Appendix A: Various samples of redistribution

Name Description Observations Mean SD Min Max Baseline All available data in Solt (2009) as long as either (1) the country has at least one observation based on a net and one based on a market inequality measure; or (2) the ratio of the difference between market and net inequality to the associated standard error is greater than 1.96, but excluding transition countries and a set of specific observations handpicked for deletion by Solt (2009) 3667 7.5 7.2 \(-\) 14.2 30.3 Full Full sample of all available data in Solt (2009) 4396 6.9 6.9 \(-\) 14.2 30.4 Restricted All available data in Solt (2009) as long as the country has at least three observations based on net and three based on market inequality measures, but excluding transition countries, all developing countries prior to 1985, all developed countries prior to 1975, and a set of specific observations handpicked for deletion by Solt (2009) 2158 7.7 7.3 \(-\) 11.9 30.3 Very restricted All available data in Solt (2009) where country-year observation from the actual survey was available 997 14.3 5.7 2.5 30.3 OECD (1975) Subsample of the baseline for OECD countries who became members prior to 1975; total of 24 countries 806 9.1 7.3 \(-\) 11.9 30.3

Appendix B: Data and summary statistics

Description Source Unit of measurement Obs Mean SD Min Max Gini of market income SWIID 3.1 Index of market income inequality (0–100) 828 46.0 8.9 24.3 73.4 Gini of net income SWIID 3.1 Index of net income inequality (0–100) 828 38.3 10.2 19.8 66.1 Redistribution (full) SWIID 3.1 Gini market—Gini net for full sample 828 7.6 7.1 \(-\) 10.6 27.9 Redistribution (baseline) SWIID 3.1 Gini market—Gini net for baseline sample 828 7.7 7.1 \(-\) 10.6 27.9 Redistribution (restricted) SWIID 3.1 Gini market—Gini net for Solt restricted sample 462 7.4 7.3 \(-\) 10.6 27.9 Redistribution (very restricted) SWIID 3.1 Gini market—Gini net for very restricted sample 334 8.0 7.2 \(-\) 10.6 27.9 Log(initial income) PWT 7.1 Real GDP per capita, PPP adjusted, chain series, in 2005 prices 828 8.6 1.3 5.7 11.2 Log(investment) PWT 7.1 Real investment to GDP, in 2005 US dollars at PPP 828 3.1 0.4 1.3 4.3 Log(population growth \(+\) 5) WEO Population growth 828 1.9 0.2 \(-\) 0.5 2.7 Log(education) Barro and Lee (2013) Average years of primary and secondary schooling in the total population over 25 751 1.8 0.6 \(-\) 0.8 2.6 Terms of trade growth (dummy) WEO 1 if in the bottom three deciles, and 0 otherwise 683 0.3 0.2 0.0 1.0 Polity 2 Polity IV Scale from \(-\) 10 (autocratic) to 10 (democratic) 705 3.6 6.8 \(-\) 10.0 10.0

Description Source Unit of measurement Obs Mean SD Min Max Openness PWT 7.1 Openness at current prices (%) 828 0.7 0.5 0.0 4.2 External debt liabilities Lane and Milesi-Ferretti (2011) External debt liabilities from WEO and Global Development Finance database 730 0.9 2.3 0.0 32.9 Summary statistics for the survival sample for h \(=\) 5, p \(=\) 10 Gini of net income SWIID 3.1 Index of net income inequality (1–100) 640 40.4 9.2 21.4 65.5 Redistribution (full) SWIID 3.1 Gini market—Gini net for full sample 640 4.8 6.0 \(-\) 6.6 26.8 Redistribution (baseline) SWIID 3.1 Gini market—Gini net for baseline sample 640 4.8 6.0 \(-\) 6.6 26.8 Redistribution (restricted) SWIID 3.1 Gini market—Gini net for Solt restricted sample 364 4.5 5.7 \(-\) 5.9 25.6 Log(Investment) PWT 7.1 Real investment to GDP, in 2005 US dollars at PPP 640 3.2 0.4 1.5 4.3 Log(population growth \(+\) 5) WEO Population growth 640 1.9 0.1 1.6 2.5 Log(education) Barro and Lee (2013) Average years of primary and secondary schooling in the total population over 25 633 1.7 0.6 \(-\) 0.4 2.5

