Technological Change, Technological Catch-up, And Capital Deepening

Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence During 90’s ∗ Oleg Badunenko† and Valentin Zelenyuk‡ October, 2004

Abstract In this paper we investigate three sources of economic growth and evolution of world income distribution during the 90’s: (i) technological change, (ii) efficiency change (the catching-up) and (iii) capital deepening. Our research is an extension to recent study of Kumar and Russell (2002), which we complement in two ways: we considering a more recent period (the 90’s instead of 1965-90) and, as a result, we include data on transitional economies. In contrast to study by Kumar and Russell (2002), which concluded that the capital deepening was the major force of growth and of changing the world income distribution over 1965-1990, our analysis shows that, during the 90’s, this major force was technological change, whereas capital accumulation played the minor role.

JEL Classification: O47, P27, P52. Keywords: Economic Growth, TFP, Transition.

∗ Authors would like to thank Daniel Henderson, and participants of seminars at the Davis Center at Harvard University, Economics Department of Central European University (CEU), Round Table on Economic Growth (Kiev, Ukraine), and a workshop at German Institute for Economic Research (DIW Berlin) for their valuable comments. † European University Viadrina, Frankfurt Oder and German Institute for Economic Research (DIW Berlin), Germany. E-Mail: [email protected]. ‡ Institut de Statistique Universit´e Catholique de Louvain, Louvain, Belgium. E-mail: [email protected].

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Introduction Our note is inspired by the recent study of Kumar and Russell (2002) that has built a bridge between the two streams of literature: macroeconomic convergence and technology frontier estimation. One of the main conclusions of their study was that: “It is primarily capital deepening, as opposed to technological catch-up, that has contributed the most to both growth and bipolar international divergence of economies”1 . Indeed, during the period they studied, 1965 to 1990, fast growing countries, as for example Asian Tigers, have undergone heavy capital accumulation (e.g., see Mankiw et al., 1992). Noteworthy, the effect of computers on economic growth during that time was found to be negligible, but quite considerable during the 90’s (e.g., see Brynjolfsson and Hitt, 2000). In this paper, we investigate the same sources of labor productivity growth and evolution of world income per worker2 distribution as in Kumar and Russell (2002), using their methodology, but now with data for 90’s. First of all, as in Kumar and Russell (hereafter K&R), we identified further (unconditional β-type) divergence in GDP per worker among countries—in the sense that the richer the countries the greater was the growth. We also find evidence for ‘Twin-Peak’ phenomenon in world income per worker distribution (earlier noticed and justified by Quah, 1996), with further divergence between the two peaks representing the ‘club of rich’ and the ‘club of poor’. Second, most importantly and opposite to period of 1965-90, we found that the technological change was the largest driving force of growth and of changing the distribution of income per worker in the world, causing further divergence. Both the poor and the rich countries have benefited from the technological change, but the richer the country the more was the benefit—again suggesting about the divergence, now driven by the technological change. Finally, the capital accumulation 1 Henderson and Russell (2004) have applied similar methodology as K&R to similar data but with human capital and found that part of the effect identified by K&R is in fact due to human capital accumulation. Lacking the human capital data for our study, we follow the K&R approach. 2 The same as K&R, we take Jones’s (1997) suggestion that GDP per worker would be most appropriate definition of welfare, and hence income, once developing countries are included into analysis.

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and efficiency change effects, on average, were a negligible source of change in the world distribution of income per worker. Our paper is structured as follows. In the next section we briefly consider the essence of methodology and data used, referring for details to K&R. The subsequent section summarizes the main results and the final section concludes.

