The role of financial development in the relationship between income inequality and economic growth: an empirical approach using cross-country panel data

Abstract

The study complements the existing literature on the role of credit constraints in the interplay between income inequality and economic growth. The question “what type of financial development matters for inequality-growth relationship” is answered empirically by adopting a multi-dimensional index of financial development. The analysis covers 35 OECD member countries and 34 non-OECD economies starting from the year 1980 with varying coverage across countries. The results of the panel estimation techniques suggest that in the non-OECD countries, income inequality is positively associated with subsequent growth of per capita GDP under sufficiently developed financial markets. If the markets are poorly developed, the partial correlation between inequality and growth is statistically insignificant. For OECD countries, the association seems to be non-existent although weak evidence for growth-dampening inequality is found if both the level of inequality is high and the financial markets are highly developed. The results imply that promoting the development of financial markets – rather than institutions – may alleviate the adverse effects of income inequality on economic growth in under-developed countries.

1 Introduction

A large body of economic literature has emphasized the role of credit market imperfections in how income distribution affects economic development. In short, the central argument of the branch pushed forward most notably by Galor and Zeira (1993) and Galor and Moav (2004) states that, under credit constraints, income inequality may suppress the accumulation of human capital at low income levels, which may eventually be harmful for economic growth. Thus, development of financial institutions and markets may alleviate the growth-dampening effects of inequality.

Moreover, setting up new firms or expanding existing ones may require sufficiently concentrated income or wealth for the entrepreneurs to cover the sunk costs associated with entrepreneurial activity. By channelling funds to the low income individual with business ideas, financial development may help to disconnect the link between economic inequality and entrepreneurial activity. Aghion et al. (1999) go even further and note that under credit frictions, inequality may be negatively associated with investment opportunities. They argue that due to decreasing returns to individual capital investment, the marginal productivity of an investment made by the rich is lower than an investment made by the poor. It is also possible that high income inequality under high financial development may hurt growth, if for example due to insufficient checks and balances, the poorer households have the possibility to over-leverage themselves, which creates an additional layer of complexity in the interplay between economic growth, inequality and financial development.

This paper adds to the existing literature by asking what type of – if any – financial development matters for the inequality-growth relationship. The question is answered empirically. A multi-dimensional index of financial development (Svirydzenka 2016) is adopted. The index not only provides an aggregate measure but also separates the institutional evolutions from the development of financial markets. Furthermore, it provides measures of depth, access and efficiency for the institutions and markets and thus follows the influential characterization of financial systems by Cihak et al. (2012).

The objective of this study is not to isolate specific mechanisms, such as the human capital channel or over-leveraging discussed above, but rather to analyze the association between income inequality and per capita growth of GDP conditional on financial development. The empirical analysis relies on a panel data set that includes 69 countries, of which 35 are the members of the OECD. The study makes use of the structure of the data by disentangling the OECD member countries from the less-developed economies. Dictated by data coverage, the analysis uses observations from 1980 to 2017 at best though many countries are observed for shorter time periods.

The findings of the empirical analysis suggest that there is a positive association between income inequality and subsequent growth of per capita GDP in the non-OECD countries given that the financial markets are sufficiently developed. The evidence for an association between inequality and growth is weak in the OECD countries: only under high inequality and highly developed financial markets there are traces of a negative relationship between inequality and growth.

Although the methodological approach of the study cannot isolate causal mechanisms, novel evidence for the role of financial markets as a mediator in the inequality-growth relationship is found. In other words, instead of analyzing financial phenomena as causes of inequality like for example Blau (2018) and Furceri and Loungani (2018), who study capital account liberalization and stock market liquidity, respectively, this paper investigates whether the consequences, namely economic growth, of inequality depend on financial development.

The findings complement the earlier studies on the role of credit constraints in the interplay between inequality and growth and the vast literature that has used reduced-form cross-country and panel growth regressions to understand whether inequality matters for economic growth.¹ First, the finding that inequality is positively associated with growth when financial markets are sufficiently developed is compatible with the theoretical work by Galor and Zeira (1993) and Galor and Moav (2004), whose results on the adverse effects of inequality arise only when there are financial frictions. Second, in terms of the empirical studies on the inequality-growth nexus, the findings of this study suggest that the role of financial conditions should be accounted for in future work on the topic. Third, although the seminal study by Rajan and Zingales (1998) and related work on financial development and growth serve as a relevant background material, this study is essentially related to another branch of literature as financial development is considered as a mediator in the inequality-growth nexus rather than as a direct facilitator of growth.

The next section of the study introduces the data and econometric techniques while the third section presents the results of the empirical analysis. The fourth section concludes the findings. Many of the regression tables and figures are located in the appendices.

2 Data and methodology

The three key data sources of this study are the version 9.1 of the Penn World Table (Feenstra et al. 2015, PWT), the fourth version of the World Income Inequality Database (UNU-WIDER 2018, WIID) and the multi-dimensional index of financial development by Svirydzenka (2016). The coverage of these sources and the control variables narrow down the sample to include 35 OECD member economies and 34 non-OECD countries.