Description Source Unit of measurement Obs Mean SD Min Max US interest rate (dummy) FED 3 month treasury bill 1 if upper three deciles, and 0 otherwise 640 0.4 0.5 0.0 1.0 Terms of trade growth (dummy) WEO 1 if in the bottom three deciles, and 0 otherwise 616 0.3 0.4 0.0 1.0 Polity 2 Polity IV Scale from − 10 (autocratic) to 10 (democratic) 614 2.1 6.7 \(-\) 9.0 10.0 Openness PWT 7.1 Openness at current prices (%) 640 86.6 74.7 8.5 433.0 External debt liabilities Lane and Milesi-Ferretti (2011) External debt liabilities from WEO and Global Development Finance database 597 163.2 490.8 3.0 3468.3

Appendix C: Correlation between market inequality and redistribution

As discussed in Sect. 3 countries with more market inequality tend to redistribute more, with a stronger effect in the OECD sample. This is so in a model with country-specific fixed effects (which focuses on the variation across time within countries) while controlling for unobserved heterogeneity, as well as with IV-GMM estimation, where market inequality is instrumented with its lagged differences.Footnote 49 The effect is modest but nontrivial: an increase in market inequality from the 50th to the 75th percentile of the sample is associated with an increase in redistribution by 3–4 Gini units (Table 8).

Table 8 Correlation between market inequality and redistribution. Full size table

Appendix D: Reconciling with the literature: alternative panel estimation methods to investigate the growth-inequality-redistribution relationship

In an attempt to reconcile disparate results in the literature, this Appendix, presents results from additional panel estimators that have been used in the literature to investigate the growth–inequality–redistribution relationship. By using the same dataset, we are able to ensure and apples-to-apples comparison and isolate differences between our results and those in the literature using alternative estimation methods.

One of the advantages of panel data estimators is that it allows modeling (or controlling for) the time-invariant, unobserved individual effect ui in Eq. (3). The standard estimator pooled OLS (POLS) ignores the ui which is correlated with the lagged dependent variable in the dynamic panel specification, as it is part of the process that generates the lagged dependent variable yi, \(t-1\), and hence, it is biased (upwards). The fixed effects (FE) estimator (obtained by OLS estimation on the time-demeaned variables) allows the individual effect ui to be correlated with the regressors. In a finite dynamic panel model with fixed T, FE will be (downward) biased of order 1/T because the transformed time varying component of the error term vt and the transformed lagged dependent variable are correlated (Nickell 1981). (FE is also called the “within” estimator, because it uses the time variation within each cross-section.) The between estimator (BE) is obtained by OLS estimation on the cross-sectional equation on time averages of the variables, and effectively ignores variables’ changes over time. As in the case of the POLS, the between estimator is biased (upwards) since the ui is correlated with the lagged dependent variable. Finally, the random effects (RE) estimator assumes that the individual effect is uncorrelated with the regressors, which is violated in the case of the dynamic panel setting.

To illustrate the effect of these estimators, Table 9 uses a specification with inequality, redistribution and standard growth determinants as controls and applies econometric techniques used in the literature. Columns [1]–[6] present results from POLS [1]; FE-within (FEw, [2]) which is based on time variation; the between (BW, [3]) which looks at the between-country effects and uses the cross section variation in averages to identify the parameters; RE [4] which is effectively a weighted average for the within and between estimators;Footnote 50 over random effects the difference GMM estimator (dGMM, [5]) which explores time series variation; and our preferred systems GMM estimator which explores both the time-series and cross sectional variation-replicating the specification in Table 2 [3]. (Unlike the rest of the estimators the two GMM estimators allow consistent estimation in the presence of a dynamic panel and potentially endogenous variables.)

Overall, our results confirm findings in the literature and the findings of Halter et al. (2014). Estimates based only on time-series variation such as the dGMM used in Forbes (2000) generally find a positive impact of inequality on growth. On the other hand, estimation methods exploiting the cross-sectional variation in the data tend to find a negative relationship (e.g. Alesina and Rodrik 1994; Persson and Tabellini 1994; Deininger and Squire 1998; Barro 2000). Combining both cross-sectional and time series variation as in sGMM is indeed important.

As an additional illustration, we explore the growth–inequality relationship in the short-run and long-run context graphically. The left column in Fig. 6 plots per capita growth rates against the (lagged) change of inequality or redistribution, thus representing short-run changes. The right column plots the level of per capita GDP against the (lagged) level of inequality or redistribution. Two distinct patterns emerge: in the long-run there is a strong negative relationship between per capita income and inequality; however, the growth–inequality relationship is (slightly) positive in the short-run. The bottom row of the figure suggests that higher transfers may increase long-run growth, but there is no significant relationship in the short-run.

Fig. 6 Market inequality, net inequality, redistribution, and growth: evidence from short-run and long-run effects Full size image