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World Development Vol. 78, pp. 386–400, 20160305-750X/� 2015 Elsevier Ltd. All rights reserved.

www.elsevier.com/locate/worlddevhttp://dx.doi.org/10.1016/j.worlddev.2015.10.038

A Meta-Analytic Reassessment of the Effects of Inequality

on Growth

PEDRO CUNHA NEVES a, OSCAR AFONSOb and SANDRA TAVARES SILVA c,*

aDepartamento de Gestao e Economic, Universidade da Beira Interior (UBI), and CEFAGE-UBI,Covilha, Portugal

bUniversidade do Porto, Faculdade de Economia, PortugalcUniversidade do Porto, Faculdade de Economia, CEFUP, Portugal

Summary. — This paper develops a meta-analysis of the empirical literature that estimates the effect of inequality on growth. It coversstudies published in scientific journals during 1994–2014 that examine the impact on growth of inequality in income, land, and humancapital distribution. We find traces of publication bias in this literature, as authors and journals are more willing to report and publishstatistically significant findings, and the results tend to follow a predictable time pattern over time according to which negative andpositive effects are cyclically reported. After correcting for these two forms of publication bias, we conclude that the high degree ofheterogeneity of the reported effect sizes is explained by study conditions, namely the structure of the data, the type of countries includedin the sample, the inclusion of regional dummies, the concept of inequality and the definition of income. In particular, ourmeta-regression analysis suggests that: cross-section studies systematically report a stronger negative impact than panel data studies;the effect of inequality on growth is negative and more pronounced in less developed countries than in rich countries; the inclusionof regional dummies in the growth regression of the primary studies considerably weakens such effect; expenditure and gross incomeinequality tend to lead to different estimates of the effect size; land and human inequality are more pernicious to subsequent growth thanincome inequality is. We also find that the estimation technique, the quality of data on income distribution, and the specification of thegrowth regression do not significantly influence the estimation of the effect sizes. These results provide new insights into the nature of theinequality–growth relationship and offer important guidelines for policy makers.� 2015 Elsevier Ltd. All rights reserved.

Key words — economic growth, inequality, meta-analysis, publication bias

*Final revision accepted: October 6, 2015

1. INTRODUCTION

The question of how inequality influences economic growthand the process of development has gained considerableattention among economists. Over the last three decades, theliterature on this topic has grown considerably, as a largenumber of theoretical and empirical studies have beenproduced in an attempt to formalize and test the effects ofinequality on growth.The theoretical literature has focused on exploring and

modeling the transmission channels through which inequalityaffects growth. The most important channels refer to: creditconstraints and impediments to human and physical capitalaccumulation (Banerjee & Newman, 1993; Galor & Zeira,1993); expensive fiscal policies and excessive taxation(Alesina & Rodrik, 1994; Persson & Tabellini, 1994); sociopo-litical instability (Alesina & Perotti, 1996); joint education andfertility decisions (Galor & Zang, 1997; Perotti, 1996); aggre-gate savings (Kaldor, 1956); and incentives to R&D(Foelmmi & Zweimuuler, 2006). While the savings and theR&D channels predict a positive impact of inequality ongrowth, the other channels imply a negative impact. 1

Within the empirical literature, two branches can be identi-fied: one aiming to test the validity of the theoretical channels,and the other, more extensive, attempting to estimate thereduced-form relationship between inequality and growth.The results obtained so far are, however, not consistent. Inparticular, works estimating the reduced-form relationshiphave reached very different conclusions regarding both thedirection and magnitude of the impact of inequality ongrowth. On the one hand, one group of studies finds empirical

386

support for a negative effect and, on the other hand, thesefindings are countered by an important number of studiesreporting a positive or an ambiguous effect. In addition, theempirical works also differ with respect to several methodolog-ical issues, such as the countries and time span of the sample,the structure of the data, the estimation techniques, the con-cept of inequality, the specification of the growth regression,and the source and quality of the data on income distribution.Neves and Silva (2014) have undertaken a comprehensive

descriptive survey of the empirical literature on this topic, sug-gesting that some of the methodological differences are likely toinfluence the estimation of the inequality–growth relationship.Thus, these differences could be important elements accountingfor the diversity in the studies’ findings. In the present paper,we complement their survey by performing a meta-analysis ofthe empirical literature that estimates the reduced-formrelationship between inequality and growth. A meta-analysisis a quantitative literature review method in which statisticalprocedures are used to combine results from different studiesinvestigating the same research question. The aim is to identifypatterns among results, sources of disagreement or otherinteresting relationships that may come to light in the contextof multiple studies (Greenland & O’Rourke, 2008). In compar-ison with traditional literature reviews, meta-analysis has theadvantage of summarizing the findings of the studies in asystematic way, thus eliminating subjectivity and reducingthe chances of making wrong interpretations and drawingmisleading review conclusions (Shadish, 1982).

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A META-ANALYTIC REASSESSMENT OF THE EFFECTS OF INEQUALITYON GROWTH 387

Used initially in medical and psychological research, meta-analysis has spread to other research fields and today it is usedin several social sciences. In economics, it has come to beincreasingly used in the last two decades, particularly inresearch fields where the empirical literature is far from beingconsensual (e.g., Ashenfelter, Harmon, & Oosterbeek, 1999;Benos & Zotou, 2014; Doucouliagos, 2005; Gorg & Strobl,2001; Iwasaki & Tokunaga, 2014; Jarrell & Stanley, 2004;Stanley, 2004).A meta-analysis of the empirical literature on the effects of

inequality on growth is desirable essentially for two reasons.Firstly, it helps to understand the causes of the divergentresults that this literature has generated over the years usinga quantitative approach, thus providing a more objective anal-ysis of the relationship between the two variables. Secondly, acorrect assessment of the different mechanisms through whichinequality influences economic growth and the circumstancesunder which they operate is crucial for correct policy guidancein this area. It allows policy-makers to have an unbiased rep-resentation of the variety of perspectives and alternative meth-ods that coexist within this research field, helping to avoidideologically based policies. This is a point of major relevance,especially considering that inequality has steadily increased inseveral developing and developed countries over the last threedecades (Cingano, 2014; Roser & Cuaresma, 2014).A meta-analysis of the empirical literature on the effects of

inequality on growth has already been performed byDominicis, Florax, and Groot (2008). This work representsan important starting point to identify and analyze the varia-tion in the studies’ results. The main conclusions are that dif-ferences in estimation methods, data quality, and samplecoverage affect the magnitude of the estimated effect ofinequality on growth. In particular, it should be stressed that:(i) the effect tends to be negative and more pronounced in lessdeveloped countries and in the long-run; (ii) when regionaldummies and additional measures of inequality are added asmoderator variables in the growth regressions of the primarystudies, the effect of inequality on growth becomes consider-ably weaker; (iii) studies that use fixed effects estimators sys-tematically report higher effects; (iv) the definition of incomeand the quality of the data on income distribution have alsoa significant impact on the outcomes.In the present paper, we further contribute to the under-

standing of this empirical literature by extending and enrich-ing Dominicis et al.’s (2008) meta-analysis in threeimportant aspects. Firstly, we include in the meta-analysismore recent studies. The latest study considered inDominicis et al. (2008) dates from 2006, and since then a sub-stantial amount of empirical work has been produced. Notice-ably, recent papers have questioned some of the assumptionsof the previous studies and attempted to conciliate their appar-ently contradictory findings by showing that inequality may begrowth-promoting in some circumstances and growth-hindering in others. Thus, the inclusion of these papers inthe meta-analysis could launch some important new ideasabout the way inequality influences growth. Secondly, whileDominicis et al. (2008) focus exclusively on income inequality,we also include studies using other concepts of inequality,namely inequality in land and human capital distribution thatrepresent an important body of the related literature. Giventhat these three forms of inequality are different in their natureand are not necessarily correlated, it is possible that they influ-ence growth in different ways and through different channels.Thirdly, we develop an extensive analysis of the effects of pub-lication bias on this empirical literature. Publication bias hasbeen generally recognized as an important threat to empirical

research and can assume different forms. Dominicis et al.(2008) have examined this problem in the inequality–growthempirical literature by testing for the presence of only oneform of publication bias that is in the direction of the results.In addition, in their meta-regression estimation the presence ofthis form of bias was not corrected, which may have distortedthe final results. Here we test for the presence of a larger num-ber of forms of publication bias and, when necessary, employthe appropriate statistical methods to correct them.Our meta-analysis reveals that publication bias is present in