The aim of the multi-dimensional financial development index (Svirydzenka 2016) is to overcome the shortcomings of the use of single indicators to track financial development. Empirical studies have typically used either private credit or stock market capitalization, as ratios to GDP. However, even if financial systems were highly developed by these two measures, they may not work as the desired lubricant if they are wasteful or accessible only to few people.

As summarized in Fig.  1, the sub-indices capture the size and liquidity (depth), the ability of individuals and companies to access financial services (access) and the ability of institutions to provide the services with sustainable revenues and the activity of the capital markets (efficiency).² The sub-indices are constructed for banks, insurance companies, mutual funds and pension funds as a group (financial institutions) and for stock and bond markets (financial markets). Finally, the development of institutions and markets are gathered into the aggregate index.

Fig. 1

Financial development index pyramid

Table 1 presents the variables that are used to form the sub-indices. The two largely used proxies for financial development – private sector credit to GDP and stock market capitalization to GDP – are included as the underlying variables. The former for the depth of institutions, the latter for the depth of markets. The construction of the indices follows a four-stage approach. First, the underlying variables are normalized, second, the normalized variables are aggregated into the sub-indices, third, the sub-indices are aggregated into the indices of institutional and market development, and finally, the aggregate index is constructed. In her paper, Svirydzenka (2016) offers a detailed discussion on the methodology, portrays overall trends and discusses differences between countries and country groups.

Table 1 The underlying variables for depth, access and efficiency measures of Fig.  1

The primary data source for income inequality in this study is the fourth version of the World Income Inequality Database (WIID) maintained by the United Nations University World Institute for Development Economics Research (UNU-WIDER 2018). It is a secondary database combining information from several sources³ and builds on the work by Deininger and Squire (1996). Each update has aimed at improving data comparability, both within countries over time and across countries, by taking seriously the issues raised in the evaluative studies by for example Atkinson and Brandolini (2001) and Jenkins (2015). The data set includes not only information on the Gini coefficient but also on the income shares of each decile. Even though the data issues cannot be fully removed, I believe that the newest version of the WIID is the best available data source for income inequality in a cross-country setting. This conclusion is founded on the well-documented choices that account for the influential critique directed to the construction of secondary databases.

The empirical studies on the linkage between income inequality and economic growth have predominantly focused on disposable income, also referred to as net or post-tax & post-transfer income. Since the aim of this study is to complement the previous empirical literature by introducing a novel measure of financial development, the same concept of inequality is adopted. Although many of the suggested mechanisms in the theoretical literature emphasize wealth inequality rather than the dispersion of income, the focus on disposable income is well-founded as our consumption, saving and investing decisions are based on income after taxes and transfers. The listed economic decisions in turn are relevant for aggregate economic activity. A detailed discussion on the general properties of inequality data, comparison of the WIID data to other alternatives and the data selection algorithm are presented in “Appendix A”.

For data on economic growth, I rely on the Penn World Table (Feenstra et al. 2015, PWT), which is a standard data source for empirical cross-country studies offering annual data on numerous variables in a global scope. Economic activity is defined as expenditure-side per capita gross domestic product (GDP) and the rate of growth corresponds to logarithmic differences.

Following a standard convention in the literature, the baseline statistical model addresses growth of per capita GDP inside five-year non-overlapping windows. The last growth window is a three-year one (2015-2017). The aim of the choice is to (i) move away from a short-run scope influenced by business cycles (ii) and to mitigate the issues of missing observation and noisiness stemming from potential measurement error in the income inequality (Gini) and financial development (Svir, Svirydzenka (2016)) time series. The panel growth regression can be written as

$$\begin{aligned}&\frac{1}{4} (lnY_{i,t+4}-lnY_{i,t}) = \gamma lnY_{i,t-1} +\varvec{\delta }' \varvec{X}_{i,t} \nonumber \\&\quad + \beta _{1}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}\right) +\beta _{2}\left( \frac{1}{5}\sum _{j=0}^{4}Svir_{i,t-5+j}\right) \nonumber \\&\quad + \beta _{3}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j} \times \frac{1}{5}\sum _{j=0}^{4}Svir_{i,t-5+j}\right) + \alpha _i + \eta _t + \varepsilon _{i,t}, \end{aligned}$$

(1)

where $\alpha _i$ and $\eta _t$ are the vectors of fixed country and year effects and $\varepsilon _{i,t}$ is the overall error term. $Y_{i,t}$ stands for expenditure-side real per capita GDP in country i in year t while $\varvec{X}_{i,t}$ contains a set of control variables⁴. The purpose of including both the country and year fixed effects is to control for the bias stemming from both the unobservable variables that change over time but are constant over countries – such as large shifts in technology or educational attainment not captured by the years of schooling – and the factors that are different across countries but are constant over time. The latter effectively means that the empirical analysis relies on variation within countries.⁵

It is worth noting that the model does not include a lagged dependent variable, i.e. the growth rate during the previous five-year period, but the log of per capita GDP just before the growth window commences to capture convergence in growth rates. The estimates change only little and remain qualitatively intact if lagged growth rates are used instead of the chosen specification, which is standard in the literature.

