# A reassessment of the relationship between income inequality and poverty

### Kristin J. Forbes - MIT Personal Faculty

This paper examines the relationship between income inequality and economic whereas it impedes growth among medium and poor areas. Key Words: Kuznets Curve, TFP Growth, Inequality Decomposition, Poverty between growth and inequality is an analysis of evolution of the income. PDF | This paper empirically investigates the effect of income inequality on economic A reassessment of the relationship between inequality and growth, American . and their effect on income inequality and poverty: Evidence from Vietnam.

A broad consensus validating the existence of this negative correlation prevailed until some authors began using panel data estimation techniques that have tended to show a positive correlation. The aim of this paper is to empirically explore the relationship between inequality and growth in light of recent developments. For this, first a broad overview of the literature in the area is conducted, at both the theoretical and empirical levels.

Section I provides such a review, focusing on the rationale of the theoretical models and includes a summary of the empirical studies, their methods, and results.

In section II the motivation for providing a new empirical estimate is presented. The results of this empirical estimation are reported and discussed in section III. The final section concludes with some comments. They found five main motives for this: Since the appearance of Kuznets' inverted U hypothesis on the relationship between inequality and economic growth empirical work has shown diverging results about its validity. Doubts have been particularly strong regarding the persistence of this relationship for a country over time.

In spite of mixed evidence on the nature of the relationship between inequality and growth, from the stand point of endogenous growth theory the independence between the two is questioned with no qualification. The move toward increased inequality within countries has spurred an ample set of explanations ranging from potential distributional effects from globalization, to government policies and social norms.

The increase in inequality between countries experienced since the s has motivated a large body of literature that has helped put inequality back on the agenda.

Clearly, one of the issues is convergence. Another set of issues refers to the seeming difficulty of some countries to break the low-income trap while others manage to do so and the consequent quest for the reasons for this difference as well as for policy recipes to achieve this jump. In examining this theme, the connection between inequality and long-term growth has provided a fruitful area of research. Theoretical Effects of Inequality on Growth An interesting body of literature on this topic mainly based upon endogenous growth theory has been developed from the s.

It has become common to classify these theories into categories according to the mechanism that links inequality and growth. The classification in use here comprises the following: Credit Market Imperfections Models featuring credit market imperfections are based upon the assumption that a limited capacity to borrow on the part of certain economic agents, leads to rates of return on investment opportunities that do not necessarily equate in the margin.

As credit access is limited, the possibility of exploiting investment opportunities depends on the individual's possession of assets and income. Hence, in the presence of decreasing returns, inequality leads to lower average returns and lower growth. Perotti uses the loan-to-value ratio for domestic mortgages as a proxy for credit availability, finding that it has a positive effect on the growth rate and that as inequality increases the impact of credit availability on growth becomes larger.

Following their work, a number of studies for instance Benabou, a, and Piketty, indicate that although education shows high rates of return, poor people tend to forego investing in education due to their inability to borrow and that this, in turn, slows the formation of human capital and lower growth rates. An important issue here is intergenerational mobility as the presence of fixed costs of investment on education may prevent a dynasty that lacks resources at the beginning from doing this type of investment generation after generation.

In contrast, if increasing returns on investment prevail for some range for example, education yields higher returns only after certain schooling level inequality may be positively related to growth as it allows some individuals to get through this threshold. Political Economy The political economy argument refers to social preference for redistributive taxation.

When mean income exceeds the median income in an economy, majority voting tends to favor taxation provided it is progressive and government redistributive spending either as direct transfers or as public expenditure programs. This provides the political mechanism for the connection between inequality and growth. On the other hand, higher taxes and transfers distort economic decisions and disincentive private savings and investment causing economic growth to decline.

This constitutes the economic mechanism of the linkage. As a consequence, the existence of high inequality is considered a cause of slow growth via its effect on taxation and redistribution through the political system. Perotti finds an expected positive relation between inequality and taxation but an unexpected positive relation between marginal taxation and growth. In either case, more equal societies must tend to grow faster. However, the relationship inequality-growth within this perspective may prove tricky, as Barro has noticed with respect to the implications of whether income inequality is measured ex-ante or ex-post.

The form of political power may matter. Benabou b builds a model that allows for deviations from the one-person-one-vote rule in a specific direction: In this context, what matters for growth is not the extent to which the political system deviates from perfect democracy but whose interests are favored by this deviation.

It then turns out that the distribution of political power matters too. Political Economy Compounded with Credit Market Imperfections The main issue within this class of models is redistribution and its effects on growth. In a strict sense, for credit market imperfections models policy is exogenous. On the other hand, complete markets characterize 'pure' political economy models.

