The short-run relationship between inequality and growth: evidence from OECD regions during the Great Recession

ABSTRACT This paper provides evidence on the relationship between income inequality and economic growth in Organisation for Economic Co-operation and Development (OECD) regions during the decade 2003–13. It combines household survey data and macroeconomic databases, covering over 200 comparable regions in 15 OECD countries. The econometric results, based on two alternative sets of instruments, highlight a general negative association between inequalities and economic growth since the start of the economic crisis. This relationship is sensitive to the type of urban structure. Higher inequalities seem to be more detrimental for growth in regions characterized by medium to large-sized cities, while regions characterized by small cities and rural areas are less affected.


INTRODUCTION
Since the start of the economic crisis of the late 2000s, concerns have emerged in most developed countries about the distributional effect of the crisis and recovery, because in most Organisation for Economic Co-operation and Development (OECD) countries the gap between rich and poor has widened. Recent evidence shows that income inequality has a negative impact on economic growth, mainly through lower levels of social mobility due to less investment in human capital. Other works distinguish between equality of opportunities and equality of outcomes as two parallel and differentiated components of inequality (World Bank, 2006), or between structural and market inequality (Easterly, 2007) having the latter an expected positive effect on economic growth. Some of the mechanisms underlying the relationship between inequality and economic growth might be particularly relevant at the regional level, as increasing evidence shows that local conditions can affect individual opportunities. For instance, analyses for the United States show that a neighbourhood's average income has a large impact on individuals' future earnings capacity, an effect that is roughly half that related to parental income (Rothwell & Massey, 2015). Glaeser, Resseger, and Tobio (2009) show that more unequal cities grow more slowly once controlling for the skill distribution. In the same vein, Chetty, Hendren, Kline, and Saez (2014) find that individual opportunities differ substantially across cities in the United States and are negatively related to inequality.
One issue that deserves particular consideration and that has been less analyzed in the literature is the length of the time horizon. Most of the literature has focused on the long-run relationship, while much less work exists in trying to understand the short-term dynamics, even though several authors recognize different channels for different time dimensions (Forbes, 2000;Perugini & Martino, 2008). The Great Recession provides an important ground for research on the role of inequality and its interaction with the regional urban structure in the last decade. Regions with different levels of inequality might respond differently to the economic cycle. At the same time, the effects of economic shocks can be heterogeneous by the type of urban structure: in Europe highly urbanized regions were found to be particularly sensitive to the Great Recession (Dijkstra, Garcilazo, & McCann, 2015).
This work provides new empirical evidence on the relationship between income inequalities and economic growth between 2003 and 2013 in a large sample of regions, including 15 OECD countries. Of the few works that have tried to explain such a relationship at the regional scale, most refer to regions within a single country, especially the United States (e.g., Fallah & Partridge, 2007;Frank, 2009;Partridge, 2005), although some analyses have covered European regions (Ezcurra, 2007(Ezcurra, , 2009Perugini & Martino, 2008;Rodríguez-Pose & Tselios, 2010). To the best of our knowledge, no works focus on the shortrun relationship between inequality and growth at the regional level or cover the periods before and after the Great Recession. Including this period makes it possible to consider the role of inequality for regional resilience to economic shocks.
This paper also focuses on the role of urban structure as a factor potentially affecting the inequality-economic growth relationship. Using a consistent definition of city helps identify the extent of urban concentration within regions while at the same time limiting the bias introduced by different administrative definitions across countries. The relationship between city size and economic growth has been recently analyzed by Frick and Rodríguez-Pose (2016) for a wide sample of countries and by Fothergill and Houston (2016) for the specific case of the UK. Their main result is that the prevailing view of a positive relationship between economic growth and city size does not hold.
We estimate panel models with country fixed effects and consider two sets of instruments for inequality, trying to mitigate endogeneity concerns. The main findings show that inequality and economic growth are negatively associated, particularly since the start of the economic crisis, suggesting that more inclusive societies might foster regional resilience to economic shocks. Moreover, the link between inequality and growth is affected by urban size, with a stronger negative relationship in regions where most people live in medium to large cities.
The paper is structured as follows. The next section provides the rationale for analyzing the relationship between inequality and growth at the subnational level. It also reviews the mechanisms through which inequality can affect economic growth. The third section presents the data and the empirical model, while the fourth section presents the main results. The fifth section concludes.