So far, the modelling choices follow standard approaches. The novelty comes from the inclusion of the terms Svir and the interaction term to evaluate the dependency of the inequality-growth relationship on financial development. Moreover, the empirical analysis aims to fully utilize the richness of the financial development index (Svirydzenka 2016) introduced above. Consequently, the aggregate index, the development of financial institutions, the development of financial markets and the sub-indices (Fig.  1 and Table 1) enter the panel regressions one after another.

Table 2 Descriptive statistics, five-year non-overlapping windows

Table 2 shows the sample means and associated standard deviations for the focal variables of this study. Clearly, the OECD and non-OECD countries are substantially different from another, which comes as a no surprise. The higher growth rates of per capita GDP in the less developed countries depict the stylized fact of growth convergence: poorer countries tend to catch up and grow faster. The sample means for the levels of economic activity are not as informative since they have been growing over time and thus portray the level of development in the middle of the sample. Still, the large difference between the groups paints the big picture. The differences also exist for the Gini coefficients and financial development. The non-OECD countries tend to be more unequal while both the financial institutions and markets are more developed in the OECD member states. The substantial differences immediately suggest that the analysis relying in the full sample of 69 countries should be complemented by focusing on the two groups separately.

As the first step to examine the interplay between economic growth, income inequality and financial development, the observations are plotted in three-dimensional illustrations (Fig.  2) separately for the OECD and non-OECD countries. Regression planes from pooled least squares regressions, where the growth of per capita GDP is regressed on the contemporaneous Gini coefficient and either market or institutional development, are also fitted over the observations. This approach does not account for growth convergence, other growth determinants, country-specific characteristics or the time that the potential effects of inequality on growth takes to manifest themselves. Rather, the illustrations offer the first glance at the inter-dependencies between the variables under investigation.

Fig. 2

Pooled least squares regression planes, per capita growth regressed on Gini and financial development measure (five-year non-overlapping windows)

Again, differences between the OECD and non-OECD countries emerge. In the former, the regression planes are fairly flat for the aggregate index and institutional development, whereas Fig.  2b portrays how the growth rates of per capita GDP are lowest when the contemporaneous values of the Gini coefficient and market development are low. This naïve approach thus suggests that inequality and financial market development are good for economic growth in the rich countries. In the non-OECD countries alternatively, all planes tilt towards the right indicating that the contemporaneous correlation between economic growth and the Gini is negative. As can be seen below, this finding is largely due to the fact that the least developed economies in the group of the non-OECD countries tend to be more unequal but also grow faster as they are catching up (growth convergence). The aggregate index plane tilts slightly towards high values of the index, the feature is more prevalent for the financial institutions, whereas the inclination is the opposite for the development of the financial markets. Altogether, the inter-dependencies between growth, inequality and financial development seem to be heterogeneous between the aggregate index, the development of institutions and the development of markets in both country groups.

3 Results

This section presents the results of the empirical analysis, which builds on the panel growth regression laid out in Eq. (1). Results corresponding to a linear functional form and further extensions are also considered. The extensions include introducing alternative measures of income inequality, incorporating the potential effect of the extent of inequality on the results and using a panel estimation technique that can under certain conditions mitigate the potential issues stemming from omitted variables and reverse causality. Finally, instead of the multi-dimensional index, private credit to GDP and stock market capitalization to GDP are taken as the proxies of financial development.

Table 3 displays the estimates of specification (1) for the aggregate index, the development of financial institutions and the development of financial markets. Because of large differences in economic development, income inequality and financial development between the OECD and non-OECD countries and the rudimentary correlational evidence of Fig.  2, the panel regressions are run for the full sample and the two sub-samples separately to investigate whether the relationship is dependent on the country coverage. Moreover, this distinction seems important based on the findings of previous studies. In their meta-analysis, Neves et al. (2016) document that the association between inequality and growth seems to be negative and more pronounced in less developed countries than in rich countries. The table – not the statistical specifications themselves – excludes the estimates for the other growth determinants while “Appendix B” provides the full regression tables with controls. Moreover, the results for the sub-indices depth, access and efficiency are also located in the “Appendix”.

Table 3 The association between the Gini and economic growth conditional on the level of financial development. Fixed effects panel estimation, dependent variable: growth of per capita GDP inside non-overlapping five-year growth windows. Columns (2), (4) and (6) correspond to equation (1) while columns (1), (3) and (5) correspond to specifications without an interaction term. Control variables are omitted from the table

In a linear form, the association between income inequality and growth of per capita GDP is statistically insignificant in the full sample (column (1)) and in the sub-sample of OECD countries (column (3)). In the non-OECD countries however, the Gini coefficient is positively related with subsequent economic growth (column (5)). The patterns hold irrespective of whether the set of control variables include the aggregate index of financial development, the development of markets, the development of institutions or whether the level of economic development is the only control alongside the country and year fixed effects (Table 7 in “Appendix B”). Institutions and growth seem to be unrelated while a positive and significant association emerges between the markets and growth in the full sample and in the OECD countries. Moreover, the aggregate index is positively related with growth in the full sample.

