Stochastic dominance and decomposable measures of inequality and poverty

In this paper, we characterize some new links between stochastic dominance and the measurement of inequality and poverty. We show that: for second-degree normalized stochastic dominance (NSD), the weighted area between the NSD curve of a distribution and that of the equalized distribution is a decomposable inequality measure; for first-degree and second-degree censored stochastic dominance (CSD), the weighted area between the CSD curve of a distribution and that of the zero-poverty distribution is a decomposable poverty measure. These characterizations provide graphical representations for decomposable inequality and poverty measures in the same manner as Lorenz curve does for the Gini index. The extensions of the links to higher degrees of stochastic dominance are also investigated.     

A general class of additively decomposable inequality measures

Summary. This paper presents and characterizes a two-parameter class of inequality measures that contains the generalized entropy measures, the variance of logarithms, the path independent measures of Foster and Shneyerov (1999) and several new classes of measures. The key axiom is a generalized form of additive decomposability which defines the within-group and between-group inequality terms using a generalized mean in place of the arithmetic mean. Our characterization result is proved without invoking any regularity assumption (such as continuity) on the functional form of the inequality measure; instead, it relies on a minimal form of the transfer principle – or consistency with the Lorenz criterion – over two-person distributions. Received: October 27, 1997; revised: March 25, 1998     

Decomposition of bivariate inequality indices by attributes

We provide, for the class of relative bidimensional inequality indices, a decomposition of inequality into two univariate Atkinson–Kolm–Sen indices and a third statistic which depends on the joint distribution of resources.     

The price of education and inequality

Constructing a simple model that includes the price of education, this paper shows that the educational expenditure of rich households could prevent poor households from escaping poverty. The paper offers an explanation for persistent inequality.     

Decomposing differences in health and inequality using quasi-objective health indices

People in Canada and the United States often make claims regarding whose country has a better health system. Several researchers have attempted to address this question by analysing subjective health measures in the two countries, thus assuming a common definition of ‘good’ health. Using data from the Joint Canada/US Survey of Health, which provides rich and comparable health information for the two countries, I generate two quasi-objective health indices and show that Canadians and Americans define ‘good’ health differently. After controlling for cross-country reporting heterogeneity, health differences between Americans and Canadians are eliminated for intermediate health statuses, while health differences at the tails of the health distribution lead to slightly better average population health in Canada. With respect to health inequality, my results show that income and education gradients increase steeply with poor health in both countries. Hence, considering differences along the health distribution is crucial when assessing population health or health inequality.     

Invariance, price indices and estimation in almost ideal demand systems

Two issues are addressed in this paper. First, we explore the issue of price index invariance in the linearized Almost Ideal demand system. We establish that the Stone index, which lacks invariance, and the recently proposed invariant Laspeyres, Paasche and Tornqvist indices all generate biased and inconsistent estimators. Monte Carlo evidence shows that invariance does not necessarily lead to better estimates of price and income elasticities insofar as the Stone and Paasche indices are unambiguously inferior to the Laspeyres and Tornqvist indices, especially if prices are not strongly positively correlated. Second, we examine the merits of the widely used conditional ML estimator of the non-linear Almost Ideal system in which a prior value is chosen for the “subsistence” parameter. We find that the bias and trace mean square error increases induced by conditional estimation are modest. The choice between the linearized and the non-linear models favors the latter although in some cases linear methods are as good as non-linear. First Version Received: January 1999 / Final Version Received: March 2000     

On the dynamics of inequality

The dynamics of inequality are studied in a model of human capital accumulation with credit constraints. This model admits a multiplicity of steady state skill ratios that exhibit varying degrees of inequality across households. The main result studies equilibrium paths. It is shown that an equilibrium sequence of skill ratios must converge monotonically to the smallest steady state that exceeds the initial ratio for that sequence. Convergence is “gradual" in that the steady state is not achieved in finite time. On the other hand, if the initial skill ratio exceeds the largest steady state, convergence to a steady state is immediate.This paper is based on unpublished notes from 1990; see http://www.econ.nyu.edu/user/debraj/DevEcon/Notes/incdist.pdf. Two considerations suggest that these results may be worth reporting in print. First, the existence of a sizeable recent literature indicates that these relatively early notes may have value outside a filing cabinet or a private webpage. Second, Mukul Majumdar’s own research on economic growth with a nonconvex technology is an even earlier precursor to some of this literature, so the current outlet – a special issue in his honor – seems appropriate. Conversations with Glenn Loury simplified the proof of the main result. I thank Dilip Mookherjee for many useful discussions, and two anonymous referees for helpful comments on an earlier draft. Funding from the National Science Foundation under grant number 0241070 is acknowledged. This paper is dedicated with much affection and warm admiration to Mukul Majumdar – or to Mukulda, as I always think of him – on the occasion of his 60th birthday.     

A note on the evolution of inequality in Poland, 1992-99

Analyses of household budget surveys, national accounts dataon functional income distribution, and data on the dispersionof wages, indicate that income inequality in Poland, after fallingover the 1993–96 period, rose significantly from 1997onwards. Farmers and the unemployed were the main losers. Theoverall position of wage-earners improved, although wage inequalityincreased sharply in the second half of the 1990s. Employersand the self-employed fared quite well. This coincided withfiscal policy changes which substantially slowed down progressionin income taxes. Over the 1993–96 period growth was highand balanced. Subsequently, growth slowed down, giving riseto serious fiscal and external deficits.     

The creation of effective states in the OECD since 1870: The role of inequality

Research shows that state capacity is crucial for economic development, yet the impact of inequality on state capacity is not well understood. This paper examines the impact of income inequality on three key dimensions of state capacity, namely legal, fiscal and collective capacity using annual data for a core of 21 OECD countries over the period 1870–2013. We find that the marked reduction in inequality over most of the last century starting from 1916 was pivotal to the significant improvements in legal, fiscal and collective capacity in the OECD countries over the same period.     

The effect of reporting errors on the cross-country relationship between inequality and crime

This paper analyzes reporting errors in crime data to see how they impact econometric estimates, particularly of the key relationship between inequality and crime. Criminal victimization surveys of 140,000 respondents in 37 industrial, transition and developing countries are used. Comparing the crimes experienced by these respondents with those reported to the police, non-random and mean-reverting errors are apparent. Time-varying factors affect the propensity of victims to report crimes to the police, undermining the use of country-specific fixed effects as a means of dealing with measurement error in official crime data. These errors substantially attenuate both cross-sectional and panel estimates of the partial correlation between inequality and crime.