THEORETICAL ARGUMENTS AND EMPIRICAL FINDINGS: A VIEW FROM THE LITERATURE
The bulk of the literature on the inequality-economic growth relationship tackles the national scale as the unit of analysis and focuses on mechanisms that play their role mostly in the long run. Ehrhart (2009) and Galor (2009) provide comprehensive overviews of theories and empirical evidence; a recent critical survey of the empirical works is provided by Neves and Tavares Silva (2014); while de Dominicis, Florax, and de Groot (2008) and Neves, Afonso, and Tavares Silva (2016) offer meta-analysis on the relationship between inequality and economic growth. Still, only a few studies have tried to explain the inequality-growth nexus at the subnational level, although it is relevant for several reasons.
First, smaller spatial entities better reflect the actual conditions experienced by people where they live, and this might reduce a potential omitted variable bias generated by national averages and incomparability across countries.
Second, the use of regional data also helps to magnify how small disparities in initial conditions affect economic growth (Partridge, 2005), and it allows researchers to better account for patterns of urban agglomeration. Such patterns are certainly linked to inequalities through mechanisms of sorting the most talented individuals, selecting the most productive firms and agglomerating the advantages of cities.
Third, many factors affecting people's well-being and the business environment (e.g., crime, access to services etc.) are also likely to be important at the local level. In particular, the socioeconomic characteristics of the communities where people actually live can affect individual opportunities (and choices), yielding different economic outcomes. Investment in human capital can be shaped by local conditions, including life expectancy (Rodríguez-Pose & Tselios, 2010), which can largely differ across regions: the difference between the best and the worst performing OECD region in terms of life expectancy is 15 years, more than double than among countries (OECD, 2014).
Finally, compared with countries, regions are also much more open economies. Capital and labourparticularly a highly educated workforcecan move across regions at a lower cost and tend to move to places where they can enjoy higher returns. Cities certainly have an advantage in attracting capital and labour, thanks to more efficient provision of public services (due to economies of scale) and agglomeration economies. In principle, perfectly mobile production factors should yield, in equilibrium, an optimal allocation of resources with no spatial inequalities. However, even in the presence of perfect factor mobility, differences in initial factor endowments, sectoral specialization and agglomeration externalities can widen interregional disparities (Rice & Venables, 2003). An initial higher level of specialization in sectors requiring more highly skilled workers can attract further highly skilled labour and increase the gap in earnings. A possible consequence is that factor mobility increases income inequalities in relatively rich regions while reducing those in worse-off regions (Perugini & Martino, 2008). This might determine the coexistence of a positive relationship between inequality and growth at the regional level, with a negative relationship at the country level (Fallah & Partridge, 2007). Glaeser et al. (2009) report a positive association at the city level in the United States, which becomes negative once skills distribution are controlled for.
Regarding the mechanisms underlying inequalitygrowth relationships, recent evidence at the national level shows that while in the short run a positive relationship Short-run relationship between inequality and growth: evidence from OECD regions during the Great Recession 575 predominates, in the long run the reverse is observed (Halter, Oechslin, & Zweimüller, 2014). 1

Long-run factors
The classical approach to the role of physical and human capital accumulation suggests that savings rates increase with wealth and that wealthier people have a higher marginal propensity to save, and as a result, in more unequal societies, aggregate investment in physical capital will be relatively higher, fostering economic growth (Barro, 2000). The modern paradigm focuses on the role of human capital accumulation rather than on investment in physical capital, the former being the major driver of growth in developed economies (Galor & Moav, 2004). According to Tselios (2008), the optimal level of schooling depends on the distribution of income, as the supply and demand curves have a different shape for different income groups. Another argument is that more equal societies give people greater opportunities to invest in human capital because of imperfections in the financial and credit markets that prevent worse-off individuals from carrying out such costly investments. In this view, more equal societies can be seen as opportunity enhancing, given the decreasing returns on investment in education at the individual level and the fact that households' wealth is a major determinant of such investments. Recent empirical analyzes further support the idea that obstacles to human capital accumulation drive the negative relationship between inequality and growth (Cingano, 2014).
Economic incentives also play an important role in the long run. Societies in which ability is rewarded stimulate individual effort, productivity and risk taking (Voitchovsky, 2005). These economic incentives also affect the accumulation of human capital and the effort to seize the returns of skills, although in the low part of the wage distribution they can be counterbalanced by feelings of unfairness (Akerlof & Yellen, 1990).
Political economy factors also matter. Persson and Tabellini (1994) and Alesina and Rodrik (1994) argue that in relatively more unequal societies, people vote for higher taxation and redistribution. Higher taxation has a negative effect on incentives to invest, which, in turn, negatively affects economic growth.