Columns (2), (4) and (6) of Table 3 correspond to the statistical model of equation (1). Panels A and C show evidence that overall financial development and the development of markets play a role in the inequality-growth relationship in the full sample and in the non-OECD countries as many of the coefficients are individually and jointly statistically significant. This does not hold for institutions (Panel B) or in the sub-sample of OECD countries for any of the measures of financial development.

Yet, based on the parameter estimates, standard errors and tests of joint significance in Table 3, it is difficult to interpret the results in terms of the relationship between the Gini coefficient and subsequent economic growth conditional on the financial development index. To visualize the interplay between income inequality, economic growth and financial development, interaction plots, which display the point estimate of $Gini + Gini \times Svir$ along with the 95 % confidence intervals for different values of financial development, are introduced (Fig.  4). Again, the interest not only lies in the aggregate index but instead the richness of the data source (Svirydzenka 2016) is allowed to flourish. Moreover, the OECD and non-OECD countries are separated, which seems essential given the results of Table 3.

The results for the sample of OECD countries are blunt: there is no evidence for a statistically significant association between the Gini coefficient and subsequent economic growth in the quadratic specifications conditional on any of the measures of financial development. The interaction plots for OECD countries, in which zero is included in the confidence intervals for all cases, are omitted.

Fig. 3

Estimated association (95 % level confidence interval) between the Gini coefficient and per capita growth conditional on different measures of financial development, non-OECD countries

In the non-OECD countries, both the aggregate index (Fig.  2a) and development of financial markets (2c) seem to play a significant role in the inequality-growth relationship, whereas modelling the interaction through the development of institutions (2b) suggests that inequality and growth are not related. Furthermore, the sub-indices of market development (2d, 2e and 2f) replicate the main result of market development: under sufficiently highly developed markets, the association between the Gini coefficient and subsequent growth is positive.

The interaction plots of Fig.  3 immediately raise the question of how relevant the regions right from the cut-off, where the lower bound of the confidence interval is above zero, are. For the aggregate index, the highest quintile of the sample values is above the cut-off, whereas the corresponding share is 25 % for market development⁶. For the sub-indices depth, access and efficiency, the shares are approximately 25 %, 30 % and 23 %, respectively. If the point estimates are considered, 90 % of the sample values of the aggregate measure are above the cut-off, whereas for the measures of financial market development, the association is always positive.

The functional form of equation (1) also produces estimates for the relationship between financial development and growth conditional on the level of the Gini coefficient. In the OECD countries, under low income inequality, there is a positive association between the development of financial markets and growth, whereas in the non-OECD countries, the association is negative for low levels of the Gini coefficient. Such dependencies are not present for aggregate development or institutional development. As the emphasis of this study is to complement the previous reduced-form analysis on the interplay between income inequality and subsequent economic growth, the potential growth-promoting or growth-dampening effect of financial development is not thoroughly examined here.

The dependency of the inequality-growth relationship to the level of economic development. A potential worry over the results is whether the inequality-growth relationship in the non-OECD countries is simply conditional on the level of economic development rather than the development of financial markets. The panel level correlations reported in Table 4 mitigate this worry: there is no strong correlation between per capita GDP and the measures of financial development in either of the country samples. If the annual observations were used instead, relatively high positive correlations emerge. This is an additional benefit of using the five-year intervals.

Table 4 Correlations between per capita GDP and the measures of financial development. Panel level correlations between $lnY_{i,t-1}$ and $\frac{1}{5}\sum _{j=0}^{4}Svir_{i,t-5+j}$

The interaction plot (Fig.  4) shows that the upward-sloping profile of Fig.  3 does not emerge if the estimated model is the following:

$$\begin{aligned}&\frac{1}{4} (lnY_{i,t+4}-lnY_{i,t}) = \gamma lnY_{i,t-1} +\varvec{\delta }' \varvec{X}_{i,t} \nonumber \\&\quad + \beta _{1}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}\right) \nonumber \\&\quad + \beta _{2}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j} \times lnY_{i,t-1}\right) + \alpha _i + \eta _t + \varepsilon _{i,t}, \end{aligned}$$

(2)

where the notation follows equation (1). Rather, in the non-OECD countries, the association between the Gini coefficient and subsequent growth is positive for low levels of per capita GDP, and negative when per capita GDP is high. This result is compatible with the theoretical analysis by Galor and Moav (2004), whose main finding state that inequality enhances growth through the accumulation of physical capital at low levels of economic development, whereas in more developed economies human capital has become the prime engine for growth and inequality hurts growth.

Fig. 4

Estimated association (95 % level confidence interval) between the Gini coefficient and per capita growth conditional on per capita GDP, non-OECD countries

Using top income shares. The main results are robust to considering the disposable income shares of either the highest-earning quintile or decile. First, for OECD countries, per capita GDP growth shows no dependency on the concentration of income. Second, in non-OECD countries, the association between income inequality and growth seems to depend on the development of financial markets irrespective of the measure of inequality. Figure 8 and 9 – similar to Fig.  3 – in “Appendix C” portray the results for the top income shares in the sample of non-OECD countries. The similarities in results are hardly surprising as the Gini coefficient and the top income shares follow one another closely⁷. The main results remain unchanged if the Palma ratio (top 10 % income share divided by the bottom 40 % income share) is used instead of the Gini coefficient or the top income shares.

