4.1 Methodology and Identification Strategy

As noted in Section 2, the relationship between income inequality and growth has proven difficult to analyze for a number of reasons. First, the two variables may be intertwined, such that income inequality has an impact on growth at the same time that growth has an impact on income inequality. The failure to account for this source of endogeneity may bias the results. Endogene-ity may also arise because of omitted variables that are correlated either with income inequality or growth. Second, dynamics are likely to be present, in the sense that the feedback between income inequality and growth occurs gradually over time, and with different intensities over different time horizons. Third, there is no reason for which these dynamic relationships would be the same across countries, regions, or income levels. In fact, they may differ because of the economic structure, institutions, policies’ inclusiveness, among others. Fourth, shocks that are common to all countries might induce cross-section dependence and omitted variable bias.

To deal with these complexities, we employ the heterogeneous panel SVAR model of Pedroni (2013).¹³ Let y_i,t be a vector of n endogenous variables (i.e., the log differences of real per capita GDP and net Gini) with country-specific time dimension t = [1, …,T_i]’ for each member i = [1…,M]’ of an unbalanced panel. As a way to deal with country-fixed effects, we demean the data as $y_{i,t}^{*}=y_{i,t}-{\overline{y}}_i$, where ${\overline{y}}_i=T_i^{-1}{\mathrm{\Sigma }}_{t=1}^{T_i}{y}_{i,t}\forall i$. Thus, we estimate the following equation:

where A_i(L) is a polynomial of lagged coefficients $(A_i\left(L\right)={\mathrm{\Sigma }}_{j=0}^{J_i}{A}_j^i{L}^j)$ with country-specific lag-lengths J_i, $A_j^i$ is a nxn matrix of coefficients, e_i,t is a vector of residuals, and B_i is a nxn matrix of contemporaneous coefficients. J_i are selected based on the Schwartz Information Criterion to assure that residuals approximate white noise. As a way to control for the uncertainty associated to the net Gini measurement, we use the inverse of the standard deviation of the 100 multiply-imputed values as weights, thereby estimating by weighted least squares (WLS).

As noted, the dynamic relationship between income inequality and growth can differ across countries. Failing to account for such heterogeneity by simply pooling data as in conventional dynamic panel methods may result in inconsistent estimation and inference of the relationships. ¹⁴ Thus, the methodology employed in this paper relaxes the assumption of homogeneous dynamics among the members of the panel by estimating and identifying a reduced-form VAR for each country i:

from which we can obtain the idiosyncratic dynamics. To the extent that correlated omitted variables have a heterogeneous impact across countries, treating each country separately can also help in dealing with the bias generated by the omissions. Another advantage of relying on the heterogeneous approach is that between-countries comparability is less of an issue as each member of the panel is treated independently.

Then, we estimate an additional VAR using cross-section averages for each period, which would serve to capture to retrieve the common dynamics:

where ${\overline{y}}_t^{*}\equiv M^{-1}{\mathrm{\Sigma }}_{i=1}^M{y}_{i,t}^{*}$.

We can now recover the SVAR representation, in which the reduced-form residuals in equation (2) and (3) are mapped into $u_{i,t}=B_i^{-1}{e}_{i,t}$ and ${\overline{u}}_t={\overline{B}}^{-1}{\overline{e}}_t$, respectively. Thus, we calculate nM correlation coefficients to construct M diagonal matrices:

where $\begin{array}{c}\rho (u_{i,t}^n,u_t^{-n})\end{array}$ denote the correlation coefficients between structural residuals of the n^th endogenous variable for each country i. We are now able to decompose the composite shocks u_i,t as:

where ${\overline{u}}_{i,t}$ are the common shocks, ${\tilde{u}}_{i,t}$ are the idiosyncratic shocks, and Λ_i are nxn diagonal matrices containing country specific loadings which account for the relative importance of common shocks. We then recover the matrices of composite responses to structural shocks for each country R_i(L), and use the loading matrices estimated in equation (5) to disentangle the composite responses into responses to common shocks and responses to idiosyncratic shocks:

It should be noted that $\begin{array}{c}{R}_i\left(L\right)={\overline{R}}_i\left(L\right)+{\tilde{R}}_i\left(L\right)\end{array}$, where $\begin{array}{c}{\overline{R}}_i\left(L\right)\equiv {\mathrm{\Lambda }}_i{R}_i\left(L\right)\end{array}$ and $\begin{array}{c}{\tilde{R}}_i\left(L\right)\equiv \left({\mathrm{\Lambda }}_i{\mathrm{\Lambda }}_i^{\prime }\right)R_i\left(L\right)\end{array}$. Thus, we rely on the cross-section distribution of $R_i\left(L\right),{\overline{R}}_i\left(L\right)$, and ${\tilde{R}}_i\left(L\right)$ to present selected descriptive statistics of the impulse response functions (IRF), such as their medians, averages, and interquartile ranges. Finally, we also calculate standard errors of medians through a re-sampling simulation with 500 repetitions.

The structural representation of the VAR requires an identification strategy. Rather than imposing economic relationships, we rely on the Cholesky decomposition. The ordering of the variables is based on the following argument. Since income is an input in the calculation of income inequality, any change in income will have a contemporaneous effect on income inequality. At the same time, changes in income inequality are likely to have only a delayed impact on income. Therefore, the identification strategy rests on lag restrictions rather than economic ones, implying that changes in the net Gini do not have contemporaneous (i.e., within a year) effect on growth.