Short-run factors
One channel through which inequalities can affect economic growth in the short run is political instability. Alesina and Perotti (1996) provide cross-country evidence that inequalities generate higher levels social discontent and political instability, which in turn yields lower levels of investment and economic growth. At the regional level, this channel would play a role through higher levels of urban segregation or crime rates rather than institutional instability. In research on US metropolitan areas, Li, Campbell, and Fernandez (2013) find that residential segregation by skills and racewhich is likely to be reflected also in income levelsis negatively correlated with economic growth.
A strand of the literature argues that increasing inequality can affect both demand for and supply of credit (Morelli & Atkinson, 2015). Low-income households tend to increase their levels of indebtedness in order to maintain the stability of their consumption patterns. From a supply side, increasing loans to more risky individuals due to financial liberalization are likely to generate further instability in the financial system (Bazilliers & Hericourt, 2012;Rajan, 2010). Thus, inequality is likely to cause unhealthy credit booms, which can suddenly degenerate into financial instability (Perugini, Hölscher, & Collie, 2016).
Short-term effects of inequality on economic growth can be determined by the existence of convex saving functions and high-risk propensity of wealthier individuals (Kaldor, 1955;Kuznets, 1955). A higher concentration of resources ensures that there will be at least a limited number of sufficiently rich investors to take on risky but high-return investment projects, which can in turn ensure higher growth rates. As these mechanisms are of a purely economic nature, they are likely to materialize relatively quickly (Halter et al., 2014).
Last, on the demand side, the link between inequalities and growth depends on the balance between two different effects: market size and the dynamic price effect. In a short time horizon, innovation is affected by the demand for new products. The latter requires innovation, which in turn drives economic growth. In a more equal society, more individuals will be able to buy a new product, stimulating innovation by firms. However, the richest individuals have a greater willingness to pay for new goods and higher prices can be applied by monopolistic producers, stimulating further innovation (Bertola, Foellmi, & Zweimüller, 2006;Foellmi & Zweimuller, 2006).
Summarizing, the existing empirical evidence on the inequality-growth nexus over the short run tends to confirm a positive association driven by different factors, as found for European regions by Perugini and Martino (2008) and Rodríguez-Pose and Tselios (2010). Grijalva (2012) found an inverse 'U'-shaped relationship over both fiveand 10-year periods using a large panel of countries. Going from the short-to the medium-run time horizon, the relationship shifts downwards, meaning that the relationship turns negative at a lower level of inequality: Ezcurra (2007) finds a negative association for a sample of European regions over a 10-year period. In the longrun (a 20-year time span) the relationship becomes linear and negative. Li and Zou (1998) and Forbes (2000) find a positive relationship over five-year periods, while Barro (2000) finds that the relationship between inequality and growth over 10-year periods is negative for poor countries and positive for rich countries.

