## Abstract

We estimate a panel model where the relationship between inequality and GDP per capita growth depends on countries’ initial incomes. Estimates of the model show that the relationship between inequality and GDP per capita growth is significantly decreasing in countries’ initial incomes. Results from instrumental variables regressions show that in Low Income Countries transitional growth is boosted by greater income inequality. In High Income Countries inequality has a significant negative effect on transitional growth. For the median country in the world, that in the year 2015 had a PPP GDP per capita of around 10000USD, IV estimates predict that a 1 percentage point increase in the Gini coefficient decreases GDP per capita growth over a 5-year period by over 1 percentage point; the long-run effect on the level of GDP per capita is around − 5%.

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## Notes

- 1.
See Hausman et al. (1987) for econometric theory for identifying simultaneous equation models with zero covariance restrictions.

- 2.
For a review of mechanism through which inequality may affect growth, see Galor (2011).

- 3.
The long-run effect is calculated as 0.0036/0.076 = 0.047 (see column (1) of Table 3 in Forbes). The relevant equation is lny

_{t}= γlny_{t-1}+ βInequality_{t-1}; see Eq. (2) in Forbes where control variables have been left out to simplify. The equation can be rewritten as Δlny_{t}= κlny_{t-1}+ βInequality_{t-1}, where κ = (γ − 1). Because |γ| < 1, a permanent increase in inequality has a permanent effect on the level of GDP per capita. This follows from solving the first-order difference equation and differentiating with respect to inequality, i.e. ∂ln(y)/∂Inequality = β/(1 − γ) = β/−κ. - 4.
Brueckner et al.'s (2015) primary data source is the UN-WIDER World Income Inequality Database. The authors filtered the data to drop low-quality observations. The data were supplemented with data from the World Bank’s POVCALNET database for developing countries. To ensure comparability between the two data sources, Brueckner et al. made adjustments to the data sets for individual countries so that the income shares consistently correspond to those of a consumption (or income) survey. The authors then identified and dropped duplicates; eliminated duplicate survey-years with inferior quality data from the WIID; eliminated survey-years for which no extra information (consumption/income; etc.) is available as well as survey-years for which the income shares add up to less than 99 or more than 101 percent. The authors then aggregated the inequality data to the 5-year level by taking a simple average of the observed annual observations over five years. In the regression analysis countries are only included for which inequality data are available for at least two or more consecutive 5-year intervals.

- 5.
One can show this by noting that least squares estimation of

*a*yields a^{LS}= cov(X,Y)/Var(Y) = a + cov(u,Y)/Var(Y) = a + (1 − ab)^{−1}bVar(u)/Var(Y) = a +bias_{1}≠ a where bias_{1}= (1 − ab)^{−1}bVar(u)/Var(Y). It follows that u^{LS}= X − a^{LS}Y = X−(a + (1 − ab)^{−1}bVar(u)/Var(Y))Y = u−((1 − ab)^{−1}bVar(u)/Var(Y))Y = u-bias_{1}*Y. IV estimation that uses u^{LS}as an instrument for X in Eq. (1) yields b^{IV1}= cov(u^{LS},Y)/cov(u^{LS}, X) = 0. This follows from noting that cov(u^{LS},Y) = cov(u − bias_{1}*Y,Y) = cov(u,Y) − bias_{1}*Var(Y) = cov(u, Y) − [(1 − ab)^{−1}bVar(u)/Var(Y)]*Var(Y) = cov(u,Y) − (1 − ab)^{−1}bVar(u) = cov(u, (1 − ab)^{−1}(bu + e)) − (1 − ab)^{−1}bVar(u) = (1 − ab)^{−1}bVar(u) − (1 − ab)^{−1}bVar(u) = 0. - 6.
- 7.
We performed the panel unit root test by Maddala and Wu (1999) and were able to reject the null hypothesis of a unit root in the level of log GDP per capita at the 1 percent significance level; both for a model with trend and for a model with drift.

- 8.
Figure S1 in the online appendix plots the bivariate relationship between inequality and residual inequality for the different Ginis used in the estimates shown in Table 1.

- 9.
As noted in Bazzi and Clemens (2013) the Stock and Yogo tabulations were developed in a pure cross-sectional context and some caution is warranted when applying them to the panel context.

- 10.
First-differencing eliminates information contained in the level of the series; first differencing also implies that the country fixed effects drop out.

- 11.
For the subsequent analysis the sample is restricted to the 1970–2010 period; i.e. GDP per capita in 1970 is the average income at the beginning of the sample period.

- 12.
GDP per capita in 1970 does not show up in Table S7 because the variable is perfectly collinear with the country fixed effects.

- 13.
The cumulative effect is calculated as the sum of coefficients on period t and t-1

*inequality*and*inequality*ln(y*_{1970}*).*For a country with income of 5000USD in 1970, a value of 8.5 needs to be plugged in for*ln(y*_{1970}*)*. - 14.
In the Galor and Zeira model there are: (1) fixed costs to human capital accumulation; (2) financial market imperfections. The financial market imperfections arise because of moral hazard, i.e. borrowers can default [see Brueckner et al. (2010) for some empirical evidence that supports the importance of moral hazard in credit markets]. A positive risk of default means that the lending rate exceeds the deposit rate. Due to the interest rate spread, only children of sufficiently rich parents accumulate human capital. In economies where average income is high, a reduction in inequality (such that rich families are made poorer but can still pay the cost of education) makes some of the relatively poorer families (that before redistribution were unable to pay the cost of education) send their children to university. This implies that the share of population ages 15 and above with tertiary education increases when inequality decreases. In economies where average income is low, a decrease in inequality (such that poor families are made richer but still cannot pay the cost of education) prevents some of the relatively richer families (that before redistribution were able to pay the cost of education) to send their children to university. This implies that the share of population ages 15 and above with tertiary education decreases when inequality decreases. Hence, inequality and education are positively related in poor countries but negatively related in rich countries. The same holds for the relationship between inequality and GDP per capita since in the Galor and Zeira model human capital has a positive effect on aggregate output. Evidence that education has a significant positive effect on GDP per capita in both rich and poor countries is provided, for example, in Barro (2013). Galor (2011) find that in the United States during 1880–1940 land inequality had a significant negative effect on educational expenditures.

- 15.
Brueckner et al. (2015) document that national income—through its effect on human capital—has a negative impact on inequality.

- 16.
In the online appendix we document robustness to including in the model additional control variables (Table S9); restricting the sample to the 1970–2010 period and using as initial income the GDP per capita of countries in 1970 (Table S10); using alternative measures of human capital such as average years of schooling of the population and the share of population with secondary education (Table S11); including in the model current and lagged inequality as well as interactions of those variables with initial income (Table S12).

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We are grateful to three anonymous referees and the associate editor for thoughtful comments that significantly improved the paper. The findings, interpretations, and conclusions of this paper do not necessarily reflect the views of the World Bank, the Executive Directors of the World Bank or the governments they represent.

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## Appendix

### Appendix

See Table 11.

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Brueckner, M., Lederman, D. Inequality and economic growth: the role of initial income.
*J Econ Growth* **23, **341–366 (2018). https://doi.org/10.1007/s10887-018-9156-4

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### Keywords

- Economic growth
- Income inequality
- Human capital

### JEL Codes

- O1