In general, countries face a tradeoff between the benefits of redistribution and its costs and both forces must be accounted for. In Benabou bunder any given policy, inequality reduces growth and intertemporal efficiency while growth is first increasing on redistribution and then decreasing, regardless of the level of initial inequality. With heterogeneous agents, highly imperfect capital markets, and technology exhibiting diminishing returns to capital, inequality has a negative impact on growth and redistribution a positive one.

Unequal access to investment opportunities, jointly with a high degree of capital market imperfection generates credit cycles and macroeconomic volatility. By increasing the share of savers that can directly invest in high return projects or by transferring idle funds from savers to investors volatility would decrease and growth would be enhanced. Efficient redistribution has a wide consensus in a fairly homogeneous society and face strong opposition in a more unequal one.

### Revisiting the Relationship Between Income, Inequality and Economic Growth

Below a threshold level no allocation of political power can lead to more than a unique social contract, whereas above it there may be multiple steady states. Therefore no unique relationship necessarily arises between inequality and growth and differing empirical results may be in fact non-comparable or be indicative of differing steady state equilibriums that bear weak or no linkage to economic performance. This form of rent-seeking behavior is wasteful as are the defensive efforts of the potential victims.

Furthermore, social unrest discourages investment as it generates uncertainty and disrupts the normal functioning of markets and labor relations.

As a consequence, economic growth declines. Benabou b synthesizes the basics of this class of models by means of an economic growth version of the prisoner's dilemma. The model shows that, as in the case of the political economy models, what seems to matter is not inequality per se but the relative distribution of income and political power.

As pointed out by Barrotransfers of economic resources may be an offsetting force in this context.

As the poor need some resource level to effectively be able to disrupt the regime, income equalizing transfers promote stability only to the extent that they can overcome the tendency towards rebellious behavior. Even though it appears to be ample empirical evidence in favor of this perspective, the specific channels through which it operates are not entirely clear. As Benabou b points out it seems to be the 'general idea' that political instability negatively affects growth what the evidence supports rather than the particular linkages that models portray.

Limited work, most notably that by Barrohas taken a simultaneous equations perspective. The usual cross-section estimation regresses a measure of economic growth or investment growth on a set of variables deemed as standard in estimating growth models, to which a measure of income inequality is added.

Most of the results of this reduced-form estimation indicate a negative relationship between inequality and growth, although a number of qualifications usually apply to them.

As reduced-form estimates are compatible with several theoretical explanations of the linkage inequality-growth, they cannot provide information on the specific channels through which this relationship takes place and therefore only structural models may supply evidence on them. However, as mentioned, few empirical works have attempted to do so.

On the other hand, the political economy approach appears to command the weakest empirical support. One of the problems associated with cross-section estimations is measurement error in income inequality data.

They assembled a relatively large and consistent data set and classified the data points according to its seeming quality level. Forbes notes that a majority of the data employed in some of the most well-known cross-section studies does not qualify as high quality data, a situation that she considers may lead to biased estimated coefficients. There is discussion however, on the extent to which data selection based upon the criteria used by Deininger and Squire should be regarded as definitive.

A set of 12 studies that have attempted to empirically measure the relationship between inequality and growth were examined.

Seven studies employ cross-section estimations, two use pooled time series-cross section, four use simultaneous equations estimation techniques, one uses panel data estimation, and one uses nonparametric methods. Typically, the growth rate measured over a long period of time 20 to 30 years is regressed on a set of variables that is a slight variation of Barro's growth regression, to which others are added the so called Barro-augmented regression. The results tend to be robust to different specifications of the models and ways of measuring inequality, but are frequently found to moderately vary in magnitude and lose significance when regional dummy variables are included.

This has been interpreted as a consequence of well known historic regional differences in inequality and as an indication of the existence of non-included variables of regional importance that have some correlation with inequality and actually influence the growth rate. In spite of the relatively large consensus on the empirical verification of this negative relationship, a handful of studies have recently 'challenged' this view.

Barro finds weak overall effects of inequality on growth and investment, and reports that the negative effect of inequality on growth that he finds for low-income countries switches to a positive effect for high-income countries. In the light of these findings, especially that of Forbes, a debate has resurfaced around the issue. Motivation for a New Empirical Estimation Seemingly, the immediate reasons for the differing result of Forbes lie in the fact that hers as is Li and Zou's is a fixed-effects model yielding estimates that should be understood as a measure of how changes in inequality relate to changes in growth within a given country instead of across countries as regular cross-section studies do.