Income inequality within regions
The data set includes 209 TL2 regions 2 from 15 OECD countries, of which 10 are European (Belgium, Czech Republic, Estonia, Finland, France, Greece, Italy, Luxemburg, Spain and the UK, accounting for 45% of all regions in the sample), four American (Canada, Chile, Mexico and the United States, accounting for 52% of all regions) and one Asian (South Korea, 3% of all regions). Indicators of inequality at the regional level are computed using microdata from household income surveys publicly available or made available through the OECD Income Distribution Database, following the method applied by Piacentini (2014). Table A2 in Appendix A in the supplemental data online provides details on the data sources. For reasons of robustness, inequalities within regions are computed using several indicators related to equivalized household annual disposable income: the Gini index, the top-bottom quintile ratio (p80-20), the top-bottom decile ratio (p90-10), the bottom decile ratio (p50-10), the top decile ratio (p90-50) and the relative poverty rate using two alternative national poverty lines, at 40% and 60% of the median income. The analysis uses the 2003-13 income reference period. As this is a yearly panel, interpolated inequality statistics were used, usually for one year, when data on inequality are not available on a yearly basis (i.e., Chile, Korea and Mexico). We work with an unbalanced panel with some attrition. For 2003, the data have 10 countries; 2010 is the only year with data for all 15 countries; 13 countries for 2012; and four countries for 2013. The only country with information for the full period is the United States, while for the UK data are available only from 2010 onwards.
The dependent variable is the annual growth rate of per capita gross domestic product (GDP) in purchasing power parity (PPP)-adjusted US dollars. A set of control variables was included to account for socioeconomic and institutional factors that can have a role in regional economic growth. The basic statistics of the income distribution indicators are summarized in Table A4 in Appendix A in the supplemental data online, which shows that, given the short period under consideration, most of the variation in inequality is due to cross-sectional differences, as the variation in time is much smaller.

Inequality, economic growth and urban concentration
The strong decline in economic growth rates subsequent to the Great Recession has been heterogeneous across regions and countries (OECD, 2013). A positive association is observed across OECD regions between GDP growth and several measures of income inequality (Table 1 and Figure 1). However, the sign of the correlations becomes negative when controlling for regions and time-fixed effects (FE).
It is documented that income inequality and urban size are positively associated (Baum-Snow & Pavan, 2013). Urbanization and income inequality can be interpreted as the spatial concentration of human and physical capital in the process of development (Castells-Quintana & Royuela, 2014). By determining the allocation of resources across space and individuals, the interaction between urbanization and inequality is therefore expected to have implications in terms of economic growth (Kim & Kim, 2003). The first step to exploring this issue is to assess the levels of inequality in regions by distinguishing the type and size of urban settlements. Urban population is identified using the functional urban areas (FUAs) defined by the OECD (2012). The use of FUAs is a relevant contribution of this study because it helps to assess the extent of urban concentration within a region without relying on countries' existing administrative definitions of cities, which can introduce biases into the analysis.
Regions were classified into three groups according to their urban structure: 99 regions that are either rural (11 regions) or where the largest urbanization share is observed in smaller cities (88 regions with cities with fewer than 500,000 inhabitants); 63 in medium-sized cities (between 500,000 and 1.5 million inhabitants); and 52 in large cities (more than 1.5 million inhabitants). Most (56%) European regions have small cities; three of seven Korean regions (43%) have large cities; while the American regions of the sample are distributed among the three categories (38% small, 32% median and 30% large cities). 3 In the sample of regions, inequalities are smaller the smaller the size of cities, though with considerable heterogeneity ( Figure 2). This general evidence is robust to the use of several indicators of inequality, and differences are particularly strong for poverty rates and for the bottom decile ratio (Table 2). Several interpretations arise: more talented individuals tend to congregate in large cities where the returns to talent are higher and where there are more productive firms paying higher wages (Behrens, Duranton, & Robert-Nicoud, 2014); agglomeration economies can be a source of additional wage premium, increasing the level of inequalities; and, as in the Harris and Todaro (1970) model, the expected income of a potential immigrant depends on the probability of finding a job, which is more likely to happen in expanding cities. As the 'Todaro Paradox' explains, it can be the case that the inflow of workers to the urban sector exceeds urban labour demand, and it can result in increasing unemployment, which in turn increases inequality. This result can also arise in Table 1. Correlation coefficients between gross domestic product (GDP) per capita growth and inequality.
Gini index p80-20 p90-50 p50-10 pov60 pov40 Raw data Short-run relationship between inequality and growth: evidence from OECD regions during the Great Recession 577 situations where international migrants are directed to gateway cities, which are usually the largest cities (Royuela, 2015).

