0,0002) 0,0993 (0,0001) 0,0879 (0,002) 0,099 (0,0003) Appendix Table 2 1990 0,113 (0,00004) 0,115 (0,00004) 1980 0,083 (0,00002) 0,0866 (0,00002) 0,125 (0,002) 0,0573 (0,002) 0,0682 (0,0001) 0,0941 (0,0003) 0,0938 (0,0005) 0,0911 (0,0003) 0,088 (0,0005) 0,0625 (0,0005) 0,0875 (0,0003) 0,0732 (0,0002) Note: estimated Mincerian coefficients and robust standard errors in parentheses 1970 figure refers to 1971 for Venezuela and 1973 for Colombia; 1980 figure refers to 1981 for Venezuela, 1982 for Jamaica, and 1983 for India; 1990 figure refers to 1987 for India and 1991 for Brazil and Jamaica; 1995 figure refers to 1993 for India and 1996 for South Africa; 2000 figure refers to 1999 for India and 2001 for Jamaica, South Africa, and Venezuela; 2005 figure refers to 2004 for India and 2007 for South Africa 1995 2000 0,109 (0,00003) 2005 0,074 (0,00002) 0,0776 (0,00001) 0,0788 (0,00001) 0,114 (0,0001) 0,117 (0,0001) 0,0614 (0,001) 0,094 (0,0001) 0,0916 (0,0005) 0,0985 (0,0005) 0,11 (0,0002) 0,0443 (0,0005) 0,116 (0,0004) 0,143 (0,0002) 1960 Brazil Colombia India Jamaica Mexico Panama Puerto Rico South Africa Venezuela 1970 14660440 3127210 Appendix Table 3 1990 24720720 33616046 1980 86928152 255720 4470106 6183300 246250 653200 367330 775220 45901965 409100 14303270 408540 698772 1540174 2567310 3548928 Note: number of observations used in the individual-level Mincerian regressions 1970 figure refers to 1971 for Venezuela and 1973 for Colombia; 1980 figure refers to 1981 for Venezuela, 1982 for Jamaica, and 1983 for India; 1990 figure refers to 1987 for India and 1991 for Brazil and Jamaica; 1995 figure refers to 1993 for India and 1996 for South Africa; 2000 figure refers to 1999 for India and 2001 for Jamaica, South Africa, and Venezuela; 2005 figure refers to 2004 for India and 2007 for South Africa 1995 2000 41010810 2005 109703806 133891583 443629 21316086 653460 732668 8299308 5038900 139597372 18762057 6775030 1000738 9360012 Appendix Table 4 Kuwait Norway Zimbabwe Uganda Vietnam Ghana Philippines Nepal Sri Lanka China Zambia Cameroon Peru Estonia Russian Federation Kenya Tanzania Bulgaria India Bolivia Indonesia Sudan Nicaragua Honduras Egypt Dominican Republic Slovak Republic Poland Croatia Paraguay Costa Rica El Salvador Czech Republic Thailand Ecuador Sweden Panama Australia Cyprus Tunisia Chile Pakistan Output in 1995 % gap with US 76562 73274 610 1525 2532 2313 5897 2008 6327 3234 2595 4490 13101 15679 16108 2979 1640 14140 3736 7624 6413 3747 5433 7599 11387 10739 22834 19960 20606 10450 18352 12182 31215 10414 15528 47480 17119 54055 37843 13927 23403 6624 ‐0.14 ‐0.10 106.79 42.13 24.99 27.44 10.16 31.76 9.40 19.34 24.35 13.65 4.02 3.20 3.08 21.08 39.10 3.65 16.61 7.63 9.26 16.56 11.11 7.66 4.78 5.13 1.88 2.30 2.19 5.30 2.58 4.40 1.11 5.32 3.24 0.39 2.84 0.22 0.74 3.72 1.81 8.93 Mincer Coeff. Estimate Year 4.5 5.5 5.57 5.1 4.8 7.1 12.6 9.7 7 12.2 11.5 6.45 5.7 5.4 7.2 11.39 13.84 5.25 10.6 10.7 7 9.3 12.1 9.3 5.2 9.4 6.4 7 5 11.5 8.5 7.6 5.65 11.5 