the inequality–growth empirical literature in two ways: (i)authors and journals are more willing to report and publishstatistically significant results,which makes the empirical effectof inequality on growth seem larger than it actually is; (ii) theresults of the studies tend to follow a predictable time pattern,according to which negative and positive effects are cyclicallyreported. After correcting for these two forms of publicationbias, we find that the heterogeneity in the studies’ results ispartially explained by differences in the data structure, the typeof countries considered, the concept of inequality and thedefinition of income. In particular, our meta-regressioncorroborates Dominicis et al.’s (2008) findings that the effectof inequality on growth is more severe in developing countries,weaker when regional dummies are included, and higher whengross income-based inequality is used. However, in contrastwith Dominicis et al. (2008), we find the impact of inequalityon growth significantly influenced by the data structure (neg-ative and stronger in cross-section studies than in panel stud-ies), but not by estimation techniques or the quality of incomedistribution data. In addition, the inclusion in the meta-analysis of studies in which inequality is defined based on con-cepts other than income allows us to derive an important newconclusion, namely that land and human capital inequalityappears to exert a stronger negative impact on growth thanincome inequality does. These results provide new insights intothe nature of the inequality–growth relationship and addi-tional guidelines for policy makers.This paper is set out as follows. The next section presents a

brief review of the empirical literature on the reduced-formrelationship between inequality and growth. Section 3 providesa description of the studies used in the meta-analysis and adetailed explanation of the criteria for their selection. InSection 4 we present a preliminary analysis of the meta-data.Section 5 assesses the issue of publication bias. In Section 6we perform meta-regression analysis to explain heterogeneityin the studies’ findings and Section 7 concludes.

2. A BRIEF REVIEW OF THE LITERATURE

The empirical literature on the effects of inequality ongrowth has increased enormously over the past two decades.The first set of studies (Alesina & Rodrik, 1994; Clarke,1995; Perotti, 1996; Persson & Tabellini, 1994), dating fromthe mid 1990s, basically consists of reduced-form estimatesof a growth regression in the form:

g ¼ a0 þXMm¼1

amZm þ dINEQþ u; ð1Þ

where g is the average annual growth rate (usually measuredas a dlog GDP per capita); INEQ is a measure of incomeinequality (usually the Gini coefficient); Zm is a set of othervariables commonly used in standard growth regressions;and u is the usual error term. All studies use cross-sectiondata from a relatively large number of countries and estimate

388 WORLD DEVELOPMENT

Eqn. (1) by OLS. In order to avoid reverse causation, inequal-ity is measured at the beginning of the time span for growth,which is measured as the average annual growth rate for a per-iod of 20–30 years. The aim was to estimate the coefficient ofthe income inequality variable, d. All studies found a negativeand statistically significant impact of inequality on subsequentgrowth. However, Persson and Tabellini (1994) and Perotti(1996) found that this impact becomes insignificant once regio-nal dummies are included as explanatory variables.By the late 1990s, the general consensus on a negative

inequality–growth relationship began to be challenged. Anew wave of papers emerged, criticizing the methodologicalprocedures used in the earlier studies. In several cases, theresult was a rejection of the negative relationship. For exam-ple, Deininger and Squire (1996) question the quality of thedata on income distribution, arguing that these were taintedby problems related to construction methods, income mea-surement, and population coverage. Based on three criteriaof reliability, they assembled a high-quality dataset for incomedistribution comprising data from several countries, whichwas used in subsequent studies.Knowles (2005) argues that, despite the huge improvement

in data quality and availability raised by the Deininger andSquire (1996) dataset, concerns regarding comparability ofincome distribution data still remain, as the definition ofincome, either gross income or expenditures, differs acrosscountries. According to Knowles (2005), mixing gross incomewith expenditure data may introduce a bias in the estimationof the effect of inequality on growth, since expenditures aremore equally distributed than gross income. He finds thatinequality has a significant negative effect on growth in coun-tries where expenditures distribution is applied and an insignif-icant effect in countries where gross income distribution isused.Another set of studies (Castello & Domenech, 2002;

Deininger & Olinto, 2000; Deininger & Squire, 1998) criticizesthe earlier papers regarding the concept of inequality. Thesemore recent studies argue that inequality in wealth distribu-tion should be used instead of inequality in income distribu-tion, given that wealth distribution, proxied by land orhuman capital distribution, is associated with fewer measure-ment errors and is the relevant distribution in many theoreticalanalyses. In general, these studies find that land and humancapital inequality have a more significant negative impact ongrowth than income inequality.Following the release of the Deininger and Squire (1996)

dataset, several authors began to estimate the reduced-formrelationship using panel data. The first studies to do so wereLi and Zou (1998), Forbes (2000), Barro (2000), andDeininger and Olinto (2000). Assessing the impact of inequal-ity on growth over five-year periods and using different panelestimation techniques, these studies reach different conclusionsregarding the way inequality influences growth: (i) Li and Zou(1998) and Forbes (2000) find a positive impact for the wholesample considered; (ii) Barro (2000) obtains a negative rela-tionship for poor countries, a positive relationship for devel-oped countries, and an insignificant one when both groupsare considered; (iii) Deininger and Olinto (2000) find a nega-tive correlation between land inequality and growth.In the light of the contradictory results found by the studies

presented above, more recent papers have adopted a differentapproach in estimating the inequality–growth reduced-form relationship. Basically, they question some of theassumptions of the previous works and suggest that inequalitymay be growth-promoting in some circumstances and growth-hindering in others.

Bleaney and Nishiyama (2004) examine the extent to whichdifferent growth model specifications change the estimationresults by testing three types of growth specifications, eachconsidering different explanatory variables. Although similarfor high- and mid-income countries, the estimated coefficientof inequality differs significantly between models, suggestinga lack of robustness to different growth specifications.Chen (2003) and Banerjee and Duflo (2003) question the lin-

earity of the regressions estimated in the previous studies,accounting for the level of inequality and for the changes ininequality as factors that can affect the direction of the rela-tionship. While Chen (2003) finds a statistically significantU-inverted relationship between inequality and growth,Banerjee and Duflo (2003) show that changes in inequalityin any direction are associated with reduced growth in theshort-run.Voitchovsky (2005) explores the idea that aggregate mea-

sures of income distribution, such as the Gini coefficient, arenot appropriate for testing the effect of inequality on growthsince the relationship might depend on the whole shape ofincome distribution. Using panel data for 21 industrializedcountries, she finds that the influence of top end inequalityon growth is positive while that of bottom end inequality isnegative.Halter et al. (2014) examine how inequality affects economic

performance at different moments in the future, finding a pos-itive moderate effect in the short-run and a strong negativeeffect in the medium/long-run.Finally, several studies (Castello, 2010; Chambers & Krause,

2010; Herzer & Vollmer, 2012; Khalifa & El Hag, 2010) havefocused on how the inequality–growth relationship changes atdifferent development levels. They all come to the conclusionthat inequality is more detrimental to growth in developingcountries, whereas in developed countries it has a weaker neg-ative or even a positive effect.

3. THE META-DATA SET

In this section, we present the empirical studies included inthe meta-analysis and explain the criteria used for selectingthem. Following Stanley’s (2001) suggestion, we started bysearching in the Econlit and Web of Science databases forany reference containing a combination of the keyword‘‘growth” with either the keyword ‘‘distribution” or thekeyword ‘‘inequality” in the title and in the abstract ofEnglish-written articles published in scientific journals. Thissearch came up with 196 articles. We then searched the refer-ences of these 196 articles and obtained 17 additional papers.Since we are interested in collecting estimates of the impact

of inequality on growth in empirical articles that use a sampleof several countries, theoretical articles, case studies, studies atthe national level, and articles that did not provide any esti-mate of the inequality–growth effect were excluded. This leftus with 32 articles. Moreover, in order to ensure a consistentset of summary measures that can be investigated analytically,we also restricted our sample to those studies that measureinequality using the Gini coefficient. Given the wide use of thisindicator in the literature, the application of this criterion ledto the exclusion of only two of the 32 studies.We then defined the summary variable to meta-analyze as

the parameter associated with the Gini coefficient, d, inEqn. (1). This is our central measure of the effect size (Glass,1976), as it measures the direction and the magnitude of theeffect of inequality on growth, after controlling for othergrowth determinants. This definition of the effect size imposes


another restriction on the inclusion of studies in our sample,namely that these must estimate a linear model linkinginequality and growth. This restriction further excluded twostudies.Applying all the above criteria to the primary list of articles,

we were left with a final set of 28 studies to be included in ourmeta-analysis. They are listed in column (1) of Table 1. Our set