Model specification
The standard procedure for estimating the impact of inequality on growth is to assume a simple linear relationship where the growth rate of GDP per capita is regressed on a number of explanatory variables, potentially explaining differences in growth rates, including a measure of income inequality. Specifically: where ln y it is the logarithm of GDP per capita in region i at time t; x it−t represents an income inequality measure (e.g., the Gini index); Z i-t is a set of control variables that account for factors underlying economic growth; and 1 it is a random error term that varies across regions and periods. In particular, Z i−t includes the degree and type of urban concentration, measured through the share of regional population living in cities, accounting for the size of the latter. More specifically, three classes of urban size were considered: fewer than 500,000 inhabitants, between 500,000 and 1.5 million inhabitants, and more than 1.5 million inhabitants. Control variables also include demographics (e.g., age structure), the sectoral shares of the economy (agriculture, industry and construction), education levels, the labour market participation rate and one variable related to religion at the country level based on a Herfindahl index of diversity in religion (as in Rodríguez-Pose & Tselios, 2010). For definitions and sources for all variables, see Table A3 in Appendix A in the supplemental data online. The estimation of the empirical model requires tackling a list of econometric problems such as reverse causality and unobserved time-invariant region-specific characteristics and spatial dependence. As former aspects, factors such as technology, climate, institutions and any other country-specific variable may be important determinants of growth rates and be correlated with the explanatory variables considered in the model. Many factors other than the controls are typically unobservable. By assuming those factors are constant over time and using longitudinal data, the suggested specification results in a modified

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Vicente Royuela et al. panel data version of the previous equation, where one can control for unobservable factors. One of the possibilities is the use of regional FE. This procedure is supposed to account for most omitted variable bias. Nevertheless, it reduces the degrees of freedom and the measurementerror bias is aggravated, as the signal-to-noise ratio is further reduced by only using variation within regions (Neves et al., 2016). The estimated coefficients would then only reflect the effect of time variation within regions, and when the phenomenon under analysis mostly varies cross-sectionally, the method may produce inaccurate results (Partridge, 2005). In our sample, the overall standard deviation (SD) of the Gini index is 0.075, the between SD being 0.072 and the within SD is 0.021. Consequently, the FE models would account for only a small fraction of the variation of inequality, and 'the long-run cross-sectional effects would be subsumed into the fixed effects' (Fallah & Partridge, 2007, p. 381), in turn producing potentially misleading results (Barro, 2000). In addition, the short time intervals considered in this work and in other similar analyses (Rodríguez-Pose & Tselios, 2010) further question the use of FE to account for the omitted variable bias. Forbes (2000) also recalls that in panels with a limited time-series length, the estimation by FE is not consistent, i.e., the size of the bias is much more important for the endogenous variable than for other right-hand side. Finally, we also take into account the possibility of spatial dependence, as reported by Ezcurra (2007) and Perugini and Martino (2008). Ezcurra estimates a spatial error model considering inverse a spatial matrix based on the distance between the centroids, while Perugini and Martino (2008) apply both a spatial lag model and a spatial error model using a binary first-order contiguity matrix.
Taking into account the previous exposition, our strategy to account for the omitted variable bias and for a large source of spatial heterogeneity is to include country dummies and a set of controls. More specifically, the model in equation (1) is modified as follows: where J c is a vector of country effects; and h t represents a vector of time-specific effects. The option of estimating a dynamic panel model using the system-based generalized method of moments (GMM-SYS) estimator was discarded for two reasons. First, the time dimension is too short for some countries, such as the UK. Second, GMM-SYS is designed with the assumption that the only available instruments are 'internal', based on lags of the instrumented variables (Roodman, 2009), and in the present case these are correlated with the error term. 4 Reverse causality is treated by means of an instrumental variables (IV) approach, as it addresses the potential endogeneity of the lagged value of GDP per capita and inequality. One of the main strengths of the work is the amplitude of the regional coverage: more than 200 regions in 15 different countries. Nevertheless, identifying valid instruments in such a sample is not straightforward. Taking this into account, we have followed a double strategy.
In the first stage we have collected the following set of instruments: the murder rate, the elderly rate and the share of registered voters who voted during general elections. These variables are used as instruments capable of capturing mainly the channels associated with political economy and political instability. Short-run relationship between inequality and growth: evidence from OECD regions during the Great Recession Atems (2013) explores the way the political affiliation of US counties affects the inequality-growth relationship and finds a strong heterogeneity. By considering the share of voters and the elderly rate, one can capture part of the political economy channel and part of the demand dynamics. In the very short term, the demographic structure of the regions is assumed to be exogenous. Similarly, the functioning of democracies is a variable that, despite affecting the way inequality is associated with economic growth, has been found to have an ambiguous relationship with the latter (Doucouliagos & Ulubaşoğlu, 2008). The murder rate can be used as an indicator of political instability. As Powell, Manish, and Nair (2010, p. 349) conclude, there is 'little evidence of the impact of crime on economic growth in cross-country studies'. While some studies report that crime has a significant negative influence on economic growth (Cárdenas, 2007;Gaibulloev & Sandler, 2008;Peri, 2004), others infer that the impact is unclear (Burnham, Feinberg, & Husted, 2004;Goulas & Zervoyianni, 2012) or even non-existent (Chatterjee & Ray, 2014;Mauro & Carmeci, 2007). We also considered the vegetation coverage of every region in order to consider permanent differences between regions (this is the only time-invariant instrument considered in this analysis). Instruments are considered in both levels and first differences. We admit that any reader can have serious concerns about this set of instruments by arguing that they hardly meet the exclusion restrictions by having an effect on economic growth beyond the indirect effect via inequality. Consequently, we are particularly careful about, first, the under-and over-identification tests and, second, the interpretation of the results: any significant effect arising from the use of these instruments might be the result of a direct effect of these political economy related instruments.
These caveats calls for a parallel strategy focused on exploiting an alternative channel through with inequality may affect economic growth. For that purpose we build a new instrument using a two-step procedure following Brückner (2012Brückner ( , 2013 and Castells-Quintana (2016). We define an instrument based on Bartik's (1991) industry mix for economic growth and use it to build a valid instrument for inequality in the growth equation. We follow a new version of this instrument developed by Détang-Dessendre, Partridge, and Piguet (2016). First, we regress inequality as a dependent variable on economic growth using an IV approach. By construction, the residual of this equation captures any variation in the inequality measure that is not due to economic growth.
As shown in more detail in Appendix B in the supplemental data online, economic growth drives subsequent increases in overall and top income inequality and decreases in bottom income inequality. The derived instruments are free of these market-driven inequality changes. Despite our efforts to demonstrate that the generated instruments are valid, we again assume they are based on the assumption that the sectoral share of every economy is not affecting subsequent inequality evolution. Again, we are particularly careful with the under-and over-identification tests and assume that the approach may lower endogeneity concerns, but is hardly likely to remove it completely. Table 3 shows the estimates of the pooled ordinary least squares (OLS) panel estimates with country FE for different inequality measures. The results report non-significant parameters for global measures of inequality (the Gini index and the 80-20 and 90-10 ratios). These measures hide a conflicting relationship with top income inequality, which is Table 3. Pooled ordinary least squares (OLS) estimates.