4.2 Integration, Cointegration, and Convergence

As a first step, we analyze the stationarity properties of the log of Gini net and the log of per capita real GDP by employing the tests by Levin et al. (2002) (LLC thereafter), Im et al. (2003) (IPS thereafter), and Maddala and Wu (1999) (MW thereafter).¹⁵ These tests differ in that LLC treats the parameter of interest as common across countries and focuses on the within-country dimension, IPS treats the parameter of interest as varying across countries and focuses on the between-country dimension, and MW treats all the parameters as potentially varying across countries and tests by pooling significance values across members of the panels.

We perform the tests on the (log) levels and the (log) first differences of the series, both including the intercept only and the intercept and the trend. As expected, the results of the different tests reported in Table 1 suggest that levels are non-stationary as the null hypothesis of unit root cannot be rejected, irrespective of the inclusion of a time trend. After first differencing, the series result stationary.

Table 1:

Panel Unit Root Tests

Source: Authors’ calculations.Notes: The null hypothesis of the panel unit root tests is that all panels contain a unit root. Fixed effects are always included. The Schwartz Information Criterion is used to select the optimal lag length. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

Table 1:

Panel Unit Root Tests

		Levels		First differences
		Intercept	Intercept and trend	Intercept	Intercept and trend
Levin, Lin, and Chu (2002)
	Ln net GINI	−0.617	−1.110	−12.488**	−6.933**
	Ln per capita real GDP	−1.419	−2.58	−23.297**	−19.438**
Im, Pesaran, and Shin (2003)
	Ln net GINI	−0.234	−2.200	−18.833**	−15.324**
	Ln per capita real GDP	8.137	−1.070	−22.258**	−19.927**
Maddala and Wu (1999)
	Ln net GINI	−0.023	−0.067	−16.687**	−14.044**
	Ln per capita real GDP	7.685	−0.524	−20.329**	−17.768**

Source: Authors’ calculations.Notes: The null hypothesis of the panel unit root tests is that all panels contain a unit root. Fixed effects are always included. The Schwartz Information Criterion is used to select the optimal lag length. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

View Table

Table 1:

Panel Unit Root Tests

		Levels		First differences
		Intercept	Intercept and trend	Intercept	Intercept and trend
Levin, Lin, and Chu (2002)
	Ln net GINI	−0.617	−1.110	−12.488**	−6.933**
	Ln per capita real GDP	−1.419	−2.58	−23.297**	−19.438**
Im, Pesaran, and Shin (2003)
	Ln net GINI	−0.234	−2.200	−18.833**	−15.324**
	Ln per capita real GDP	8.137	−1.070	−22.258**	−19.927**
Maddala and Wu (1999)
	Ln net GINI	−0.023	−0.067	−16.687**	−14.044**
	Ln per capita real GDP	7.685	−0.524	−20.329**	−17.768**

Source: Authors’ calculations.Notes: The null hypothesis of the panel unit root tests is that all panels contain a unit root. Fixed effects are always included. The Schwartz Information Criterion is used to select the optimal lag length. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

The presence of unit roots in levels warrants the investigation of the existence of a long-run relationship between (the log of) Gini net and (the log of) per capita real GDP. We employ the tests by Kao (1999) and Pedroni (1999, 2004). The former treats all parameters except fixed effects as homogeneous, and therefore is mispecified if heterogeneous dynamics exist. The latter treat all parameters as heterogeneous across countries and include within- and between-country dimension tests, both parametric and non-parametric.

The results of the cointegration tests reported in Table 2 suggest the existence of a long-run relationship between inequality and income per capita. In particular, in the majority of cases and irrespective of the inclusion of a trend, both homogeneous and heterogeneous tests reject the null hypothesis of no cointegration, providing evidence of comovements between the series in the long run.

Table 2:

Panel Cointegration Tests

Source: Authors’ calculations.Notes: The null hypothesis of the panel cointegration tests is that there is no cointegration between ln Gini net and ln real per capita GDP. For Pedroni (1999, 2004), we present the versions of the statistics that are not weighted by the member specific long-run conditional variances. The Schwartz Information Criterion is used to select the optimal lag length. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

Table 2:

Panel Cointegration Tests

			Intercept
		Intercept	and trend
Kao (1999)
	ADF	−3.109**
Pedroni (1999, 2004)
	Panel v -Statistic	0.833	3.921**
	Panel ρ -Statistic	−1.681*	0.710
	Panel t -Statistic (non-parametric)	−6.224**	−2.252*
	Panel t -Statistic (parametric)	−3.774**	−5.022**
	Group ρ -Statistic	1.168	4.185
	Group t -Statistic (non-parametric)	−4.191**	0.674
	Group t−Statistic (parametric)	−5.782**	−5.662**

Source: Authors’ calculations.Notes: The null hypothesis of the panel cointegration tests is that there is no cointegration between ln Gini net and ln real per capita GDP. For Pedroni (1999, 2004), we present the versions of the statistics that are not weighted by the member specific long-run conditional variances. The Schwartz Information Criterion is used to select the optimal lag length. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