Table 1. List of selec

(1) (2) (3Study d x

Alesina and Rodrik (1994) �0.0358 0.0Alesina and Rodrik (1994) �0.0500 0.0Clarke (1995) �0.0691 0.0Perotti (1996) �0.0700 0.0Perotti (1996) �0.0300 0.0Galor and Zang (1997) �0.0396 0.0Deininger and Squire (1998) �0.0470 0.0Deininger and Squire (1998) �0.0190 0.0Deininger and Squire (1998) �0.0340 0.0Li and Zou (1998) 0.1490 0.0Li and Zou (1998) 0.0310 0.0Li and Zou (1998) �0.0890 0.0Tanninen (1999) �0.1220 0.0Deininger and Olinto (2000) �0.0111 0.0Deininger and Olinto (2000) 0.0033 0.0Forbes (2000) 0.1300 0.0Sylwester (2000) �0.0700 0.0Barro (2000) 0.0001 0.0Barro (2000) 0.0540 0.0Barro (2000) �0.0330 0.0Castello and Domenech (2002) �0.0170 0.0Banerjee and Duflo (2003) 0.1550 0.0Banerjee and Duflo (2003) �0.0300 0.0Banerjee and Duflo (2003) 0.1580 0.0De la Croix and Doepke (2003) �0.0300 0.0Bleaney and Nishiyama (2004) 0.0280 0.0Bleaney and Nishiyama (2004) 0.0230 0.0Odedokum and Round (2004) �0.042 0.0Knowles (2005) �0.0170 0.0Knowles (2005) �0.0130 0.0Knowles (2005) �0.1350 0.0Voitchovsky (2005) �0.0090 0.1Bengoa and Sanchez-Robles (2005) 0.0322 0.0Sarkar (2007) �0.0110 0.0Castello (2010) �0.0480 0.0Castello (2010) �0.0150 0.0Castello (2010) �0.0170 0.0Chambers and Krause (2010) �0.0079 0.0Khalifa and El Hag (2010) �0.1222 0.0Khalifa and El Hag (2010) 0.0656 0.0David and Hopkins (2011) �0.0737 0.0David and Hopkins (2011) �0.0285 0.0Woo (2011) �0.0560 0.0Woo (2011) �0.0330 0.0Herzer and Vollmer (2012) �0.0130 0.0Herzer and Vollmer (2012) �0.0130 0.0Halter et al. (2014) 0.0684 0.0Halter et al. (2014) �0.1144 0.0Thewissen (2014) 0.0100 0.2

Legend: d: estimate of the effect size; x: estimate of the standard error of d; t: t-size; t0: publication bias-corrected t-statistic associated to d.Notes: The effect size is interpreted as the increase in average annual growth rFor example, the effect of �0.0358 reported by Alesina and Rodrik (1994) meanreduction in the average annual growth rate of 0.0358 percentage points. Foconversions of the collected values were made.

of studies differs from that of Dominicis et al. (2008) essen-tially in three aspects. Firstly, it does not include studies atthe national level, working papers and other unpublishedworks. We opted to exclude studies at the national level asthey reflect the specific characteristics of only one economyand, therefore, mixing them with studies that use a sampleof several countries could bias the results. Following

ted observations

) (4) (5) (6)t d0 t0

198 �1.8100 �0.0008 �0.0386095 �5.2400 �0.0331 �3.4686276 �2.5000 �0.0201 �0.7286246 �2.8400 �0.0263 �1.0686166 �1.8100 �0.0006 �0.0386179 �2.2110 �0.0079 �0.4396168 �2.8000 �0.0173 �1.0286200 �0.9500 0.0164 0.8214084 �4.0700 �0.0192 �2.2986612 2.4360 0.0407 0.6646459 0.6750 �0.0504 �1.0964268 �3.3180 �0.0415 �1.5466449 �2.7200 �0.0425 �0.9486029 �3.8276 �0.0060 �2.0562023 1.4348 �0.0008 �0.3366600 2.1667 0.0237 0.3953300 �2.3333 �0.0169 �0.5619180 0.0056 �0.0318 �1.7659250 2.1600 0.0097 0.3886210 �1.5714 0.0042 0.2000055 �3.0800 �0.0073 �1.3195630 2.4603 0.0434 0.6889430 �0.6977 0.0462 1.0737680 2.3235 0.0375 0.5521100 �3.0000 �0.0123 �1.2286185 1.5100 �0.0048 �0.2614168 1.3700 �0.0067 �0.4014467 �0.8993 0.0383 0.8208082 �2.0800 �0.0025 �0.3086241 �0.5400 0.0296 1.2314758 �1.7800 �0.0007 �0.0086232 �0.0733 0.0639 1.0382943 0.3419 �0.1347 �1.4295055 �2.0000 �0.0013 �0.2286170 �2.8235 �0.0179 �1.0521140 �1.0714 0.0098 0.7000260 �0.6538 0.0291 1.1176258 �0.3062 0.0378 1.4652746 �1.6381 0.0099 0.1333591 1.1100 �0.0391 �0.6614240 �3.0708 �0.0312 �1.2994190 �1.5000 0.0052 0.2714230 �2.4348 �0.0153 �0.6634110 �3.0000 �0.0135 �1.2286037 �3.5100 �0.0064 �1.7386019 �6.8800 �0.0097 �5.1086358 1.9100 0.0161 0.0899472 �2.4327 �0.1660 �0.7033762 0.3620 �0.0375 �0.1357

statistic associated to d; d0: publication bias-corrected estimate of the effect

ate induced by an increase in the Gini coefficient of one percentage point.s that an increase in the Gini coefficient of one percentage point leads to ar the studies that do not use these measurement units, the appropriate


Doucouliagos, Haman, and Stanley (2012) and Iwasaki andTokunaga (2014), we also exclude working papers and otherunpublished research material since they report results thatcould be subject to revision and have not been validatedthrough the peer review process. Secondly, while Dominiciset al. (2008) focus exclusively on income inequality, we alsoinclude in the meta-analysis studies that use inequality onwealth distribution, proxied by land or human capital, which,as we have seen in the previous section, represent a relevantbody of the related literature. Thirdly, we include in themeta-analysis more recent studies: we have selected ninepapers published between 2006 (the year of the latest paperconsidered in Dominicis et al., 2008) and 2014.A frequent problem in conducting a meta-analysis occurs

when more than one estimate of the effect size is given in astudy. For example, in one single paper, Li and Zou (1998)report 20 estimates of the effect of inequality on growth. Ifthese estimates were considered as 28 independent observa-tions, we would be overweighing Li and Zou (1998) paper incomparison with other papers that present only one estimate.To avoid this problem, we follow Stanley’s (2001) principle ofcollecting one estimate or very few from each study.To choose the estimate to be collected from each study,

Stanley (2001) and Rose and Stanley (2005) propose usingthe average estimate, the median estimate or the estimatepreferred by the author. We opted to choose the estimatepreferred by the author because the author believes it the bestand takes it as a reference in the paper. In addition, the use ofthe average or the median estimate would make the estimationof the meta-regression in Section 6 virtually impossible. 2

The ‘‘preferred estimate” in each paper was chosen on thebasis of the results highlighted by the authors in the abstractor conclusion. If these were unclear or absent, we opted tochoose the estimates of the baseline regressions. In somepapers, more than one ‘‘preferred estimate” was presented.In these cases, to avoid subjectivity and minimize potentialselection bias, we considered various ‘‘preferred estimates”,up to a maximum of three per article. 3, 4

The application of these criteria led to a total of 49 estimatesof the impact of inequality on growth, which constitute ourmeta-sample. Columns (2)–(4) of Table 1 list these 49 estimates,as well as the respective standard errors andt-statistics. 5Table 2presents a summary of the main characteristics of the selectedstudies.