Variables
(1) (2) (3) (4) (5) (6) (7) Gini p80-20 p90-10 p90-50 p50-10 pov40 pov60 ln GDP per capita -0.0032  marginally positive (10% of confidence), and bottomincome inequality and poverty indicators, which are significant and negative. Such results call for a specific focus on the different types of inequality and accommodate both to positive results (Perugini & Martino, 2008;Rodríguez-Pose & Tselios, 2010) and negative ones (Ezcurra, 2007). Regarding the coefficients of the other control variables, displayed in Table A5 in Appendix A in the supplemental data online, those related to GDP per capita and urban concentration are never significantly different from zero. On the other hand, the coefficients related to educational attainment and labour participation are positive and negative in sign respectively, and statistically significant. The sectoral composition shows significant parameters, which are significantly positive for regions with high shares in agriculture and industry. Finally, the coefficient related to religious diversity was always positive and significant. Table 4 shows results obtained with the random effects specification, including those with IV regressions considering standard instruments (IV1) and regressions considering industry mix-derived instruments (IV2). As reported above, there may be some concerns about the suitability of the procedures for treating endogeneity. Consequently, from now on we will interpret the results in terms of association rather than being strict in terms of causality interpretation. The estimates are performed for a global inequality statistic (the Gini index) and for the 90-50 and 50-10 ratios in order to capture any complex relationship between inequality resulting from different parts of the income distribution. 5 The random effects estimates of the Gini index replicate the results obtained in Table 3 for the pooled OLS regressions. The heterogeneous results are in line with the meta-analysis of Neves et al. (2016) at the country level, who highlight that 'although the average impact of inequality is not significant, there is a high degree of heterogeneity in the reported effect sizes' (p. 397). The previous section found a heterogeneous association between economic growth and inequality by city size. Columns 2, 4 and 6 of Table 4 show incremental parameters of income inequality as the shares of population in medium and large cities increase. Column 2 shows the random effects results and displays significant and negative parameters for inequality measures in larger cities. This result is also obtained for top and bottom income inequality, although again a positive and significant parameter is found for top income inequality. At this stage we take into account the possibility of spatial effects, which are well documented in regional growth regressions in European Union regions (Ezcurra, 2007;Perugini & Martino, 2008). We performed a list of panel regressions by considering spatial error models, assuming both contiguity and inverse distance matrices, and a balanced panel of regions, as required by these procedures. Table A6 in Appendix A in the supplemental data online displays the main results, including the Pesaran (2004) cross-sectional dependence test for spatial models. The results show that in fact there is spatial dependence in the residuals. Nevertheless, and consistently with what was found by Ezcurra (2007) and Perugini and Martino (2008), the main results hold after addressing the residual's spatial dependence: a positive impact of top income inequality on economic growth plus significant and negative parameters for inequality larger cities. Even though we assume the potential consequences of not considering spatial dependence and as far as the main results of the analysis are robust to its consideration, as in Perugini and Martino (2008), we next provide separate regressions for accounting for endogeneity.
Thus, when we instrument inequality with so-called political instability channels (IV1), inequality turns statistically significant, though this does not occur for the marketfree instruments (IV2). 6 The coefficient related to top income inequality is negative and statistically significant under IV1, but not significant under IV2, while the coefficient related to bottom income inequality is always negative and statistically significant.
IV regressions display significant and negative parameters for the Gini index in larger cities. This result is also obtained for top and bottom income inequality, although it is not robust for IV2 sets of instruments.
As a robustness, separate regressions for groups of regions according to their city size were performed (see Table A7 in Appendix A in the supplemental data online). 7 We again find the significant and negative association between inequality on economic growth in regions with medium and large cities, particularly when using the bottom income ratio. Overall, inequality is higher in regions with larger cities, but further increases of inequality in these regions are associated with lower economic growth rates.
Credit market imperfections and market size effects are potential mechanisms underlying the negative effects of inequality on economic growth. Possible explanations include stronger social ties in small cities and rural areas, which could limit the consequences of the imperfections in the credit markets. As for the market size effect, this might be linked to the high costs of living in cities (Combes, Duranton, & Gobillon, 2012), which are likely to depress particularly fixed salaries as well as government transfers and social benefits, usually established nationally rather than adjusted to local prices.

