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Cross-country growth regressions

Cross-country growth regressions. Francesco Daveri. Outline. Numerical implications of the Solow model Pitfalls of cross-country growth regressions Conclusions. Numerical implications of the Solow model. Does the Solow model make sense?

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Cross-country growth regressions

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  1. Cross-country growth regressions Francesco Daveri

  2. Outline • Numerical implications of the Solow model • Pitfalls of cross-country growth regressions • Conclusions

  3. Numerical implications of the Solow model • Does the Solow model make sense? • One possibility is to take it seriously as it is, append a Cobb-Douglas production function and see whether its implications are consistent with the data • By doing so, three numerical puzzles arise • The baseline Solow model: • under-predicts actual cross-country income differences • over-predicts the actual convergence rate • over-predicts actual rate-of-return variation

  4. Back to basics first Production function Y=K(AL)1- y=k (in efficiency units; divided by AL) Ay= GDP per worker K accumulation dk/dt=sk - (+n+g)k (g=exog. technical change) Steady state (dk/dt=0  dy/dt=0) y*=[s/(+n+g)] /(1-) dy*/y*= [/(1-)][ds/s – d(+n+g)/(+n+g)] Now ready to discuss numerical puzzles

  5. Puzzle 1: magnitude of income differences • What’s the predicted income gap between R (rich) and P (poor) country according to the Solow model? • Assumptions • (+g) = 0.05 for both R&P • Technology = freely transferable public good • sR=0.2 sP=0.05 • R saves four times as much as P • nR=0.01 nP=0.03 • Child bearing less costly in P than in R •  = 1/3 (value added share of capital)

  6. Puzzle 1: magnitude of income differences Predicted income gap between R and P? (ARy*R)/(APy*P) = y*R/y*P = 2.3 Now take World Bank data and compute actual income difference between rich and poor countries. It’s about 10 Why such an under-estimate? Tech is NOT an international public good If AR=4AP, the puzzle disappears Or not? If tech gap is this size, huge incentives for tech transfer & imitation. What keeps AR so much different from AP?

  7. Puzzle 2: convergence rate • gy =  [sy [(-1)/] - (+n+g)] • Taylor expansion of gy=f(y) around y* • gy= gy*+ f’(y*)(y-y*) • where • gy*=0 • f’(y*)=s(-1)y*(-1/) • After some rewriting • dy/dt= (-1)(+n+g)(y-y*) = - (y-y*) •  = convergence coefficient, measure of how much of the (y-y*) gap is bridged in each period

  8. Puzzle 2: convergence rate • Numerical estimates of R and P? • R=.66  0.06 = 0.04 • P=.66  0.08 = 0.055 • Econometric estimate? • Much lower and statistically equal across countries • = 0.02 • Implications • initial conditions matter for quite a long time (35 years of half-life convergence) • They do so for much longer than implied by the Solow model

  9. Puzzle 3: rate of returns If yP<yR, then kP<kR and MPKP>MPKR With perfectly competitive capital markets, r=MPK Hence (if AP=AR and =1/3) rP / rR = (kP/kR)-1= (yR/yP)(1-)/=(yR/yP)2 With actual income gaps (=10) Implied rate of return differential between P and R is huge (=100!) With AR=4AP , it is still an unbelievable 25

  10. Three puzzles, one solution • The baseline Solow model: • under-predicts actual cross-country income differences • over-predicts the actual convergence rate • over-predicts actual rate-of-return variation • Solution • Actual  must be higher than 1/3. With =0.8, puzzles disappear

  11. Why might  be = 0.8? • Two explanations • Externalities • but their size should be substantial • and geographically localized • Human capital • A fraction of labor income rewards human capital, not raw labor • How much goes to raw labor? Minimum wage is one third of average wage, so 2/3 of labor income may go to HK • Also: solution to puzzle of lack of K flows to developing countries. No collateral on HK, borrowing constraints matter

  12. Alternative route • The Solow model as such is wanting, and needs being augmented if it has to be used to explain growth gaps between rich and poor • Barro regressions do that • Less attention of specific derivation from functional form • Long list of growth determinants to be tested against data

  13. Barro regressions: basics • Many countries (100 or so) • One period of time (e.g. averaged data through 1960-85) • Regression analysis Y = a + bX + error term • Y = dependent variable • X = independent variable(s) • b = not observed, to be estimated from data set. Estimate of b tells us how large Y in response to X. • If many Xs, each b (say b1) gives us effect of X1 on Y, while holding X2, X3, .. constant

