## Abstract

Inequality affects economic performance through many mechanisms, both beneficial and harmful. Moreover, some of these mechanisms tend to set in fast while others are rather slow. The present paper (i) introduces a simple theoretical model to study how changes in inequality affect economic growth over different time horizons; (ii) empirically investigates the inequality–growth relationship, thereby relying on specifications derived from the theory. Our empirical findings are in line with the theoretical predictions: Higher inequality helps economic performance in the short term but reduces the growth rate of GDP per capita farther in the future. The long-run (or total) effect of higher inequality tends to be negative.

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## Notes

Estimates based on time-series variation only (e.g., those in Li and Zou 1998; Forbes 2000) are often positive. Estimates which also or exclusively rely on cross-sectional variation tend to be negative, however. Examples include Barro’s (2000) random-effects approach or earlier cross-country OLS studies (e.g., Alesina and Rodrik 1994; Persson and Tabellini 1994; Clarke 1995; Deininger and Squire 1998). Using different estimation methods, Banerjee and Duflo (2003) find that changes in inequality (both positive as well as negative ones) are associated with lower growth rates in the subsequent period.

Moreover, if the number of time series observations is small and the variables are highly persistent (as is the case here), the first-difference GMM estimator has been shown to do worse in terms of biases and imprecision than the System GMM estimator (see Blundell and Bond 1998).

It has also been argued that, with convex technologies and financial markets imperfections, higher inequality worsens economic performance because investment returns are more heterogeneous. However, as shown by Foellmi and Oechslin (2008), this is by no means a robust theoretical prediction.

The large-scale investment channel as well as the demand-side channel may be of different relevance in low and high-income countries, reflecting differences in the severity of financial frictions (more severe in low-income countries) and the importance of R&D (more important in high-income countries).

The empirical picture is mixed. Earlier papers (e.g., Perotti 1996) find little evidence of a systematic association between the distribution of the disposable income and fiscal variables. Milanovic (2000), on the other hand, documents a strong positive link between factor-income inequality and the extent of redistribution towards the poor. Interestingly, however, the middle class does not appear to be a net beneficiary of such redistribution, a finding that casts doubt on the relevance of the median voter channel.

More generally, based on the experience of the colonization of the New World, Sokoloff and Engerman (2000) argue that huge wealth inequalities may promote institutions that protect the privileges of the elites and restrict opportunities for the broad masses—with adverse consequences for economic development.

The existence of a positive short-term effect of inequality does not require the absence of financial markets. In combination with technology (2), a simple imperfection (such as unreliable ex-post contract enforcement) is sufficient to imply that (i) not the entire supply of resources is used in the most productive way; (ii) higher inequality may mitigate resource misallocation (see, e.g, Matsuyama 2000, Sect. 4).

Note that the short-term effect of inequality would be negative if the endowment of the poor were greater than \(\omega ^{c}\) in the state of low inequality but less than \(\omega ^{c}\) if \(D_{t}=H\) (as discussed in the influential paper by Galor and Zeira (1993), which started the literature on the impact of inequality in presence of financial frictions and indivisibilities in human capital investments). However, our short-term channel is not meant to capture the (long-run) effect of inequality on human capital accumulation. Rather, it is meant to reflect that in presence of financial frictions higher wealth inequality may quickly increase the stock of physical capital invested in large high-return investment projects (as discussed in Section 2.1). In this context, assuming \( \omega ^{P}(L)<\omega ^{c}\) seems natural.

If condition (R2) were violated, there would never be a change in the level of the public good. As a result, \(\theta _{2}\) would be equal zero (while \(\theta _{1}\) would be unchanged).

There are some important exceptions, however. Deininger and Squire (1998), for instance, explore the impact of land inequality (i.e., a specific form of asset inequality) on growth; similarly, Castelló and Doménech (2002) investigate how human capital inequality affects subsequent growth rates. More recently, by simultaneously including measures of the distributions of human capital and income, Castelló-Climent (2010) explores whether asset and income inequality have different effects on growth.

It is straightforward to check that this approximation relies on the fact that the product of the three shares \((a^{h}-a^{l})/a^{h},\ \sigma \), and \( \omega ^{P}\) is close to zero. In practice, it is clear that factors unrelated to the asset distribution may affect \(D_{t}^{y}\), which could be mirrored in expression (7) through an additional additive term (constant or variable). Obviously, the higher the variability of this term (relative to the variability of \(D_{t}\)), the lower is the quality of \(D_{t}^{y}\) as a proxy for \(D_{t}\) in an empirical setting.

Next to ensuring comparability with existing studies, we too chose to include these standard regressors because the Gini index could proxy for them if they were omitted. For instance, suppose that the implementation of economic reforms jointly increases investment and inequality. If that were the case, and if we did not control for the investment rate, we would run the risk that the estimated coefficient on the current Gini index is biased because it captures investment-driven increases in short-run growth.

The problem with the RE estimator is that \(\eta _{i}\) and \(y_{it-1}\) are correlated by construction; WG does not work because the transformed error term will be correlated with the transformation of \(y_{it-1}\).

More recently, relying on Monte Carlo simulations, Hauk and Wacziarg (2009) have demonstrated that these biases can be greatly exacerbated in presence of measurement error.