Also, the time period break of 5 years that she uses to build the unbalanced panel data on which the estimation is done, makes the coefficients short to medium run in nature instead of long run indicators as is usual in other studies. For these reasons, Forbes considers that these results do not necessarily contradict other studies. While currently there is no sufficient data to estimate a long run fixed-effects relationship between inequality and growth, it is possible to think of theoretical channels that in the long run may hamper or even reverse this positive relationship.

Besides, Forbes argues that, contrary to what is commonly claimed, most estimates lack robustness and that the drop in significance that the inequality coefficient suffers when regional dummies are included in the models shows this fact. Furthermore, two econometric problems potentially affect the quality of most studies. First, as mentioned before, is the issue of measurement error in inequality. Second, the omitted- variable bias is a potentially important problem in the context of these studies.

The particular relation between inequality and growth that is found in a country may be due to the effect of variables that are not included in the model. In other words, there is a strong possibility that 'unobserved' characteristics of a country determine to a large extent either the degree of inequality or the growth rate or both but are not explicitly accounted for in the model.

There are two possibilities for taking into account the 'unobserved' characteristics of a country: Interestingly, as noted, the two studies that have recently found positive associations between inequality and growth were estimated by using some variant of the fixed-effects approach. Forbes notes how data quality, period length, and estimation technique influence the sign and significance of the coefficient for inequality for the same specification of the model.

According to them, there are theoretical and empirical reasons to believe that in the short-run both increases and decreases in inequality are followed by a reduction in the growth rate. That is, there exists a U-shaped relationship between changes in inequality in any direction and changes in the growth rate. The direction of this relationship i. As a consequence, they consider that Forbes' estimate extrapolates this relationship by means of the linear structure that she imposes on her model.

In what follows I generate a new estimation of the relationship between inequality and growth by using a panel data model that tries to take into account some of the just mentioned criticisms of Forbes' model. The Model and the Data A commonly used model specification is employed for estimating the relationship between inequality and growth. The basic model can be described as follows: The set of control variables comprises the logarithm of per capita GNP Incomeit-1the Gini coefficient Giniit-1a measure of market distortions PPPIit-1average secondary school attainment for the female population aged over 25 Feducit-1and average secondary school attainment for the male population aged over 25 Meducit Given the short to medium term nature of the panel data sets used to estimate the model five-year and ten-year breaks per capita GNP was averaged over five-year periods to smooth out possible yearly serial correlation from business cycles.

As usual in these models, income level controls for convergence effects. Educational attainment is meant to proxy for the level of human capital available and is preferred to enrollment since it is a stock variable. The purpose of using stock variables measured at the start of the time breaks, rather than flow variables measured throughout the periods is to reduce potential endogeneity.

Table 1 summarizes the definition of the variables employed, indicates the data sources, and provides basic statistics for them. The data set basically employed for estimation includes 52 countries and observations distributed along 7 five-year periods covering from to Following Barrothe data for the Gini coefficients includes, besides the 'high quality' data, the observations that are not considered 'high quality' by Deininger and Squire due to lack of a clear reference to their source.

This allows expanding the database used by Forbes without major loss in comparability. Since the purpose of the estimations to be presented is to make a comparison with Forbes' results, no attempt is made to experiment with the set of control variables. This was done on the idea of preserving comparability. Also, for doing sensibility analysis of the results no other measures of inequality were considered since it would have implied an impracticable reduction in the size of the database.

The fourth section defines and discusses the database. The fifth section analyzes the results obtained from the estimate of the econometric model and, finally, the sixth section offers a conclusion with some final considerations. Kuznets scrutinizes this topic in a unique way, exploring the nature and consequences of long-term changes in income distribution. The author believes that there are at least two groups of forces in the long-term development of countries that lead to increasing inequality in the distribution of income — the industrial structure of the income distribution and the concentration of savings in the upper-income brackets.

As a result of industrialization and urbanization, rural migration came about in search of better living conditions.

With that, to analyze the income distribution of the population in its totality is essential to understand the way in which income is shared between cities and rural environments, considering that the inequality of distribution and average rural per capital income are commonly lower than in urban settings, mainly due to the lower productivity inherent to activities in each realm.

Because the distribution of savings is more unequal than the distribution of personal income and assets, only the wealthiest strati of society have the capacity to save and this leads, ceteris paribus, to the concentration of a growing proportion of income in the hands of the upper groups.

In this same work, Kuznets poses a few questions on income distribution, including the following. What factors determine long-term income inequality? Generally speaking, these questions confirm his concern with the degree of inequality in the income distribution, whose origin may be associated with economic growth. According to the author, the aforementioned questions are broad, in a field of study that has few definitions, scarce data and the pressure of strongly defended opinions.