11.8 3.56 13.7 8 5.2 8 12.1 15.4 1983 1995 1994 1992 1992 1995 1998 1999 1981 1993 1994 1994 1990 1994 1996 1995 1991 1995 1995 1993 1995 1989 1996 1991 1997 1995 1995 1996 1996 1990 1991 1992 1995 1989 1995 1991 1990 1989 1994 1980 1989 1991 % gain using (19) % gain using (20) % of gap closed 0.275 0.132 0.337 0.535 0.411 0.477 0.330 1.197 0.355 0.769 1.084 0.683 0.207 0.169 0.165 1.135 2.225 0.214 1.067 0.498 0.661 1.248 0.947 0.674 0.452 0.528 0.229 0.280 0.274 0.719 0.362 0.680 0.186 0.934 0.606 0.076 0.568 0.046 0.162 0.829 0.442 2.180 0.317 0.141 0.370 0.572 0.425 0.578 0.411 1.518 0.408 0.964 1.342 0.753 0.239 0.181 0.172 1.353 2.676 0.235 1.421 0.658 0.758 1.417 1.303 0.763 0.511 0.652 0.265 0.302 0.299 0.851 0.411 0.776 0.210 1.084 0.820 0.080 0.770 0.038 0.178 1.006 0.546 3.439 ‐1.95 ‐1.29 0.00 0.01 0.02 0.02 0.03 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.06 0.06 0.06 0.07 0.07 0.08 0.09 0.09 0.09 0.10 0.12 0.12 0.13 0.14 0.14 0.15 0.17 0.18 0.19 0.20 0.20 0.21 0.22 0.22 0.24 0.24 Argentina Korea, Rep. Botswana Cote d'Ivoire Mexico Morocco Malaysia South Africa Colombia Guatemala Turkey Hungary Venezuela, RB Jamaica Canada Brazil Israel Slovenia Iran, Islamic Rep. Greece Portugal Denmark Finland Ireland Japan Netherlands Hong Kong United Kingdom Spain Switzerland Austria France Germany Italy Belgium Singapore United States Iraq Taiwan 23222 33210 17280 4512 25835 7759 23194 22638 18808 10530 22996 27326 26164 14588 54026 16676 53203 32991 22339 42141 35336 52032 45289 52868 51674 59684 57093 51901 50451 57209 56728 58784 56992 63260 64751 63009 65788 n.a. n.a. Note: output per worker from PWT 1.83 0.98 2.81 13.58 1.55 7.48 1.84 1.91 2.50 5.25 1.86 1.41 1.51 3.51 0.22 2.95 0.24 0.99 1.95 0.56 0.86 0.26 0.45 0.24 0.27 0.10 0.15 0.27 0.30 0.15 0.16 0.12 0.15 0.04 0.02 0.04 0.00 n.a. n.a. 10.3 13.5 12.6 20.1 7.6 15.8 9.4 11 14.5 14.9 9 8.9 9.4 28.8 8.9 14.7 6.2 9.8 11.6 7.6 8.73 5.14 8.2 9.81 13.2 6.4 6.1 9.3 7.54 7.5 7.2 7 7.85 6.19 6.3 13.1 10 6.4 6 1989 1986 1979 1986 1992 1970 1979 1993 1989 1989 1994 1995 1992 1989 1989 1989 1995 1995 1975 1993 1994 1995 1993 1994 1988 1994 1981 1995 1994 1991 1993 1995 1995 1995 1999 1998 1993 1979 1972 0.448 0.262 0.751 3.660 0.426 2.109 0.524 0.562 0.787 1.674 0.605 0.501 0.579 1.621 0.106 1.451 0.126 0.553 1.095 0.318 0.569 0.185 0.337 0.234 0.264 0.117 0.190 0.342 0.449 0.255 0.300 0.300 0.392 0.305 0.154 0.634 0.000 0.567 0.330 0.542 0.406 1.056 7.593 0.496 3.550 0.657 0.668 1.044 2.193 0.736 0.588 0.689 2.268 0.108 1.903 0.149 0.693 1.483 0.368 0.658 0.197 0.374 0.266 0.333 0.127 0.229 0.405 0.541 0.314 0.331 0.347 0.480 0.344 0.171 0.724 0.000 0.664 0.293 0.24 0.27 0.27 0.27 0.28 0.28 0.29 0.29 0.32 0.32 0.32 0.36 0.38 0.46 0.49 0.49 0.53 0.56 0.56 0.57 0.66 0.70 0.74 0.96 0.97 1.14 1.25 1.28 1.48 1.70 1.88 2.52 2.54 7.63 9.58 14.36 n.a. n.a. n.a. CENTRE FOR ECONOMIC PERFORMANCE Recent Discussion Papers 1101 Alan Manning Barbara Petrongolo How Local Are Labour Markets? Evidence from a