A rise in the Gini coefficient by \(3\) points (which is about the size of the within-country standard deviation) leads to a rise in the subsequent 5-year growth rate in the range of \(0.42\)–\(0.97\) percentage points and to a fall in the following 5-year growth rate in the range of \(1.35\)–\( 1.71\) percentage points.

The \(p\)-values for the specifications that do not include the lagged Gini coefficient (columns 1 and 2) are substantially lower (\(0.19\) and \(0.23\), respectively), which could be a sign of mis-specification.

Note also that we ran additional regressions treating persistent explanatory variables like \(\textit{GINI}\) and \(\textit{SCHOOL}\) as predetermined (rather than endogenous). The results are virtually unchanged (quantitatively and also in terms of statistical significance) and so we chose not to report them here. We return to this issue in greater detail when we discuss the first-difference GMM results below.

To save space, we present only the one-step System GMM results based on the \( \textit{GINI}^{y}\) \((Q12)\)-series. The two-step results, no matter whether based on \( \textit{GINI}^{y}\) \((Q1)\) or \(\textit{GINI}^{y}\) \((Q12)\), are very similar.

The 10-year growth spells are 1965–1975, 1975–1985, 1985–1995, 1995–2005. The set of instruments is again restricted to lag 2 of \(W\) (differenced equation) and the lagged first difference of \(W\) (level equation).

To see exactly why this approach of treating missing instruments implies that the two estimators rely on different numbers of observations, consider the following example. Suppose that there are two consecutive observations of the Gini coefficent, \(D_{it-1}\) and \(D_{it-2}\), while \(D_{it-3}\) is missing. Then, the calculation of the error term in levels, \((\eta _{i}+v_{it}),\) is feasible, whereas the difference \((D_{it-2}-D_{it-3})\) in the associated instrument vector \((W_{it-1}-W_{it-2})\) is missing. Yet,

*xtabond2*converts the missing instrument value to zero and lets the observation stay in the System GMM regression. Consider now the error term in first differences, \((v_{it}-v_{it-1})\). To calculate this difference, \( D_{it-3}\) is required. As a result, \((v_{it}-v_{it-1})\) cannot be found and the observation drops out of the first-difference regression.A predetermined variable is uncorrelated with the present as well as all future realizations of the error term. An endogenous variable may be correlated with the present realization (but is also uncorrelated with all future ones). So suppose that \({\tilde{\mathbf{x}}}_{i}\) is a vector of predetermined variables. Then, \(E\left\{ (v_{it}-v_{it-1}){\tilde{\mathbf{x}}} _{it-1}\right\} ,\) \(t\ge 2,\) are valid moment conditions that are used by the first-difference GMM estimator.

Note further that the investment rate is calculated as an average over the entire 5-year growth period considered. If investment were measured at the beginning of the growth period (as is the case when we use the System GMM estimator), the impact of \(INV\_RATE\) would be negative, reflecting cyclical short-run fluctuations that are captured in the time-series dimension of the dataset.

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## Appendix 1

### Appendix 1

###
*Proof of Proposition 1*

We prove the proposition by showing that the proposed policy functions are in fact solutions to the recursive problem (4), given that the relevant parameter constellation holds. One way to do so is to establish that in any given period \(t\) it is indeed optimal to stick to the proposed policy function, provided that this policy function is applied in all future periods, \(t+1\), \(t+2\), \(\cdot \cdot \cdot \).

Suppose now first that parameter constellation (R2) holds. Then, we have to establish that – irrespective of the value of \( G_{t} \) – the representative poor agent finds it optimal to choose (\(a\)) \( G_{t+1}=1\) if \(D_{t}=L\) and (\(b\)) \(G_{t+1}=0\) if \(D_{t}=H\) (again, provided that this rule is invariably applied in the future). The formal condition for point (\(a\)) to hold is

where the second line in the above expression gives the value if the decision is in favor of the alternative choice, \(G_{t+1}=0.\) Rearranging terms yields the much simpler restriction

which is indeed independent of \(G_{t}.\) Similarly, for point (\(b\)) to be true, we must have

which is again independent of the current level of the public good, \(G_{t}\).

To proceed, we have to find explicit expressions for the differences \( V^{P}(L,1)-V^{P}(L,0)\) and \(V^{P}(H,1)-V^{P}(H,0)\) which show up in (12) and (13). Assuming that the proposed policy function is applied in all (future) periods, the two differences are given by

with \(D\in \{L,H\}.\) Using this last expression in conditions (12) and (13) confirms that points (a) and (b) indeed hold (given that parameter constellation R2 holds).

A corresponding approach can be chosen to verify the proposed policy functions under the possible alternative parameter constellations. Note in this regard that there exist just the two alternatives stated in the proposition since the first expression in (R2) must be strictly greater than the last one \(\left( {\text {as}}\; \pi >1/2 {\text { and }} \omega ^{P}(L)>\omega ^{P}(H)\right) \).

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Halter, D., Oechslin, M. & Zweimüller, J. Inequality and growth: the neglected time dimension.
*J Econ Growth* **19**, 81–104 (2014). https://doi.org/10.1007/s10887-013-9099-8

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DOI: https://doi.org/10.1007/s10887-013-9099-8