  14. Barro regressions: Ys and Xs • Y = Avg. growth rate of per capita or per worker GDP • X = bunch of variables: (predicted sign of b in parentheses) • Initial level of p.c. GDP (-). Captures ‘convergence effect’. • Fertility rate (-). Captures ‘population effect’ • Gov’t consumption (-), fin’l development (+). Capture ‘saving effect’. • Level of education (years of schooling, +) and health (infant mortality,-). Political instability (#coups, -). Rule of law (+), market distortions (-). Capture ‘efficiency effects’.

  15. Findings from Barro regressions Variables listed above: all ‘statistically significant’ (bs precisely estimated, i.e. their size can be trusted) Overall goodness of fit of such regressions quite remarkable: about 75% of total cross-sectional variability of growth rates explained by a few variables Remark. This is striking: in spite of huge cultural, religious, ethnic differences, simple cross-country regression does a good job explaining growth gaps

  16. Pitfalls in Barro regressions • Cross-country growth regressions became popular. An appealing way to learn about quantitative aspects of growth. Less popular among hard-nosed econometricians. Why? Five main reasons • Lack of robustness • Endogeneity of explanatory variables. • Sampling issue • Averaging = wasting valuable info? • Cross-country growth regressions are in “reduced form”. What do we really learn? • Durlauf, Johnson and Temple (Handbook of Economic Growth, sect.III, 2005): issue review

  17. Lack of robustness Size & significance of estimated bs varies depending on variables included in the regression. Few exceptions: e.g. convergence coefficient=0.02. Its statistical significance says that the gain from being initially poor, holding other things constant, is there; its small size says that this effect is small Levine and Renelt (AER, 1992): very negative conclusions

  18. Endogeneity of explanatory variables • Or: Why is Y ‘Y’ and not ‘X’ ? • Or: What comes first, chicken or egg? • Examples are many • Economic instability and growth • Savings ands growth • Human capital and growth • You name them

  19. Sampling Lumping countries such as Ghana and the U.S. together in the same sample: NOT the most obvious thing to do. ‘Sampling’ implies drawing from underlying population

  20. Averaging = wasting valuable information? Why not use available yearly data ? Potential waste of info ? Some variables (e.g. human capital) not measured or mis-measured at yearly frequencies Growth theory vague about precise timing of effects at high frequencies

  21. What do we learn from reduced forms? Cross-country growth regressions are meant to be in reduced form. In other words, estimates of b do not bear ‘behavioral’ interpretation If neoclassical growth model to be tested for, learning about size of those bs is not enough Unless link between underlying theory and estimated coefficient is made clear Example: political instability may negatively affect growth, but how? By discouraging foreign investment or technical change or what else?

  22. An alternative: Testing growth theories with time series data Less popular strand of research Study time series properties of Ys and contrast with time series properties of Xs They should be consistent if Xs determine Ys

  23. Findings with US time series data Jones (1995): Long-run (1880-1987) US data shows that per-capita GDP growth is CONSTANT, while growth determinants (implied by growth theory; such as Investment / GDP; # scientists & engineers / labor force; R&D spending; human capital; population growth; tax rates and Gov’t size) are NOT CONSTANT Conclusion: Link between (alleged) growth determinants and growth is at most temporary  Solow is right, EG is wrong

  24. Findings with OECD time series data • So much for the US. How about other countries ? • Jones’ evidence for other OECD countries is mixed • Contentious issue: How to treat World Wars • If war years taken out, downward trend in growth rates is there for postwar years in most OECD countries (until 1987) • Evidence for LDCs: not there (too short time series)

  25. Evaluating applied growth findings Applied growth: pick simple theories of complicated facts, and go ahead confronting them with data Cross-sectional evidence: impressive explanatory power, seriously unresolved methodological issues. Still, bunch of partial correlation detected, somehow unexpectedly Time series evidence: speaks against EG. But perhaps EG theory deserves one more chance In any case, given estimated slow pace of convergence and relatively short span of available data, distinguishing empirically Solow and EG may prove hard task

  26. Mankiw’s take on What we learn from growth regressions http://gregmankiw.blogspot.com/2007/02/growth-regressions-and-policy-advising.html

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