Methodology and data For the sake of brevity of this paper we refer readers to Kumar and Russell (2002) and F¨are et al. (1994) for details of methodology, notation, related literature, etc., but mentioning here only the main issues of estimation and our main results. The key relation of our analysis is the K&R (see their eq.6, p. 535) decomposition given by:

∆y = ∆EF F × ∆T ECH × ∆CAP where ∆y =

³

Yt Lt

´ ³

/

Ys Ls

´

(1)

is the labor productivity index between periods s and t, which is

decomposed into three sources: (i) efficiency change (∆EF F ), representing the notion of ‘catching-up’ with the world ‘best practice frontier’, (ii) technological change (∆T ECH), representing the shifts of the world ‘best practice frontier’, and (iii) the capital deepening (∆CAP ), representing the movement along the frontier due to change in the level of capital per worker. The world ‘best practice frontier’ is estimated as the ‘upper’ boundary of the smallest convex free disposal cone of the observed data on inputs and outputs in each period s and t, using data envelopment analysis (DEA) estimator3 . We apply this estimator to sample of 73 countries over the period 1992-2000. One important distinctive feature of the 90’s (relative to K&R period of study) is the emergence of new transitional countries, 15 of which we have in our sample. We use series for variables pop, rgdpch, rgdpwok and 3

Kneip et al. (1998) shows consistency of the DEA estimator and derives its rate of convergence. The limiting distribution of the DEA estimator is provided by Kneip et al. (2003).

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ikon from Penn World Tables (PWT) 6.1 to retrieve data on aggregate output (Y ) and aggregate employment (L); we also apply perpetual inventory method to construct the capital stock variable (K)4 .

Results Upon making appropriate computations5 , we observe that Luxembourg, United Kingdom and United States appeared on the “best-practice” frontier in 1992 and Argentina, Ireland, Luxembourg and United Kingdom were on the frontier of 2000 (United States’ efficiency score being 0.99 in 2000). The results of estimation of components of conceptual decomposition are illustrated on four panels of Figure 16 , made analogously to those of K&R. Panel A suggests that relatively poorer countries have grown slower than relatively richer ones. This endorses previous findings on divergence of economies in the world (e.g. DeLong, 1988, Quah, 1996, Kumar and Russell, 2002, etc). According to Panel B, the efficiency has collapsed in the majority of countries. This can be explained by at least two major reasons. Firstly, many transitional countries in the sample have experienced sudden decrease in their total output while stocks of inputs did not drop as much (e.g., Azerbaijan, Belarus, Bulgaria, Czech Rep., Poland, Romania, Slovenia). Theoretical explanation for this can be given via, for example, the disorganization argument of Blanchard and Kremer (1997). Some transitional countries (China, Estonia, Kazakhstan, Kyrgyzstan, Russia and Ukraine), however, have experienced positive efficinecy change or ‘catching-up’ impact, but mainly due to a low efficiency level in the base period. Secondly, some countries have moved the technological frontier so fast that even most devloped 4

For constructing K we used PWT methodology (Summers and Heston, 1991). Only those countries, for which all the data for Y , L, and K were available, were included into our sample. 5 Results may be found in Table 2, in Appendix. 6 Bold lines on four panels of Figure 1 are OLS fitted lines with Huber/White/Sandwich estimators of variance used (slope coefficients on panels A and C are significant at 0.1%, and 8% levels of significance respectively; slope coefficients on panel B and D are insignificant; see Table 3 in Appendix for details).

BADUNENKO AND ZELENYUK

10000 20000 30000 40000 50000 60000 70000

0

10000 20000 30000 40000 50000 60000 70000

Panel (C)

Panel (D)

Output per Worker in 1992

−75 −50 −25 0

Percentage Change in Capital Accumulation Index

40 20 0

10000 20000 30000 40000 50000 60000 70000

25 50 75 100 125

Output per Worker in 1992

60

Output per Worker in 1992

−20

Percentage Change in Technology Index

0

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Percentage Change in Efficiency Index

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Percentage Change in Output per Worker

0

20 40 60 80 100

Panel (B)

75

Panel (A)

5

0

10000 20000 30000 40000 50000 60000 70000

Output per Worker in 1992

Note: Each panel contains a GLS regression line. Figure 1: Percentage Changes between 1992 and 2000 in Output per Worker and three Decomposition Indexes, plotted against 1992 Output per Worker.