View Table

Table 2:

Panel Cointegration Tests

			Intercept
		Intercept	and trend
Kao (1999)
	ADF	−3.109**
Pedroni (1999, 2004)
	Panel v -Statistic	0.833	3.921**
	Panel ρ -Statistic	−1.681*	0.710
	Panel t -Statistic (non-parametric)	−6.224**	−2.252*
	Panel t -Statistic (parametric)	−3.774**	−5.022**
	Group ρ -Statistic	1.168	4.185
	Group t -Statistic (non-parametric)	−4.191**	0.674
	Group t−Statistic (parametric)	−5.782**	−5.662**

Source: Authors’ calculations.Notes: The null hypothesis of the panel cointegration tests is that there is no cointegration between ln Gini net and ln real per capita GDP. For Pedroni (1999, 2004), we present the versions of the statistics that are not weighted by the member specific long-run conditional variances. The Schwartz Information Criterion is used to select the optimal lag length. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

We now turn to investigate if income inequality data show long-run convergence or divergence across countries. Previous studies of income inequality convergence include Sala-i-Martin (2006) and Chotikapanich et al. (2012), that use non-parametric or parametric methods to estimate world inequality indexes and assess convergence by looking at the trend in the world distribution of income. We take a different approach. Borrowing from the literature on income convergence (Evans, 1998; Pedroni and Yao, 2006), we define convergence as the reduction of the inequality gap between any pair of countries. As noted by Pedroni and Yao (ibid.), an empirical formalization differs from the graphical inspection in that it requires that properties of the data must be consistent with the fact that differences are eliminated eventually. This is something harder to detect using graphical analysis, where we can only observe if differences become smaller at any point in time.

Empirically testing for convergence is equal to testing for the stationarity of the difference between the levels of the series for any pair of countries.¹⁶ This would imply that the series are coin-tegrated. Formally:

where y is (the log of) net Gini, and (i, j) are country pairs. Similarly, testing for convergence across multiple countries requires that every possible country pair within the sample exhibits convergence. However, Evans showed that if the the condition in equation 7 holds, then:

Thus:

So:

In other words, convergence requires that $(y_{it}-{\overline{y}}_t)$ is stationary for each country in the sample. Therefore, the null hypothesis of nonconvergence can be resumed in the unit root null of panel unit root tests. As in Pedroni and Yao (2006), we employ the IPS and the MW panel unit root tests, leveraging on the fact that the autoregressive parameter in the income inquality differentials is allowed to vary across countries.

Table 3 presents the results of the tests of conditional convergence for (the log of) net Gini (and market Gini). Beyond the full sample, we also consider regions and income groups to investigate the existence of convergence clubs. The first column reports the Augmented Dickey-Fuller t-statistic of the IPS test along with its significance level. For the full sample, we reject the null hypothesis of unit root presence, suggesting convergence. When looking at the t-statistic for every country, the majority of them cannot reject the null hypothesis at 5 percent level. However, the signal from the latter is not neutral as it lies on the tail of the distribution, and when combined, is sufficient to warrant the rejection of the null hypothesis for the panel as a whole. This finding is supported by the Fisher statistic of the MW test.

Table 3:

Convergence in Income Inequality

Source: Authors’ calculations.Notes: The null hypothesis of the unit root tests is that all panels contain a unit root, i.e. there is no convergence. Fixed effects are always included. The Schwartz Information Criterion is used to select the optimal lag length. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

Table 3:

Convergence in Income Inequality

			Net Gini		Market Gini
		Countries	Im, Pesaran, and Shin (2003)	Maddala and Wu (1999)	Im, Pesaran, and Shin (2003)	Maddala and Wu (1999)
Full sample
	$(y_{it}-{\overline{y}}_t)\forall i$	77	−3.939**	−3.392**	−2.506*	−3.204*
Regions
$(y_{it}-{\overline{y}}_t)\forall i$		11	−0.461	−0.430	−0.460	−0.473
	$(y_{it}-{\overline{y}}_t)\forall i$	12	−0.905	−0.903	−1.649*	−1.624
	$(y_{it}-{\overline{y}}_t)\forall i$	29	−4.513**	−3.706**	−3.686**	−3.275**
	$(y_{it}-{\overline{y}}_t)\forall i$	9	−4.296**	−4.086**	−4.043**	−3.582**
	$(y_{it}-{\overline{y}}_t)\forall i$	16	−1.184	−0.872	−0.432	−0.091
Income groups
	$(y_{it}-{\overline{y}}_t)\forall i$	28	−3.705**	−2.665**	−4.864**	−4.470**
	$(y_{it}-{\overline{y}}_t)\forall i$	36	−0.890	−0.595	−2.404	−1.927
	$(y_{it}-{\overline{y}}_t)\forall i$	13	−0.463	−0.523	−1.260	−1.254

Source: Authors’ calculations.Notes: The null hypothesis of the unit root tests is that all panels contain a unit root, i.e. there is no convergence. Fixed effects are always included. The Schwartz Information Criterion is used to select the optimal lag length. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

View Table

Table 3:

Convergence in Income Inequality

			Net Gini		Market Gini
		Countries	Im, Pesaran, and Shin (2003)	Maddala and Wu (1999)	Im, Pesaran, and Shin (2003)	Maddala and Wu (1999)
Full sample
	$(y_{it}-{\overline{y}}_t)\forall i$	77	−3.939**	−3.392**	−2.506*	−3.204*
Regions
$(y_{it}-{\overline{y}}_t)\forall i$		11	−0.461	−0.430	−0.460	−0.473
	$(y_{it}-{\overline{y}}_t)\forall i$	12	−0.905	−0.903	−1.649*	−1.624
	$(y_{it}-{\overline{y}}_t)\forall i$	29	−4.513**	−3.706**	−3.686**	−3.275**
	$(y_{it}-{\overline{y}}_t)\forall i$	9	−4.296**	−4.086**	−4.043**	−3.582**
	$(y_{it}-{\overline{y}}_t)\forall i$	16	−1.184	−0.872	−0.432	−0.091
Income groups
	$(y_{it}-{\overline{y}}_t)\forall i$	28	−3.705**	−2.665**	−4.864**	−4.470**
	$(y_{it}-{\overline{y}}_t)\forall i$	36	−0.890	−0.595	−2.404	−1.927
	$(y_{it}-{\overline{y}}_t)\forall i$	13	−0.463	−0.523	−1.260	−1.254

Source: Authors’ calculations.Notes: The null hypothesis of the unit root tests is that all panels contain a unit root, i.e. there is no convergence. Fixed effects are always included. The Schwartz Information Criterion is used to select the optimal lag length. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

We then analyze convergence across regions and income groups. The fact that countries are generally converging to the average for the sample does not exclude the possibility that countries are also converging to, for example, a regional average. The results of the unit root tests suggest that convergence is occurring in Europe and in the Middle East and Central Asia, as well as in advanced economies. Such findings are once again corroborated by the results of the MW test. While these conclusions are in general valid also in the case of market Gini, the null hypothesis for the full sample is rejected at a higher significance level both for IPS and MW, suggesting that the signal is weaker when redistribution effects are not netted out.

4.3 (Heterogeneous) Dynamics

We now present the IRF for the full sample. Figure 2 reports the median, the average, as well as the 25^th and 75^th percentile responses of real per capita GDP growth and net Gini growth among the 77 countries in the sample over a 12-year horizon. As noted by Goes (2016), this is an informative way of presenting the results, which would not be available if we had imposed homogeneity in the estimation. Particularly, we would not be able to know how many countries were actually behaving as the average dynamics, and inference would be biased in presence of heterogeneity (Pe-saran and Smith, 1995).

Composite IRFs

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.

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Composite IRFs

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.

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Composite IRFs

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.

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We find a large heterogeneity in the results. While the median impact of income inequality growth on real per capita GDP growth is negative and lasts for about two years, this is by no means true for all countries, as shown in the bottom left panel. Indeed, the results for the 25^th percentile show that there is a subset of countries for which the estimated impact is actually positive and longer lasting. Conversely, the results for the 75^th percentile suggest that the negative impact is about four times larger than the negative median response, and takes longer to die out. Importantly, the average response can be quite noisy in presence of heterogeneous slopes and dynamics. For the median response, a one percentage point (pp) shock in the growth rate of income inequality is associated with a 0.14 pp fall in real per capita GDP growth.

The results in Figure 2 are also informative regarding the impact of real per capita GDP growth on income inequality growth. The top right panel shows that the median response is negative and reverts to about zero after two years. However, once again, the variation across countries is considerable, as shown by the 25^th and 75^th percentile. The effects of the shocks in real per capita GDP growth and income inequality growth on themselves are positive as expected, and much more homogeneous (top left and bottom right panels).

As an illustration of the large heterogeneity, we present the cases of two different countries at the tails of the distribution. Figure 3 shows the estimated response of real per capita GDP to a shock in income inequality over a 12-year horizon for Nigeria and Finland. For Nigeria, the response is negative and large. It reaches its maximum magnitude three years after the shock (eight pp fall in real per capita GDP growth in response to a pp change in the net Gini) and still shows negative values 11 years after the shock. For Finland, the response is positive over the entire horizon considered, reaching its maximum magnitude one year after the shock (1.2 pp). While single-country results might be noisy, they still provide a suggestive picture of the heterogeneity in the strength of the effect.

Composite Response of Real per Capita GDP Growth to Income Inequality Growth for Nigeria and Finland

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.

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Composite Response of Real per Capita GDP Growth to Income Inequality Growth for Nigeria and Finland

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.

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Composite Response of Real per Capita GDP Growth to Income Inequality Growth for Nigeria and Finland

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.

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Our results so far suggest that the sign and the strength of the relationship between the two variables varies widely across countries. We now turn to investigate if such heterogeneity persists across regions (Africa, Asia and Pacific, Europe, Middle East and Central Asia, and Western Hemisphere) and income levels (advanced economies, emerging markets, and low-income developing countries).¹⁷

Figure 4 compares the median, the average, as well as the 25^th and 75^th percentile response of real per capita GDP growth to a shock in income inequality growth. With the exception of Asia and Pacific (which shows an erratic behavior) and the advanced economies (which present a mildly positive reaction in the second year), the median response remains negative. In terms of magnitude, the negative response to a one pp shock in the net Gini is largest in the Middle East and Central Asia and the Western Hemisphere (about -0.3 pp during the second and the third year after the shock, respectively), and in emerging economies (-0.4 pp one year after the shock). Even at the country group level, the median response can be deceiving.