Spatial Job Search Model 1100 Fabrice Defever Benedikt Heid Mario Larch Spatial Exporters 1099 John T. Addison Alex Bryson André Pahnke Paulino Teixeira Change and Persistence in the German Model of Collective Bargaining and Worker Representation 1098 Joan Costa-Font Mireia Jofre-Bonet Anorexia, Body Image and Peer Effects: Evidence from a Sample of European Women 1097 Michal White Alex Bryson HRM and Workplace Motivation: Incremental and Threshold Effects 1096 Dominique Goux Eric Maurin Barbara Petrongolo Worktime Regulations and Spousal Labor Supply 1095 Petri Böckerman Alex Bryson Pekka Ilmakunnas Does High Involvement Management Improve Worker Wellbeing? 1094 Olivier Marie Judit Vall Castello Measuring the (Income) Effect of Disability Insurance Generosity on Labour Market Participation 1093 Claudia Olivetti Barbara Petrongolo Gender Gaps Across Countries and Skills: Supply, Demand and the Industry Structure 1092 Guy Mayraz Wishful Thinking 1091 Francesco Caselli Andrea Tesei Resource Windfalls, Political Regimes, and Political Stability 1090 Keyu Jin Nan Li Factor Proportions and International Business Cycles 1089 Yu-Hsiang Lei Guy Michaels Do Giant Oilfield Discoveries Fuel Internal Armed Conflicts? 1088 Brian Bell John Van Reenen Firm Performance and Wages: Evidence from Across the Corporate Hierarchy 1087 Amparo Castelló-Climent Ana Hidalgo-Cabrillana The Role of Educational Quality and Quantity in the Process of Economic Development 1086 Amparo Castelló-Climent Abhiroop Mukhopadhyay Mass Education or a Minority Well Educated Elite in the Process of Development: the Case of India 1085 Holger Breinlich Heterogeneous Firm-Level Responses to Trade Liberalisation: A Test Using Stock Price Reactions 1084 Andrew B. Bernard J. Bradford Jensen Stephen J. Redding Peter K. Schott The Empirics of Firm Heterogeneity and International Trade 1083 Elisa Faraglia Albert Marcet Andrew Scott In Search of a Theory of Debt Management 1082 Holger Breinlich Alejandro Cuñat A Many-Country Model of Industrialization 1081 Francesca Cornaglia Naomi E. Feldman Productivity, Wages and Marriage: The Case of Major League Baseball 1080 Nicholas Oulton The Wealth and Poverty of Nations: True PPPs for 141 Countries 1079 Gary S. Becker Yona Rubinstein Fear and the Response to Terrorism: An Economic Analysis 1078 Camille Landais Pascal Michaillat Emmanuel Saez Optimal Unemployment Insurance over the Business Cycle 1077 Klaus Adam Albert Marcet Juan Pablo Nicolini Stock Market Volatility and Learning 1076 Zsófia L. Bárány The Minimum Wage and Inequality - The Effects of Education and Technology 1075 Joanne Lindley Stephen Machin Rising Wage Inequality and Postgraduate Education 1074 Stephen Hansen Michael McMahon First Impressions Matter: Signalling as a Source of Policy Dynamics 1073 Ferdinand Rauch Advertising Expenditure and Consumer Prices The Centre for Economic Performance Publications Unit Tel 020 7955 7673 Fax 020 7955 7595 Email info@cep.lse.ac.uk Web site http://cep.lse.ac.uk