countries (except Denmark, Finland, Ireland and Norway) were not able to catch-up with it to maintain their 1992-efficiency level. This finding goes hand in hand with general purpose technology argument, emphasizing that it takes time before newly implemented technology can be utilised 100% efficiently (Helpman and Rangel, 1999). Estimated positive slope here suggests that, on average, relatively richer countries benefited slightly more (or rather lost less) from efficiency change than relatively poorer countries, i.e., the richer the country the better its catch-up (or the smaller its lagging-behind); the estimate however is not statistically significant from zero.

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Table 1: Distribution Hypotheses Tests.

H0 : Distributions are equal Value of HA : Distributions are not equal statistic f (y1992) vs. g(y2000) 1.3160 E f (y1992) vs. f (y1992 · ∆EF F ) 0.0554 f (y1992) vs. f T (y1992 · ∆T ECH) 1.8737 f (y1992) vs. f C (y1992 · ∆CAP ) 0.0107 CT f (y1992) vs. f (y1992 · ∆CAP · ∆T ECH) 2.2904 f (y1992) vs. f ET (y1992 · ∆EF F · ∆T ECH) 1.0735 f (y1992) vs. f EC (y1992 · ∆EF F · ∆CAP ) 0.0394

Bootstrap p-value 0.0554 0.9358 0.0268 0.9886 0.0140 0.0896 0.9560

Conclusion of the test Reject at 10% Do not reject Reject at 5% Do not reject Reject at 5% Reject at 10% Do not reject

Notes: f (·) and g(·) are density functions for distributions of income per worker in 1992 and 2000, respectively. f E , f T , f C , f CT , f ET and f EC are densities for the counterfactual distributions obtained by adjusting the 1992 data for the effects of, respectively, efficiency changes, technological change, capital deepening, both capital deepening and technological change, both efficiency changes and technological change, and, finally, both efficiency changes and capital deepening.

Panel C suggests that technological change have contributed to productivity growth positively in most of the countries. Moreover, relatively richer countries have benefited from this technological change more than relatively poorer countries—as indicated by the positive and significant coefficient. Most remarkably, the impact of technological change was the largest among the three components of the decomposition. Panel D reveals that the capital deepening impact on labor productivity was negligible for all countries with some exceptions (e.g., Brazil, China). Notably, the last two results are very different from those obtained for 1965-1990 period by Kumar and Russell (2002). We now consider the world income per worker distributions, a l´a K&R, by using the kernel density estimator to visualize estimated densities of ‘actual’ and ‘counterfactual’ income (per worker) distributions (Figure 2) and by applying the Li (1996) test for equality of density functions (Table 1).7 First thing to note is that the bi-modal or the “Twin-Peak” distribution of income (per 7

In all cases we used Gaussian kernel. For computation of the optimal bandwidth, we used the Sheather and Jones (1991) method in case of density estimation, while in the bootstrap for the Li (1996) test we used Silverman (1986) adaptive (robust) rule of thumb (for computational reasons).

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.00001

.00002

y_1992 * TECH

60000

90000

115000

0

30000

60000

Output per Worker

Panel (C)

Panel (D) .00003

Output per Worker

115000

y_2000

.00002

y_1992 * TECH * EFF * CAP

0

0

.00001

.00002

y_1992 * TECH * EFF

Kernel Distribution

y_2000

90000

.00001

30000

.00003

0

Kernel Distribution

y_2000

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.00001

.00002

y_1992

Kernel Distribution

y_2000

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Kernel Distribution

.00003

Panel (B)

.00003

Panel (A)

7

0

30000

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Output per Worker

90000

115000

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30000

60000

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115000

Output per Worker

Note: In each panel solid vertical line represents sample mean value of output per worker for 2000; dashed lines represent corresponding counterfactual sample means. Figure 2: Counterfactual Distributions of Output per Worker.