4. PRELIMINARY ANALYSIS OF THE META-DATA

The empirical analysis performed in the selected studies cov-ers the 20 years from 1994 to 2014. As Table 2 shows, 33 of the49 estimates that compose our meta-sample set were obtainedusing a sample of both developed and developing countries,while the remaining 16 were collected from studies using oneor the other group of countries. Most of the estimates (42)were selected from studies that use income distribution tomeasure inequality. As for the structure of the data, themeta-sample contains 23 observations from cross-section stud-ies and 26 from panel studies. While all cross-section studiesemployed the same estimation technique (OLS), panel studiesemployed a wide range of estimators.The effect size estimates vary between a minimum of

�0.1350 (Knowles, 2005) and a maximum of 0.1580(Banerjee & Duflo, 2003), with 36 negative and 13 positive.To compute the average of the effect size, we employ twocommonly used estimators in meta-analysis: the fixed effectsestimator and the random effects estimator. 6

The fixed effects estimator assumes there is no heterogeneityacross studies, as there is only one ‘‘true” effect size. In thiscase, differences in the estimates of the effect size arise onlyfrom sampling variation. The fixed effects estimator is aweighted average of all the estimates of the effect sizes reported

in the primary studies, dj, with weights given by the inverse oftheir variance, 1=x2

j .7

The random effects estimator assumes a heterogeneityamong the studies’ results, as each study has its own ‘‘true”effect size. As a consequence, the observed variability insample estimates of the effect size has two sources: one thesampling error variation and the other the random variabilityin the ‘‘true” population effect size. Like the fixed effectsestimator, the random effects estimator is an inverse-variance

weighted estimator of dj, with weights now equal to

1 x2j þ s2

� �., where x2

j is a measure of the sampling error

variation and s2 a measure of the variation in population effectsize (Dominicis et al., 2008).The fixed and the random effect estimates for our meta

sample are equal to dFE ¼ �0:0111 and ^dRE ¼ �0:0145,respectively, both statistically significant at the 5% level. Theseresults are very close to those obtained by Dominicis et al.(2008) and suggest that the average impact of inequalityon growth is negative and statistically significant, but noteconomically meaningful. In fact, an estimated effect of�0.0111/�0.0145 implies that a substantial increase of10 percentage points in the Gini coefficient reduces theaverage annual growth rate by only 0.111/0.145 percentagepoints. Such small magnitude has little practical significance.To test the assumption of homogeneity of the effect sizes, we

use the so-called Q-test (Hedges, 1982), based on the statistic:

Q ¼XNj¼1

ðdj � dFEÞ2x2

j; ð2Þ

which, under the null hypothesis of homogeneity, has anasymptotic chi-squared distribution with N � 1 degrees offreedom. In our case, Q ¼ 196:6370, which is much higherthan the 95% critical value. Therefore, the hypothesis ofthe existence of homogeneity of the effect sizes is clearlyrejected.The amount of heterogeneity can be quantified using the I2

index developed by Higgins and Thompson (2002). This indexdescribes the proportion of total variation across studies dueto heterogeneity and is equal to:

I2 ¼ Q� ðN � 1ÞQ

� 100%: ð3Þ

In our sample, I2 is equal to 75.59%, which denotes a highdegree of heterogeneity.The results provided by the Q-test and the I2 index have

three important implications. Firstly, the random effects esti-mator is preferable to the fixed effects estimator, as the latterrelies on an assumption that does not hold. Secondly, thereis excess variation in the reported estimates of the effect sizethat needs to be explained. We do so is Section 6 by meansof a meta-regression analysis. Thirdly, such excess variationis not only due to sampling error in the original estimatesbut also to the existence of different ‘‘true” effects. Thus, thelow average effect size obtained above may result not from areal weak association between the two variables but fromthe existence of several different effects that operate in differentdirections and that may be statistically and economically sig-nificant when considered separately.

Table 2. Characteristics of the selected studies

Study Estimate of effect size Number of obs. Countries included in the sample Structure of the data Estimation technique Concept of inequality Quality of income inequality data

Alesina and Rodrik (1994) �0.0358 70 Developing Developed Cross-section OLS Income Low

Alesina and Rodrik (1994) �0.0500 49 Developing Developed Cross-section OLS Wealth –

Clarke (1995) �0.0691 74 Developing Developed Cross-section OLS Income Low

Perotti (1996) �0.0700 67 Developing Developed Cross-section OLS Income Low

Perotti (1996) �0.0300 67 Developing Developed Cross-section OLS Income Low

Galor and Zang (1997) �0.0396 73 Developing Developed Cross-section OLS Income Low

Deininger and Squire (1998) �0.0470 87 Developing Developed Cross-section OLS Income High

Deininger and Squire (1998) �0.0190 87 Developing Developed Cross-section OLS Income High

Deininger and Squire (1998) �0.0340 64 Developing Developed Cross-section OLS Wealth –

Li and Zou (1998) 0.1490 185 Developing Developed Panel Fixed effects Income High

Li and Zou (1998) 0.0310 185 Developing Developed Panel Random effects Income High

Li and Zou (1998) �0.0890 37 Developing Developed Cross-section OLS Income High

Tanninen (1999) �0.1220 49 Developing Developed Cross-section OLS Income High

Deininger and Olinto (2000) �0.0111 300 Developing Developed Panel System GMM Wealth –

Deininger and Olinto (2000) 0.0033 108 Developing Developed Panel System GMM Income High

Forbes (2000) 0.1300 135 Developing Developed Panel First-difference GMM Income High

Sylwester (2000) �0.0700 54 Developing Developed Cross-section OLS Income High

Barro (2000) 0.0001 146 Developing Developed Panel Three-stage least squares Income High

Barro (2000) 0.0540 80 Developed Panel Three-stage least squares Income High

Barro (2000) �0.0330 66 Developing Panel Three-stage least squares Income High

Castello and Domenech (2002) �0.0170 83 Developing Developed Cross-section OLS Wealth –

Banerjee and Duflo (2003) 0.1550 98 Developing Developed Panel Fixed effects Income High

Banerjee and Duflo (2003) �0.0300 98 Developing Developed Panel Random effects Income High

Banerjee and Duflo (2003) 0.1580 98 Developing Developed Panel First-difference GMM Income High

De la Croix and Doepke (2003) �0.0300 83 Developing Developed Panel GMM Income High

Bleaney and Nishiyama (2004) 0.0280 42 Developed Cross-section OLS Income High

Bleaney and Nishiyama (2004) 0.0230 42 Developing Cross-section OLS Income High

Odedokum and Round (2004) �0.0420 63 African Cross-section OLS Income High

Knowles (2005) �0.0170 40 Developing Developed Cross-section OLS Income High

Knowles (2005) �0.0130 27 Developed Cross-section OLS Income High

Knowles (2005) �0.1350 30 Developing Cross-section OLS Income High

Voitchovsky (2005) �0.0090 81 Developed Panel System GMM Income High

Bengoa and Sanchez-Robles (2005) 0.0322 80 Developed Panel First-difference GMM Income High

Sarkar (2007) �0.0110 62 Developing Developed Cross-section OLS Income High

Castello (2010) �0.0480 474 Developing Panel System GMM Wealth –

Castello (2010) �0.0150 236 Developed Panel System GMM Wealth –

Castello (2010) �0.0170 119 Developing Panel System GMM Income High

Chambers and Krause (2010) �0.0079 240 Developing Developed Panel * Income High

Khalifa and El Hag (2010) �0.1222 70 Developing Panel * Income High

Khalifa and El Hag (2010) 0.0656 70 Developed Panel * Income High

David and Hopkins (2011) �0.0737 63 Developing Developed Cross-section Two-stage least squares Income High

David and Hopkins (2011) �0.0285 450 Developing Developed Panel Random effects Income High

Woo (2011) �0.0560 61 Developing Developed Cross-section OLS Income High

Woo (2011) �0.0330 57 Developing Developed Cross-section OLS Wealth –

Herzer and Vollmer (2012) �0.0130 572 Developing Developed Panel * Income High

Herzer and Vollmer (2012) �0.0130 624 Developing Panel * Income High

Halter et al. (2014) 0.0684 227 Developing Developed Panel System GMM Income High

Halter et al. (2014) �0.1144 227 Developing Developed Panel System GMM Income High

Thewissen (2014) 0.0100 122 OECD Panel Fixed effects Income High

Notes: The estimation methods used in the studies marked with * are not textbook methods, having been separately developed for specific studies (for details on these methods, please see Chambers andKrause, 2010; Khalifa and El Hag, 2010; Herzer and Vollmer, 2012). Income inequality data are considered of high-quality if they satisfy Deininger and Squire’s three criteria for high-quality data(please see Section 6(f) for more details).

AMETA-A

NALYTIC

REASSESSMENTOFTHE

EFFECTSOFIN

EQUALIT

YON

GROWTH

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5. TESTING AND CORRECTING FOR THE PRESENCEOF PUBLICATION BIAS

Before using meta-regression analysis to explain heterogene-ity in effect sizes, we investigate whether and how the studies’estimates are distorted by the presence of publication bias.Distortions generated by publication bias have been recognizedas an important threat to empirical research, as they preventobtaining reliable estimates of the phenomenon under analysis.Several forms of publication bias have been identified in theliterature, which have been thoroughly systematized byDoucouliagos, Laroche, and Stanley (2005) and Stanley (2005).Dominicis et al. (2008) have investigated this problem in the

inequality–growth empirical literature by using the funnel plotand the related Funnel Asymmetry Test developed by Egger,Smith, Scheider, and Minder (1997). In this section, we extendtheir analysis by testing for the presence of a larger number offorms of publication bias and, when necessary, employ theappropriate statistical methods to correct them.