Composite Response of Real per Capita GDP Growth to Income Inequality Growth by Region and Income Level

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

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Composite Response of Real per Capita GDP Growth to Income Inequality Growth by Region and Income Level

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.

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Composite Response of Real per Capita GDP Growth to Income Inequality Growth by Region and Income Level

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.

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While looking at the median gives an idea of the typical country in the subset, the interquartile range is telling about the dispersion. As in the case of the full sample, the dispersion is vast across regions and income groups. Only in Western Hemisphere the 25^th percentile answer is negative, in all other cases it remains positive, suggesting that heterogeneity is present even at regional level. However, the extent of the positive effect is as large as the full sample or larger only for Asia and Pacific, the Middle East and Central Asia, and advanced economies; in all other cases, the magnitude is reduced.

We now move to look at the statistical significance of the median response of real per capita GDP growth to shocks in income inequality growth, both for the full sample and for sample subsets. Figure 5 reports the median response along with the associated 95 percent bootstrapped confidence intervals. The median effect is significant for the full sample at five percent level. Converted in index numbers and real PPP terms, these responses suggest that for the median country in the sample, an increase in the net Gini by 0.3 decreases per capita income by $24. However, a look at the regional and country group dynamics suggests that the effect remains significant only in the Middle East and Central Asia, the Western Hemisphere, and in emerging markets. In contrast, we cannot find any significant and positive effect in any sample subsets.

Composite Response of Real per Capita GDP Growth to Income Inequality Growth by Region and Income Level and Confidence Intervals

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Notes: Confidence intervals are calculated from a resampling simulation with 500 repetitions.Source: Authors’ calculations.

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Composite Response of Real per Capita GDP Growth to Income Inequality Growth by Region and Income Level and Confidence Intervals

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Notes: Confidence intervals are calculated from a resampling simulation with 500 repetitions.Source: Authors’ calculations.

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Composite Response of Real per Capita GDP Growth to Income Inequality Growth by Region and Income Level and Confidence Intervals

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Notes: Confidence intervals are calculated from a resampling simulation with 500 repetitions.Source: Authors’ calculations.

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Interestingly, also the time needed for the effect of the shock to phase out is heterogeneous across country groups. For the full sample, the median response dies out three years after the shock. However, in emerging economies, it takes longer, as the median response reaches zero only five years after the shock. In the Middle East and Central Asia and the Western Hemisphere, the median response is significant two years after the shock and settles in two to three years.¹⁸

Figure 6 reports the corresponding median response of the level of real per capita GDP to shocks in income inequality growth for the full sample and sample subsets. To ease visualization, the median response is presented in terms of percent deviation from the steady state.¹⁹ For the full sample, real per capita GDP is about 0.3 percent lower with respect to the steady state after a one pp shock in income inequality growth. The effect is more sizable in the Middle East and Central Asia (0.9 percent), the Western Hemisphere (1 percent), and in emerging markets (0.8 percent).

Composite Response of Real per Capita GDP to Income Inequality Growth by Region and Income Level

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

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Composite Response of Real per Capita GDP to Income Inequality Growth by Region and Income Level

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.

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Composite Response of Real per Capita GDP to Income Inequality Growth by Region and Income Level

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.

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Finally, we decompose the responses into those associated to idiosyncratic and common shocks.²⁰ As noted, loading factors contain information about the relative importance of common shocks for each country and can be used to decompose the aggregate response. Thus, in Figure 7 we present such decomposition for the response of real per capita GDP growth to income inequality growth. The results indicate that the great majority of the response is explained by idiosyncratic shocks.

Idiosyncratic and Common Median Response of Real per Capita GDP Growth to Income Inequality Growth by Regions and Income Levels

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Notes: Median responses are decomposed into idiosyncratic and common shocks by using the loading factors.Source: Authors’ calculations.

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Idiosyncratic and Common Median Response of Real per Capita GDP Growth to Income Inequality Growth by Regions and Income Levels

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Notes: Median responses are decomposed into idiosyncratic and common shocks by using the loading factors.Source: Authors’ calculations.

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Idiosyncratic and Common Median Response of Real per Capita GDP Growth to Income Inequality Growth by Regions and Income Levels

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Notes: Median responses are decomposed into idiosyncratic and common shocks by using the loading factors.Source: Authors’ calculations.

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4.4 A Look into the Relationship’s Determinants

In order to explore the determinants of the variation in the IRF, we examine the cross-section association between certain country characteristics and the strength of the IRF. In particular, we test whether a better institutional framework could lead to a smaller negative effect of income inequality on growth. The benefits of a bad institutional environment tend to accrue to the more powerful higher income groups through the subversion of legal, regulatory, and political institutions, making them richer and worsening inequality (Glaeser et al., 2003 and Batabyal and Chowd-hury, 2015). Thus, a higher institutional quality could soften the negative impact of inequality on growth. Another channel could be the one for which governments characterized by high institutional quality are often the more meritocratic ones, which provide incentives to compete and increase productivity, hence attenuating the deleterious effect of income inequality on economic activity. Also, we test if higher education has any effect on the extent to which income inequality reduces economic activity. One of the reasons this may happen is because better educated people may value education more strongly. Thus, even if the distribution of income becomes more unequal, they will refrain from reducing investment in education, which would contribute to mute the effect of income inequality on economic growth.