worker) in the world, which theoretically was explained by Quah (1996) and empirically identified by a number of studies including K&R, has persisted through the end of XX century. Most remarkably, the major source of further divergence in the two modes was no longer the capital accumulation, as in period studied by K&R, but the technological change. This is inferred from comparing panel B of Figure 2, (which gives the counterfactual distribution of variable y1992 · ∆T ECH, thus isolating the effect of technological change) to other panels. One can see that the technological change effect alone has constituted the most of the shift of y1992 distribution towards that of y2000 —causing statistically significant change at less than 5% level, according to the bootstrap p-value of the Li test

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(Table 1). None of the two other effects alone has contributed to a (statistically) significant change in the distribution over the 8 years, according to the Li test (or to just visual inspection). Moreover, efficiency change and capital change even when taken together also did not introduce statistically significant change over this period. Interestingly, capital change taken together with the technological change have slightly improved significance of the difference to almost 1% level, while efficiency change taken together with the technological change yielded smaller significance (about 9%) than when the technological change was considered alone. This again suggests that efficiency change has mostly contributed to regress rather than progress in the world income per worker distribution. Finally, both figures (1 and 2) give evidence that the divergence of growth rates in labor productivity between the rich and the poor countries has persisted during 90’s. Figure 2.A, for example illustrates that the right (smaller) mode of the estimated density of income per worker distribution in the world (i.e., the mode of the ‘club of rich’), have shifted further to the right over 8 years, while the left mode (for the ‘club of poor’) has virtually remained the same. Also recall that the positive and significant slope on Figure 1.A also supported the hypothesis that, on average, the richer the country the higher was the rate of growth of income (per worker). One may wonder that the reason our results for 90’s are radically different from those for 1965-90 of K&R might be because our sample also includes transitional countries (some of which did not even exist before 1991). So did we—and thus have checked for this by performing same analysis for updated K&R sample of countries for 1992-20008 —and found that our conclusions are qualitatively the same (and also statistically significant) as those obtained when the transitional countries were in the sample.

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Six countries were dropped from K&R sample since data were not available for them. Tables and Figures for this sample are available from authors as Supplement 2, upon request.

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Conclusions The approach originally employed by Kumar and Russell (2002) enables decomposing the growth of labor productivity into efficiency change, technological change and capital deepening. In this comment we have extended the Kumar and Russell (2002) study to cover the period of 90’s. We have identified further (unconditional β–type) divergence in income per worker in the world—in the sense that the richer the countries the greater the growth, on average. The distribution of income per worker persisted to be bi-modal, with evidence for further divergence between the ‘club or rich’ and the ‘club of poor’. Most remarkably, we discovered that during the 90’s it was the technological change and not the capital deepening (as it was during K&R study for 1965-1990) that constituted the major (significant) source of change in income per worker distribution in the world, towards further divergence. Moreover, the capital deepening and the efficiency change (catching-up) effects on the income per worker (or labor productivity) were negligible for causing such changes. Overall, these results have shed additional light onto the World development during the era of 90’s—the time of major structural changes in the world—shaped by the collapse of the Soviet empire in one part of the globe and the High-Tech boom in other parts.

References [1] Blanchard, Oliver and Michael Kremer. “Disorganization.” The Quarterly Journal of Economics, November 1997, volume 112, issue 4, pp. 1091-1126.

