Income Inequality And Economic Growth: A Panel VAR Approach
Empir Econ (2015) 48:1541–1561DOI 10.1007/s00181-014-0841-7Income inequality and economic growth: a panel VARapproachBebonchu Atems · Jason JonesReceived: 18 July 2012 / Accepted: 18 April 2014 / Published online: 23 July 2014 Springer-Verlag Berlin Heidelberg 2014Abstract The paper uses a new and improved comprehensive dataset on inequalityto examine the effects of inequality on per capita income and the effects of per capitaincome on income inequality. The use of such a comprehensive cross-state panelallows for the estimation of the dynamic responses of inequality and per capita incomeusing panel vector autoregressive (VAR) models. Cumulative impulse responses froma baseline bivariate VAR model indicate that shocks to the Gini index of inequalitysignificantly decrease the level of per capita income. This finding is robust to changesin the measures of inequality used, as well as to the estimation of a three-variablemodel. We also find that the relationship between inequality and per capita incomevaries over time and is sensitive to particular episodes in history.KeywordsInequality · Growth · Panel vector autoregressionsJEL Classification040 · C33 · I241 IntroductionThere has been a recent surge in the number of papers studying the relationship betweenincome inequality and economic growth. Such renewed interest has been fueled byrecent increases in income inequality in the U.S., as well as by empirical studies thatdocument conflicting results on the relationship between inequality and the level of perB. Atems (B)School of Business, Clarkson University, 8 Clarkson Avenue, Potsdam, NY 13699, USAe-mail: batems@clarkson.eduJ. JonesDepartment of Economics, Furman University, 3300 Poinsett Highway, Greenville, SC 29613, USA123
1542B. Atems, J. Jonescapita income or growth [Partridge (1997); Li and Zou (1998) and Forbes (2000) findpositive relationships, while Alesina and Perotti (1994) and Alesina and Perotti (1996)find negative relationships). These results have generated a good deal of discussionbecause they pose significant challenges to policy makers.A particular challenge, from a policy standpoint, is that while several theoreticalmodels show positive (see e.g., Li and Zou 1998; Galor and Tsiddon 1997) or negative(see e.g., Alesina and Perotti 1994; Persson and Tabellini 1994) effects of inequalityon the level or growth of per capita income, their empirical counterparts rely oncorrelations and not necessarily on causality between inequality and per capita income.However, one cannot make informed public policy based on correlations because thesesimple correlations may lead to misguided policy.Several empirical studies use cross-sections or panels of countries to examine therelationship between economic performance and inequality. Partridge (1997); Fallahand Partridge (2007), and Panizza (2002), among others, all point out that a problemwith many cross-country studies is the quality and comparability of the inequalitydata. These quality and comparability issues in cross-country data can result in measurement error, which may induce numerical instability into the regression estimates,thus having dire consequences on their precision. Forbes (2000) notes that randommeasurement error for example can lead to an attenuation bias, which decreases thesignificance of the results. A potentially more pervasive problem, Forbes notes, issystematic measurement error, which can generate a positive or negative bias basedon the correlation between the measurement error and other variables in the regressionmodel. 1 This line of argument caused Kanbur (2000) to make the following argumentagainst cross-country studies:A superior approach is one which looks at country experiences in their historical and policy detail, and approaches the issues of policy directly and specifically.relying on cross-country regressions of inequality on per capita incomeor growth to support or contradict a policy “tradeoff” between the two does notseem to have been very productive (p. 832).Furthermore, the relationship between inequality and the level or growth of per capitatends to vary depending on the time intervals under consideration. In general, studiesthat examine the short- and/or medium-run relationship tend to find a positive relationship, whereas studies that examine their longer-run relationship tend to find a negativerelationship. Li and Zou (1998) and Forbes (2000), who use data averaged over 5year periods find a positive relationship. Forbes (2000) shows that when the data areaveraged over 10-year periods, the coefficient on inequality remains positive, but dramatically decreases to the extent that it becomes insignificant. Persson and Tabellini(1994) and Alesina and Rodrik (1994), who use data averaged over longer periods findnegative relationships. It is worth mentioning that this set-up (averaging over n periods)is not without criticism. Attanasio et al. (2000) note that annual data provide information that is lost when averaging. They also argue that the length of business cycles1 For example, Forbes states that “if more unequal countries tend to underreport their inequality statisticsand also tend to grow more slowly than comparable countries with lower levels of inequality, this couldgenerate a negative bias in cross-country estimates of the impact of inequality on growth”.123
