Growth, inequality and poverty : a robust relationship?

Empirical Economics (2022) 63:725–791 https://doi.org/10.1007/s00181-021-02152-x Growth, inequality and poverty: a robust relationship? Gustavo A. Marrero1,2 ·Luis Servén3 Received: 12 October 2020 / Accepted: 30 September 2021 / Published online: 23 November 2021 © The Author(s) 2021 Abstract The consequences of poverty and inequality for growth have long preoccupied academics and policy-makers. This paper revisits the inequality-growth and povertygrowth links. Using a panel of 158 countries between 1960 and 2010, we find that the correlation of growth with poverty is consistently negative: A 10 p.p. decrease in the headcount poverty rate is associated with a subsequent increase in per capita GDP between 0.5 and 1.2% per year. In contrast, the correlation of growth with inequality is empirically fragile—it can be positive or negative, depending on the empirical specification and econometric approach employed. However, the indirect effect of inequality on growth through its correlation with poverty is robustly negative. Closer inspection shows that these results are driven by the sample observations featuring high poverty rates. Keywords Growth ·Inequality ·Poverty ·Indirect impacts JEL Classification O40 ·O11 ·O15 ·E25 1 Introduction Whatistheeffectofpovertyonaggregateincomegrowth?Andtheeffectofinequality? Academicsandpolicy-makershavelongbeenconcernedwiththesequestions.Butthey have typically been explored as separate issues. Yet properly answering them requires BGustavo A. Marrero [email protected] Luis Servén [email protected] 1Departamento de Economía, Contabilidad y Finanzas, CEDESOG, Universidad de La Laguna, San Cristóbal de La Laguna, Spain 2EQUALITAS, Madrid, Spain 3CEMFI, Madrid, Spain 123 726 G. A. Marrero, L. Servén taking them up jointly, because poverty and inequality are interrelated features of the same income distribution (Bourguignon 2004). This paper attempts to fill that gap by providing an empirical exploration of the growth effects of both poverty and inequality and, in particular, of their respective robustness. The effects of poverty have been analyzed by numerous theoretical papers highlighting a variety of mechanisms through which poverty may become selfperpetuating. But empirical work has been more limited and largely inconclusive. Indeed, a basic implication of the theoretical models of poverty traps—namely, that countries suffering from higher levels of poverty should grow less rapidly than comparable countries with lower poverty—has been largely overlooked. This is the key hypothesis pursued in this paper. It can be viewed as a weak version of the poverty trap hypothesis, in that to support it we do not need to find evidence of multiple equilibria or income stagnation, but just empirical proof that, other things equal, poverty tends to hold back growth. In contrast, the effects of inequality have attracted massive empirical literature, albeit with sharply conflicting results. The present paper adds to existing work by highlighting a novel angle, namely the indirect effect of inequality on growth accruing through the impact of inequality on poverty: given the poverty line and the overall population’s mean income, an increase in inequality will typically raise poverty, by pushing more individuals below the poverty line.1If poverty affects growth, so will inequality through this indirect channel—in addition to any direct effects that inequality might exert on growth. To assess the respective growth impacts of poverty and inequality, we estimate a reduced-form growth equation with inequality and poverty added separately and jointly to an otherwise standard set of growth determinants (educational attainment, investment prices, government size, degree of openness, public infrastructures, etc.). For the estimation, we assemble a large panel data set of non-overlapping five-year observations comprising 158 countries over the period 1960–2010. The sample is heavily unbalanced, and its size exceeds by far that found in earlier studies of the poverty-growth link. Our econometric approach is based on GMM estimation employing internal instruments (Arellano and Bover 1995; Blundell and Bond 1998; Roodman 2009). In our setting, the choice of this approach is dictated by the short time dimension and large cross-sectional dimension of our panel dataset—which makes panel time-series methods unsuitable—and by the potential endogeneity of the regressors—which demands an instrumental variable approach. These issues affect also much of the empirical literature on the links between poverty, inequality and growth, which—like our paper—has to contend with the potential problem of two-way causality between the variables at the core of the analysis. In this context, GMM represents a natural methodological choice, which we also share with much of the related empirical literature.2Moreover, this common empirical 1The consequences of inequality for poverty are highlighted for example by Bourguignon (2003,2004)or Ravallion (2005). Marrero and Servén (2018) provide numerical simulations illustrating the magnitude of the effect of inequality on poverty, for given average income. 2Empirical analyses of the links between aggregate growth, poverty and inequality commonly use an instrumental variable approach. A few papers feature external instruments—e.g., Brueckner et al. (2015), 123 Growth, inequality and poverty: a robust relationship? 727 methodologyalsomakesourpapermoreeasilycomparablewithexistingwork.Finally, while our use of GMM for growth empirics is not novel, our paper is among the first to examine rigorously, in a system GMM setting, the potential problem of weak instruments plaguing much of the empirical growth literature, as first raised by Kraay (2015) in the context of the empirical relationship between inequality and growth. Our main finding is that poverty has a robust negative and significant effect on growth. As for inequality, we find that the sign and significance of its direct effect on growth are fragile. However, its indirect effect (through poverty) is robustly negative. Further inspection reveals the presence of nonlinearities, in that these results are driven by the sample observations featuring high poverty: when poverty is low, its impact on growth is not significant, and the indirect effect of inequality on growth is therefore absent. We reach a similar conclusion when we let the growth impact of poverty differ between developed and developing countries: It is negative and significant for the latter, but not for the former. Our results survive a battery of robustness checks, including the use of alternative sets of instruments and specifications in the GMM estimation, different poverty lines and poverty measures, alternative poverty data, nonlinear and nonparametric specifications, or the use of alternative sets of control variables. We also find that our preferred GMM specification can address in a satisfactory manner the endogeneity, under-identification and weak instruments problems often encountered in macroeconomic applications of dynamic panel models (Bazzi and Clemens 2013). Our paper is embedded in an extensive literature (recently surveyed by Cerra et al. 2021a) analyzing the multidirectional links among growth, inequality and poverty. Three strands are especially relevant in our context. They, respectively, focus on the impactofpovertyongrowth,theimpactofinequalityongrowth,andthecontributionof inequality and income growth to poverty. We provide a brief review of these literature works in the next section. The rest of the paper is structured as follows. As just noted, Sect. 2is devoted to a selective summary of the literature on the growth-inequality-poverty nexus. In Sect. 3, we describe the data and we lay out the empirical strategy to test for the effects of poverty and inequality on growth. In Sect. 4, we report the main empirical results for our baseline specification. Section 5reports extensive robustness checks on our empirical results. Section 6analyzes how the links of poverty and inequality with growthmight depend onthe prevailing degreesof poverty and/or inequalityand gauges the direct and indirect effects of inequality on growth. Finally, Sect. 7concludes. 2 The growth-inequality-poverty nexus: a review The seminal work of Kuznets (1955) is the starting point of an extensive literature analyzing the growth-inequality-poverty nexus (see Bourguignon 2004, and the recent surveys by Cerra et al. 2021a,b). Our paper relates to several strands of this literature. Footnote 2 continued assessing the effect of GDP growth on inequality—but GMM using internal instruments (given by suitably lagged and transformed regressors) is much more commonly used: for example, by Partridge (1997), Forbes (2000), Panizza (2002), or Berg et al. (2018), all of which are concerned with the opposite direction of causality, from inequality to growth. 