[2] Brynjolfsson, Erik and Lorin M. Hitt. “Beyond Computation: Information Technology, Organizational Transformation and Business Performance.” Journal of Economic Perspectives, 2000, vol. 14, issue 4, pp. 23-48

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[3] DeLong, J. Bradford. “Productivity Growth, Convergence, and Welfare: Comment.” The American Economic Review, Volume 78, Issue 5, December 1988, pp. 1138-1154. [4] F¨are, Rolf; Shawna Grosskopf; Marry Norris; and Zhongyang Zhang. “Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries.” The American Economic Review, March 1994, 84(1), pp. 63-83. [5] Henderson, Daniel J. and R. Robert Russell. “Human Capital and Convergence: A Production-Frontier Approach.” International Economic Review, forthcoming. [6] Helpman, Elhanan and Antonio Rangel. “Adjusting to a new technology: experience and training.” Journal of Economic Growth, December 1999, 4(4), pp. 359-383. [7] Jones, Charles. “On the evolution of world income distribution.” The Journal of Economic Prospective, Summer 1997, volume 11, issue 3, pp. 19-36. [8] Kumar, Subodh and R. Robert Russell. “Technological Change, Technological Catchup, and Capital Deepening: Relative contributions to Growth and Convergence.” The American Economic Review, June 2002, Vol. 92, No. 3, pp. 527-548 [9] Kneip, Alois; Byeong U Park; and Leopold Simar. “A Note on the Convergence of Nonparametric DEA Estimators for Production Efficiency Scores”, Econometric Theory, 1998, 14, 783-793. [10] Kneip, Alois; Leopold Simar; and Paul Wilson. “Asymptotics for DEA Estimators in Non-parametric Frontier Models”, Discussion Paper #0317, 2003, Institut de Statistique, Universit´e Catholique de Louvain, Belgium. [11] Li, Qi. “Nonparametric Testing of Closeness between Two Unknown Distribution Functions,” Econometric Reviews, 1996, 15, 261-274.

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[12] Mankiw, N. Gregory; David Romer; and David N. Weil. “A Contribution to the Empirics of Economic Growth.” Quarterly Journal of Economics, Volume 107, issue 2, May 1992, pp. 407-437. [13] Quah, Danny. “Twean Peaks: Growth and Convergence in Models of Distribution Dynamics.” The Economic Journal, July 1996, 106 (437), pp. 1045-55. [14] Sheather, Simon J. and Michael C. Jones, “A reliable Data Based Bandwidth Selection Method for Kernel Density Estimation.” Journal of Royal Statistical Society, Series B, 1991, Vol.53, 683-690. [15] Silverman, Bernard W. Density Estimation for Statistics and Data Analysis, Chapman and Hall, London, 1986. [16] Summers, Robert and Alan Heston. “The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950–1988.” Quarterly Journal of Economics, May 1991, volume 106, issue 2, pp. 327–68.

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Appendix Table 2: Percentage Change of Tripartite Decomposition Indexes, 1992-2000 Contribution to percentage change in output per worker of: Country Argentina Armenia Australia Austria Azerbaijan Belarus Belgium Brazil Bulgaria Canada Chile China Colombia Costa Rica Czech Republic Denmark Dominican Republic Ecuador Estonia Finland France Germany Greece Guatemala Hong Kong Hungary Iceland India Indonesia Ireland Israel Italy Jamaica Japan Kazakhstan Kenya Korea, Republic of Kyrgyzstan Lithuania Luxembourg

TE1 0.78 0.09 0.79 0.76 0.09 0.22 0.77 0.75 0.25 0.79 0.28 0.18 0.18 0.21 0.41 0.72 0.19 0.19 0.23 0.67 0.80 0.78 0.46 0.29 0.73 0.32 0.55 0.12 0.12 0.98 0.70 0.72 0.14 0.53 0.21 0.07 0.40 0.27 0.38 1.00

TE2 1.00 0.08 0.79 0.70 0.06 0.16 0.68 0.85 0.18 0.80 0.24 0.19 0.12 0.18 0.35 0.74 0.25 0.11 0.26 0.73 0.73 0.71 0.34 0.29 0.76 0.28 0.44 0.09 0.09 1.00 0.66 0.52 0.11 0.38 0.23 0.05 0.36 0.38 0.35 1.00