There are several indicators of institutional quality or development. We consider here a subset composed by control of corruption, rule of law, government effectiveness, and political stability from the Worldwide Governance Indicators and the Economic Freedom of the World Index from the Fraser Institute. As for education, we use years of schooling from the Barro-Lee database and education expenditure from the IMF’s Fiscal Affairs Department database.

Measuring the impact of these variables on the strength of the relationship using the IRF coefficients is complicated by the fact that the response coefficients typically vary period by period, implying that no single number provides an unambiguous measure of the size of the response. Accordingly, we examine the magnitude of each of the responses one to four years after the shock (which correspond to the years where most countries present a significant marginal response), as well as by the magnitude of the average response coefficient and the accumulated response coefficient over a 12-year horizon.²¹ More formally, we estimate the following equation with an OLS estimator:

where $\left|IR{F_i}^t\right|$ is the absolute value of, alternatively, the IRF coefficient at time t, the average response coefficient, or the accumulated response coefficient for country i; IQ is the institutional quality variable; EDUC is the proxy for education attainment; and e is a white noise error term.

As a first step, we examine the bivariate correlation between the IRF coefficients and the potential correlates. The scatter plots of Figure 8 only shows the relationship for the IRF coefficients one year after the shock and the accumulated ones for space reasons. The signs of almost all the bivariate correlations (13 out of 14) are consistent with the hypotheses outlined above. Higher institutional quality and more years of schooling (or higher education spending) are associated with a smaller reduction in economic growth in response to an income inequality shock. With the exception of the correlation between years of schooling and the accumulated IRF coefficients, the bivariate regression coefficient is always significant.

Bivariate Correlations

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.Notes: The minimum of the vertical axis for the accumulated IRF coefficients has been set to -20 to ease the visualization of the data. This leaves out Nigeria, which is however part of the sample to calculate the regression coefficient.

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Bivariate Correlations

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.Notes: The minimum of the vertical axis for the accumulated IRF coefficients has been set to -20 to ease the visualization of the data. This leaves out Nigeria, which is however part of the sample to calculate the regression coefficient.

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Bivariate Correlations

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.Notes: The minimum of the vertical axis for the accumulated IRF coefficients has been set to -20 to ease the visualization of the data. This leaves out Nigeria, which is however part of the sample to calculate the regression coefficient.

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The multivariate regression results are presented in Table 4. Each panel reports the results of the regressions of the IRF coefficients one to four years after the shock, the average coefficients over the 12-year horizon, and the accumulated IRF coefficients on a specific institutional quality variable and years of schooling. ²² We report here the results using years of schooling as a proxy for education attainment. The results are generally robust to substituting years of schooling with education expenditure.

Table 4:

Multivariate Correlations

Source: Authors’ calculations.Notes: Robust standard errors are reported. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

Table 4:

Multivariate Correlations

	(1)	(2)	(3)	(4)	(5)	(6)
	IRF coefficients 1 year after the shock	IRF coefficients 2 years after the shock	IRF coefficients 3 years after the shock	IRF coefficients 4 years after the shock	Average IRF coefficients	Accumulated IRF coefficients
Control of corruption	−0.005	−0.006	−0.004*	−0.003*	−0.002**	−0.028**
	(0.004)	(0.004)	(0.002)	(0.002)	(0.001)	(0.012)
Years of schooling	−0.024	0.022	0.012	0.012	0.008	0.092
	(0.046)	(0.043)	(0.027)	(0.018)	(0.011)	(0.137)
Constant	1.070**	0.702**	0.486**	0.295**	0.224**	2.691**
	(0.332)	(0.310)	(0.190)	(0.131)	(0.082)	(0.979)
Observations	74	74	74	74	74	74
R-squared	0.040	0.032	0.043	0.045	0.072	0.072
Rule of law	−0.006	−0.006	−0.004*	−0.003*	−0.002**	−0.029**
	(0.004)	(0.004)	(0.002)	(0.002)	(0.001)	(0.013)
Years of schooling	−0.016	0.024	0.013	0.014	0.009	0.108
	(0.047)	(0.044)	(0.027)	(0.019)	(0.012)	(0.140)
Constant	1.062**	0.683**	0.473**	0.286**	0.217**	2.606**
	(0.329)	(0.309)	(0.190)	(0.131)	(0.081)	(0.975)
Observations	74	74	74	74	74	74
R-squared	0.047	0.031	0.042	0.045	0.072	0.072
Government effectiveness	−0.004	−0.005	−0.004	−0.003	−0.002**	−0.030**
	(0.005)	(0.005)	(0.003)	(0.002)	(0.001)	(0.014)
Years of schooling	−0.025	0.019	0.012	0.013	0.010	0.118
	(0.050)	(0.047)	(0.029)	(0.020)	(0.012)	(0.149)
Constant	1.059**	0.695**	0.488**	0.299**	0.227**	2.720**
	(0.333)	(0.313)	(0.192)	(0.132)	(0.082)	(0.987)
Observations	74	74	74	74	74	74
R-squared	0.033	0.017	0.030	0.030	0.061	0.061
Political stability	−0.006	−0.005	−0.003	−0.002	−0.001	−0.016
	(0.004)	(0.004)	(0.002)	(0.002)	(0.001)	(0.013)
Years of schooling	−0.018	0.019	0.007	0.008	0.002	0.020
	(0.046)	(0.043)	(0.027)	(0.019)	(0.012)	(0.140)
Constant	1.040**	0.665**	0.461**	0.278**	0.206**	2.475**
	(0.328)	(0.309)	(0.190)	(0.131)	(0.083)	(0.995)
Observations	74	74	74	74	74	74
R-squared	0.047	0.026	0.030	0.024	0.026	0.026
Economic Freedom of the World Index	−0.321**	−0.107	−0.103	−0.053	−0.049	−0.587
	(0.159)	(0.154)	(0.094)	(0.065)	(0.041)	(0.487)
Years of schooling	−0.004	0.001	0.003	0.004	0.003	0.033
	(0.050)	(0.049)	(0.030)	(0.020)	(0.013)	(0.154)
Constant	2.886**	1.291	1.037*	0.560	0.467*	5.605*
	(0.940)	(0.914)	(0.557)	(0.382)	(0.240)	(2.882)
Observations	67	67	67	67	67	67
R-squared	0.086	0.010	0.024	0.012	0.026	0.026