123 728 G. A. Marrero, L. Servén First, a long-standing theoretical literature has studied a variety of mechanisms through which poverty may deter economic growth. Its arguments are mostly based on the existence of poverty traps, i.e., mechanisms through which poverty prevents a significantshareofthepopulationfromhelpingignitethegrowthengine(Azariadisand Stachurski2005;Bowlesetal.2006;Haider etal. 2018). Underappropriate conditions, those mechanisms may lead to multiple equilibria and make the negative impact of poverty on growth self-reinforcing. In general, the mechanisms highlighted in the literature operate by reducing the incentives and/or abilities of the poor to undertake risky entrepreneurial activities, and/or to accumulate physical and human capital. A prominent mechanism involves ‘threshold effects’ (Azariadis and Drazen 1990), resulting, for example, from indivisibilities or increasing returns to scale.3For example, if poverty is coupled with credit constraints, the result is that below a certain level of income or wealth economic agents may be too poor to afford the investments (in human or physical capital) or the technologies necessary to raise their income (Galor and Zeira 1993; Banerjee and Newman 1993). Malnutrition provides another example. In developing countries, poverty is associated with high rates of malnutrition (Dasgupta and Ray 1986), which impacts cognitive abilities and school absenteeism and is transmitted to the children’s capacity to learn. The resulting educational inequality is also growth-deterring (Galor and Moav 2004). Institutional arrangements that place economic opportunities beyond the reach of the poor can likewise result in reduced income growth (Mookherjee and Ray 2002; Engerman and Sokoloff 2006). Another poverty-perpetuating mechanism is related to risk aversion (Banerjee 2000): Because poorer individuals are typically more risk averse, in the absence of well-functioning insurance and credit markets, they will skip profitable investment opportunities that they deem too risky.4Poverty can also alter the decision-making process of individuals toward less growth-enhancing activities. For instance, the poor devote a significant fraction of their income to satisfying basic needs (Shah et al. 2012) and to “temptation” goods (Banerjee and Mullainathan 2010) and reduce the resources devoted to education, health and investment. Poor individuals show also lower aspirations, as they anticipate that their current status will impede their future success (La Ferrara 2019). In spite of the diversity of these analytical models, evidence on their empirical relevance remains largely inconclusive. A few papers (see Durlauf 2006,forareview) have searched for various empirical regularities consistent with those models, such as aggregate non-convexities (Azariadis and Stachurski 2005) and convergence clubs (Quah 1993). A broader empirical review of different mechanisms advanced in the literature finds little evidence that they may be at work, except perhaps in remote or disadvantaged areas (Kraay and McKenzie 2014). More recently, large-scale randomized evaluations, such as the one developed by Bandiera et al. (2017) in Bangladesh, 3Poverty traps arising from threshold effects have often been offered as a rationale for a ‘big push’ approach to policy. In particular, when large aid programs are coordinated in a multi-faceted way, a ‘big push’ can be effective to engineer growth takeoffs (Banerjee et al., 2015). However, in a cross-country dataset, Easterly (2006) finds that takeoffs are rare and, in general, they are not associated with ‘big push’ strategies. 4The argument that risk aversion leads to underinvestment goes back to Stiglitz (1969). See also Agenor and Aizenman (2011), who argue that aid volatility could induce poverty traps in poor countries through a similar mechanism. 123 Growth, inequality and poverty: a robust relationship? 729 yield strong evidence that the poor face imperfections in capital markets that keep them in a low asset-low employment poverty trap. Somewhat surprisingly, just a few papers have taken up the fundamental aggregate implication of the poverty trap literature—that, ceteris paribus, countries with higher poverty should grow more slowly. The list is limited to our working paper version, Marrero and Servén (2018), plus López and Servén (2015) and Ravallion (2012), all of which conclude that poverty is growth-deterring5;Easterly(2006) shows a nonsignificant impact of poverty on growth. The second strand of literature to which our paper is related is concerned with the impact of inequality on growth. It includes a large number of empirical contributions reaching conflicting conclusions; for overviews, see Voitchovsky (2011), Berg et al. (2018), and Cerra et al. (2021a). For example, Alesina and Rodrik (1994) and Perotti (1996) found a negative relationship between inequality and growth in cross section data, but subsequently, Li and Zou (1998) and Forbes (2000) obtained the opposite result using panel data. Barro (2000) found that inequality might affect growth in different directions depending on the country’s level of income, while Panizza (2002) found that results might depend on the model specification and the quality and type of data (see also Deininger and Squire 1998). In turn, Banerjee and Duflo (2003) concluded that the response of growth to inequality changes has an inverted U-shape. Themultiplicityof factorsaffectingbothinequalityandgrowthmightexplainsthese contradictory results. For example, rising inequality could be the result of growthenhancing technological change whose returns are captured by talented individuals at the top of the distribution (Goldin and Katz 2008). In contrast, if rent-seeking is the fundamental force behind growing incomes of the rich, the increase in inequality could come along with declining growth (Stiglitz 2012). In this line of enquiry, Galor and Moav (2004) argue that the replacement of physical capital accumulation by human capital accumulation as a prime engine of economic growth has changed the qualitative impact of inequality on growth. Marrero and Rodríguez (2013) emphasize that the sign of the effect of inequality on growth depends on the type of inequality considered (i.e., inequality of opportunity or of effort). Voitchovsky (2005) and, more recently, van der Weide and Milanovic (2018) argue that the effect of inequality is negative for the income growth of the poor but positive for the income growth of the rich—i.e., inequality tends to be self-reinforcing. The effects of inequality on growth might also depend on the sectoral structure of the economy (Erman and te Kaat 2019) and on the degree of intergenerational mobility (Aiyar and Ebeke 2020).6 In general, different mechanisms affecting growth in opposite directions through different channels act all simultaneously, leading to conflicting inferences. In the empirical literature, an emerging consensus view is that the long-run effect of inequalityongrowthissignificantlynegative,andonlywhenlookingatrelativelyshort periods 5Easterly (2006) investigates (and rejects) a more extreme hypothesis, namely that high poverty countries should show no growth. 6Erman and te Kaat (2019) show that higher inequality increases growth in physical capital-intensive industries, while it harms grow in industries using skilled labor intensively. 123 730 G. A. Marrero, L. Servén of time, the relationship may turn positive (Halter et al. 2014; Brueckner et al. 2015; Berg et al. 2018; Brueckner and Lederman 2018).7 A third strand of the literature explores the links between growth and inequality, on the one hand, and poverty, on the other. The bulk of this literature, which is quite extensive (Cerra et al. 2021a), focuses on the poverty-reducing effect of growth and the factors that shape it (Dollar and Kraay 2002; Bourguignon 2003; Ravallion 2004). This angle of the poverty-growth link is the opposite to that pursued in this paper. Empirically, there is ample consensus that growth reduces poverty—i.e., it is “good for the poor.” Dollar and Kraay (2002), and the subsequent updates using alternative databases and empirical approaches (Kraay 2006, Dollar et al. 2016) find that the income of the poorest deciles varies in the same proportion as average income, hence fostering aggregate growth is pro-poor (see also Ferreira et al. 2010, or Loayza and Raddatz 2010). Recent work confirms this result (Fosu 2017; Bluhm et al. 2018; Bergstrom 2020). For example, Bergstrom (2020) finds that, in a large cross-country sample, 90% of the variation in poverty is explained by variation in per capita GDP. However, the reason is that the sample variation in per capita income is much larger thanthatofinequality;indeed,inmost of the sample countries, theestimatedinequality elasticity of poverty exceeds the income elasticity of poverty—which suggests that declines in inequality offer a large potential (as yet unrealized) to reduce poverty rates. Comparatively, the literature has paid less attention to the impact of inequality on poverty (Bourguignon 2003; Ravallion 2005; Ferreira et al. 2010; Kalwij and Verschoor2007).Thisis preciselythemechanismbehindtheindirectinequality-to-growth channel analyzed in this paper, and not covered in earlier literature. More recently, Sehrawat and Giri (2018), the aforementioned Bergstrom (2020) and Lakner et al. (2020) find evidence supporting the role of declining inequality for poverty reduction. 