(a) Bias in the direction of the results

One of the most frequent forms of bias in empirical studiesis the tendency for authors, motivated by their prior expecta-tions, beliefs or ideological positions, to publish results in acertain direction, positive or negative (Stanley, 2005). A widelyused tool for detecting the presence of this form of bias is thefunnel plot. This is a scatter diagram that compares the esti-

mate of the effect size from each study, dj, against its precision,measured by the inverse of the estimate of the standard error

of dj, 1=xj. In the absence of publication bias, dj varies ran-domly and symmetrically around the ‘‘true” value independentof xj. In this case, the funnel plot should assume a symmetricinverted funnel-like pattern. However, if there is a bias in acertain direction, studies with smaller samples and hencehigher standard deviations tend to report an effect biasedtoward that direction and, therefore, the graph will be asym-metric and overweight on the left or the right side, especiallyat the bottom. Thus, the key to identifying this form of biasis the funnel plot’s asymmetry.Figure 1 presents the funnel graph for the observations of

our meta-sample. There does not seem to be evidence of the

Figure 1. Funnel plot of the inequality–growth estimate.

existence of publication bias in favor of a certain direction,as the graph is not significantly asymmetric around the ‘‘true”effect size, which, in line with the fixed and random effectsestimates of d presented in Section 4, is slightly negative.The asymmetry of the funnel plot can be formally tested

using the Funnel Asymmetry Test (FAT). The FAT (Eggeret al., 1997) involves running a regression between a study’sreported effect size and its estimated standard error:

dj ¼ c0 þ c1xj þ ej: ð4ÞThe conventional t-test of the coefficient c1 is a test for pub-

lication bias and the sign of its estimate indicates its direction.As noted by Stanley (2005), Eqn. (4) has a problem ofheteroscedasticity, 8 which can be eliminated using the stan-dard procedure of dividing it by xj, yielding:

tj ¼ c1 þ c01

xjþ e�j ; ð5Þ

where tj ¼ dj=xj is the conventional t-statistic associated withparameter d, reported in the primary studies. 9 Because theintercept and the slope coefficients are now reversed, theFAT is the t-test for the intercept in (5).Column (1) of Table 3 reports the results of the estimation

of Eqn. (5) by OLS for our meta-sample, with standard-errors calculated using the Newey–West procedure. 10 TheFAT confirms the previous interpretation of the funnel graph:given that c1 is not significantly different from zero, there areno signs of publication bias in a given direction. This resultis different from that obtained by Dominicis et al. (2008),who have found a bias in favor of negative effects of inequalityon growth.

(b) Bias in the magnitude of the results

Another important form of bias arises when studies thatreport statistically significant results are published morepromptly. In fact, ‘‘insignificant results may not be as interest-ing to readers and, given that journal space is a scarceresource, journals may prefer that insignificant results arenot published, choosing instead to devote space to whatare regarded more informative results” (Doucouliagos, 2005,p. 324). The main problem arising from this form of bias isthat it leads to a truncated pool of published studies andmakes empirical effects appear larger.In general, studies with smaller samples find it more difficult

to produce significant results than studies with larger samples,as they usually present higher standard errors and lowert-statistics. When there is a bias for statistical significance,authors of small-sample studies are then tempted to manipu-late their specifications to find required large estimates of theeffect size. Thus, this type of publication bias implies a positiverelationship between the magnitude of a study’s estimate ofthe effect size and its standard error (Ashenfelter et al., 1999;Gorg & Strobl, 2001). This provides the basis for testing thisform of bias, which involves estimating the regression:

jdjj ¼ c0 þ c1xj þ ej: ð6ÞThis regression is similar to (4), the only difference is that the

dependent variable is the absolute value of d. This is becausenow we are not interested in analyzing the direction of

the bias, but the magnitude of d, regardless of its sign. The testfor this form of publication bias is thus H 0 : c1 ¼ 0 (absenceof bias) vs. H 1 : c1 > 0 (presence of bias). Heteroscedasticityin (6) requires the estimation of:

Table 3. Results of the test detecting the presence of publication bias

Columns (1) (2) (3) (4) (5) (6)Testing for: Direction bias Magnitude bias Time patterns Nationality patterns Journal type patterns Journal impact factor

patterns

Dependent variable tj jtjj tj tj tj tjConstant �0:5857 1.6918***

ð�1:5055Þ ð7:2824Þ1=xj �0:0084� 0.0061** �0:0482�� 0:0118�� 0:0181�� 0:0089�

ð�1:9862Þ ð2:2168Þ ð�3:7262Þ ð�3:8900Þ ð�3:5029Þ ð�1:9802Þtime�j 0.0083***

ð3:1445Þtime2�j �0:0003��

ð�3:1806ÞEurope�j 0.0037

ð1:698ÞOthers�j 0.0075*

ð1:9984ÞDevelop�j 0.0079

ð1:2260ÞGrowth�j 0.0075

ð0:5611ÞImpact�j �0:0016

ð�0:5547ÞNotes: Coefficients are estimated by OLS.Moderator variable x�j corresponds to variable xj divided by x.t-Statistics reported in brackets, calculated from heteroscedasticity-autocorrelation consistent standard errors.

***, ** and * denote statistical significance at the 1%, 5% and 10% level, respectively.

Figure 2. Distribution of the reported effect sizes over time.


jtjj ¼ c1 þ c01

xjþ e�j : ð7Þ

As can be seen from the results reported in column (2) ofTable 3, the null hypothesis is rejected at 1% of significance.Thus, there is clear evidence that the reported results of theeffect of inequality on growth are likely to be overstated dueto the desire to report significant results.In this context, it is necessary to correct the estimates of d

provided by the primary studies. To do so, we followStanley’s (2005) procedure of first estimating the magnitudeof each observation’s bias, which is given by c1xj, and thenreducing each reported effect size toward 0 by c1xj. The cor-

rected effect sizes for our meta-sample, d0j, and the associatedcorrected t-statistic, t0j, are listed in columns (5) and (6) of

Table 1. We can use the values of d0j to recalculate the randomeffects estimator of our effect sizes. The value is now equal to�0.0062, which is considerably lower than the value presentedin Section 4 and is no longer statistically significant at the 5%level.

(c) Publication patterns across time

Goldfarb (1995) has suggested that empirical economicsresearch follows a predictable time pattern. According to thispattern, there is an initial tendency for the empirical results toconfirm a newly suggested theory, which will continue untileventual further confirmations fail to provide substantiallynew information. After some time, an inverted tendency islikely to emerge, as further empirical research tends to reportresults rejecting the initial theory. The entire process is succes-sively repeated, thus generating an ‘‘economics research cycle”as defined by Doucouliagos et al. (2005).Figure 2 reflects the time pattern followed by the empirical

literature that estimates the impact of inequality on growth.As referred to in Section 2, in the early to mid 1990s, when this

literature began to emerge, the tendency was for authors andjournals to publish negative effects. This was possibly associ-ated with the desire to lend support to the flourishing theoret-ical literature, which at that time began to model thetransmission channels between inequality and growth, gener-ally predicting a negative relationship. With the passage oftime, this tendency to publish negative effects was reversedas in the beginning of the century studies reporting a positiveeffect have become increasingly important. In recent years,several studies have attempted to reconcile the twoperspectives so that positive and negative findings have beenevenly produced and reported. Thus, there seems to be an‘‘economics research cycle” in the estimation of the effect of


inequality on growth, which is reflected in Figure 2 by meansof a quadratic time pattern.In order to formally test Goldfarb’s (1995) conjecture, we

run a regression where the reported effect size depends on thevariables timej and time2j , with timej defined as the year ofpublication of study j minus 1993. 11 The heteroscedasticity-corrected version of this regression is:

tj ¼ c01

xjþ c1time

�j þ c2time

2�j þ e�j ; ð8Þ

where time�j ¼ timej=xj; time2�j ¼ time2j=xj, and e�j ¼ ej=xj.Column (3) of Table 3 shows that the estimate of c2 is negativeand both timej and time2j are significant at the 1% level, whichconfirms the statistical significance of the quadratic time trendreflected in Figure 2. Thus, we can conclude that, in additionto the existence of a bias in the magnitude of the effect sizes,there is also a bias associated to the existence of a‘‘Goldfarb-type” time pattern in the empirical literature onthe inequality–growth effect.