Addressing the extent of inequality. One aspect that may affect the above-stated results, is potential dependency on the extent of income inequality. To investigate this possibility, piece-wise panel growth regressions are introduced:

$$\begin{aligned}\frac{1}{4} (lnY_{i,t+4}-lnY_{i,t}) &= \gamma lnY_{i,t-1} +\varvec{\delta }' \varvec{X}_{i,t} \nonumber \\&\quad + \beta _{1}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}^{top25}\right) +\beta _{2}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}^{bottom75}\right) +\beta _{3}\left( \frac{1}{5}\sum _{j=0}^{4}Svir_{i,t-5+j}\right) \nonumber \\&\quad + \beta _{4}\left( \frac{1}{5}\sum _{j=0}^{4}Gini^{top25}_{i,t-5+j} \times \frac{1}{5}\sum _{j=0}^{4} Svir_{i,t-5+j}\right) \nonumber \\&\quad + \beta _{4}\left( \frac{1}{5}\sum _{j=0}^{4}Gini^{top75}_{i,t-5+j} \times \frac{1}{5}\sum _{j=0}^{4} Svir_{i,t-5+j}\right) \nonumber \\&\quad + \alpha _i + \eta _t + \varepsilon _{i,t}, \end{aligned}$$

(3)

where the notation follows equation (1). This approach allows for different coefficients above and below a certain cut-off in the distribution of the Gini coefficient. The analysis uses the 75th percentile as the cut-off – the results show only little sensitivity to alternative choices. The reported one is consistent with the study by Berg et al. (2018).

Table 5 reports the piece-wise panel regression results for the OECD and non-OECD countries separately when the relationship between income inequality and subsequent growth is allowed to depend on financial market development and the extent of inequality. Again, the additional growth determinants are excluded from the table for readability. As above, the development of financial markets seems to play a role in the inequality-growth relationship while institutional development does not.

Clearly, the parameter estimates for the Gini coefficient and for the interaction term are different conditional on the level of the Gini in the OECD countries. In the less developed economies, the two coefficients for the Gini are not statistically different from one another while the null hypothesis of equality of the interaction terms is rejected.

Table 5 The association between the Gini and economic growth conditional on financial market development and the extent of inequality. Fixed effects panel estimation (equation (3)), dependent variable: growth of per capita GDP inside non-overlapping five-year growth windows. Control variables are omitted from the table

As above, the interaction plots are more suitable than regression tables to demonstrate the inter-dependencies studied in this paper. The results for the non-OECD countries (Figs.  5b and d) are very similar between the low and high inequality cases and portray a very similar picture to Fig.  2c. In the sub-sample of OECD countries, however, the results are dependent on the extent of income inequality as the results of Table 5 already suggested. At the bottom 75 % of the distribution of the Gini coefficient, the association between income inequality and growth seems non-existent (Fig.  5c). This holds across specifications with linear functional form and ones that incorporate non-linearities to different measures provided by Svirydzenka (2016). Under both high inequality and high financial market development, income inequality is negatively associated with subsequent growth. This non-linearity is not present for the aggregate index or the development of institutions.

Fig. 5

Estimated association (95 % level confidence interval) between the Gini coefficient at the top 25 % and at the bottom 75 % percent and per capita growth conditional on development of financial markets (FM)

The panel regressions of this analysis suggest that financial markets, rather than institutions, matter for the interplay between income inequality and per capita growth of GDP. For the non-OECD countries the relationship is found not to depend on the level of income, whereas for the OECD countries, incorporating the extent of inequality seems essential to get the right picture. However, the statistical approach used so far can only capture a partial correlation between the variables of interest despite the chosen timing convention and controlling for several other determinants of economic growth and country and year fixed effects.

Controlling for endogeneity. The limitations of simple panel estimation techniques are well-recognized in the literature. To address the identification issues caused by both omitted variables and reverse causality, researchers have increasingly started to apply generalized method of moments (GMM) estimators. The so-called system GMM or sGMM (Arellano and Bover 1995; Blundell and Bond 1998)⁸ has been particularly popular. In short, the sGMM estimates equation (1) and its first-difference as a system using suitably lagged values of the regressors as instrument variables for the first-differenced equation and lagged variables of first-differences as instruments for the level equation. The estimator can therefore exploit both variation in time and across individuals since the individual-specific characteristics are not removed from the equation in levels.

To inspect the validity of the lagged levels and differences of the regressors as instruments, the Arellano-Bond autocorrelation test, the Hansen test for overidentifying restrictions and the difference-in-Hansen tests are nowadays often reported alongside the number of instruments. This is a clear improvement on past practices, where the tractability of the choices regarding the use of the sGMM was often poor. In this study, for each sGMM estimation, Windmeijer (2005) small sample correction is used for robust standard errors; in the a priori estimate of the covariance matrix, the upper right and lower left quadrants are zeroed out; and the two-step estimator is favored over the one-step one. Moreover, the set of instruments is narrowed down to include only the observations during twice lagged windows for the regressors to reduce the risk of instrument proliferation.