3 Growth, inequality and poverty: data and empirical implementation We turn to the description of our empirical strategy. First we describe the data and then the econometric approach employed in the estimation. 3.1 Data Sinceourfocusisnotoncyclicalgrowthfluctuations,wefollowtheempiricalliterature on inequality and growth and construct a panel data set of non-overlapping 5-year observations on the three variables of interest: inequality, growth and poverty. We focus on the 1960–2010 period, as done by the recent empirical literature on inequality and growth. Growth is measured as the log difference of real per capita income over the entire 5-year interval, while poverty and inequality are measured at the beginning 7Amorelimitedliterature hasexaminedtheinequality-growthlinkfrom theopposite perspective,assessing how income growth affects inequality. Its results are mostly inconclusive, however. For instance, while Brueckner et al. (2015) and Blau (2018) find that GDP growth reduces inequality, Krusell et al. (2000)and Aghion et al. (2019) reach the opposite conclusion. 123 Growth, inequality and poverty: a robust relationship? 731 of the interval. This means we only need to collect poverty and inequality data up to 2005. We use the Gini index to measure inequality and take the UN-WIID2 (2008) database as our primary source of data on income inequality. It includes 5313 surveys for 154 countries from 1950 to 2006. We complete the WIID2 data with information fromPovcalNet,whichadds another122country-year(16countries)observationsover the 1960–2010 period. In a number of instances, there are multiple surveys referring to the same country-year, but they offer different coverage or use different concepts of income. We restrict our sample to Gini indexes based on nationally representative surveys. Moreover, data are sometimes based on income and other times on expenditure figures; income is net of transfers and taxes in some cases and not in others; the unit of analysis may be the individual or the household, etc. To correct at least in part for this heterogeneity, we adjust the original Gini data following Dollar and Kraay (2002).8 For economic growth, we use national accounts purchasing-power-parity (PPP)- adjusted per capita GDP data from the Penn World Tables 7.1, the same source used by Berg et al. (2018) and many other studies of inequality and growth, which facilitates comparability with them. Sala-i-Martin (2006) and Dollar and Kraay (2002), among many others, emphasize the advantages of using per capita GDP instead of the mean level of income obtained directly from household surveys. The survey mean usually does not match per capita income from the national accounts, because of differences in concepts and methodology, inconsistent data collection methods, misreporting, etc. Additionally,formanyofthecountry-yearobservationsforwhichwehaveinformation on inequality, we do not have matching information on mean income from the same source, which hampers the construction of a large panel dataset. In contrast, national accounts data are reported yearly for all countries, using a homogenous methodology, which, in addition, allows us to compare our empirical results with those of the ample macroeconomic literature on income inequality and growth. Regarding poverty data, we follow the strategy proposed by Dollar and Kraay (2002), López and Servén (2015), Sala-i-Martin (2006) and Pinkovskiy and Sala-iMartin (2013). These authors point out that combining poverty and income growth data from household surveys and national accounts may lead to misleading conclusions, because of the inconsistencies between the two sources just noted. To avoid this problem, they use PWT data to construct both income growth and poverty measures, with the latter computed assuming that household income follows a lognormal distribution. Thus, we construct a set of poverty measures (the headcount ratio P0, the poverty gap P1 and the squared poverty gap P2) using a lognormal approximation on the basis of the observed per capita GDP levels and Gini coefficients.9We also 8Specifically, we pool the sample and regress the Gini coefficient on a constant, regional dummies and dummy variables indicating whether the survey is stated in terms of gross income or consumption (the omitted category is income net of taxes and transfers). We then subtract the estimated mean difference between these two alternatives and the omitted category to arrive at a set of Gini indices that notionally correspondtothedistributionofincomenetoftaxesandtransfers.Theresultsoftheseadjustmentregressions are available upon request, but they show similar conclusions as in Dollar and Kraay (2002). 9The UN-WIID2 Gini index is not always available for the first year of each 5-year interval. In such cases, we allocate the available observation(s) to the closest starting year of a 5-year interval, with a limit of 2 years 123 732 G. A. Marrero, L. Servén experiment with alternative, widely used poverty lines: US$ 1.25, US$ 2 and US$ 4 per person per day, in 2005 PPP US$ (see Appendix 1for details). This approach allows a considerable increase in sample size. Despite the progress made in recent years, mainly through the PovcalNet project, survey-based poverty data are still relatively scarce, at least in comparison with the size of the standard crosscountry time-series growth dataset. Using the lognormal approximation, we assemble 746observationsonpovertyovernon-overlapping5-yearintervals,covering156countries between 1960 and 2005 (an average of almost five observations per country).10 In contrast, using the January 2020 version of PovcalNet over the same 1960–2005 time span, we can construct a dataset of 383 poverty observations over non-overlapping 5-year intervals for 144 countries, roughly half the size of our sample—i.e., an average of less than 3 observations per country, with data for the vast majority of countries starting in 1990 or later.11 As far as we are aware, ours is the largest sample used to date to study the impact of poverty on growth. It exceeds by far the samples used by the two earlier papers analyzing the poverty-growth nexus in a panel regression setting: López and Servén (2015) assemble a sample comprising 325 observations from 85 countries over 1960–2000, while Ravallion (2012) uses unbalanced panel data from PovcalNet covering up to 97 developing countries over a shorter time span, 1981–2005. Table 1presents summary statistics on annual growth, mean income, inequality and poverty for the common sample of these variables in the unbalanced 1960–2010 panel. The table shows the wide range of per capita income levels (expressed in 2005 US dollars in PPP terms) in the sample—from just over $200 (the Democratic Republic of Congo in the mid-2000s) to about $73,000 (Luxembourg in 2005). The median observation corresponds to Brazil in the mid-1970s, with per capita income about $5500. The overall sample mean is about $9800, much larger than the median, which reflects a world income distribution skewed to the right. Regardinginequality,boththemedianandthemeanoftheGinicoefficientequal0.4, which matches the values found for the U.S. (in 2000), Burkina Faso (in 1995), Turkey (in 2010) or Singapore (in 1970). The maximum value (above 0.74) corresponds to Footnote 9 continued of difference. When more than one observation is available within the 2-year limit, we take the average. Because of the strong inertia of inequality and poverty time series, using a 1-year limit instead of 2 years, or not using means, yields very similar results (Dollar and Kraay 2002). 10 Our data comprise 121 data points corresponding to 32 low-income countries, 180 to 41 lower-middle income countries, 240 to 44 upper-middle income, 57 to 11 high-income non-OECD, and 206 to 30 highincome OCDE countries. The sample includes 18 observations (2 countries) from North America, 248 (48 countries) from Europe and Central Asia, 159 (28 countries) from Latin American and the Caribbean, 53 (12 countries) from Middle East and North Africa, 144 (40 countries) from Sub-Saharan Africa, 56 (9 countries) from South Asia and 126 (19 countries) from East Asia and the Pacific. 11 This sample size would be too small for many of our exercises, and thus for the robustness tests using PovcalNet data reported in Section V below, we resort to the interpolated PovcalNet series, which allows increasing the sample size to 556 observations. These interpolated information start in 1981 and are reported every three years. Thus, to construct a non-overlapping 5-year panel data similar to the one used in our baseline specification and match the timing of poverty data with that of the other variables (growth and other controls), we use a “closest” criterion or take the average if two poverty observations are one year above and one below the assigned year. We should also note that the current PovcalNet series uses a poverty line of 1.90 2011 US$, which replaces its previous line of 1.25 2005 US$ (see Ferreira et al. 2016,formore details). 123 Growth, inequality and poverty: a robust relationship? 