Impact of the business cycle: inequality and growth before and after the Great Recession
Empirical findings about the inequality-growth relationship importantly can be affected by the time span considered. 8 Results obtained in the short-time horizon considered here are hardly comparable with works such as by Partridge (2005), which covers a period of 40 years for US states and finds a positive link between inequality and long-run economic growth, while FE results were much more ambiguous. Rodríguez-Pose and Tselios (2010) over the period -2001and Perugini and Martino (2008 over two samples (1995-2004 and 2000-04) also find a positive link in OLS estimates and non-significant results for the FE results, in line with the present results, while Ezcurra (2007) over the period 1993-2002 reports a negative estimate. The analysis includes the years before and after the economic crisis began in 2008. This makes Short-run relationship between inequality and growth: evidence from OECD regions during the Great Recession 581 it possible to verify whether the role of inequality on economic growth changed in a period of economic shocks. The hypothesis is that less unequal regions might show higher resilience to economic shocks, especially among regions in which inequality is relatively high, such as those with large metropolitan areas.  Table A5 in Appendix A in the supplemental data online. *p < 0.10; **p < 0.05; ***p < 0.01.

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Vicente Royuela et al. Table 5 presents the results of a model that considers separate estimates for two sub-periods. The first model reports estimates of inequality on economic growth until 2006 (including the growth rate for 2006-07). The next subperiod already takes into account the downturn, as it considers inequality in 2007 and economic growth from 2007-08 onwards. 9 The results, which are robust to the type of inequality indicator, point to a clear effect of the Great Recession in turning the parameter negative and significant.
These results confirm the idea that lower levels of inequality might have been relevant as an element of regional resilience against the shock of the crisis. Regions with smaller cities were less harmed by inequality during the Great Recession than regions with large cities. Even though the difficulty in reporting causality in this relationship, we believe there is a significant association even after several aspects are considered. A possible interpretation is that places with lower levels of inequalitysuch as regions with relatively small citiesmight have more room for growing inequality by increasing the spatial concentration of economic activity. The benefits of agglomeration might, in fact, overcome the costs of higher levels of inequality.

