Nripesh Podder

Efficient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations

The Lorenz curve is widely used to represent and analyze the size distribution of income and wealth. The purpose of this paper is to introduce a new coordinate system for the Lorenz curve, with particular attention to a special case of wide empirical validity. Four alternative methods have been used to estimate the proposed Lorenz curve from the grouped observations. The well-known inequality measures are obtained as the function of the estimated parameters of the Lorenz curve. The procedure of estimating the asymptotic standard errors of the inequality measures is also provided. In addition, the frequency distribution is derived from the equation of the Lorenz curve. A new representation of the Lorenz curve is introduced and related to a number of conventional measures of income inequality. The report describes a number of estimation methods and reports some empirical results based on the data from the Australian survey of Consumer Expenditure and Finances.

Sharing the national cake in post reform New Zealand: income inequality trends in terms of income sources

Abstract Using Household Economic Survey (HES) data in unit record form, this paper examines the trends of household income inequality in New Zealand over the period 1984–96, a period that saw New Zealand implement a wide range of economic and social policy reform. The observed changes in the overall income inequality are then decomposed by income components to measure the contributions of the different sources of personal income to the overall inequality. To our knowledge, this is the first time that the methodology for disaggregating the Gini co-efficient, including its more recent extensions by Lerman and Yitzhaki [Review of Economics and Statistics 63 (1985) 151]; Podder [Review of Income and Wealth 39 (1993) 51]; and Mookherjee and Shorrocks [Economic Journal 92 (1982) 886], has been applied to micro-level New Zealand data for computing income inequality and other, related, indices and measures reported in this study. The findings, which indicate a steady upward trend in income inequality, are examined in the light of the reform policies used at the time. Their implications for policy are also addressed.

The implications of economic inequality for social welfare and social conflict

In this article, first, we show how equity considerations, in the guise of inequality of income, enters into a social welfare function. In this connection the important properties of a social welfare function are also discussed. Second, contrary to the popular belief, we contend that the degree of inequality is not an appropriate indicator of the degree of social discontent. Third, the appropriate indicator of social discontent is shown to be the level of social envy which is a non‐monotonic function of inequality. It is also demonstrated that the sociological term “relative deprivation” is equivalent to the economic definition of envy.

Bounding Lifetime Income Using a Cross Section of Data

Measures of income inequality based on current income are well known to overstate lifetime income inequality for two reasons: intracohort mobility and the shape of the age-earnings profile. Utilizing the concept of age equivalence scales along with varying assumptions concerning the extent of intracohort mobility, the method presented bounds lifetime income inequality using only cross-sectional data from the CPS, 1967-86. As a result, we are able to analyze changes in lifetime inequality over this period. Copyright 2003 by the International Association for Research in Income and Wealth.

Some Ethnic Dimensions of Income Distribution from Pre- to Post-Reform New Zealand, 1984-1998

Based on unit record data from four household surveys conducted by Statistics New Zealand for the years 1983/1984, 1991/1992, 1995/1996 and 1997/1998, this paper addresses some ethnic dimensions of income inequality among New Zealanders over the period of the surveys. It applies alternative techniques of decomposition of the Gini coefficient of inequality by subgroups of population. It then analyses how changes in the incomes of specific population subgroups affect the overall inequality. The results help quantify the economic distances among the different ethnic populations of New Zealand, and indicate how and why these distances have been changing over time.

Welfare Disparity Among Subgroups of Population: The Method of Analysis with an Application

The aim of this paper is to examine the properties and then disaggregate a social welfare function (SWF) by subgroups of population. The functional form of the SWF was axiomatically derived by Sen and has recently been given a utilitarian foundation by Dagum. Since the function contains the Gini coefficient as the inequality parameter, it could not be disaggregated by subgroups of population in the conventional manner. In this paper, using an alternative method of subgroup decomposition of the Gini coefficient recently suggested by Podder (1993), the SWF has now been disaggregated. Among other things, with the application of this method it is now possible to identify the disadvantaged groups by their relative shares in total welfare. However, the main use of the method is probably the determination of the effect of economic growth in specific subgroups on total social welfare of the society as a whole. The method has been empirically illustrated with Australian Household Expenditures data of 1988–89 . The subgroups are based on the geographical region of residence. The effect of a percentage change in income of a specific group on total welfare is also computed. This information is crucially important in a variety of social decision making situations including optimum social security decisions and cost benefit analysis.

Intrinsic Uncertainty - An Explanation of the St. Petersburg Paradox

Consider any situation involving uncertainty, where the random variable of interest (e.g., payoff) is X. Let there exist a random variable, say Y, which represents the uncertainty intrinsic to the situation, and let there exist a function g such that X=g(Y). Our contention is that, once the intrinsic uncertainty has been identified, the relevant summary value is g(E(Y)), even though this may not be equal to the expectation E(g(Y)) of the variable of interest. We discuss two examples in which we can identify the random variable representing the intrinsic uncertainty. One of these examples is the St. Petersburg Paradox, where we argue that the intrinsic uncertainty is represented by the length of the game, and therefore, the variable of interest is the (finite) payoff received at the expected length of the game, as opposed to the infinite expected payoff of the game. As a result, we are able to resolve the St. Petersburg Paradox even under risk neutrality, i.e., without recourse to the strong risk aversion represented by a bounded utility function in the expected utility framework.

Equity, efficiency and social welfare: An application of generalised Lorenz Dominance to New Zealand incomes data 1984-1998

This paper examines the changes in the level of social welfare in New Zealand over the period 1984 to 1998 in the context of the countrys economic reform process since the early 1980s. The earlier part of this period was also characterized by a largely policy-induced economic recession in New Zealand. In this paper, we make an attempt to identify the sections of the population that became better off in terms of real income, and those that became worse off during the period chosen. In addition, we examine the changes to the overall level of social welfare. The methods used are both ordinal and cardinal. The ordinal method is based on the criterion of generalized Lorenz dominance, and the cardinal method is based on a social evaluation function that provides complete ordering of all possible social states. The social welfare changes, derived with the help of the cardinal method, and measured in terms of real income, are then attributed to the twin influences of mean income changes and changes in measured inequality. In addition to showing up the dramatic increase in the Gini coefficient of income inequality overall, the results also track the changes in real income of the different income groups over time, and quantify how these changes, coupled with the increased inequality, affected the well-being of New Zealanders over a period of extensive economic reform. The study is based on unit record data from four Household Surveys conducted by Statistics New Zealand in the years 1983/84, 1991/1992, 1995/1996 and 1997/1998.