733 Table 1 Growth, inequality and poverty data: summary statistics Median Mean Std P10 P90 Min Max GDP per capita growth 0.025 0.025 0.030 −0.012 0.061 −0.086 0.201 Real per capita income 5651.1 9792.5 10,462.5 816.4 26,053.7 207.5 73,243.0 Gini coefficient 0.394 0.402 0.100 0.280 0.543 0.157 0.742 P0 (US$ 1.25) 0.005 0.096 0.177 0.000 0.364 0.000 0.906 P0 (US$ 2) 0.023 0.162 0.247 0.000 0.610 0.000 0.969 P0 (US$ 4) 0.130 0.287 0.336 0.000 0.881 0.000 0.999 P1 (US$ 1.25) 0.001 0.040 0.086 0.000 0.146 0.000 0.602 P1 (US$ 2) 0.006 0.073 0.132 0.000 0.270 0.000 0.722 P1 (US$ 4) 0.038 0.151 0.212 0.000 0.523 0.000 0.855 P2 (US$ 1.25) 0.000 0.023 0.056 0.000 0.077 0.000 0.497 P2 (US$ 2) 0.002 0.044 0.089 0.000 0.158 0.000 0.594 P2 (US$ 4) 0.016 0.100 0.156 0.000 0.356 0.000 0.750 Headcount poverty rate (P0); poverty gap (P1); squared poverty gap (P2); alternative poverty lines: US$ 1.25, US$ 2 and US$ 4, per person per day (2005 PPP). Poverty is obtained from a lognormal approximation on the basis of the observed per capita GDP (PWT 7.1) levels and Gini coefficients (UNU-WIDER 2008). See Appendix 1for details Zimbabwe in 1995, and the minimum (below 0.16) corresponds to Bulgaria in 1975. Around 80% of the observations fall in the range between 0.28, a value found among Western European countries, and 0.54, a value found among Latin American and Sub-Saharan African countries. Poverty rises by construction with the poverty line and declines as the poverty measure changes from P0 to P2 (i.e., as one considers more bottom-sensitive measures). For our lognormal poverty estimates, the table shows that median headcount poverty P0 is 0.6% using US$ 1.25 per day as poverty line, but it raises to 2.3% with a US$ 2 poverty line, and to 13% with US$ 4. Likewise, the median P1 ranges from less than 0.1% for US$ 1.25 to about 4% for US$ 4, while the median P2 ranges from less than 0.1% for US$ 1.25 to almost 2% for US$ 4. Although the mean and the median of these poverty measures are relatively small, the heterogeneity in the sample is quite high, since the ranges of the various poverty measures run from a minimum of zero (reflecting the presence of high-income countries in the sample) to a maximum whose 123 740 G. A. Marrero, L. Servén Table 2 Growth, poverty and inequality: panel OLS estimates M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P0, lag − 0.0450*** (−5.70) − 0.0440*** (−5.71) − 0.0328*** (−3.88) − 0.0334*** (−4.02) − 0.0382*** (−4.58) − 0.0380*** (−4.70) − 0.0424*** (−3.84) −0.0430*** (−4.03) Gini, lag − 0.0415*** (− 3.63) − 0.0393*** (−3.50) −0.0252** (−2.12) −0.0266** (−2.31) − 0.0399*** (−3.35) − 0.0396*** (−3.36) −0.0354** (−2.44) −0.0366*** (−2.60) log y,lag − 0.00781*** (−5.43) −0.00143 (− 1.61) − 0.00873*** (−5.88) − 0.00892*** (−4.80) − 0.00381*** (−3.08) − 0.00952*** (−5.05) − 0.00803*** (−5.43) − 0.00303*** (−3.20) − 0.00920*** (−5.97) − 0.0213*** (−6.13) − 0.0143*** (−4.18) −0.0215*** (−6.31) Inv. deflator, lag − 0.00482** (−2.23) − 0.00629** (−2.20) −0.00453* (−1.91) Female educ., lag −0.00299 (−1.16) −0.00300 (−1.09) −0.00176 (−0.66) 0.00560*** (3.79) 0.00370** (2.44) 0.00509*** (3.48) Male educ., lag 0.00747*** (2.89) 0.00671** (2.40) 0.00567** (2.13) Inflation −0.00728 (−1.41) −0.00409 (−0.84) −0.00728 (−1.41) − 0.0232*** (−3.66) −0.0165** (−2.58) −0.0217*** (−3.31) Trade openness (log) 0.0113*** (4.25) 0.0136*** (5.05) 0.0115*** (4.34) Gov. size (log) −0.00110 (−0.40) −0.00191 (−0.67) −0.00135 (−0.48) Infrastructure, lag 0.00847*** (2.94) 0.00830*** (2.78) 0.00754*** (2.70) 123 Growth, inequality and poverty: a robust relationship? 741 Table 2 (continued) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures Num. obs 745 745 745 676 676 676 656 656 656 477 477 477 R2-adjusted 0.096 0.072 0.112 0.124 0.108 0.130 0.120 0.107 0.135 0.149 0.125 0.161 Unbalanced panel with data at 5-year intervals over 1960–2010. The dependent variable is the annual growth rate of per capita GDP. The explanatory variables are real per capita GDP (in logs), the headcount poverty rate (P0) using US$ 2 as poverty line, the Gini coefficient, and alternative sets of additional controls that vary across models M1 (skeleton model), M2 (education and investment prices), M3 (policy variables) and M4 (policy variables and infrastructures). Explanatory variables are all lagged one period (5 years), with the exception of the policy variables in models M3 and M4, which are taken as contemporaneous 5-year averages. A constant term and time dummies are included in all models. Robust tstatistics in parentheses: ***denotes significance at 1%, **at 5%, *at 10% 123 742 G. A. Marrero, L. Servén Table 3 Growth, poverty and inequality: within-group estimates M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P0, lag − 0.0665*** (−3.79) − 0.0764*** (−4.45) − 0.0664*** (−3.89) − 0.0792*** (−4.65) − 0.0716*** (−3.86) − 0.0861*** (−4.53) − 0.0514** (−2.46) − 0.0633*** (−2.82) Gini, lag 0.0378 (1.27) 0.0643** (2.27) 0.0454 (1.46) 0.0742** (2.46) 0.0576** (2.00) 0.0865*** (2.98) 0.0457 (1.48) 0.0641** (2.05) log y,lag − 0.0409*** (−6.28) − 0.0303*** (−4.91) − 0.0429*** (−6.18) − 0.0394*** (−5.51) − 0.0256*** (−4.02) − 0.0426*** (−5.86) − 0.0667*** (−8.31) − 0.0557*** (−6.62) − 0.0709*** (−8.38) − 0.0643*** (−8.11) − 0.0580*** (−8.04) − 0.0674*** (−8.18) Inv. deflator, lag − 0.00916** (−2.33) − 0.0116** (−2.33) − 0.00899** (−2.31) Female educ., lag −0.00122 (−0.15) −0.0124 (−1.63) −0.00196 (−0.26) 0.00471* (1.79) 0.00261 (1.04) 0.00603** (2.39) Male educ., lag 0.00637 (0.75) 0.0148* (1.85) 0.00935 (1.15) Inflation − 0.0224*** (−3.87) − 0.0221*** (−3.87) − 0.0219*** (−3.72) − 0.0368*** (−4.93) − 0.0369*** (−5.45) − 0.0366*** (−5.10) Trade openness (log) 0.0258*** (3.50) 0.0312*** (3.57) 0.0238*** (3.49) Gov. size (log) − 0.0237*** (−2.94) − 0.0196** (−2.57) − 0.0251*** (−3.26) Infrastructure, lag 0.0177*** (3.75) 0.0236*** (5.90) 0.0170*** (3.44) Num. obs 745 745 745 676 676 676 656 656 656 477 477 477 123 Growth, inequality and poverty: a robust relationship? 743 Table 3 (continued) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures R2-adjusted 0.202 0.171 0.216 0.218 0.192 0.236 0.325 0.302 0.348 0.336 0.329 0.350 Num. countries 156 156 156 131 131 131 147 147 147 88 88 88 See note in Table 2 123 744 G. A. Marrero, L. Servén (inM4)carrypositiveandsignificantcoefficients(Calderónetal.2015).Incontrast,the effectsofmaleandfemalesecondaryeducationdependonmodelspecification.Female education carries a positive and significant coefficient in M4, but turns insignificant in M2, while the coefficient of male education is generally positive. Similarly, among the policy variables, the coefficient of government size is generally negative, but it is significant only for the WG estimates. Table 4shows estimation results for first-difference GMM, while Table 5shows the results for the baseline system GMM specification (limiting the instrument matrix to two lags). In Appendix 3(Tables 15 and 16), we report results under alternative approaches to reducing the dimension of the system GMM instrument set: collapsing the matrix of instruments while using all lags as instruments (Table 15), and limiting them to two lags and collapsing the instruments at the same time (Table 16). For first-difference GMM (Table 4), we use three lags in the matrix of instruments so as to have the same number of orthogonality conditions as in the baseline system GMM estimation, thus making the results more easily comparable.18 The pvalues of the Hansen tests suggest that in virtually every case, the null of joint validity of all instruments cannot be rejected. Moreover, the Difference-in-Hansen test results, whose pvalues always exceed 0.10, point toward the superiority of system GMM over first-difference GMM. The parameter estimates of the variables of interest follow the same pattern found earlier. The coefficient on the poverty headcount is consistently negative and highly significant, regardless of the choice of model and specification. In contrast, the coefficient of the inequality variable varies in sign and significance depending on the GMM approach and the controls used in the estimation. It is always positive and in one case significant for first-difference GMM, consistent with our results for the WG estimates in Table 3and part of the earlier literature (e.g., Forbes 2000). However, it is negative and, in some cases, significant for system GMM, consistent with our results for pooled-OLS and another strand of the literature (e.g., Berg et al. 2018, and references therein). The negative effect of poverty on growth is robust to changes in model specification and estimation method, while the effect of inequality on growth, which has been the focus of a massive literature, is not. The theoretical model outlined in López and Servén (2015) and explored in Marrero and Servén (2018) helps rationalize our empirical results. In that model, poor individuals—i.e., those whose initial endowment is below a minimum consumption level—do not save and do not contribute to the economy’s aggregate growth. In the absence of financial markets, the model shows that poverty is unambiguously growth-deterring, while inequality can affect growth directly, through the savings of the non-poor, and indirectly, through its effect on poverty. While the indirect effect is negative, the direct effect is ambiguous (as found by the empirical literature), and so is the overall impact of inequality on growth. As a further diagnostic check on the GMM estimates of Tables 4,5,15,16,we inspectedtheresiduals for cross-sectionaldependence,usingPesaran’s(2021)CDtest, 18 Data for the infrastructure index included in M4 are available for only 88 countries under system GMM and 79 under the first-difference GMM specification. Using two lags as instruments to estimate this model would result in the number of instruments exceeding the cross section dimension of the data. Thus, we limit the number of instruments to just one lag. 123 Growth, inequality and poverty: a robust relationship? 