(d) Publication patterns across nationalities and journals

Several studies (e.g., Neary, Mirrlees, & Tirole, 2003;Stanley, 2005) have mentioned authors’ nationalities as apotentially important determinant of research findings. Otherstudies (e.g., Doucouliagos et al., 2005) suggest that journalsfrom different fields or with different ranking positions maypublish considerably different results. To test for the presenceof these forms of bias, we estimate three separate regressions.For the first regression, taking into account that a consider-

able number of the authors of our selected studies are affiliatedto the US and European institutions, we divide our meta-sample into three groups: group 1, consisting of those studiesin which all the authors are affiliated to US institutions; group2, comprising those studies in which at least one of the authorsis affiliated to European institutions; group 3, composed of theremaining studies. We then defined group 1 as the referencecategory and created the dummies Europej and Othersj, whichassume the value 1 if study j belongs to groups 2 and 3, respec-tively. The effect sizes were regressed on these two dummies totest for the presence of systematic differences among the threegroups. For the second regression, we used the Categorizationof Journals in Economics and Managementcompiled by theFrench Committee of Scientific Research, and also groupedthe journals in our sample into three categories: general eco-nomics, development and economic growth. The dummiesused in this regression were Developj and Growthj, whichassume the value 1 for studies published in journals of thefields of development and growth, respectively. In the thirdregression, we used the ISI Web of Science’s 2010 impact fac-tor as the only explanatory variable.The results of the heteroscedasticity-corrected version of

these three regressions are presented in columns (4)-(6) ofTable 3. None of the explanatory variables are statistically sig-nificant at 5% and only variable Othersj is significant at 10%,meaning that there is no clear evidence to support the exis-tence of publication bias across nationalities and journals inthe inequality–growth literature.

6. META-REGRESSION ANALYSIS

In this section we try to explain the heterogeneity of thereported effect sizes using meta-regression analysis.Meta-regression is a tool of meta-analysis which has been

widely used in quantitative literature reviews in economics toinvestigate the extent to which excess variation among studies’results can be related to studies’ characteristics (Gorg &Strobl, 2001; Stanley & Jarrell, 1989). It involves estimatinga standard regression of the form:

Y j ¼ b0 þXKk¼1

bkX kj þ ej; j ¼ 1; 2; . . . ;N ; ð9Þ

where the dependent variable, Y j, is the estimate of the effectsize reported in study j in a literature comprised of N studies;Xkj are meta-independent variables capturing relevant charac-teristics of the empirical primary studies that could explain thevariation in Y j; bk are the meta-regression coefficients reflect-ing the effect of each characteristic on Y j; and ej is the meta-regression disturbance term.We choose as independent variables those reflecting charac-

teristics of the primary studies that, according to Dominiciset al. (2008) and Neves and Silva (2014), are expected to influ-ence the estimates of the inequality effect on growth. Thesecharacteristics are: (i) the structure of the data; (ii) the inclu-sion of regional dummies as moderator variables in theprimary growth regression; (iii) the estimation techniques;(iv) the development level of the countries included in the sam-ple; (v) the concept of inequality; (vi) the quality and compa-rability of the income distribution data; and (vii) thespecification of the growth regression.Contrary to Dominicis et al. (2008), in the estimation of the

meta-regression we account for the presence of the two formsof publication bias detected in the previous section. While themagnitude bias is filtered by considering the publication bias-corrected estimate of the effect size, d0j (rather than the directestimate of the effect size, d) as the dependent variable, the biasassociated to the existence of an ‘‘economic research cycle” isaccounted for by including timej and time2j .Themeta-regressionwas estimated byOLS, correcting for the

presence of both heteroscedasticity by dividing all the variablesby xj and autocorrelation using the Newey–West procedure.Table 4 reports the estimation results. Below we discuss theseresults presenting the main differences and similarities withthe results obtained by Dominicis et al. (2008) and emphasizingtheir contribution for a better understanding of the nature of theinequality–growth relationship. Following the common prac-tice, we consider 5% of significance as the reference level todefine whether or not a variable is statistical significant.

(a) Structure of the data

In order to assess whether the structure of the data used inthe primary studies has a systematic influence on the reportedeffect sizes, we include in the meta-regression a dummy, crossj,which assumes the value 1 if observation j is taken from across-section study and 0 if it is taken from a panel study.As can be seen in Table 4, variable crossj is statistically signif-icant at the 1% level, meaning that the structure of the data isrelevant in explaining differences in the effect sizes. This resultdiffers from the one obtained by Dominicis et al. (2008), whohave found an insignificant influence. Moreover, the negativeestimate of the coefficient of crossj confirms the idea advancedin Section 2 that cross-section studies typically report a nega-tive relationship between inequality and growth, whereaspanel studies present more diverse results.We advance with three possible explanations for this fact.

The first explanation relies on differences in the time horizonimplicit in both types of studies. While cross-section studiesexamine the inequality–growth relationship in the long-run

Table 4. Results of the meta-regression estimation

Dependent variable: t0jExplanatory variables Coefficient estimates t-statistics

constant� �0:0327�� ð�3:5699Þtime�j 0.0055*** ð5:0685Þtime2�j �0:0002�� ð�4:3967Þcross�j �0:0055�� ð�2:8348Þreg:cross�j 0.0208*** ð4:2105Þfixedð1� crossÞ�j �0:0005 ð�0:0203Þrandomð1� crossÞ�j 0.0069 ð0:6019Þdevelop�j �0:0038�� ð�3:0908Þdoecd�j �0:0061 ð�1:0405Þincome�j 0.0127*** ð3:3508Þhq:income�j �0:0073� ð�1:8426Þexpend:income�j �0:0069�� ð�2:3025Þspecif �

j 0.0012 ð0:1877ÞN = 49; R2 ¼ 0:6544; corrected R2 ¼ 0:6138 F ratio ¼ 2:9029��

Notes: Coefficients are estimated by OLS.Moderator variable x�j corresponds to variable xj divided by x.t-Statistics reported in brackets, calculated from heteroscedasticity-autocorrelation consistent standard errors.

***, ** and * denote statistical significance at the 1%, 5% and 10% level, respectively.


(recall that they usually estimate the impact of inequality onthe average annual growth rates of the subsequent 20–30 years), panel studies do so in the short-medium-run (mostof them assess the impact of inequality on growth over five-year periods). According to Knowles (2005) and Halter et al.(2014), the theoretical transmission channels between bothvariables are likely to operate differently in both time hori-zons. In particular, the positive effects of inequality on growth,associated to the increase of aggregate savings, large-scaleinvestments and R&D incentives, relying basically on eco-nomic mechanisms, are likely to operate in the short-run.On the other hand, the negative effects, associated to excessivetaxation, constraints to human capital accumulation, increasesin fertility and sociopolitical instability, are more likely tooperate in the long-run, since they involve changes in the polit-ical process, institutions, education attainments and demogra-phy, which materialize only with a considerable lag. Therefore,we should expect stronger evidence of a negative impact ofinequality on growth in cross-section studies.

(b) Regional dummies

The second possible explanation for the fact that the effectsreported in cross-section studies are negative and those ofpanel studies are more diverse is that the impact of inequalityon growth may differ substantially across countries andregions. Given that panel data, contrary to cross-section data,control for time-invariant unobservable country-specific char-acteristics, the existence of such specificities may make panelfindings quite diverse.If this explanation is true, then the inclusion of regional

dummies as explanatory variables in the growth regressionof cross-section primary studies should weaken the negativeeffect of inequality on growth. To test this hypothesis, we cre-ate the dummy regj, which is equal to 1 if the primary studyincludes regional dummies and equal to 0 if it does not. Giventhat regional dummies are never included in panel studies, regjis multiplied by crossj. The coefficient associated withreg:crossj is positive and is statistically different from zero,thus confirming the hypothesis advanced above. As inDominicis et al. (2008), the effect of reg:crossj is particularlystrong (p-value of 0.0002), meaning that country and regional

specificities play a crucial role in explaining the heterogeneityfound in the reported effect sizes.

(c) Estimation techniques

The third possible explanation for the diversity of resultsfound in panel studies relates to estimation techniques.Whereas almost all cross-section studies estimate the inequal-ity–growth effect using OLS, panel studies use several estima-tors, which, given the differences in their underlyingassumptions, could lead to different results.The standard panel estimation techniques are fixed and ran-

dom effects. The fixed effects estimates are calculated form dif-ferences within each country across time, while the randomeffects estimates incorporate information across countries aswell as across periods. However, as noted by several authors(e.g., Forbes, 2000), neither of these two techniques is the mostappropriate to estimate the inequality–growth relationship.The fixed estimator can lead to biased results when variablesare persistent over time or when their variation is mostlycross-section, as in the case of inequality. The random effectsestimator is inconsistent, since the explanatory variables usedin the standard growth regression are typically correlated withthe country-specific effects. Moreover, neither of them dealsproperly with the potential problem of endogeneity causedby effects of growth on inequality.As a consequence of these problems, many panel studies have

used more adequate estimation techniques instead, the mostcommon being the first-difference and the system GMM esti-mators. The first-difference GMM, developed by ArellanoandBond (1991), removes the unobserved time-invariant effectsand uses the lagged values of the explanatory variables asinstruments to control for endogeneity and measurementerrors. However, this ‘‘differencing procedure may discardmuch of the information in the data since the largest share ofvariation in income inequality is cross-sectional”(Voitchovsky, 2005, p. 284). The system GMM estimator,developed by Arellano and Bover (1995) and Blundell andBond (1998), addresses this problem by considering an instru-mentmatrix composed of two components: the lagged variablesin levels as instrument for the first-difference equations, and thefirst-differences as instruments for the equation in levels.