Despite restricting the size of the instrument matrix, the sGMM tends to run into issues in small samples. Namely, the p-value of Hansen J can be suspiciously high implying that the estimator suffers from instrument proliferation, which weakens the power of testing for the validity of the instruments. Consequently, dividing the sample into OECD and non-OECD countries is out of reach. Moreover, as the instrument counts increases with the number of regressors, only the level of economic development is included as an additional growth determinant. To circumvent the problem, an approach, which uses the full sample of 69 countries together with cross-terms that indicate whether a country is a member of the OECD or not, is introduced (see equation (4) in “Appendix D”). These choices of modelling reduce the number of instruments relative to the number of countries compared to the sub-sample analysis. Still, the tests for overidentifying restrictions speak for proliferation and the number of instruments clearly exceeds the number of countries (Table 14 in “Appendix D”) violating the rule of thumb provided by Roodman (2009), who offers an influential guide for the use of the sGMM.

The results of the sGMM estimations are illustrated by interaction plots familiar from above. Figure 10 in “Appendix D” replicates Fig.  5. The results for the non-OECD countries are very similar between the fixed effects estimator and the sGMM. On the contrary, the result of growth-hurting inequality under high inequality and high development of financial markets in the OECD countries is not robust to the introduction of the sGMM.

The sGMM allows for heteroskedasticity and autocorrelation within countries but not across them. The assumption of no heteroskedasticity across countries is a strong one and since the Arellano-Bond autocorrelation test and the estimation of robust standard errors make the assumption, it is not innocent. Unfortunately, testing for conditional homoskedasticity is not straight-forward in a GMM framework⁹ and thus it is not clear whether the sGMM improves on the simple panel estimation techniques even if the autocorrelation test and Hansen J were to support appropriateness of the model specification. Moreover, it has been shown that the sGMM estimates tend to be associated with wide weak-instrument robust confidence intervals (Bazzi and Clemens 2013; Kraay 2015).

Although the sGMM estimator is not a remedy to isolate the effects of inequality to growth in cross-country panels, its use is also motivated by controlling for the so-called dynamic panel bias (Nickell 1981). The GMM estimators account for the correlation between lagged dependent variables and the fixed effects in the error term, and thus from this perspective too, the similarities between the fixed effects and sGMM estimates suggest that the main findings for the non-OECD sample are not driven by any apparent source of misspecification.

4 Conclusion

This study empirically investigated the role of financial development in the interplay between income inequality and growth of per capita GDP. Although financial frictions are recognized as an integral part of the inequality-growth nexus in theoretical work and the linkages between financial development and inequality have been widely-studied empirically, previous empirical studies have not investigated whether the association between inequality and growth is conditional on the development of financial institutions or markets. The empirical analysis relied on panel data techniques and a multi-dimensional index of financial development together with survey-based evidence on the distribution of disposable income and a standard data source for overall economic activity.

A positive partial correlation was found between income inequality and subsequent growth of per capita GDP in the non-OECD countries given that the financial markets were sufficiently developed. The results were similar between standard fixed effects estimator and a technique that controls for endogeneity. The evidence for an association between inequality and growth was weak in the sample of OECD countries – irrespective of financial development. The fixed effects estimates suggested that under both high income inequality and highly developed financial markets the association between inequality and economic growth was negative. However, this finding was not robust to controlling for endogeneity.

Typically, panel growth regressions have two main limitations. First, it is not clear whether a parameter estimate corresponds to causal mechanisms or whether it is for example driven by some underlying institutional traits not captured by the controls. Second, the policy relevance of a finding that could be read as inequality causing a decrease or an increase in economic growth would still be limited. The policy actions aiming to affect income inequality are controlled by national policy-makers and the set of possible tools is large and associated with country-specific limitations, whereas the result necessarily relies on data that have been pooled from many countries.

The first concern is relevant in the context of this study. Even though the main result regarding the non-OECD countries was robust between different estimation techniques, the findings do not warrant a causal interpretation.

The second concern is perhaps less relevant in the context highlighted in this study as opposed to a case, where only inequality and growth are considered. The findings of this study suggest that it may be possible to focus on the development of financial markets as a tool to mitigate the potential adverse effects of income inequality on economic growth. The distinction is important if policies affecting financial markets are easier to coordinate supra-nationally than predistributive and redistributive actions.

Appendices

Appendices

A Data selection for the WIID

As informatively summarized by Jenkins (2015), Atkinson and Brandolini (2001) state that non-comparability in secondary data sets may arise because of differences in the definitions of income, in the data sources or in the processing of the income data in the original source. Differences both within countries in time and across countries may emerge. Many of the differences are associated with predictable patterns on inequality if their nature is not drastically heterogeneous over time and across countries. Unfortunately, the assumption of homogeneity is unlikely to hold for the WIID despite major improvements on the earlier databases and thus the practical implications need to assessed by comparing the WIID series with other sources of at least as good a quality.