745 Table 4 Growth, poverty and inequality: first-difference GMM estimates M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P0, lag − 0.0941*** (−2.59) − 0.0981*** (−2.63) − 0.150*** (− 3.35) − 0.150*** (−5.16) − 0.0997* (− 1.79) − 0.0947** (− 2.19) − 0.117** (− 2.25) − 0.103*** (−2.75) Gini, lag 0.0253 (0.37) 0.113 (1.10) 0.0330 (0.47) 0.131** (2.01) 0.0690 (0.73) 0.112 (1.56) 0.0434 (0.43) 0.115 (1.32) log y,lag − 0.106*** (−4.15) − 0.0876*** (−3.89) − 0.119*** (−5.45) − 0.100*** (− 3.48) − 0.0756*** (−4.60) − 0.0948*** (−4.47) − 0.154*** (− 3.71) − 0.105*** (− 4.50) − 0.149*** (− 4.47) − 0.103*** (− 3.24) − 0.0883*** (−4.01) − 0.106*** (−5.25) Inv. deflator, lag −0.0117 (− 1.19) −0.0177 (−1.47) −0.00942 (−0.90) Female educ., lag 0.0616** (2.39) 0.0148 (0.82) 0.0465*** (2.70) 0.00688 (0.71) −0.00271 (−0.20) 0.00611 (0.57) Male educ., lag − 0.0525* (− 1.92) −0.0140 (−0.59) −0.0319 (−1.51) Inflation 0.0005** (2.51) 0.0005** (2.26) 0.0004* (1.91) 0.0001 (0.06) 0.0017 (0.98) 0.0009 (0.83) Trade openness (log) 0.0396 (1.56) 0.0532** (2.24) 0.0457* (1.95) 123 746 G. A. Marrero, L. Servén Table 4 (continued) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures Gov. size (log) −0.0265 (− 1.50) −0.0350 (− 1.51) − 0.0407** (− 2.05) Infrastructure, lag 0.00750 (0.37) 0.0245* (1.78) 0.00778 (0.42) m2-test (p value) 0.854 0.924 0.568 0.565 0.503 0.336 0.505 0.833 0.750 0.658 0.641 0.622 AR(3) (p value) 0.0261 0.00635 0.0238 0.117 0.102 0.416 0.186 0.155 0.264 0.142 0.146 0.187 Hansen (p value) 0.167 0.199 0.0571 0.412 0.269 0.330 0.581 0.431 0.759 0.397 0.575 0.424 Num. obs 502 503 502 467 468 467 248 249 248 345 346 345 Num. countries 130 130 130 113 113 113 84 84 84 79 79 79 Num. instruments 39 39 54 84 84 99 59 59 70 47 47 55 SeeNoteinTable2. Estimations are done using 2-step first-difference GMM reducing the number of instrument lags to three. The instrument set starts at t−3, and the variance covariance matrix is computed using the small sample correction of Windmeijer (2005). Robust tstatistics in parentheses. ***denotes significance at 1%, **at 5%, *at 10% 123 Growth, inequality and poverty: a robust relationship? 747 Table 5 Growth, poverty and inequality: system GMM estimates M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P0, lag − 0.117*** (−3.81) − 0.121*** (−5.34) − 0.0883*** (−3.71) − 0.0846*** (−4.12) − 0.0666*** (−2.96) − 0.0697*** (−3.85) −0.0506* (−1.88) −0.0503** (−2.32) Gini, lag − 0.107*** (− 2.92) − 0.0955** (−2.12) −0.0553 (− 1.44) −0.0587 (−1.57) − 0.0908*** (−3.30) − 0.106*** (−4.10) − 0.00339 (− 0.08) −0.0346 (−1.25) log y,lag − 0.0200*** (−4.60) − 0.00156 (− 0.61) − 0.0228*** (−6.19) − 0.0166*** (−4.61) − 0.00210 (− 0.92) − 0.0173*** (−5.30) − 0.0160*** (−4.72) − 0.00653** (−2.50) − 0.0184*** (−5.95) − 0.0362*** (−4.72) −0.0168 (− 1.53) − 0.0299*** (−3.29) Inv. deflator, lag −0.00137 (−1.38) − 0.00339* (− 1.93) − 0.000830 (−0.70) Female educ., lag 0.00122 (0.20) 0.00267 (0.44) 0.00385 (0.57) 0.00714** (2.47) 0.000557 (0.15) 0.00557* (1.83) Male educ., lag 0.00241 (0.36) − 0.00158 (− 0.23) −0.00144 (−0.19) Inflation 0.001* (1.93) 0.0012*** (2.91) 0.001*** (2.60) 0.0004 (0.68) 0.001** (2.02) 0.001* (1.83) Trade openness (log) 0.0255*** (3.26) 0.0264*** (2.83) 0.0217*** (2.58) 123 748 G. A. Marrero, L. Servén Table 5 (continued) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures Gov. size (log) −0.00306 (−0.42) −0.00861 (−0.91) −0.00349 (−0.44) Infrastructure, lag 0.0222*** (3.07) 0.0189** (2.03) 0.0166** (2.01) m2-test (p value) 0.108 0.223 0.215 0.0574 0.117 0.117 0.279 0.434 0.493 0.227 0.203 0.313 AR(3) (p value) 0.942 0.659 0.671 0.735 0.729 0.785 0.622 0.609 0.474 0.845 0.773 0.746 Hansen (p value) 0.138 0.160 0.279 0.225 0.242 0.572 0.224 0.295 0.616 0.163 0.269 0.477 Diff-Hansen for levels (p value) 0.220 0.640 0.248 0.382 0.490 0.848 0.375 0.662 0.783 0.372 0.617 0.850 Num. obs 745 745 745 676 676 676 656 656 656 477 477 477 Num. countries 156 156 156 131 131 131 147 147 147 88 88 88 Num. instruments 54 54 76 120 120 142 116 116 138 82 82 97 See note Table 4Estimations are done using 2-step system GMM reducing the number of instrument lags to two. The instrument set starts at t−3, and the variance covariance matrix is computed using the small sample correction of Windmeijer (2005). The difference Hansen test assesses the validity of the instruments for the level equation in system GMM. Robust tstatistics in parentheses. *** denotes significance at 1%, ** at 5%, * at 10% 123 Growth, inequality and poverty: a robust relationship? 749 and focusing on the model versions including both poverty and inequality. Results are shown in Table 17 (Appendix 4). In the majority of cases, the test results are supportive of the empirical specification. This is particularly the case for the models including policy variables (models M3 and M4 in the aforementioned tables), for which the test fails in all cases to reject the null of cross-sectional independence. For the strippeddown model M1, which omits all controls, results are more mixed, as the test fails to reject the null at the conventional 5% level in some exercises (those in Tables 4and 5) but rejects it in others (those in Tables 15,16). The exception is model M2, for which the test consistently finds significant evidence of cross-sectional dependence.19 Overall, we take these results as supporting the view that models M3 and M4 are correctly specified. However, the presence of residual cross-sectional correlation in model M2—first explored by Perotti (1996) and Forbes (2000), suggests that the model’s estimated standard errors may be incorrect.20 4.1 Weak instruments analysis Bazzi and Clemens (2013) have raised the potential problem of weak instruments when using system GMM estimation in growth regressions. Weak identification arises when the instruments are only weakly correlated with the endogenous regressors, and its consequence is that estimators perform poorly (Nelson and Startz 1990). To assess the strength of the instruments employed in our system GMM estimations—in particular, the identification of the poverty and inequality parameters—we use tools designed for settings featuring multiple endogenous regressors. We follow Sanderson and Windmeijer (2016) (SW hereafter), who propose a conditional Fstatistic based on Angrist and Pischke (2009) to test whether, in a multivariate setting, a particular endogenous regressor is weakly instrumented. For each such regressor, a conditional test is constructed by “partialing-out” linear projections of the remaining endogenous regressors. SW show that the conditional Fstatistic can be assessed against the Stock and Yogo critical values, and the weakness can then be expressed in terms of the size of the bias of the IV (or 2SLS) estimator relative to that of the OLS estimator. The null hypothesis is that the instruments are weak. It is rejected if the conditional Fstatistic exceeds the corresponding critical value, and we use a critical value allowing for a 30 percent maximal relative bias. We also perform a Chi-square under-identification test separately for each regressor. Here, the null hypothesis is that the matrix of coefficients from the first-stage conditional regressions is not full rank, signaling a complete 19 The robustness exercises in section V follow the same pattern regarding cross-sectional dependence tests: The residuals of models M3 and M4 show no evidence of dependence, while in most cases, those of model M3 yield the opposite conclusion. Model M1 again yields mixed results. 20 The absence of cross-sectional dependence in models M3 and M4 (and, to a lesser extent, M1) may seem surprising given that short-term growth fluctuations typically display significant international comovement. However, our use of 5-year averages greatly mitigates the comovement usually found at annual (or higher) frequency. In addition, the inclusion of time dummies in our empirical specifications also helps soak up common factors affecting growth in multiple countries. Lastly, the presence of statistically significant policy variables in models M3 and M4 likely helps soak up any remaining cross-sectional correlation in these specifications, unlike in models M1 and M2. 