In our meta-regression, dummies fixedj and randomj assumethe value one if the primary study uses fixed or random effects,respectively, and equal to zero if it uses another estimator,such as the first-difference or the system GMM. Since thisanalysis applies to panel studies only, both dummies are mul-tiplied by ð1� crossjÞ. Neither of them is statistically signifi-cant at the 5% level. Thus, there is no evidence to suggestthat the heterogeneity of the effects sizes reported by panelstudies is explained by differences on estimation techniques.This is another result that differs from Dominicis et al.(2008), who have found that studies using fixed effects tendto report higher estimates.

(d) Development level of the countries included in the sample

We also investigate if the estimates of the inequality–growthrelationship are significantly affected by the development levelof the countries included in the sample of the primary studies.We defined studies that include only OECD countries as thereference category and created two dummies: dummydevelopj assumes the value 1 when the study includes onlydeveloping countries, and dummy doecdj is equal to 1 whenthe study includes both OECD and developing countries. Onlydevelopj is statistically significant and its coefficient estimate isnegative. This result, which is in line with Dominicis et al.(2008), suggests that income inequality is more perniciousfor subsequent growth in less developed economies.This confirms the idea already advanced by several authors

that the transmission channels from inequality to growth mayoperate very differently depending on a country’s developmentlevel. In particular, Alesina and Perotti (1996), Barro (2000)and Castello (2010) state that the channels predicting a nega-tive relationship may be stronger in less developed countries,as in these countries constraints to human capital accumula-tion, political instability and social unrest are more severe.On the other hand, Barro (2000) suggests that in richer econo-mies the growth-promoting aspects of inequality, related tosavings and incentives, are also relevant.

(e) Concept of inequality

As previously mentioned, one of the contributions of ourmeta-analysis is that it includes not only studies using incomeinequality, but also studies that use inequality in wealth distri-bution. To check if these two groups of studies systematicallyreport different results, we included in the meta-regressiondummy incomej, which assumes the value 1 if the study usesincome and 0 if it uses wealth, proxied by land or human cap-ital. This dummy has a positive coefficient and is statisticallysignificant at the 1% level, meaning that inequality in wealthdistribution has a stronger negative effect on growth thaninequality in income distribution.Again transmission channels may be at the root of this

result. While in the savings channel income distribution isclearly the one that matters because savings rates are deter-mined as a fraction of income, in the other channels, especiallythose associated to constraints to human capital accumula-tion, sociopolitical instability and fertility decisions, the distri-bution of wealth is also relevant.

(f) Quality and comparability of income distribution data

Another explanation for the fact that income inequality hasa weaker effect on growth than wealth inequality may be asso-ciated to problems of quality and comparability of data onincome distribution. When a variable is badly measured, its

coefficient is biased toward zero, resulting in a weaker impacton the dependent variable (Dominicis et al., 2008).Regarding the problem of data quality, Deininger and

Squire (1996) argue that high-quality data on income distribu-tion should be: (i) based on household surveys and not onnational accounts; (ii) based on comprehensive coverage ofall sources of income or uses of expenditure thus including,for example, non-wage income and income from householdproduction, which in some countries account for a significantshare of the total income; and (iii) representative of the popu-lation at the national level thus including both urban and ruralpopulation. The studies published after 1996 make use ofdatabases that meet these three criteria for high-quality dataon income distribution, such as that of Deininger and Squire(DS), the UNU-WIDER, the Luxembourg Income Study(LIS), the University of Texas Inequality Project (UTIP), theStandardized World Income Inequality Database (SWIID)and the World Bank’s ‘‘All the Ginis dataset”. 12 We createdthe dummy hqj to distinguish between studies that use high-quality data, drawn from these datasets, and studies that donot. Since this analysis is restricted to data on income distribu-tion, hqj is multiplied by incomej. As Table 4 shows, hq:incomejis not statistically significant at 5% but only at 10%, which,contrary to Dominicis et al. (2008), suggests that using ornot high-quality data does not make a big difference in theestimation of the inequality–growth effect.As for the problem of data comparability, stressed by

Knowles (2005), we examine the effect of the use of differentdefinitions of income, namely gross income versus expendi-ture. Dummy expendj assumes the value 1 if the study’s datasetuses inequality based on both gross income and expenditure,and 0 if it uses inequality based on gross income only. Thecoefficient associated with expend:incomej is statistically differ-ent from zero and presents a negative estimate. That is, in linewith Dominicis et al. (2008), we find that when only grossincome-based inequality is considered the reported impact ofinequality on growth is higher.

(g) Specification of the growth regression

We also check if differences in the specification of thegrowth regression used in the primary studies have an influ-ence on the reported results. To assess the impact of inequalityon growth, all the studies in our meta-sample estimated aregression in the form of Eqn. (1), where output growth rateis explained as a function of inequality and a set of other vari-ables, Zm, widely accepted in the literature as important deter-minants of growth. Several of these studies adopt the standardPerotti (1996) specification, which includes the initial GDP percapita, the level of investment, and the level of human capitalas explanatory variables. In this case, dummy specifj takes thevalue 1. When the growth regression does not assume aPerotti-type specification, it takes the value 0. Table 4 showsthat the effect sizes are not significantly affected by the specifi-cation of the growth regression as dummy specifj is not statis-tically significant.Summing up, from the estimation results of the meta-

regression, we can conclude that the structure of the data,regional specificities, the countries’ development level, the con-cept of inequality, and the definition of income are particularlyimportant factors that explain the heterogeneity of collectedestimates. Moreover, the meta-regression performs well inexplaining such heterogeneity: the F-ratio shows that themodel is statistically significant overall at the 1% level andthe corrected R-squared (61.38%) is considerably high com-pared to most of meta regressions in economics. 13 It also

Table 5. Battery of diagnostic tests to meta-regression

Test Test-statistic P-Value

White for heteroscedasticity v2ð26Þ ¼ 18:5711 0.8540Breusch–Godfrey LM for serial correlation v2ð3Þ ¼ 12:9791 0.0047Ramsey RESET for model specification F ð2;36Þ ¼ 0:4195 0.6607Jarque–Bera for normality of disturbances v2ð2Þ ¼ 0:7052 0.7029

Notes: Given the considerable number of explanatory variables in the meta regression, cross-terms were excluded in White’s heteroscedasticity test. Sincethe maximum number of observations collected from each primary study is three, Breusch–Godfrey’ LM test was executed with three lags. Following thestandard procedure, Ramsey’s RESET test was executed with one fitted term.

Table 6. Robustness analysis

Dependent variable: t0jExplanatory variables (1) (2)

Coefficient estimates t-statistics Coefficient estimates t-statistics

constant� �0:0292�� ð�2:7147Þ �0:0293�� ð�3:3406Þtime�j 0:0041�� ð3:1480Þ 0:0054�� ð4:9991Þtime2�j �0:0001�� ð�2:0277Þ �0:0002�� ð�3:9638Þcross�j �0:0056�� ð�2:5257Þ �0:0052�� ð�3:3129Þreg:cross�j 0:0178�� ð4:2597Þ 0:0206�� ð2:3222Þfixedð1� crossÞ�j �0:0234� ð�1:9163Þ �0:0019 ð�0:0859Þrandomð1� crossÞ�j 0.0034 ð0:4151Þ 0.0030 ð0:2555Þdevelop�j �0:0030�� ð�2:9617Þ �0:0035�� ð�3:2197Þdoecd�j �0:0035 ð�0:3710Þ �0:0086 ð�1:4524Þincome�j 0:0136�� ð2:3406Þ 0:0125�� ð3:1357Þhq:income�j �0:0073� ð�1:8426Þ �0:0073� ð�1:8246Þexpend:income�j �0:0089 ð�1:5551Þ �0:0031 ð�0:8331Þspecif �

j 0.0024 ð0:4047Þ 0.0024 ð0:4223Þcapital�j �0:0065�� ð�2:0808Þ


passes several standard diagnostic tests: despite the expectedpresence of serial correlation (which is confirmed by theBreusch–Godfrey’s LM test), White’s test finds no trace ofheteroscedasticity, Ramsey’s generic misspecification test doesnot detect any evidence of omitted-variable or simultaneousequation bias, and Jarque–Bera’s test does not reject thehypothesis that the disturbance terms have a normal distribu-tion (see Table 5).To assess the robustness of the meta-regression, we run two