Income inequality and economic growth1543varies over time and across space, and because the interval over which these averagesare computed is arbitrarily fixed, there is no guarantee that business cycles are cut inthe right way. In addition, they insist that if averaging indeed measures the long-runeffects, it prevents the analysis of short-run effects which usually include the interesting dynamic interplay of forces acting in opposite directions or different magnitudes.In this paper, we address the aforementioned problems using a new comprehensivepanel of annual state-level income inequality from 1930 to 2005 assembled by Frank(2009a, b). Our goal was to examine the response of per capita income to shocks ininequality and the effects of inequality on the level of per capita income using a panelvector autoregression (VAR) approach. The new dataset, together with our empiricalmethodology, addresses the above mentioned problems in several ways. Firstly, whilewe are under no illusions that our dataset is free of measurement error, using state-leveldata decrease the problem significantly. Frank (2009b) points out that:The greater homogeneity of state-level data helps mitigate the difficulty in adequately capturing structural differences across international panels of earlierstudies such as Forbes (2000) and Barro (2000). Corruption levels, labor marketflexibility, tax neutrality, tradition of entrepreneurship, and many other factorsare only poorly measured, if at all (Barro 2000, pp. 10–11), and these sources ofheterogeneity are much more likely to contribute to omitted variable bias acrosscountries than across states (Frank 2009b).Secondly, a panel VAR approach allows not only for the examination of the correlationbetween income inequality and per capita income, but also the dynamic responses ofthese variables. Thirdly, prior studies on the relationship between the level or growth ofper capita income and inequality have traditionally followed one of two paths: the firstpath, motivated by the work of Kuznets (1955), examines how economic performanceaffects inequality. The other line of research examines rather the effect of inequalityon economic performance. Our panel VAR methodology unifies these two approachesbecause our approach simultaneously examines the effect of changes in inequality onper capita income and the effect of per capita income on inequality. Finally, by usingannual state-level data, we are able to examine both the short-run and long-run effectsof inequality and per capita income. To check for robustness, we also identify theresponse of the level of per capita income to several other inequality measures. Toour knowledge, this paper is the first that uses a panel VAR approach to examine theeffect of inequality on per capita income and per capita income on inequality usingU.S. state-level data.Our empirical approach is certainly not without limitations. A potential limitation isthat the baseline estimates of our model come from a bivariate panel VAR model of percapita income and changes in inequality. While bivariate VAR models have frequentlybeen used in the traditional time-series VAR literature (Blanchard and Gali 2007;Kilian and Vigfusson 2011; Bachmeier and Cha 2011), it is possible that several shocksmight be simultaneously affecting per capita income growth. The use of state-leveldata limits the series that can be added to the panel VAR model. In addition, we do notbelieve that this limitation is significant enough for the purposes of this paper becauseour primary purpose is on the cumulative responses of per capita income and inequality,and our empirical approach allows for a parsimonious, valid identification framework.123
1544B. Atems, J. JonesThe impulse response functions (IRFs) from the estimated baseline bivariate panelVAR models show a pattern in which real per capita income tends to decrease following a shock to the Gini index. The maximum effect on real per capita income levelsoccurs approximately 5 years after the shock. This finding is robust to changes in themeasures of inequality used. We also find that income inequality decreases followinga one percentage point increase in per capita income, although the initial direction andsignificance differ depending on the measure of inequality used. To examine how stable our estimated impulse responses are, and to what extent they are driven by eventssuch as World War II and the Great Moderation, we split our sample into three subsamples: 1930–1947, 1948–1984, and 1985–2005. The IRFs for the first subsample arequalitatively identical to those shown