123 756 G. A. Marrero, L. Servén Table 7 (continued) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P0, lag − 0.142*** (− 4.86) − 0.152*** (− 6.15) − 0.101*** (−4.93) − 0.0944*** (−4.78) − 0.0652*** (−3.12) − 0.0765*** (−4.41) −0.0557 (− 1.54) − 0.0629*** (−2.62) Gini, lag − 0.107*** (− 2.92) −0.0689 (− 1.55) − 0.0553 (− 1.44) −0.0412 (−1.24) − 0.0908*** (−3.30) − 0.107*** (−3.74) − 0.00339 (− 0.08) −0.0206 (−0.58) Hansen (p value) 0.124 0.160 0.207 0.292 0.242 0.688 0.195 0.295 0.618 0.181 0.269 0.543 Poverty Gap, P1, Poverty line US$ 1.25 P1, lag − 0.263*** (− 3.74) − 0.227*** (− 4.57) − 0.145*** (−3.35) − 0.138*** (−2.90) − 0.200*** (−4.89) − 0.158*** (−4.49) − 0.144** (− 2.28) −0.121** (−2.45) Gini, lag − 0.107*** (− 2.92) − 0.0658* (− 1.66) − 0.0553 (− 1.44) −0.0486 (−1.21) − 0.0908*** (−3.30) − 0.0789*** (−2.63) − 0.00339 (− 0.08) −0.0182 (−0.57) Hansen (p value) 0.319 0.160 0.346 0.184 0.242 0.620 0.194 0.295 0.520 0.129 0.269 0.630 Poverty gap, P1, poverty line US$ 2.0 123 Growth, inequality and poverty: a robust relationship? 757 Table 7 (continued) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P1, lag − 0.191*** (− 3.65) − 0.176*** (− 5.08) − 0.118*** (−3.46) − 0.111*** (−3.66) − 0.141*** (−4.17) − 0.119*** (−4.20) − 0.0895** (− 1.98) −0.0854** (−2.57) Gini, lag − 0.107*** (− 2.92) − 0.0756* (− 1.93) − 0.0553 (− 1.44) −0.0524* (−1.72) − 0.0908*** (−3.30) − 0.0925*** (−3.45) − 0.00339 (− 0.08) −0.0356 (−1.10) Hansen (p value) 0.210 0.160 0.290 0.253 0.242 0.491 0.217 0.295 0.493 0.134 0.269 0.470 Poverty gap, P1, poverty line US$ 4.0 P1, lag − 0.169*** (− 3.57) − 0.183*** (− 5.61) − 0.125*** (−3.41) − 0.120*** (−4.23) − 0.0993*** (−3.76) − 0.104*** (−4.71) − 0.0706* (− 1.86) −0.0709** (−2.33) Gini, lag − 0.107*** (− 2.92) − 0.0871** (− 2.03) − 0.0553 (− 1.44) −0.0451 (−1.15) − 0.0908*** (−3.30) − 0.102*** (−3.78) − 0.00339 (− 0.08) −0.0326 (−1.08) Hansen (p value) 0.0985 0.160 0.267 0.208 0.242 0.581 0.208 0.295 0.683 0.191 0.269 0.540 Squared poverty gap, P2, poverty line US$ 1.25 123 758 G. A. Marrero, L. Servén Table 7 (continued) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P2, lag − 0.413*** (− 4.15) − 0.347*** (− 4.18) − 0.197*** (−2.85) −0.177** (−2.36) − 0.300*** (−4.54) − 0.237*** (−4.22) − 0.230** (− 2.35) −0.197** (−2.56) Gini, lag − 0.107*** (− 2.92) −0.0518 (− 1.07) − 0.0553 (− 1.44) −0.0370 (−1.15) − 0.0908*** (−3.30) − 0.0709** (−2.52) − 0.00339 (− 0.08) −0.00956 (−0.30) Hansen (p value) 0.431 0.160 0.420 0.172 0.242 0.567 0.212 0.295 0.528 0.153 0.269 0.662 Squared poverty gap, P2, poverty line US$ 2.0 P2, lag − 0.266*** (− 3.70) − 0.239*** (− 4.81) − 0.150*** (−3.63) − 0.149*** (−3.77) − 0.203*** (−4.90) − 0.164*** (−4.45) − 0.139** (− 2.19) −0.116** (−2.41) Gini, lag − 0.107*** (− 2.92) − 0.0652* (− 1.68) − 0.0553 (− 1.44) −0.0442 (−1.31) − 0.0908*** (−3.30) − 0.0820*** (−2.79) − 0.00339 (− 0.08) −0.0241 (−0.81) Hansen (p value) 0.270 0.160 0.318 0.210 0.242 0.587 0.211 0.295 0.521 0.127 0.269 0.622 Squared poverty gap, P2, poverty line US$ 4.0 123 Growth, inequality and poverty: a robust relationship? 759 Table 7 (continued) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P2, lag − 0.201*** (− 3.58) − 0.196*** (− 5.44) − 0.131*** (−3.06) − 0.127*** (−3.78) − 0.132*** (−3.98) − 0.123*** (−4.59) − 0.0850* (− 1.85) −0.0833** (−2.26) Gini, lag − 0.107*** (− 2.92) − 0.0801** (− 2.03) − 0.0553 (− 1.44) −0.0493 (−1.53) − 0.0908*** (−3.30) − 0.0980*** (−3.89) − 0.00339 (− 0.08) −0.0327 (−1.55) Hansen (p value) 0.136 0.160 0.285 0.248 0.242 0.499 0.188 0.295 0.487 0.160 0.269 0.603 See note in Table 4 123 760 G. A. Marrero, L. Servén 14). Further inspection reveals that the correlation is higher for the more recent data, reaching 0.93 in 2005 and 0.96 in 2010. Table 8shows estimation results for models M1, M2, M3 and M4 using the PovcalNet interpolated poverty series and our preferred system GMM specification. Comparison with Table 4reveals that the results are robust to the use of this alternative source of poverty data: Poverty consistently carries a negative coefficient, significant in all cases but one. In turn, the coefficient on inequality is also negative in most instances, but insignificant in three out of eight cases. 5.4 Additional controls Next, we assess the robustness of our results to the use of alternative controls. We focus on two extensions. First, we consider alternative measures of education to proxy for human capital. Second, we consider a set of institutional quality variables. Results are shown in Table 19 in the Appendix 6. In model M2, we added male and female education separately, following Perotti (1996) and Owen et al. (2002). Here, we estimate several variants of model M2, using average years of schooling, on the one hand, and the percentage of the population with at least primary or secondary education, on the other hand (first and second columns in Table 19). In turn, we consider two of the most widely used measures of the quality of institutions (see also Table 13 in Appendix 2): an index of democratic accountability (“democracy”), and an index of government stability (“stability”), information taken from the political risk module of the International Country Risk Database.22 Columns 3, 4 and 5 of Table 19 extend models M2, M3 and M4 with these institutional variables; column 6 reports the estimation results when jointly including all the variables from M2, M3 and M4. Finally, and just for illustrative purposes, we report (in the last column of the table) estimates of a model including all the controls. They should be taken with caution, however, given the sharp reduction in sample size (by almost half relative to columns 1–2) and the high degree of collinearity among the regressors. Estimated coefficients for the percentage of population with primary and secondary education are positive and significant. In the extended specifications with institutional variables, the coefficients of both the quality of democracy and government stability are positive and, in most cases, significant, confirming that the quality of institutions is positively correlated with growth. More importantly, the baseline estimation results for poverty (consistently negative) and inequality (its sign and significance depends on the particular specification) are robust to the inclusion of all these additional controls. 22 There are other institutional dimensions, such as the control of corruption, the military in power, the degree of international conflicts, or the Polity2 variable (from the Polity IV project). Including all these dimensions/variables simultaneously would introduce serious problems of collinearity in the estimated model. 123 Growth, inequality and poverty: a robust relationship? 761 Table 8 System GMM estimates: robustness to the use of PovcalNet data M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P0, lag − 0.0959*** (0.0244) − 0.103*** (0.0325) − 0.0675** (0.0272) −0.0537* (0.0323) − 0.0637** (0.0285) − 0.0635** (0.0323) −0.0327* (0.0183) −0.0206 (0.0448) Gini, lag − 0.0794* (0.0407) −0.0271 (0.0571) − 0.0783** (0.0366) − 0.0777** (0.0383) − 0.105*** (0.0363) − 0.0865** (0.0412) 0.0218 (0.0491) 0.000979 (0.0694) log y,lag − 0.0134*** (0.00496) − 0.000522 (0.00322) − 0.0166*** (0.00498) − 0.00978** (0.00465) 0.00155 (0.00333) − 0.00822* (0.00498) − 0.0141** (0.00594) − 0.00678** (0.00290) − 0.0160*** (0.00576) − 0.0246** (0.0103) − 0.0289** (0.0123) −0.0351*** (0.0121) Inv. deflator, lag − 0.0256*** (0.00749) − 0.0355*** (0.0119) − 0.0270*** (0.00792) Female educ., lag 0.000286 (0.00584) 0.00111 (0.00629) 0.000747 (0.00695) 0.000651 (0.00376) 0.00286 (0.00440) 0.00464 (0.00476) Male educ., lag 0.00145 (0.00634) −0.00156 (0.00668) − 0.0000402 (0.00700) Inflation − 0.000204 (0.000193) 0.000531* (0.000297) 0.000430 (0.000353) − 0.000114 (0.000248) 0.000823 (0.000520) 0.000887 (0.000602) Trade openness (log) 0.0284** (0.0117) 0.0320** (0.0144) 0.0280* (0.0144) Gov. size (log) −0.00351 (0.0125) 0.00171 (0.0102) 0.00139 (0.0118) Infrastructure, lag 0.0208*** (0.00773) 0.0284*** (0.0105) 0.0286* (0.0151) 123 762 G. A. Marrero, L. Servén Table 8 (continued) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures m2-test (p value) 0.125 0.345 0.140 0.00886 0.0692 0.0129 0.115 0.990 0.383 0.0668 0.219 0.109 AR(3) (p value) 0.0812 0.231 0.383 0.152 0.255 0.475 0.247 0.478 0.470 0.136 0.0734 0.466 Hansen (p value) 0.0304 0.102 0.0159 0.0934 0.153 0.173 0.114 0.318 0.206 0.246 0.182 0.196 Diff-Hansen for levels (p value) 0.422 0.459 0.087 0.710 0.586 0.556 0.432 0.932 0.816 0.618 0.317 0.205 Num. obs 522 522 522 474 474 474 491 491 491 360 360 360 Num. countries 136 136 136 116 116 116 130 130 130 81 81 81 Num. instruments 32 43 48 102 100 96 102 97 96 80 67 68 See note in Table 5. From PovcalNet, the poverty line is 1.90 US$ 2011, which updates the previous line of 1.25 US$ 2005 (Ferreira et al. 2016). We use the interpolated poverty series provided in PovcalNet, which start in 1981 and are reported every 3 years. To construct a non-overlapping 5-years panel data similar to the one used in our baseline specification, and match poverty data with all other variables (growth and other controls), we use a “closest” criteria or take the average if two poverty observations are 1 year above and one below the assigned year 123 Growth, inequality and poverty: a robust relationship? 