Moreover, he points out that while the resulting difficulties cannot entirely be avoided, it may be helpful to specify the characteristics of the size of income distributions to be examined and the movements to explain.

The empirical data in the Kuznets study suggest that inequality is reduced in developed countries only in the later phases of the growth process and as a function of its benefits. Society gains greater access to healthcare networks and education, which leads to greater productivity, which leads to rapid industrialization and urbanization. It also reasons that as economies experience growth, access to education can provide better opportunities, reduce inequalities and make the poorest strati of the population more political and able to modify government policies.

The consequences of the shift from the agricultural revolution to the industrial age, along with population growth due to rapidly declining mortality rates and the maintenance, or in some cases increase, of birth rates, leads to the increase in inequality, principally in early stages. According to Kuznets, the population growth rate can be considered as part of both the cause and effect of the long shift in income inequality. In addition, in the words of Kuznets, it is worthwhile to note that in this phase there may have been a preponderance of factors favoring maintenance or increase in the shares of top-income groups, insofar as their position was bolstered by gains arising out of new industries.

In light of the above, a dynamic inequality model can be proposed, dependent on a specific growth regime able to characterize the secular structure of income distribution, in which inequality increases in the early stages of economic growth, is consolidated for a time and then decreases in later phases. This temporal model is adjusted to the poorest population, but the results acquired indicate that this process of decreasing inequality, analyzed in developed countries, is marked by the eventual upswing of inequality over time, simulated in the inverted U curve.

Various studies and methods have been created to explore the nature of the relationship between income distribution and growth, both for developed and developing countries. Aiming to illuminate the proposal of this work, the next section will offer a literature review of work related to the Kuznets proposal, describing its theoretical foundation and the empirical evidence found.

In Economic Growth and Inequalitywith regard to the dynamic of income distribution during industrialization and urbanization, Kuznets illustrates his theory through a dualist economic model, working with one agricultural and one non-agricultural sector to analyze the relationship between income inequality and economic growth.

He conjectured that income inequality would increase in the short term and, with economic growth, it would decrease, making an inverted U. Switching the population from one sector to another, from a traditional agricultural population to a modern industrialized sector, income inequality would increase, given that this more dynamic sector is also wealthier and more unequal. This phenomenon happens due to the income differential of the populations between two sectors, which can be analyzed as average per capita industrial income of the share of sector income, with respect to total income and inequality in the two population shares, which tends to be higher in urban populations than in rural Salvato et al.

With regard to the data, Kuznets attempts to classify income into different categories with various dimensions, despite the setbacks resulting from the lack of data for long time periods.

To study this dynamic, the author uses time series from the United States, United Kingdom and a limited sample for Germany Prussia and Saxonyand suggests that relative income distribution, estimated by annual income incidence in rather broad classes, revealed greater changes in equality in the s, with evidence also in the time period before the First World War. In the United States, it was found that income between groups was similar between the crisis and after the Second World war.

The same development was noted in England between andas a result of the wealthier becoming poorer, while the income value of the poorest remained constant until and then rose between and After these influential works by Simon Kuznets were published in the s and s, debates on the relationship between per capita income and income inequality played a larger role in the broader economic discussion. Since then, various studies and methods have been created to measure income inequality, both in developed and developing countries Taquez and Mazzutti, Fields ascertains that the literature has divided into two groups with regard to these Kuznets studies, one that tends to use models that analyze the shape of the inverted U — based on level of economic development — and the other that uses empirical methods to corroborate or refute the Kuznets proposal.

Aiming to prove the inverted Y hypothesis, various estimates have been made. Cross-sectional and time series methods were widely used in subsequent decades, at the suggestion of Kuznets, but other authors continued to point out their limitations.

As an alternative, panel data estimates have been broadly adopted and produce more statistically significant results Taques and Mazzutti, That identification could help establish averages, where levels of inequality observed in specific countries could be compared. By choosing data on developed and developing countries, Fields and Jakubson assume that some countries are either above or below the Kuznets curve.

Then, the central line can be estimated using the fixed effects approach. Various results of other authors have challenged this based on the econometric method used, because the difference could be explained by observing the results between countries and in a single country.

The majority of empirical studies that include groups of both developed and developing countries in the international literature mention or praise the Kuznets hypothesis, even if they use other approaches.

## Kristin J. Forbes

With that said, KravisOshimaAdelman y MorrisPaukertAhluwaliaRobinsonRamPerottiDawsonOgwang and Sylvester are all studies based on cross-sectional data, which report evidence favorable to the hypothesis in question. In addition, Hsing and Smithusing time series data for the American economy, do not reject the Kuznets hypothesis.