In the WIID, each observation is labeled as one of possible income, consumption or expenditure concepts as strongly recommended by the seminal evaluative studies. Following the assertive conclusion of Jenkins (2015), I explicitly report the data selection algorithm inspired by Jäntti et al. (2018) in “Appendix A”. After separating the net income observations from the rest, two issues remain for empirical work: the observations are of varying quality and there are often multiple observations for each country-year pair. Some of the multiple observations are due to multiple surveys but predominantly the measurements come from the same survey and it is just the computation (and the statisticians in charge) that change. Helpfully, the WIID team has introduced a variable called a quality score, which ranks the observations from 3 to 13. By ranking the observations based on this score, presented in “Appendix A”, and picking the highest, I can use the observations of best possible quality to form the final country panel and get rid of many of the duplicate observations. In case of observations tied on the quality score for a given country-year pair, a simple average is taken to obtain unique observations. I believe that this data selection procedure may be helpful for future researchers who need to merge the WIID into some other cross-country panel.

Many recent studies, of which some have received much attention (Ostry et al. 2014), have used the Standardized World Income Inequality Database (Solt 2016, SWIID) as their source for data on the Gini coefficients. The SWIID is based on the WIID, supplemented by other sources and all observations come from its imputation model. In his conclusions, Jenkins (2015) states that costs associated with the use of the WIID are present for the SWIID too. Additionally, he urges to set questions about the imputation model against the benefits of coverage and draws a conclusion that the WIID should be used instead of the SWIID given that the use of the WIID is accompanied by a tractable data selection algorithm.

Data selection in practice. The observation is defined as net income if the WIID4 variable resource_detailed, previously labeled as welfare definition, is one of the following: “Earnings, net”, “Income, net”, “Monetary income, net”, “Monetary income, net (excluding property income)” or “Taxable income, net”; as consumption income if resource_detailed is “Consumption”; and as market income if resource_detailed is one of the following: “Earnings, gross”, “Factor income”, “Income, gross”, “Market income”, “Monetary income, gross”, “Taxable income, gross” or “Taxable income, gross (including deductions)”.

Based on the variable quality_score running from 3 to 13, I rank the observations and pick the highest to use the observations of best possible quality to form the final country panel and get rid of many of the duplicate observations. In case of observations tied on the quality score for a given country-year pair, a simple average is taken to obtain unique observations.

The quality score is defined in the following way by the WIID team (UNU-WIDER 2018): We award points to the observations based on their attributes in the following way (maximum is 13 points). Gini coefficient is available (1). Resource concept: Consumption, Income (net), Income (gross), Monetary income (gross), Monetary income (net) (5), Income, Monetary income, Market income (3), Factor income, Primary income, Taxable income, Earnings (1). Equivalence scale: Per capita or equivalized (3), No adjustment (2). Area coverage: All, Urban, Rural (1). Population coverage: All (1). Distributional share information: All of d1-q5 are available (2), All of q1-q5 are available (at least one of d1-d10 is missing) (1).

Comparative analysis between different data sources. The OECD Income Distribution Database (OECD 2019)¹⁰ provides data on the net income Gini coefficients for its member states. All series correspond to same OECD income definitions and thus they should be more comparable across time and across the OECD countries than the WIID ones. Therefore, the OECD database offers a point of reference to evaluate whether the WIID series differ from series of likely higher quality in a subsample of OECD countries. For non-OECD countries, a comparative exercise would be a cumbersome task since the reference series would have to be gathered from various sources listed under footnote$^{3}$ and improvements on comparability relative to the WIID would be difficult to establish.

Following Atkinson and Brandolini (2001), the WIID, the OECD data and the Standardized World Income Inequality Database (Solt 2016, SWIID)¹¹ are used to form cross-country inequality rankings and to compare within-country inequality trends. The WIID series correspond to the result of the above-described data selection algorithm and thus the observations are averages over the periods 2000–2004 and 2010–2014. Due to gaps in the WIID and OECD data, the comparison is restricted to 14 countries. Other choices of reference years would reduce the ranking sample even further. A single major glitch clearly emerges: the 2010 WIID ranking places Denmark as fifth while all others rank the country in the top two. As can be seen in Fig.  6, the WIID very likely overestimates the level of inequality in Denmark in 1995 and 2000. Otherwise, the rankings are fairly stable although changes occur especially within the Nordic countries who share low levels of income inequality and whose values for the Ginis are close to one another irrespective of the data source. All pairwise correlations between the rankings in a point in time are well above 0.95. (Tables 6 ,7,8,9)

Table 6 Inequality rankings in a subset of 14 OECD countries. Countries are ranked based on the value of the Gini coefficient. The smallest Gini is marked by 1, the largest by 14

Based on graphical analysis, of which Fig.  6 is an example, the WIID in general matches the data provided by the OECD modestly well although some of the time variation is undoubtedly due to differences between surveys or calculations of the income distributions. Canada is an example of a case where all three alternatives paint a similar picture, the SWIID probably underestimates the extent of inequality in Mexico while the WIID series show lower values than the OECD ones for the US (Figs. 7, 8) (Tables 10,11,12,13)

B Full fixed effects panel regression tables

See Tables 7, 8, 9, 10, 11, 12, 13.