763 5.5 Alternative econometric specifications We also performed a number of other robustness checks concerning the empirical specification and estimation approach. To save space, we just provide a brief summary here (results are available upon request). First, we modified the system GMM estimation employing different lag structures—e.g., using yit−s,pit−s,git−sand xit−s, for s≥4 for the first-difference equation and yit−4,pit−4,git−4and xit−4for the level equation—or using 1-step instead of 2-step estimates. We also experimented with a modified version of the basic empirical equation including a quadratic term in the Gini coefficient. The main conclusion is that the significantly negative effect of poverty on growth is quite robust to all these variations in specification and estimation approach, while the inequality-growth relationship is highly fragile. Finally, we also re-estimated the models in a pure cross section of countries, with the variables expressed as averages over the entire sample period, capturing what could be viewed as the long-run relationship between them. The estimated poverty coefficient remains uniformly negative and significant, although its precision declines somewhat relative to the panel estimates. In turn, inequality tends to show a negative and significant coefficient, more frequently than in the panel estimates, consistent with recent evidence (e.g., Halter et al 2014;Bergetal.2018) that inequality exerts a negative long-run impact on growth. 6 Poverty regimes 6.1 The effect of poverty and inequality on growth Thenonparametricanalysisintheprecedingsectionhintedatpossiblenonlineareffects of poverty and inequality on growth. To take a deeper look, we estimate alternative versions of Eqs. (1)–(3) allowing for different coefficients on lagged poverty and lagged inequality depending on whether the lagged value of P0 lies above or below the sample median (2.7% for our baseline P0, see Table 1). We follow the same strategy conditioning instead on the lagged level of inequality, and estimate Eqs. (1)–(3) allowing for different coefficients on poverty and inequality depending on whether the lagged Gini coefficient lies above or below its sample median (39.8%, see Table 1). Table 9 reports estimates distinguishing whether poverty is above or below the median—what we shall label the ‘high poverty regime’ and ‘low poverty regime,’ respectively. In turn, Table 10 reports the estimates distinguishing whether inequality is above or below the median—the ‘high inequality regime’ and ‘low inequality regime,’ respectively. In both cases, we use the baseline system GMM specification (Table 5). Table 9shows that, under the low poverty regime, the impact of poverty on growth is negative but statistically insignificant. However, it is negative and highly significant under the high poverty regime. In turn, the estimated coefficient on the Gini index is in most cases negative, but it turns significant only for high poverty rates and for the M1 and M3 model specifications. Thus, like with the unconditional estimates, while the result for poverty is robust, the result for inequality is not. In contrast, Table 10 shows that, when we condition on the lagged level of inequality, the estimated coefficients on 123 764 G. A. Marrero, L. Servén Table 9 Estimation results by poverty regimes: baseline system GMM M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P0, lag (P0 ≤ Median) 0.427 (0.49) −0.101 (− 0.16) −0.729 (− 0.92) −0.944 (− 1.29) −0.293 (− 0.44) −0.430 (− 0.61) 1.230 (1.44) −0.320 (− 0.41) −1.019 (−0.84) P0, lag (P0 > Median) − 0.125*** (− 4.30) − 0.124*** (− 5.04) − 0.0881*** (− 4.08) − 0.0928*** (− 5.25) − 0.0733*** (− 3.25) − 0.0784*** (− 3.65) − 0.0868*** (− 2.84) − 0.0586*** (− 2.66) −0.0927** (−2.31) Gini, lag (P0 ≤ Median) −0.0553 (− 0.81) −0.0589 (− 1.24) − 0.00103 (− 0.02) −0.00504 (− 0.10) −0.0689 (− 1.52) −0.0759 (− 1.50) −0.0285 (− 0.46) −0.0224 (− 0.55) −0.0114 (−0.14) Gini, lag (P0 > Median) − 0.138*** (− 2.83) − 0.0980*** (− 2.63) − 0.0544 (− 1.23) −0.0547 (− 1.46) − 0.0969*** (− 2.85) − 0.107*** (− 3.17) −0.0546 (− 1.00) −0.0409 (− 1.40) −0.0759 (−0.95) log y,lag − 0.0208*** (− 4.56) − 0.0153*** (− 2.73) − 0.0275*** (− 5.31) − 0.0160*** (− 4.45) − 0.0115* (− 1.89) − 0.0236*** (− 6.43) − 0.0179*** (− 4.86) − 0.0134*** (− 2.73) − 0.0243*** (− 5.32) − 0.0420*** (− 2.98) − 0.0374*** (− 3.29) − 0.0344*** (− 4.65) − 0.0504*** (−6.72) m2 (pvalue) 0.097 0.294 0.205 0.106 0.138 0.168 0.379 0.527 0.539 0.195 0.456 0.389 0.652 Hansen (p value) 0.0990 0.0476 0.256 0.211 0.111 0.354 0.408 0.238 0.476 0.163 0.425 0.990 0.122 Num. obs 745 745 745 676 676 676 655 655 655 477 477 477 477 Num. countries 156 156 156 131 131 131 147 147 147 88 88 88 88 Num. Instruments 55 55 85 100 100 130 97 97 127 77 77 127 41 Baseline system GMM estimates: 1 lag in the instrument matrix, starting at t−3. See also the note to Table 4. In the last column of the table, to further reduce the number of instruments in model M4, we consider the case with 2 lags, starting at t−3, and using the collapse option. The sample is divided according with the sample median of P0, which is 2.7% for our baseline P0 with poverty line of 2US$ 123 Growth, inequality and poverty: a robust relationship? 765 Table 10 Estimation results by inequality regimes: baseline system GMM M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P0, lag (Gini ≤ Median) − 0.109*** (− 3.33) − 0.0957*** (− 4.04) − 0.0789*** (− 4.54) − 0.0924*** (− 4.64) − 0.0561** (− 2.51) − 0.0681*** (− 3.09) − 0.0529** (− 2.06) −0.0527* (− 1.68) −0.0700** (−1.97) P0, lag (Gini > Median) − 0.146*** (− 4.87) − 0.115*** (− 3.93) − 0.0976*** (− 4.15) − 0.0696*** (− 2.93) − 0.105*** (− 4.03) − 0.0821*** (− 3.64) − 0.102*** (− 3.50) − 0.0530** (− 2.13) −0.0935** (−2.57) Gini, lag (Gini ≤ Median) 0.0343 (0.32) −0.0374 (− 0.48) 0.119* (1.86) 0.0885 (1.60) −0.0408 (−0.52) −0.0461 (− 0.73) 0.0405 (0.36) 0.00487 (0.08) 0.0931 (0.71) Gini, lag (Gini > Median) −0.0397 (−0.53) −0.0484 (− 0.91) 0.0345 (0.71) 0.0223 (0.55) −0.0683 (−1.22) −0.0647 (− 1.51) −0.00858 (− 0.10) −0.00988 (− 0.22) 0.0139 (0.17) log y,lag − 0.0230*** (− 5.98) − 0.00713*** (−2.91) − 0.0203*** (− 6.25) − 0.0152*** (− 5.05) − 0.00585* (− 1.82) − 0.0163*** (− 5.55) − 0.0186*** (− 4.63) − 0.00851*** (−3.26) − 0.0190*** (− 6.22) − 0.0262*** (− 2.73) − 0.0301*** (− 3.68) − 0.0353*** (− 4.53) − 0.0368*** (−3.86) m2 (pvalue) 0.1000 0.130 0.142 0.0681 0.0628 0.0770 0.352 0.475 0.441 0.203 0.359 0.277 0.285 Hansen (pvalue) 0.116 0.0375 0.168 0.130 0.0793 0.430 0.242 0.137 0.377 0.0907 0.232 0.988 0.254 Num. obs 745 745 745 676 676 676 655 655 655 477 477 477 477 Num. countries 156 156 156 131 131 131 147 147 147 88 88 88 88 Num. Instruments 55 55 85 100 100 130 97 97 127 77 77 127 41 Baseline system GMM estimates: 1 lag in the instrument matrix, starting at t−3. See also the note to Table 4. In the last column of the table, to further reduce the number of instruments in model M4, we consider the case with 2 lags, starting at t−3, and using the collapse option. The sample is divided according with the sample median of the Gini index, which is 39.8% 123 772 G. A. Marrero, L. Servén is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/ by/4.0/. Appendix 1: Lognormal approximation of alternative poverty measures Following Dollar and Kraay (2002), López and Servén (2015) or Pinkovskiy and Sala-i-Martin (2013), we construct a set of poverty figures (the headcount ratio, P0, the poverty gap, P1 and the squared poverty gap, P2) using a lognormal approximation on the basis of the observed per capita income levels and Gini coefficients, which are available much more widely than survey-based poverty data. The use of the lognormal approximation to the distribution of income dates back to Gibrat (1931). The literature employs also other functional forms, such as the Pareto, the gamma or the Weibull distribution, but the lognormal is the more widely used. Indeed, López and Servén (2006) compare the quintile income shares generated by a lognormal distribution with their observed counterparts using data from over 1000 household surveys and find the lognormal approximation fits the data extremely well, so that they are unable to reject the null hypothesis that per capita income follows a lognormal distribution. Under lognormality, given the Gini coefficient (g), the standard deviation (σ)of the log of income is given by σ−11+g 2, where (·) is the standard normal cumulativedistributionfunction.Usingthisexpressionandthelogofpercapitaincome (y), we can compute the FGT family of poverty measures for a given poverty line zas: P0log(z)−y σ+σ 2 P1log(z)−y σ+σ 2−ey zlog(z)−y σ−σ 2 P2log(z)−y σ+σ 2−2ey zlog(z)−y σ−σ 2+ey z2eσ2log(z)−ν σ−3σ 2. Appendix 2: Data description and cross-correlations See Tables 13,14. 123 Growth, inequality and poverty: a robust relationship? 