A Contribution to the Empirics of Economic Growth
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Why are some countries so much richer than others, and will poor countries catch up? This 1992 paper tests the classic explanation that richer countries save more and have fewer children, using data from 98 countries, 1960 to 1985. That explanation gets the direction right but the sizes come out too large on its own. Adding one missing piece -- how much a country invests in schooling -- fixes this, since together savings, population growth, and schooling explain about 80 percent of the income gap between countries. Once those three are held constant, poor countries do catch up toward their own potential, just more slowly than a simpler theory implies.
What this paper finds — and why it matters
This 1992 Quarterly Journal of Economics paper by Mankiw, Romer, and Weil tests whether Robert Solow’s (1956) neoclassical growth model, augmented to include accumulation of human as well as physical capital, can account for the enormous cross-country variation in income per capita. Using Summers-Heston national accounts data for three samples of countries (98 non-oil countries, a 75-country intermediate sample excluding low-data-quality and very small countries, and 22 OECD countries) over 1960-1985, the authors first show that the textbook Solow model (with only physical capital) gets the signs of the effects of the investment rate and population growth right and explains a majority of cross-country income variation, but implies an unrealistically high capital share of income – roughly 0.6-0.8 in the estimated regressions rather than the roughly one-third value implied by independent data on factor shares. Adding a proxy for human-capital investment (the fraction of the working-age population enrolled in secondary school) to the regression raises the explained variance to about 80 percent and brings the implied capital and human-capital shares close to their independently known values of about one-third each, without rejecting the restriction that the model’s coefficients should sum to zero. The paper further argues that the well-documented absence of unconditional convergence across countries does not contradict the Solow model, because the model predicts only “conditional convergence” – convergence toward each country’s own steady state, determined by its own saving, population growth, and human-capital investment rates – and the data show a statistically and economically significant conditional convergence at a rate, implying a roughly 35-year half-life to steady state, reasonably close to what the augmented model predicts. Finally, the paper argues that apparently puzzling patterns in international interest-rate differentials and capital flows (the Feldstein-Horioka finding that capital does not flow from high-saving to low-saving countries) do not straightforwardly contradict the model once one allows for imperfect capital markets and expropriation risk, and that direct evidence on profit rates and returns to schooling is, if anything, consistent with the Solow model’s prediction of higher returns to capital in poorer countries. The authors are careful to note that this defense of the Solow model does not make it a complete theory of growth, since it still treats saving rates, population growth, and worldwide technological change as exogenous, and that endogenous-growth models may still be needed to explain those more fundamental determinants.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. What is the paper’s central question, and what is its headline conclusion relative to the contemporaneous rise of endogenous-growth theory?
The paper asks whether the textbook Solow growth model, augmented with human capital, is consistent with the enormous international variation in living standards and with the failure of countries to converge in income, and concludes that it is: “one can explain much of the cross-country variation in income while maintaining the assumption of decreasing returns.” The authors are explicit that this is a qualified defense, not a claim that the Solow model is a complete theory of growth, since it still treats saving rates, population growth, and worldwide technological change as exogenous, and endogenous-growth models may still be the right explanation for the latter (Introduction, pp. 407-410, 421-422).
Q2. What is the textbook Solow model’s key testable prediction, and what magnitude does it imply given a capital share of about one-third?
With a Cobb-Douglas production function, exogenous saving rate, and exogenous population and technology growth, steady-state income per capita is predicted to rise with the log of the saving rate and fall with the log of the sum of population growth, technology growth, and depreciation, with both coefficients equal in magnitude to alpha/(1-alpha), where alpha is capital’s share of income (Sec. I.A, eq. 6, p. 410). Because capital’s share is roughly one-third, the model implies an elasticity of income per capita with respect to the saving rate of about +0.5 and with respect to (n+g+depreciation) of about -0.5 (p. 410).
Q3. What three country samples does the paper use, and why?
The paper uses (1) a 98-country “non-oil” sample excluding countries whose GDP mainly reflects resource extraction, (2) a 75-country “intermediate” sample that further excludes countries with poor-quality (“D”-grade) Summers-Heston data or populations under one million, and (3) a 22-country OECD sample with populations over one million, chosen for uniformly high-quality data but at the cost of discarding most cross-country variation (Sec. I.C, pp. 412-413).
Q4. In what specific sense does the textbook Solow model “fail” in Table I, even though it explains a majority of the variance?