Table 7 Parsimonious linear panel growth regression. Fixed effects panel estimation results with only convergence term and the Gini coefficient as explanatory variables, dependent variable: growth of per capita GDP inside non-overlapping five-year growth windows

Table 8 Financial development (aggregate index). Fixed effects panel estimation, dependent variable: growth of per capita GDP inside non-overlapping five-year growth windows. Columns (2), (4) and (6) correspond to equation (1), where Svir is replaced with FD. Columns (1), (3) and (5) correspond to specifications without an interaction term

Table 9 Development of financial institutions. Fixed effects panel estimation, dependent variable: growth of per capita GDP inside non-overlapping five-year growth windows. Columns (2), (4) and (6) correspond to equation (1), where Svir is replaced with FI. Columns (1), (3) and (5) correspond to specifications without an interaction term

Table 10 Development of financial markets. Fixed effects panel estimation, dependent variable: growth of per capita GDP inside non-overlapping five-year growth windows. Columns (2), (4) and (6) correspond to equation (1), where Svir is replaced with FM. Columns (1), (3) and (5) correspond to specifications without an interaction term

Table 11 Depth of financial markets. Fixed effects panel estimation, dependent variable: growth of per capita GDP inside non-overlapping five-year growth windows. Columns (2), (4) and (6) correspond to equation (1), where Svir is replaced with FMD. Columns (1), (3) and (5) correspond to specifications without an interaction term

Table 12 Access to financial markets. Fixed effects panel estimation, dependent variable: growth of per capita GDP inside non-overlapping five-year growth windows. Columns (2), (4) and (6) correspond to equation (1), where Svir is replaced with FMA. Columns (1), (3) and (5) correspond to specifications without an interaction term

Table 13 Efficiency of financial markets. Fixed effects panel estimation, dependent variable: growth of per capita GDP inside non-overlapping five-year growth windows. Columns (2), (4) and (6) correspond to equation (1), where Svir is replaced with FME. Columns (1), (3) and (5) correspond to specifications without an interaction term

C Association between the top income shares and growth of per capita GDP

Fig. 6

The disposable income Gini coefficients in Canada, Denmark, Mexico and the United States

Fig. 7

The distributions of top disposable income shares in OECD and non-OECD countries

Fig. 8

Estimated association (95 % level confidence interval) between the top 20 % income share and per capita growth conditional on different measures of financial development, non-OECD countries

D Controlling for endogeneity: system GMM

Fig. 9

Estimated association (95 % level confidence interval) between the top 10 % income share and per capita growth conditional on different measures of financial development, non-OECD countries

$$\begin{aligned}\frac{1}{4} (lnY_{i,t+4}-lnY_{i,t}) &= \gamma lnY_{i,t-1} +\beta _{1}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}^{top25}\right) + \beta _{2}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}^{bottom75}\right) \nonumber \\&\quad + \beta _{3}\left( \frac{1}{5}\sum _{j=0}^{4}FM_{i,t-5+j}\right) + \beta _{4}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}^{top25} \times OECD\right) \nonumber \\&\quad + \beta _{5}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}^{bottom75} \times OECD\right) \nonumber \\&\quad + \beta _{6}\left( \frac{1}{5}\sum _{j=0}^{4}FM_{i,t-5+j} \times OECD\right) + \beta _{7}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}^{top25} \times \frac{1}{5}\sum _{j=0}^{4}FM_{i,t-5+j}\right) \nonumber \\&\quad + \beta _{8}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}^{top75} \times \frac{1}{5}\sum _{j=0}^{4}FM_{i,t-5+j}\right) \nonumber \\&\quad + \beta _{9}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}^{top25} \times \frac{1}{5}\sum _{j=0}^{4}FM_{i,t-5+j} \times OECD\right) \nonumber \\&\quad + \beta _{10}\left( \frac{1}{5}\sum _{j=0}^{4}Gini_{i,t-5+j}^{top25} \times \frac{1}{5}\sum _{j=0}^{4}FM_{i,t-5+j} \times OECD\right) + \alpha _i + \eta _t + \varepsilon _{i,t}, \end{aligned}$$

(4)

where FM stands for the development of financial markets while otherwise the notation follows equation (1). Since the sGMM estimator is for numerical issues ill-suited for subsample analysis due to the limited data coverage of this study, additional interactions are introduced.

Fig. 10

System GMM estimates (95 % level confidence interval) for the Gini coefficient at the top 25 % and at the bottom 75 % percent on per capita growth conditional on development of financial markets (FM)

Table 14 System GMM estimates for the association between the Gini coefficient and economic growth conditional on financial market development and the level of inequality. System GMM panel estimation, dependent variable: growth of per capita GDP inside non-overlapping five-year growth windows. The model is given in equation (4)