773 Table 13 Description of the variables Name Description Source Num.Obs. (restricted to P0 and Gini sample) Sample average Standard deviation Per capita real GDP Level of activity and degree of development: PPP Converted GDP Per Capita (Chain Series), at 2005 constant prices Penn World Tables 7.1 749 9793 US$ (PPP2005) 10,462 (PPP-2005) Poverty The headcount ratio P0 (level of poverty), the poverty gap P1 (intensity), and the squared poverty gap P2 (severity). For the log-logistic measure, the baseline poverty line is US$ 2; for PovcalNet, we use US$ 1.90 as poverty line Own calculation based on lognormal approximation; PovcalNet 749 (lognormal) 556 (Povcal.) 16.18% (P0) 7.34 (P1) 4.40% (P2) 18.56 (Povcal.) 24.75% (P0) 13.22% (P1) 8.92% (P2) 21.14% (Povcal.) Gini coefficient Measure of income inequality (between 0 and 1). Based only on nationally representative surveys (area, population and age), and based on income (net of transfers and taxes) and expenditure figures UN-WIID2 (2008); PovcalNet 749 40.20% 9.98% Years of secondary education (total, male and female) Average years of secondary education of the male population and the average years of secondary education of the female population Barro and Lee (2013) Educational Attainment Data 684 1.95 (total) 1.77 (female) 2.15 (male) 1.42 (total) 1.44 (female) 1.44 (male) 123 774 G. A. Marrero, L. Servén Table 13 (continued) Name Description Source Num.Obs. (restricted to P0 and Gini sample) Sample average Standard deviation Attained education (primary and secondary) Percentage of population (total) with at least primary or secondary education Barro and Lee (2013) Educational Attainment Data 684 19.5 (primary) 16.2 (secondary) 12.8 (primary) 13.3 (secondary) Investment prices Domestic price of investment goods relative to that of the U.S. as a measure of market distortions Penn World Tables 7.1 745 0.65 (relative to US) 0.31 (relative to US) Inflation GDP deflator, as an indicator of macroeconomic stability World Development Indicators, World Bank 667 16.35% 32.05% Degree of openness Volume of trade with respect to its GDP Penn World Table 7.1 749 75.8% 49.7% Government size The ratio of public consumption to GDP: as an indicator of the burden imposed by the government on the economy Penn World Table 7.1 749 9.65% 5.41% 123 Growth, inequality and poverty: a robust relationship? 775 Table 13 (continued) Name Description Source Num.Obs. (restricted to P0 and Gini sample) Sample average Standard deviation Infrastruct. Index Composite index of public infrastructure including: telecommunication sector (number of main telephone lines per 1000 workers), the power sector (the electricity generating capacity in MW per 1000 workers), the transportation sector (the length of the road network—in km. per sq. km. of land area) World Development Indicators, World Bank. Based on Calderón et al. (2015) 528 0.39 1.33 Democracy Degree of Democracy: whether there are free and fair elections and the degree of government’s accountability. Range of values between 0—minimum democracy—and 6—maximum democracy) International Country Risk Database 474 4.15 1.46 123 776 G. A. Marrero, L. Servén Table 13 (continued) Name Description Source Num.Obs. (restricted to P0 and Gini sample) Sample average Standard deviation Government stability Degree of Government stability: measures the government’s ability to carry out its declared program(s) and its ability to stay in office. Range of values between 1—minimum stability—and 12—maximum stability International Country Risk Database 474 7.71 2.06 123 Growth, inequality and poverty: a robust relationship? 777 Table 14 Correlation matrix Growth pcGDP (log) P0 (US$ 2) lognormal P0 (Povcalnet) Gini Second.yr total Second.yr female Second.yr male Primary attain. (%) Growth 1.000 pcGDP(log) 0.152 1.000 P0 (US$ 2) −0.176 −0.828 1.000 P0 (Povcal.) −0.162 −0.843 0.892 1.000 Gini −0.184 −0.484 0.357 0.363 1.000 Sec.yr total 0.198 0.766 −0.592 −0.651 −0.447 1.000 Sec.yr female 0.195 0.777 −0.595 −0.650 −0.409 0.989 1.000 Sec.yr male 0.196 0.738 −0.575 −0.638 −0.477 0.988 0.956 1.000 Prim.att 0.007 0.202 −0.154 −0.193 −0.088 −0.151 −0.146 −0.150 1.000 Sec.att 0.214 0.641 −0.529 −0.579 −0.404 0.877 0.865 0.871 −0.184 Inv.Price −0.008 0.280 −0.033 −0.139 −0.220 0.238 0.235 0.235 0.012 Inflation −0.079 −0.058 −0.022 0.000 0.071 −0.031 −0.033 −0.029 −0.072 Open 0.298 0.143 −0.168 −0.192 −0.087 0.266 0.285 0.240 −0.120 Gov.Size −0.115 −0.332 0.381 0.453 0.080 −0.267 −0.248 −0.282 −0.071 Infrast 0.197 0.922 −0.781 −0.812 −0.499 0.741 0.743 0.722 0.218 Democ 0.126 0.682 −0.443 −0.516 −0.377 0.503 0.539 0.456 0.219 Gov.Stab 0.354 0.164 −0.094 −0.150 −0.099 0.225 0.221 0.223 0.020 123 778 G. A. Marrero, L. Servén Table 14 (continued) Second. attain. (%) Inv. price (relativ. US) Inflat Open, adjust. (log) Gov. size (log) Infrast (index) Democ (0–6 index) Gov. stab. (0–12 index) Growth pcGDP(log) P0 (US$ 2) P0 (Povcal.) Gini Sec.yr total Sec.yr female Sec.yr male Prim.att Sec.att 1.000 Inv.Price 0.173 1.000 Inflation −0.017 −0.051 1.000 Open 0.308 −0.014 −0.138 1.000 Gov.Size −0.182 −0.104 −0.041 −0.129 1.000 Infrast 0.657 0.251 −0.120 0.228 −0.307 1.000 Democ 0.432 0.306 −0.133 0.173 −0.214 0.704 1.000 Gov.Stab 0.186 −0.040 −0.098 0.267 −0.110 0.259 0.158 1.000 Variables are transformed in the same way as for the regression analysis. For example, per capita GDP in logs; poverty and the Gini coefficient in levels; openness in logs and adjusted by population, kilometers, to be oil exporters and landlock; government size in logs, etc. We consider two alternative measures of the headcount poverty rate: first, using a lognormal approximation (Dollar and Kraay 2002; Sala-i-Martin 2006; López and Servén 2015), and, for a reduced sample, using the PovcalNet database 123 Growth, inequality and poverty: a robust relationship? 779 Appendix 3: Alternative system GMM estimation results See Tables 15,16. Table 15 Growth, poverty and inequality: system GMM estimates (collapse, all lags) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P0, lag − 0.157*** (−4.14) − 0.138*** (−4.06) − 0.104*** (−3.85) − 0.0860*** (−3.77) − 0.0963*** (−4.17) − 0.0918*** (−4.61) − 0.0626** (−2.06) −0.0581** (−2.08) Gini, lag − 0.165** (− 2.53) − 0.153*** (−3.01) − 0.0798* (− 1.77) −0.0444 −0.0289 (−0.87) − 0.0766** (−2.30) 0.0105 (0.32) −0.0215 (−0.60) (−1.05) log y,lag − 0.0264*** (−4.83) − 0.00454 (− 1.35) − 0.0271*** (−5.36) − 0.0216*** (−4.22) − 0.00310 (− 1.18) − 0.0181*** (−4.37) − 0.0172*** (−5.09) − 0.0057** (−2.20) − 0.0194*** (−5.80) − 0.0324*** (−3.87) − 0.0174** (−2.13) − 0.0303*** (−3.58) Inv. deflator, lag − 0.00251* (−1.66) − 0.0032 (− 1.42) −0.0021 (−0.91) Female educ., lag 0.00284 (0.60) 0.00890 (1.54) 0.00805 (1.40) 0.0068*** (2.61) 0.0022 (0.59) 0.0059** (2.20) Male educ., lag 0.00123 (0.27) − 0.00899 (− 1.35) −0.00664 (−1.03) Inflation 0.0008** (2.13) 0.0011*** (2.81) 0.0006 (1.49) 0.0009*** (3.57) 0.0009*** (2.79) 0.0007** (2.14) 123 780 G. A. Marrero, L. Servén Table 15 (continued) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures Trade openness (log) 0.0202* (1.79) 0.0372*** (4.17) 0.0159* (1.65) Gov. size (log) 0.0199 (1.52) 0.00859 (0.88) 0.00910 (0.97) Infrastructure, lag 0.0165** (2.32) 0.0175*** (2.61) 0.0143* (1.90) m2-test (p value) 0.147 0.313 0.332 0.0710 0.179 0.115 0.236 0.427 0.397 0.226 0.179 0.262 AR(3) (p value) 0.832 0.527 0.575 0.817 0.837 0.955 0.631 0.544 0.532 0.802 0.887 0.804 Hansen (p value) 0.00333 0.000907 0.0517 0.0972 0.0428 0.114 0.118 0.0331 0.293 0.266 0.286 0.499 Diff-Hansen, levels (p value) 0.135 0.108 0.636 0.463 0.413 0.470 0.746 0.462 0.845 0.569 0.442 0.756 Num. obs 745 745 745 676 676 676 656 656 656 477 477 477 Num. countries 156 156 156 131 131 131 147 147 147 88 88 88 Num. instruments 40 40 55 85 85 100 82 82 97 82 82 97 See Note Table 4. Estimations are done using 2-step system GMM (all lags starting at t−3), but collapsing the matrix of instruments. The instrument set starts at t−3. The difference Hansen test assesses the validity of the instruments for the level equation in system GMM. Robust tstatistics in parentheses. ***denotes significance at 1%, **at 5%, *at 10% 123 Growth, inequality and poverty: a robust relationship? 781 Table 16 Growth, poverty and inequality: system GMM estimates (collapse, reduce) M1. Skeleton model M2. Extended with education and inv. prices M3. Extended with policy variables M4. Extended with policy and infrastructures P0, lag − 0.183*** (−5.21) − 0.167*** (−4.98) − 0.143*** (−5.55) − 0.141*** (−5.96) − 0.131*** (−2.82) − 0.126*** (−3.59) − 0.0888*** (−3.31) − 0.0849*** (−3.40) Gini, lag − 0.161* (− 1.65) −0.0798 (−0.96) −0.136 (− 1.54) −0.0411 (−0.70) −0.0575 (−1.50) − 0.0972** (−2.19) 0.0447 (0.86) −0.0322 (−0.91) log y,lag − 0.0306*** (−5.34) 0.00134 (0.29) − 0.0299*** (−5.03) − 0.0296*** (−5.08) 0.00413 (0.78) − 0.0280*** (−5.10) − 0.0255*** (−3.80) − 0.00586* (−1.82) − 0.0260*** (−4.04) − 0.0449*** −0.0218 (−1.63) − 0.0431*** (−5.02) (−4.50) Inv. deflator, lag 0.000917 (0.26) 0.00168 (0.36) 0.00159 (0.39) Female educ., lag 0.00563 (0.60) 0.00250 (0.29) 0.00329 (0.37) 0.00757** (2.06) −0.00199 (−0.39) 0.00654* (1.85) Male educ., lag −0.00274 (−0.30) − 0.00947 (− 1.00) −0.00197 (−0.22) Inflation 0.0009** (1.96) 0.0007 (0.89) 0.0003 (0.34) 0.0013** (2.33) 0.0017* (1.90) 0.0014** (2.44) Trade openness (log) 0.0199 (1.29) 0.0385*** (3.86) 0.0179 (1.43) 123 788 G. 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