Source: Authors’ calculations.Notes: Robust standard errors are reported. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

View Table

Table 4:

Multivariate Correlations

	(1)	(2)	(3)	(4)	(5)	(6)
	IRF coefficients 1 year after the shock	IRF coefficients 2 years after the shock	IRF coefficients 3 years after the shock	IRF coefficients 4 years after the shock	Average IRF coefficients	Accumulated IRF coefficients
Control of corruption	−0.005	−0.006	−0.004*	−0.003*	−0.002**	−0.028**
	(0.004)	(0.004)	(0.002)	(0.002)	(0.001)	(0.012)
Years of schooling	−0.024	0.022	0.012	0.012	0.008	0.092
	(0.046)	(0.043)	(0.027)	(0.018)	(0.011)	(0.137)
Constant	1.070**	0.702**	0.486**	0.295**	0.224**	2.691**
	(0.332)	(0.310)	(0.190)	(0.131)	(0.082)	(0.979)
Observations	74	74	74	74	74	74
R-squared	0.040	0.032	0.043	0.045	0.072	0.072
Rule of law	−0.006	−0.006	−0.004*	−0.003*	−0.002**	−0.029**
	(0.004)	(0.004)	(0.002)	(0.002)	(0.001)	(0.013)
Years of schooling	−0.016	0.024	0.013	0.014	0.009	0.108
	(0.047)	(0.044)	(0.027)	(0.019)	(0.012)	(0.140)
Constant	1.062**	0.683**	0.473**	0.286**	0.217**	2.606**
	(0.329)	(0.309)	(0.190)	(0.131)	(0.081)	(0.975)
Observations	74	74	74	74	74	74
R-squared	0.047	0.031	0.042	0.045	0.072	0.072
Government effectiveness	−0.004	−0.005	−0.004	−0.003	−0.002**	−0.030**
	(0.005)	(0.005)	(0.003)	(0.002)	(0.001)	(0.014)
Years of schooling	−0.025	0.019	0.012	0.013	0.010	0.118
	(0.050)	(0.047)	(0.029)	(0.020)	(0.012)	(0.149)
Constant	1.059**	0.695**	0.488**	0.299**	0.227**	2.720**
	(0.333)	(0.313)	(0.192)	(0.132)	(0.082)	(0.987)
Observations	74	74	74	74	74	74
R-squared	0.033	0.017	0.030	0.030	0.061	0.061
Political stability	−0.006	−0.005	−0.003	−0.002	−0.001	−0.016
	(0.004)	(0.004)	(0.002)	(0.002)	(0.001)	(0.013)
Years of schooling	−0.018	0.019	0.007	0.008	0.002	0.020
	(0.046)	(0.043)	(0.027)	(0.019)	(0.012)	(0.140)
Constant	1.040**	0.665**	0.461**	0.278**	0.206**	2.475**
	(0.328)	(0.309)	(0.190)	(0.131)	(0.083)	(0.995)
Observations	74	74	74	74	74	74
R-squared	0.047	0.026	0.030	0.024	0.026	0.026
Economic Freedom of the World Index	−0.321**	−0.107	−0.103	−0.053	−0.049	−0.587
	(0.159)	(0.154)	(0.094)	(0.065)	(0.041)	(0.487)
Years of schooling	−0.004	0.001	0.003	0.004	0.003	0.033
	(0.050)	(0.049)	(0.030)	(0.020)	(0.013)	(0.154)
Constant	2.886**	1.291	1.037*	0.560	0.467*	5.605*
	(0.940)	(0.914)	(0.557)	(0.382)	(0.240)	(2.882)
Observations	67	67	67	67	67	67
R-squared	0.086	0.010	0.024	0.012	0.026	0.026

Source: Authors’ calculations.Notes: Robust standard errors are reported. ** and * next to a number indicate statistical significance at 1 and 5 percent, respectively.