Although the coefficients on saving and population growth have the predicted signs and are highly significant, and the regression’s adjusted R-squared reaches 0.59 for the intermediate sample, the implied value of capital’s share – backed out from the coefficient in the restricted regression – is about 0.59, far above the roughly one-third value that data on factor shares imply it should be. When the authors instead impose the theoretically correct value of one-third (a “growth-accounting” approach) rather than estimating it freely, the adjusted R-squared for the intermediate sample falls sharply from 0.59 to 0.28, showing that the textbook model’s good unconstrained fit is not, by itself, support for the model as specified (Sec. I.D, Table I, pp. 413-415).
Q5. How does adding human capital change the model’s predictions, and why does omitting it bias the coefficients on saving and population growth?
In the augmented model, output depends on physical capital, human capital, and effective labor (Y = K^alpha H^beta (AL)^(1-alpha-beta)), and steady-state income depends on the investment rates in both physical and human capital as well as on population growth (Sec. II.A, eqq. 8-11, pp. 416-418). Because higher saving or lower population growth raises the steady-state level of human capital as well as physical capital, and because human-capital investment tends to be correlated with saving and population-growth rates across countries, omitting human capital from the regression biases the estimated coefficients on saving and population growth upward in absolute value – which is exactly the anomaly found in Table I (Sec. II.A, p. 418).
Q6. How does the paper measure human-capital investment, and what do the augmented-model regressions in Table II show?
The paper constructs SCHOOL, a proxy for the human-capital investment rate, as the fraction of the eligible population (ages 12-17) enrolled in secondary school multiplied by the fraction of the working-age population that is of school age (15-19) – an admittedly imperfect measure that ignores primary and higher education and the input of teachers (Sec. II.B, pp. 418-420). Adding this variable to the regression raises the adjusted R-squared to about 0.78 for the non-oil and intermediate samples, and the restriction that the coefficients on investment, SCHOOL, and (n+g+depreciation) sum to zero is not rejected in any sample; the implied values of alpha and beta are both close to one-third and highly significant for the non-oil and intermediate samples (Sec. II.C, Table II, pp. 420-421).
Q7. What is “conditional convergence,” and how does it differ from the unconditional convergence that earlier authors had found lacking?
The Solow model predicts convergence only after controlling for the determinants of each country’s own steady state (saving, population growth, and human-capital investment) – a phenomenon the authors call “conditional convergence” – rather than convergence toward a single common income level across all countries (“unconditional convergence”). Table III reproduces the well-known finding that there is no tendency for poor countries to grow faster than rich ones in the non-oil and intermediate samples (though there is significant unconditional convergence within the more homogeneous OECD sample); but once investment and population growth are added as controls (Table IV), and then human capital as well (Table V), the coefficient on initial income becomes significantly negative in all three samples, indicating genuine conditional convergence (Sec. III.A-B, pp. 422-427).
Q8. What speed of convergence does the augmented model imply, and how does this compare with the textbook model’s prediction?
The augmented Solow model predicts a convergence parameter lambda = (n+g+depreciation)(1-alpha-beta), which – for alpha=beta=1/3 and n+g+depreciation=0.06 – implies lambda is about 0.02, so that an economy closes half the gap to its steady state in about 35 years; the textbook model without human capital (beta=0) implies a much faster lambda of about 0.04, or a half-life of about 17 years (Sec. III.A, eq. 13, p. 423). The estimated convergence rates in Table V, once human capital is controlled for, are closer to the slower, augmented-model prediction than to the textbook model’s prediction, resolving another empirical anomaly (Sec. III.B, pp. 427-428).
Q9. How does the paper address the apparent puzzle that measured international interest-rate differentials and capital flows seem inconsistent with the model’s prediction of large cross-country differences in the marginal product of capital?
The Solow model implies that low-saving, high-population-growth countries should have a higher net marginal product of capital, yet observed real interest-rate differentials appear smaller than predicted, and (per Feldstein and Horioka [1980]) capital does not flow systematically from high-saving to low-saving countries. The authors argue this is not necessarily a rejection of the model, since inferring the marginal product of capital from real interest rates on financial assets requires optimizing investors and perfect capital markets, both of which are questionable in poor countries facing financing constraints or expropriation risk; direct evidence – Sachs’s (1979) roughly constant capital-income shares combined with capital-output ratios that vary from about one in low-saving countries to about three in high-saving countries, Williams’s (1975) finding that governments nationalized about 19 percent of foreign capital between 1956 and 1972 with only about 41 percent compensation, and Psacharopoulos’s (1985) cross-country evidence that the return to an additional year of schooling is larger in poorer countries – is, if anything, consistent with the Solow model’s prediction of a higher return to capital in poor countries (Sec. IV, pp. 430-432).