in the entire sample except that they are twice aslarge in magnitude. For the 1948–1984 subsample, per capita income has no significant responses following inequality shocks, while the response of inequality to incomeshocks is negative. For the 1985–2005 period, per capita income decreases slightlyafter a Gini shock, while the Gini response to an income shock is mostly insignificant,although there is an initial positive response within the first 2 years after the shock.Because some researchers argue that bivariate models may omit relevant information,we include a measure of human capital, and estimate a trivariate panel VAR model.The general results hold, indicating that the identified shocks from the bivariate VARmodel are not contaminated by shocks other than income or inequality shocks.Some researchers have argued that the results obtained when examining the shortrun relationship between income inequality and per capita income or growth may bespurious if these results are not robust to medium-run and long-run situations (Partridge1997). Consequently, we estimate the dynamic responses of the level of per capitaincome and inequality using data averaged over 5- and 10-year periods. We find thatin general, in the medium run (5 year averages) and the long run (10 year averages),the aforementioned results hold. That is, in the medium- and long-run inequality(Gini) decreases per capita income, and per capita income shocks decrease inequality.The literature on the relationship between inequality and growth also stresses theimportance of initial conditions on the level and growth of per capita income (Durlaufand Quah 1999). To this end, we examine how initial inequality affects growth in themedium and long terms. We find that in the medium run, initial inequality has a positiveimpact on the level of per capita income, however, the effect turns and stays negativeafter two periods. When we estimate the long-run response of per capita income to aninitial inequality shock, the response is negative and persistent.The rest of the paper proceeds as follows. Section 2 provides an overview of the data.Section 3 discusses the empirical methodology, while Sect. 4 estimates and presentsthe key results of the panel VAR model relating real per capita income and incomeinequality as measured by the Gini index. Section 5 concludes.2 Overview of the dataThis section presents a brief overview of the data as a prelude to the estimation of the structural VAR. Our dataset consists of annual data on the percentagechange in per capita real income and various income inequality measures for the 48123
Income inequality and economic growth1545b1940196019802000Years 0.15 0.10 0.05 0.00 0.05 0.108.08.59.09.50.15a1940196019802000YearsFig. 1 State-level average of real income per capita and real income per capita growth: 1930–2005. aAverage log of real per capita income. b Real per capita income growthcontiguous states of the US (and DC) from 1930 to 2005. The data on nominal incomeper capita were collected from the regional economic information systems of theBureau of Economic Analysis (BEA-REIS) and deflated using the consumer priceindex (1982 1984 100). Data on income inequality were downloaded from Professor Mark Frank’s website. Figure 1 shows the state-averaged real income per capitafor all 48 states and DC, and the corresponding average growth rate. It is difficult todistinguish the cyclical movements in per capita income because the overall upwardtrend is so strong. A slowdown in the rate of growth beginning in the early 1970s isapparent from the graph, however. Figure 1b shows the growth rate real income percapita. The most noteworthy feature of this graph is the decrease in volatility of percapita income growth after 1945 and again in the beginning of the early 1970s.Figure 2 shows state-averaged measures of inequality from 1930 to 2005. All theseindices of inequality usually lie between 0 and 1. An index that is close to 1 indicates asociety characterized by high income inequality. These graphs display that in general,income inequality in the U.S. was low until the early 1980s after which a distinct risein inequality is apparent. This pattern of inequality is similar to those found in Pikettyand Saez (2003).22.1 Panel unit root testsWe begin our analysis by conducting a series of unit root tests. Nonstationarity isa property very common to economic data. It can be thought of as a phenomenonwhereby a variable has no clear tendency to return to a constant value or linear trend.Several procedures exist for testing the presence of unit roots in panel data, notablythe Fisher-type augmented Dickey–Fuller (ADF) test (Maddala and Wu 1999; Choi2001), the Levin–Lin–Chu (LLC) (2002) test, the IM–Pesaran–Shin (IPS) (2003), theHarris–Tzavalis (HT) (1999) test, and the Hadri (2000) LM test.2 We do not plot individual state’s income growth rates or inequality because these graphs are not original,and can be found in Frank (2009b, p. 59).123