The results for control of corruption, rule of law, and government effectiveness are generally consistent with the bivariate correlations in Figure 8. In the case of control of corruption and rule of law, we find that there is a negative and significant relationship at nearly all the horizons considered, as well as for the average and accumulated IRF coefficients. In the case of government effectiveness, the result holds only for the average and accumulated IRF coefficients.²³ This is particularly relevant considered that we have only 75 observations in a regression that is designed to explain the cross-section values of very heterogeneous estimated parameters. At the same time, we find little or no evidence suggesting that stronger political stability, a higher value of the Economic Freedom of the World Index, and more years of schooling act as absorbers of income inequality shocks on economic activity.

4.5 Robustness

The estimation methodology employed in this paper should address to the best extent possible issues related to endogeneity caused by reverse causality, cross-country comparability, bias induced by assuming homogeneity across countries, and cross-section dependence. Nonetheless, other issues common to the literature may persist. First, measurement error may bias the estimates. Second, since the adopted identification strategy is based on some assumptions, these may be driving the thrust of the results. Third, endogeneity may be present due to some time-varying omitted variable with an idiosyncratic dynamic and correlated to any of the endogenous variables in the empirical model. Fourth, dropping countries for which income inequality data is stationary may bias the results.

We discuss here the results from a battery of robustness tests which address some of these concerns. Figure 9 compares the marginal response of real per capita GDP growth to income inequality growth of the baseline model to the one obtained from some variations of it. As a first step, we substitute net Gini with market Gini. This is not strictly a robustness test as post-redistribution data measure the effects of various policy interventions, however they can still provide insights about the strength of the relationship.²⁴ Results in the top left panel confirm the negative and significant relationship between the variables.

Robustness Tests for the Composite Response of Real per Capita GDP Growth to Income Inequality Growth

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.Notes: Confidence intervals are calculated from a resampling simulation with 500 repetitions. The panels report the response of real per capita GDP growth to a shock in income inequality growth from a PSVAR with the following variables and orderings: real per capita GDP growth and market Gini (top left); net Gini and real per capita GDP growth (top center); redistribution, real per capita GDP growth, and net Gini (top right); real per capita GDP growth, real investment growth, and net Gini (bottom left); terms of trade, real per capita GDP growth, and net Gini (bottom center); real per capita GDP growth and net Gini including data for countries with stationary series (bottom right).

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Robustness Tests for the Composite Response of Real per Capita GDP Growth to Income Inequality Growth

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.Notes: Confidence intervals are calculated from a resampling simulation with 500 repetitions. The panels report the response of real per capita GDP growth to a shock in income inequality growth from a PSVAR with the following variables and orderings: real per capita GDP growth and market Gini (top left); net Gini and real per capita GDP growth (top center); redistribution, real per capita GDP growth, and net Gini (top right); real per capita GDP growth, real investment growth, and net Gini (bottom left); terms of trade, real per capita GDP growth, and net Gini (bottom center); real per capita GDP growth and net Gini including data for countries with stationary series (bottom right).

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Robustness Tests for the Composite Response of Real per Capita GDP Growth to Income Inequality Growth

Citation: IMF Working Papers 2016, 244; 10.5089/9781475560527.001.A001

Source: Authors’ calculations.Notes: Confidence intervals are calculated from a resampling simulation with 500 repetitions. The panels report the response of real per capita GDP growth to a shock in income inequality growth from a PSVAR with the following variables and orderings: real per capita GDP growth and market Gini (top left); net Gini and real per capita GDP growth (top center); redistribution, real per capita GDP growth, and net Gini (top right); real per capita GDP growth, real investment growth, and net Gini (bottom left); terms of trade, real per capita GDP growth, and net Gini (bottom center); real per capita GDP growth and net Gini including data for countries with stationary series (bottom right).

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While our identification strategy is based on the fact that income inequality is an input in the calculation of income inequality and therefore it is contemporaneously determined, we test the robustness of the results by inverting the ordering of the Cholesky decomposition. As shown in the top middle panel, such modification of the identification scheme allows changes in net Gini growth to have an immediate effect on real per capita GDP growth. Although with a different timing, such modification of the specification still replicates the negative and significant effect observed in the baseline results.

Similar to other papers employing different methodologies, we then try to add to our specification one variable at a time that is potentially correlated with any of the endogenous variables.²⁵ As a first test, we add redistribution from the SWIID 5.1 in a PSVAR with real per capita GDP growth and net Gini. The top right panel confirms the negative and significant response of income inequality growth on economic growth, even though with a somewhat delayed effect. The same experiment is repeated in the bottom left panel by adding real investment growth to the specification, without substantial changes to the estimates. Also, we add terms of trade growth and the results in the bottom center panel confirm that the marginal response is consistent with that estimated using the baseline specification.²⁶

Finally, we augment the dataset by adding data for the 9 countries presenting stationary series of net Gini and rerun the PSVAR. The results for the augmented dataset comprising 86 countries are shown in the bottom right panel. The estimated impact of income inequality on growth is very similar to that of the baseline sample of 77 countries. Also, the significance of the effect is maintained. In general, all the robustness tests provide broad support to the results obtained in the baseline empirical model.