CONCLUSIONS
This paper analyzes the association between income inequality and economic growth. The patterns of association between income inequality, urban size and economic growth were investigated using a panel of regions from 15 OECD countries covering three continents over the period 2003-13. The obtained results provide support for a negative association between inequality and economic growth, especially when the former is measured focusing on the lower part of the income distribution. Such relationships are stronger in large cities, while in regions characterized by rural areas and small cities the relationship is non-significant. These findings are stronger from the start of the economic crisis.
Credit market imperfections and market size effects are potential mechanisms underlying the obtained results. If imperfections in the credit market are lower in less populated areas due to less asymmetric information flows, and closer contacts, this could lead to lower levels of inequality and to better incentives for wealth accumulation and higher economic growth. The market size channel could operate in the opposite direction: the higher costs of living in an urban area are not equally shared by its inhabitants, thus increasing within-region inequalities and depressing economic growth as fewer consumers can afford to buy goods.
Future research could advance in three different, although related, directions: first, exploring the reasons for the increasing importance of inequality within cities and metropolitan areas and between regions is a relevant and scarcely analyzed topic; second, testing alternative theories on the mechanisms through which urban size can alter the relationship between inequality and economic growth, especially in the short run; and third working with city observations, which would improve the definition of the units of analysis.

DISCLOSURE STATEMENT
No potential conflict of interest was reported by the authors.

FUNDING
This work was supported by the Secretaría de Estado de Investigación, Desarrollo e Innovación [grant number ECO2016-75805-R].  (2016) under-identification test of individual endogenous regressors. The Hansen J-statistic tests the null hypothesis of instrument validity under the assumption of heteroskedasticity. All estimates include country and time fixed effects. All regressions are pool IV and include time and country fixed effects and all controls listed in Table A5 in Appendix A in the supplemental data online. *p < 0.10; **p < 0.05; ***p < 0.01.
Short-run relationship between inequality and growth: evidence from OECD regions during the Great Recession 583 NOTES 1. Table A1 in Appendix A in the supplemental data online summarizes the main theoretical arguments that have been put forward to uncover such a complex relationship and distinguishes mechanisms operating in the long run from those having a role in a short-time horizon as well as growthenhancing factors from growth-hindering factors. 2. Territorial level (TL) 2 regions are the higher level of OECD regions, which correspond in most cases to the principal subnational unit of government (states or provinces). There are 214 regions in the selected countries.
Owing to lack of data on individual income, inequality statistics of five of these regions are not considered: three for Canada (Yukon, Northwest Territories and Nunavut), one for Finland (Åland), and one for Korea (Jeju). 3. Figure A1 in Appendix A in the supplemental data online displays the relative distribution of urban population by country. 4. The Hansen test with a reasonable number of instruments was robustly rejected for different geographical areas due to lags of the internal instruments, methods differences (between GMM and orthogonal GMM-SYS), endogenous/predetermined consideration of the other control variables and inclusion of external instruments. 5. Results are robust to the use of other indicators of income inequality and are available from the authors upon request. 6. As the instruments used in the growth equation are generated regressors, standard errors on the slope coefficients are usually incorrect for hypothesis testing. However, as noted by Brückner (2013), in the special case of testing that slope coefficients are equal to zero, these standard errors are correct. 7. We also considered additional regressions by splitting the subsample of regions with smaller cities above and below 200,000 inhabitants. The obtained results remained unchanged, but we agree with one referee that it is an interesting aspect to be considered as further research. 8. In fact, it is also reasonable to argue that the results might be affected by alternative definitions of the dependent variable. We also developed our estimates considering two-year growth rates and exponentially smoothed data for both one-and two-year growth rates. The main conclusions of our work hold. The results can be obtained from the authors upon request. 9. We also tried with subsamples to divide the period with observations until 2007 and 2008. The results are robust for such alternative specifications.