∆y 9.36 16.31 22.64 16.39 -0.07 6.00 16.47 15.88 -12.06 23.81 31.75 69.56 -6.62 7.81 7.75 28.70 55.50 -13.62 40.08 34.46 12.14 11.17 13.14 5.82 29.33 36.96 21.86 9.98 9.98 71.40 15.84 10.62 -5.64 7.06 29.43 -4.86 36.51 -4.83 2.87 52.22

∆EF F 29.00 -4.65 0.00 -7.75 -34.34 -30.28 -12.16 14.53 -29.42 0.80 -13.38 6.17 -34.09 -12.34 -14.18 2.22 26.60 -43.23 14.17 8.76 -8.76 -9.22 -25.94 -3.14 3.79 -12.50 -20.09 -27.75 -27.75 2.00 -5.30 -27.23 -22.81 -29.70 7.06 -21.53 -10.36 41.83 -8.10 0.00

∆T ECH -13.87 23.39 22.08 24.49 52.19 52.18 28.19 -13.38 23.08 22.39 49.97 -13.19 45.66 27.95 23.41 23.52 22.23 52.24 22.21 22.57 22.36 22.10 52.57 6.15 23.00 29.94 42.96 52.17 52.27 7.13 22.08 51.69 22.74 52.20 22.91 3.14 52.18 -13.59 -7.84 39.81

∆CAP -1.57 -1.14 0.46 1.34 0.01 -0.10 3.43 16.82 1.23 0.36 1.42 83.99 -2.73 -3.88 1.74 1.93 0.49 -0.04 0.40 0.87 0.45 0.29 0.12 2.92 1.31 20.45 6.67 0.04 -0.03 56.85 0.20 0.20 -0.40 0.05 -1.64 17.54 0.07 -22.34 21.46 8.88

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Table 2: Percentage Change of Tripartite Decomposition Indexes, 1992-2000, Continued Contribution to percentage change in output per worker of: Country Madagascar Malaysia Mauritius Mexico Morocco Netherlands New Zealand Nigeria Norway Paraguay Peru Philippines Poland Portugal Romania Russia Sierra Leone Singapore Slovak Republic Slovenia Spain Sri Lanka Sweden Switzerland Syria Thailand Ukraine United Kingdom Uruguay USA Venezuela Zambia Zimbabwe Average

TE1 0.03 0.39 0.36 0.41 0.21 0.85 0.64 0.05 0.77 0.23 0.41 0.14 0.53 0.43 0.12 0.33 0.05 0.67 0.35 0.38 0.57 0.12 0.69 0.85 0.25 0.19 0.52 1.00 0.36 1.00 0.32 0.05 0.16

TE2 0.02 0.43 0.45 0.37 0.17 0.79 0.60 0.02 0.78 0.10 0.43 0.13 0.37 0.34 0.08 0.34 0.03 0.78 0.34 0.32 0.43 0.12 0.67 0.72 0.24 0.19 0.88 1.00 0.32 0.99 0.19 0.03 0.31

∆y -3.81 33.67 55.93 12.86 2.96 15.38 18.26 -28.66 26.57 -34.31 4.27 11.49 53.71 20.54 4.55 -9.47 -18.79 43.92 22.78 39.35 13.83 18.09 19.80 4.18 15.35 22.93 -44.30 22.98 10.61 21.16 -17.21 -10.16 -5.20 12.68

∆EF F -25.99 11.64 26.24 -8.21 -15.68 -6.35 -5.42 -54.21 0.78 -56.88 4.76 -8.72 -29.63 -21.02 -31.28 4.83 -32.98 17.19 -2.40 -14.79 -25.21 -3.94 -3.36 -14.49 -5.46 1.35 69.03 0.00 -9.42 -0.99 -40.04 -32.86 98.12 -9.91

∆T ECH 26.99 18.67 22.68 22.37 22.12 22.61 19.28 12.54 23.56 52.29 -13.72 22.15 -1.46 51.14 52.24 14.22 22.55 22.87 23.44 39.44 51.97 22.33 23.03 22.08 22.80 22.56 -13.61 -4.85 22.22 19.32 44.91 24.78 -13.90 21.98