The same is true in studies by ForbesDeininger y SquireBarro and Thorntonwhich used panel data.

And Fields and Jakubsonone of the principal works that does not support the inverted U hypothesis, drew on estimates for panel data with fixed effects. Other studies have offered alternative explanations for the shape of the inverted U and the correlation between inequality and economic growth, subsequent to Kuznets and Robinson In that line, Barro attributes this peculiarity to deficiencies in the financial market that exist in underdeveloped economies.

Deficiencies in the credit market would significantly affect the poorest swath of the population, which faces greater difficulties in accessing credit, reducing their capacity to make investments that would lead to the accumulation of physical or human capital.

On the national level, there are also works that would appear to provide proof of the inverted U behavior espoused by Kuznets. Using panel data for municipalities in Rio Grande do Sul, Bagolin, Gabe and Pontual also demonstrated the inverted U relationship between per capita income and the Theil index, for the time period ofand Jacinto and Tejada used cross-section and panel data for cities in northeastern Brazil, analyzing the years and and also finding evidence of the aforementioned curve.

Using a non-parametric local regression, they looked at municipal demographic density and per capita income by sector and inequality, both for agricultural and livestock income as well as industrial and service sector income. The results confirmed the Kuznets inverted U, but only for some municipalities, when the explanatory variable of municipal demographic density was included. Moreover, in Brazil, local economic inequality indices grew in the s and remained high until the mids.

This situation began to change after the implementation of the "Real Plan," when inequality indices began to fall. Despite this recent decrease, inequality in Brazilian income remains fairly high. This work analyzes the behavior of inequality in 27 Brazilian states as related to income, education and life expectancy of individuals from to The relationship between income inequality and economic growth is analyzed with a panel data regression model, in the following equation: The subscript i represents the state and t the time period.

Arellano and Bond discuss what happens with two econometric problems when the model is calculated using traditional estimation methods. In this case, omitting the individual fixed effects in the dynamic panel model returns deformed and inconsistent ordinary least squares OLS estimators. Second, there is the problem of the likely endogeneity of the explanatory variables. In this case, the endogeneity on the right side of the equation 2 should be treated to prevent possible deformation due to problems of simultaneity.

One way to solve this problem, according to Arellano and Bond is to use the generalized method of moments estimator difference GMMwhich consists of eliminating the fixed effects through the first difference of the equation 1. The other explanatory variables can be considered as a strictly exogenous, if not correlated with past, present and future error terms, b weakly exogenous, if correlated only with past values of error terms and c endogenous, if correlated with past, present and future error terms.

In the second case, the values of the lagged variable in one or more periods are valid instruments in estimating equation 2 and, in the latter case, the lagged values in two or more periods are valid instruments in estimating that equation. In that way, they produce an inconsistent and distorted difference GMM estimator for panels with small T.

With that said, Arellano and Bover and Blundell and Bond recommend a system that combines the set of equations in differences, equation 2 with the set of equations in level, equation 1to reduce this issue of distortion. This system has been designated as the generalized method of moments system system GMM. For equations in differences, the set of equations is the same as previously mentioned. For the regression in levels, the appropriate instruments are the lagged differences of the respective variables.

As such, the estimator used was suggested by Arellano and Bond in two steps. The first stage supposes that the error terms are independent and homoscedastic across states and over time.

And in the second period, the residuals obtained in the first stage are used to build a consistent estimate of the variance-covariance model, thereby relaxing the hypotheses of independence and homoscedasticity.

The estimator for the second period is asymptotically more efficient than the estimator of the first stage. The consistency of the system GMM estimator depends on the assumption of the absence of serial correlation in the error term and the validity of additional instruments. In that way, initially, null hypotheses on the absence of first and second order autocorrelation of the residuals are proved.

In order for the estimators of the parameters to be consistent, the hypothesis of the absence of first order autocorrelation must be rejected and the second order accepted. Then, the Hansen test is conducted to verify if the additional instruments required by the system GMM method are valid, as Arellano and Bond recommend.

According to Vanhoudtstudies with a global scope make it difficult to compare data, as research methodologies and data collection are carried out differently in each country. As such, this work benefits from only using variables that were calculated with the same methodology in each state, which makes it possible to more precisely estimate the indicators and compare the data.

The Gini coefficient, used as a measure of inequality, is taken from per capita household income. This index is frequently used to express the degree of income inequality and may be associated with the Lorenz curve determined by the set of points which, based on incomes ordered by increasing level, relate the cumulative proportion of people and income.