Q10. What is the paper’s key identifying assumption for estimating equation (7) by ordinary least squares, and how do the authors defend it?
The regressions assume that saving and population-growth rates are independent of the country-specific shock to the level of technology; the authors defend this assumption on three grounds: it holds in any model (including Solow’s) in which saving and population growth are endogenous but preferences are isoelastic; it allows a systematic test of informal claims by Romer [1987, 1989a] and Lucas [1988] that saving and population growth have implausibly large effects on income; and because the model predicts specific magnitudes (not just signs) for the coefficients, large discrepancies from those magnitudes let the authors judge whether the identifying assumption, the model, or both, are wrong (Sec. I.B, pp. 411-412).
Q11. What four main conclusions does the paper draw about the augmented Solow model’s overall implications?
The conclusion highlights four points (pp. 432-433). First, the estimated elasticity of income with respect to physical capital is close to capital’s actual income share, indicating – in contrast to Romer’s suggestion of positive externalities to capital accumulation – that capital receives approximately its social return, with no substantial externality. Second, despite this absence of externalities, physical-capital accumulation has a larger effect on income than the textbook model implies (an elasticity of about 1, versus 0.5 in the textbook model), because higher saving also raises the steady-state level of human capital. Third, population growth similarly has a larger effect than the textbook model implies (elasticity of about -2 versus -0.5), because higher population growth spreads both physical and human capital more thinly. Fourth, the model correctly predicts that countries converge, but more slowly (roughly a 35-year half-life) than the textbook model’s 17-year prediction.
Q12. What do the authors identify as the natural next steps for growth research, given their defense of the (augmented) Solow model?
The authors argue that future research should explain why the variables the Solow model treats as exogenous – saving rates, population growth rates, and the rate of worldwide technological change – vary so much across countries, suggesting that differences in tax policy, education policy, tastes for children, and political stability are likely candidates, and explicitly note that endogenous-growth models “may provide the right explanation of worldwide technological change” even though the paper’s evidence does not support using them to explain the cross-country income variation addressed here (Conclusion, pp. 421-422, 433).
Key terms in this paper
Definitions below follow the paper's own usage.
- Textbook Solow model
- The paper's baseline model (following Solow 1956): a Cobb-Douglas production function in physical capital and labor-augmenting technology, with exogenous, constant saving, population growth, and technology-growth rates. It predicts steady-state income per capita rises with the log of the saving rate and falls with the log of the sum of population growth, technology growth, and depreciation, with coefficients pinned by capital's income share (about one-third), implying elasticities of about +0.5 and -0.5 respectively (Sec. I, eqq. 1-6).
- Augmented Solow model
- The paper's extension of the Solow model to include a second accumulable factor, human capital, with its own investment share and its own accumulation equation paralleling physical capital's. This predicts a larger, not smaller, impact of saving and population growth on income than the textbook model, because higher saving or lower population growth also raises the steady-state level of human capital (Sec. II, eqq. 8-12).
- Conditional convergence
- The Solow model's actual prediction about convergence -- that a country's income converges over time to its OWN steady state, determined by its own saving, population growth, and human-capital investment rates, not to a single common cross-country level. Unconditional convergence (no controls) is not observed in the data, but once these steady-state determinants are held constant, a statistically and economically significant convergence emerges at approximately the rate the model predicts (Sec. III.A, eqq. 13-16).
- SCHOOL (proxy for human-capital investment)
- The paper's proxy for the rate of human-capital investment, constructed as the fraction of the eligible population (ages 12-17) enrolled in secondary school multiplied by the fraction of the working-age population that is of school age (15-19); an admittedly imperfect measure that ignores teachers, primary and higher education, but one whose inclusion substantially improves the model's fit and brings implied factor shares in line with independent estimates (Sec. II.B).
- Implied factor shares as a specification check
- The paper's diagnostic of backing out the values of capital's share (alpha) and human capital's share (beta) implied by the estimated regression coefficients and comparing them to independently known factor-share values of roughly one-third each, used throughout the paper as a check on whether a regression's high explanatory power (R-squared) reflects a correctly specified model rather than a coincidentally good fit (Sec. I.D, II.C).