alternative specifications. Firstly, we reestimate the meta-regression using the technique employed in Dominicis et al.(2008)—a hierarchical linear model in which each observationis weighted by 1=Mj, where Mj is the number of observationsdrawn from study j. The results are presented in column (1) ofTable 6. We can see that all coefficients maintain their signsand, considering 5% as the reference significance level, all vari-ables maintain their statistical significance. The only exceptionis variable expend:incomej, which is no longer statistically sig-nificant.Secondly, we recall Doucouliagos and Ulubasoglu (2005),

who, in a meta-regression analysis of the relationship betweeneconomic freedom and economic growth, conclude that the lit-erature is affected by specification bias due to the omission ofphysical capital as control variable in the growth regression.Failing to include physical capital results in larger estimatesof the economic freedom–economic growth relationship, whichindicates that economic freedom not only affects growthdirectly, but also indirectly by increasing capital accumulation.Through the savings channel, a similar effect can be expected inthe inequality–growth literature. Specifically, higher inequalitymay increase savings, which will lead to an increase in physicalcapital and, as a consequence, to an increase in economicgrowth. Thus, if both inequality and capital are included in

the growth regressions, the coefficient on inequality will under-estimate the positive impact of inequality on growth. One wayto test whether this happens is to include a dummy in the meta-regression,Capitalj, that is equal to 1 if study j includes physicalcapital as an explanatory variable and 0 otherwise. This can beseen as a specification test of themeta-regression. Column (2) ofTable 6 shows that Capitalj has a negative coefficient and is sta-tistically significant, meaning that studies including capital inthe growth regressions tend to underestimate the impact ofinequality and that one of the mechanisms through whichinequality influences growth is, in fact, the savings channel.As for the other variables of the meta-regression, they maintaintheir statistical significance and coefficients’ signs, the exceptionis again variable expend:incomej. This shows that, apart fromthe result associated to expend:incomej, the results of themeta-regression are robust.

7. CONCLUDING REMARKS

We performed a meta-analysis of the empirical literature onthe relationship between inequality and growth that extendsand enriches Dominicis et al.’s (2008) meta-analysis in threeways: it includes more recent studies; it is not restricted tostudies focusing on income inequality; and it tests and correctsfor the presence of several forms of publication bias.We found that, although the average impact of inequality on

growth is not significant, there is a high degree ofheterogeneity in the reported effect sizes. This suggests thatthere are several ‘‘true” effects of inequality on growth, whichmay occur in opposite directions. We also found the presenceof publication bias, as authors and editors are more prone to


report and publish statistically significant effects, and theresults tend to follow a predictable time pattern over time,according to which negative and positive effects are cyclicallyreported.After correcting for these two forms of publication bias, we

investigated the sources of heterogeneity by means of a meta-regression. As in Dominicis et al.’s (2008) our results suggestthat for a 5% level of significance: the effect of inequality ongrowth is negative and more pronounced in less developedcountries than in rich countries; the inclusion of regional dum-mies in the growth regression of the primary studies consider-ably weakens such effect; expenditure and gross incomeinequality tend to lead to different estimates of the effect size.However, contrary to it Dominicis et al. (2008), we find that:the impact of inequality on growth is not significantly influ-enced by the quality of the data on income distribution orby the use of different panel estimation techniques; cross-section studies systematically report a stronger negativeimpact than panel data studies. Furthermore, our results sug-gest that wealth inequality is more pernicious to subsequentgrowth than income inequality is. With the exception of theimpact of using expenditure versus gross income, all theseresults are robust.These findings provide deeper insights into the nature of the

inequality–growth relationship. In fact, we can say that themechanisms through which inequality influences growthoperate differently in different circumstances. For example,inequality affects growth differently in developing and devel-oped countries, which suggests that the transmission mecha-nisms are not the same in both groups of countries. Besidesthe fact that panel studies lead to more diverse and less conclu-sive results than cross-section studies suggests that, on the onehand, the inequality–growth relationship is influenced bycountry/regional specificities and that, on the other hand, itacts differently in the short and in the long-run. Additionally,inequality in wealth distribution has a stronger negativeimpact on growth than inequality in income distributionpossibly because the transmission channels that are relevantin both types of distribution are not the same.

These insights have important policy implications. Policymakers should avoid thinking of a global, single pattern forthe inequality–growth relationship because such a patterndoes not exist. Instead, they should take into considerationthe existence of specific and particular effects that differ fromcountry to country and region to region and that vary withthe type of inequality and the time span considered. In partic-ular, policies designed to reduce inequality in developing coun-tries are desirable, as they are likely to have a positive impacton economic growth. Such policies involve, for example, thepromotion of more equitable tax and transfer systems, theimplementation of labor market reforms aimed at reducingearning gaps and unemployment or the reduction of con-straints to the access of credit markets. In addition, giventhe significant negative impact of human capital and landinequality on growth, policies directed to promote a moreequitable distribution of property, to improve the qualityand reach of education, and to guarantee a more equitable dis-tribution of educational opportunities can enhance economicgrowth.Finally, it is worth mentioning some possible extensions of

this paper. Firstly, it would be interesting to include in themeta-analysis all estimates reported in each study, as thiswould allow more information and employing meta-analytical techniques with more observations. Secondly, itwould be also interesting to conduct a separate meta-analysis composed only by working papers and other unpub-lished material, and then check for significant differencesbetween the results of published and unpublished materialsin this field. Thirdly, it would also be useful to complementthe meta-analysis of the reduced-form relationship with ameta-analysis of the empirical literature on the transmissionchannels from inequality to growth. This last extension wouldpermit testing the conjectures made in this paper regarding themechanisms that link the two variables and the circumstancesunder which they materialize. Incorporating the three exten-sions into the analysis would certainly improve our under-standing of the inequality–growth relationship and would bea fruitful direction for future research.

NOTES

1. For a summary of the theoretical literature, please see, for example,Neves and Silva (2014) and Halter, Oechslin, and Zweimuller (2014).

2. The use of the average or the median estimate would imply that eachobservation in Eqn. (9) would present multiple values for a singleexplanatory variable, Xk .

3. We defined a maximum of three estimates per article to avoid theabove-mentioned problem of disproportionate importance among studies.

4. The reduction of potential selection bias and the increase in thesample size resulting from considering more than one estimateperstudy come at a price, namely the introduction of statistical depen-dence between observations. According to Hunter and Schmidt (1990),a study can be regarded as statistically independent in this context if ituses the same dataset as a previous study but involves differentauthors, or if the same authors use different datasets. Therefore, whentwo estimates are drawn from the same study, albeit resulting fromdifferent modeling or estimation techniques, they are likely to bestatistically dependent. We deal with this problem using theappropriate procedures, described in Section 5.

5. Columns (5) and (6) of Table 1 will be analyzed in Section 5.

6. The terms ‘‘fixed effects” and ‘‘random effects” in meta-analysis do nothave the same meaning as in the estimation of panel regressions ineconometrics, as they refer to different estimators of the underlying effectsize rather than different coefficients’ panel-data estimation techniques.For more detailed explanations regarding these estimators in the contextof meta-analysis, please see Hedges and Olkin (1985) and Dominicis et al.(2008).

7. x2j stands for the estimate of the variance of dj and is collected from

the results reported in each study. The value of xj associated with eachobservation of our meta-sample is in column (3) of Table 1.

8. The dependent variable, dj, is an estimated regression coefficientdrawn from each original model. Consequently, its estimated standarderror, xj, varies with j.

9. See column (4) of Table 1 the t-statistics associated to eachobservation of our meta-sample.

10. This procedure consistently estimates standard errors in the presenceof heteroscedasticity and/or non-specified autocorrelation between distur-bances (for more details, see Newey &West, 1987). From here forward, werefer to these as heteroscedasticity-autocorrelation consistent standard


errors. This technique is necessary in our case, given the above mentionedpresumable existence of correlation between observations drawn from thesame study.

11. timej assumes the value 1 for a study published in 1994, the value 2for a study published in 1995 and so on.

12. See Neves and Silva (2014) for further information on some of thesedatabases.

13. Note that the R-squared presented in Table 4 (equal to 65.44%) is anincorrect reflection of the meta-regression’s ability to explain the variationin reported effects sizes, dj, because the dependent variable of the meta-regression is not dj, but t0j ¼ dj 0=xj. After using the estimates of thecoefficients b reported in Table 4 to predict the effect sizes corrected for thepresence of publication bias, ~d0j, and after adding to these the respectivemagnitude of the bias, we obtained the predicted values of the effect size,~dj, for each observation. The comparison of these values with the reportedeffect sizes resulted in a corrected R-squared of 61.38%.

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