∆CAP 2.35 0.89 0.68 0.48 -0.01 0.49 4.83 38.44 1.65 0.05 15.36 -0.01 121.66 0.98 -0.07 -24.39 -1.11 -0.05 1.90 17.28 0.16 0.50 0.76 -0.20 -0.64 -1.04 -61.85 29.26 -0.10 2.55 -4.72 7.23 -44.43 2.54

Table 3: Regression results regression (A) regression (B) regression (C) regression (D) constant 3.91 (0.411) -9.6 (0.125) 19.37 (0.000) -5.56 (0.315) slope 0.00047 (0.001) 0.00009 (0.593) 0.00022 (0.08) -0.00004 (0.748) Notes: p-value in parentheses; Regression (A) means regression for Panel (A) of Figure 1, etc.

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Supplement 2 Table 4: Percentage Change of Tripartite Decomposition Indexes, 1992-2000. ‘Updated’ Kumar and Russell Sample. Contribution to percentage change in output per worker of: Country Argentina Australia Austria Belgium Canada Chile Colombia Denmark Dominican Republic Ecuador Finland France Germany Greece Guatemala Hong Kong Iceland India Ireland Israel Italy Jamaica Japan Kenya Korea, Republic of Luxembourg Madagascar Malaysia Mauritius Mexico Morocco Netherlands New Zealand Nigeria Norway Paraguay Peru Philippines Portugal Sierra Leone

TE1 0.78 0.79 0.76 0.77 0.79 0.28 0.18 0.72 0.19 0.19 0.67 0.80 0.78 0.46 0.29 0.73 0.55 0.12 0.98 0.70 0.72 0.14 0.53 0.07 0.40 1.00 0.03 0.39 0.36 0.41 0.21 0.85 0.64 0.05 0.77 0.23 0.41 0.14 0.43 0.05

TE2 1.00 0.79 0.70 0.68 0.80 0.24 0.12 0.74 0.25 0.11 0.73 0.73 0.71 0.34 0.29 0.76 0.44 0.09 1.00 0.66 0.52 0.11 0.38 0.05 0.36 1.00 0.02 0.43 0.45 0.37 0.17 0.79 0.60 0.02 0.78 0.10 0.43 0.13 0.34 0.03

∆y 9.36 22.64 16.39 16.47 23.81 31.75 -6.62 28.70 55.50 -13.62 34.46 12.14 11.17 13.14 5.82 29.33 21.86 9.98 71.40 15.84 10.62 -5.64 7.06 -4.86 36.51 52.22 -3.81 33.67 55.93 12.86 2.96 15.38 18.26 -28.66 26.57 -34.31 4.27 11.49 20.54 -18.79

∆EF F 29.00 0.00 -7.75 -12.16 0.80 -13.38 -34.09 2.22 26.60 -43.23 8.76 -8.76 -9.22 -25.60 -3.14 3.79 -20.09 -27.75 2.00 -5.30 -27.23 -22.81 -29.70 -21.53 -10.36 0.00 -25.99 11.64 26.24 -8.21 -15.68 -6.35 -5.42 -54.21 0.78 -56.88 4.76 -8.72 -21.02 -32.98

∆T ECH -13.87 22.08 24.49 28.19 22.39 49.97 45.66 23.52 22.23 52.24 22.57 22.36 22.10 52.22 6.15 23.00 42.96 52.17 7.13 22.08 51.69 22.74 52.20 3.14 52.18 39.81 26.99 18.67 22.68 22.37 22.12 22.61 19.28 12.54 23.56 52.29 -13.72 22.15 51.14 22.55