19800.700.60Relative Mean Deviation19600.500.550.50Gini Index0.450.4019400.80B. Atems, J. .400.350.30Top Decile Income Share0.80.70.6Theil . 2 State-level average of various inequality measures: 1930–2005The first four tests usually test the hypothesis of a unit root for each individual seriesin a panel (Pesaran 2011). The formulation of the alternative hypothesis is the rathercontroversial issue that critically depends on the assumptions made about the natureof the homogeneity/heterogeneity of the panel. Therefore, in the event of a rejectionof the null hypothesis of these tests, one must interpret the results as implying thata statistically significant proportion of the units, and not necessarily all the units arestationary. The Hadri test on the other hand has a null of stationarity around a deterministic level or a unit-specific deterministic trend. It allows for homoskedastic errorprocesses across the panel, or heteroskedastic error processes across cross-sectionalunits. The test allows for the correction of autocorrelation using a Newey–West estimator of the long-run variance. Because each of these tests has the advantages anddisadvantages, we test for stationarity of our panel using all five tests. Table 1 presentsthe results.Table 1 shows the results of the various unit root tests. For the LLC test, we applythe Newey–West bandwidth selection algorithm, while the HT, LPS, and ADF teststatistics are robust to cross-sectional correlation of the error terms. Lag lengths werechosen using the Akaike information criteria (AIC). Our inferences are based on a5 % level of significance. As suggested by Levin et al. (2002), all the tests are carriedout on demeaned data to mitigate the effects of cross-sectional dependence. Panel Aof Table 1 shows the various unit root tests for the Gini inequality index. As can beseen from the table, the first four tests, namely the LLC, HT, IPS and ADF, rejectthe null hypothesis of a unit root for each series in the panel. From these results,one might be tempted to conclude that the Gini coefficient of inequality is stationary.However, it must be stressed that a rejection of the null hypothesis only implies that astatistically significant proportion of the series of Gini coefficients is stationary, andnot necessarily all the series in the panel. Consequently, we use the Hadri test to testthe hypothesis that there is no unit root in any series (stationarity). The p value of 0123
Income inequality and economic growth1547Table 1 Panel unit root testsTestInterceptIntercept and trendInterceptIntercept and trendA. Gini coefficient of inequalityLLCHTIPSADFHadri*Gini coefficient—levelChange in Gini coefficient 7.2845 6.5877 43.5202 8 0.2423 0.2346(0.0000)(0.0000)(0.0000)(0.0000) 10.4094 9.3574 62.2892 59.7336(0.0000)(0.0000)(0.0000)(0.0000) 9.1217 5.9655 22.8941 9811 3.5310 4.5688(0.0000)(0.0000)(0.9998)(1.0000)B. Real per capita personal income (level) and growthPer capita income—LevelLLCHTIPSADFHadri*Per capita income growth4.21720.2873 26.5674 0 0.2175 0.2026(0.9288)(0.0315)(0.0000)(0.0000)0.9867 3.4512 45.1076 45.9714(0.8381)(0.0003)(0.0000)(0.0000)0.3330 3.4903 22.5493 .0953 1.6142 5.5251(0.0000)(0.0000)(0.9468)(1.0000)The t statistics reported are the Levin–Lin–Chu bias-adjusted t statistic* Null hypothesis: stationary. p values in parenthesesrejects this hypothesis, indicating that some of the series in the panel are nonstationary.Consequently, we first-difference each series to achieve stationarity. As shown in thesame table, all five tests indicate that the series of Gini coefficients are now stationaryafter first differencing. Similarly, while the HT, IPS, and ADF tests reject the unit roothypothesis for the level of per capita income when intercept and trend are included,the Hadri (and the LLC) test indicates nonstationarity. All five tests, however, indicatestationarity of the growth rate of per capita income. As a result, we proceed to theestimation of the panel vector autoregression model with the variables in differences.3 MethodologyThe baseline specification is a bivariate panel vector autoregression model of thegrowth rate of real per capita income and the change in the Gini index. Denote thepercentage change (or growth rate) of real per capita income of state i in year t by123
1548B. Atems, J. Jones yi,t and the change in the Gini coefficient of inequality of state i in year t by gi,t .Then a reduced-form panel VAR model of the variables can be written as:Yit A(L)Yi,t 1 δi ϕi εit εi,t N (0, i ),(1) y g where Yi,t yit git , εi,t εit εit , t indexes time, L is the lag operator,A(·) is a polynomial matrix in L, δt denotes the unobservable time effects, a
Income inequality and economic growth 1545 Years 1940 1960 1980 2000 8.0 8.5 9.0 9.5 0.15 0.10 0.05 0.00 0.05 0.10 0.15 ab Fig. 1 State-level average of real income per capita and real income per capita growth: 1930–2005. a Average log of real per capita income. b Real per capita income growt
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