∆CAP -1.57 0.46 1.34 3.43 0.36 1.42 -2.73 1.93 0.49 -0.04 0.87 0.45 0.29 -0.10 2.92 1.31 6.67 0.04 56.85 0.20 0.20 -0.40 0.05 17.54 0.07 8.88 2.35 0.89 0.68 0.48 -0.01 0.49 4.83 38.44 1.65 0.05 15.36 -0.01 0.98 -1.11

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Table 4: Percentage Change of Tripartite Decomposition Indexes, 1992-2000. ‘Updated’ Kumar and Russell Sample, Continued Contribution to percentage change in output per worker of: Country Spain Sri Lanka Sweden Switzerland Syria Thailand United Kingdom Uruguay USA Zambia Zimbabwe MEAN

TE1 0.57 0.12 0.69 0.85 0.25 0.19 1.00 0.36 1.00 0.05 0.16

TE2 0.43 0.12 0.67 0.72 0.24 0.19 1.00 0.32 0.99 0.03 0.31

∆y 13.83 18.09 19.80 4.18 15.35 22.93 22.98 10.61 21.16 -10.16 -5.20 13.06

∆EF F -25.21 -3.94 -3.36 -14.49 -5.46 1.35 0.00 -9.42 -0.99 -32.86 98.12 -11.26

∆T ECH 51.97 22.33 23.03 22.08 22.80 22.56 -4.85 22.22 19.32 24.78 -13.90 24.43

∆CAP 0.16 0.50 0.76 -0.20 -0.64 -1.04 29.26 -0.10 2.55 7.23 -44.43 2.39

Table 5: Regression results, ‘Updated’ Kumar and Russell Sample regression (A) regression (B) regression (C) regression (D) constant -0.156 (0.975) -12.01 (0.167) 20.7875 (0.000) 1.54 (0.699) slope 0.00057 (0.000) 0.00013 (0.550) 0.0001853 (0.136) 0.00006 (0.602) Notes: p-value in parentheses; Regression (A) means regression for Panel (A) of Figure 1, etc.

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10000 20000 30000 40000 50000 60000 70000

0

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Output per Worker in 1992

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Note: Each panel contains a GLS regression line. Figure 3: Percentage Changes between 1992 and 2000 in Output per Worker and three Decomposition Indexes, plotted against 1992 Output per Worker, ‘Updated’ Kumar and Russel Sample.

BADUNENKO AND ZELENYUK

.00001

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Kernel Distribution

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Note: In each panel solid vertical line represents sample mean value of output per worker for 2000; dashed lines represent corresponding counterfactual sample means. Figure 4: Counterfactual Distributions of Output per Worker, ‘Updated’ Kumar and Russell Sample.

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Table 6: Distribution Hypotheses Tests, ‘Updated’ Kumar and Russell Sample. H0 : Distributions are equal Value of HA : Distributions are not equal statistic f (y1992) vs. g(y2000) 1.5689 E f (y1992) vs. f (y1992 · ∆EF F ) 0.1148 f (y1992) vs. f T (y1992 · ∆T ECH) 2.7059 f (y1992) vs. f C (y1992 · ∆CAP ) 0.0468 f (y1992) vs. f CT (y1992 · ∆CAP · ∆T ECH) 3.5566 f (y1992) vs. f ET (y1992 · ∆EF F · ∆T ECH) 1.0690 f (y1992) vs. f EC (y1992 · ∆EF F · ∆CAP ) 0.0094

Bootstrap p-value 0.0478 0.8802 0.0132 0.9506 0.0036 0.0826 0.9918

Conclusion of the test Reject at 5% Do not reject Reject at 1% Do not reject Reject at 1% Reject at 10% Do not reject

Notes: f (·) and g(·) are density functions for distributions of income per worker in 1992 and 2000, respectively. f E , f T , f C , f CT , f ET and f EC are densities for the counterfactual distributions obtained by adjusting the 1992 data for the effects of, respectively, efficiency changes, technological change, capital deepening, both capital deepening and technological change, both efficiency changes and technological change, and, finally, both efficiency changes and capital deepening.