Kuan Xu

International Comparisons of Poverty Intensity: Index Decomposition and Bootstrap Inference

This paper proposes an alternative formulation for the Sen-Shorrocks-Thon (SST) index of poverty intensity that is appropriate for survey data with sampling weights. It also decomposes the SST index into the poverty rate, the average poverty gap ratio among the poor, and the overall Gini index of poverty gap ratios. To account for sampling variation in estimates of poverty intensity, this paper uses the bootstrap method to compute confidence intervals and presents international comparisons using Luxembourg Income Study (LIS) data from the 1970s to the 1990s. Cross-sectional and longitudinal analyses indicate that the percentage change in poverty intensity can be approximated by the sum of percentage changes in the poverty rate and average poverty gap ratio, since changes in the overall Gini index of poverty gap ratios are negligible. In the early 1970s poverty intensity in Canada and the United States was almost indistinguishable, but in the 1970s Canadian poverty intensity decreased. Large increases in poverty intensity occurred in the 1980s in the United States, the United Kingdom, and Sweden.

Poverty Intensity - How Well Do Canadian Provinces Compare?

This paper uses estimates of the Sen-Shorrocks-Thon measure of poverty intensity in Canadian provinces, and the 95 percent confidence interval surrounding such estimates, for 1984, 1989 and 1991-96 to compare Canadian provinces over time and internationally. Coinciding with a more general social assistance support, poverty intensity in Ontario declined in the late 1980s to a level similar to Northern Europe, but since 1994 cuts to social assistance have coincided with a significant rise in poverty intensity. Prince Edward Island has done relatively well in reducing poverty intensity. Nationally, the 1980s were a period of declining poverty intensity, but these gains have been eroded since 1994.

The Social Welfare Implications, Decomposability, and Geometry of the Sen Family of Poverty Indices

In this paper, we propose a unified framework for the Sen indices of poverty intensity that shows an explicit connection between the indices and the common underlying social evaluation function. We also identify the common multiplicative decomposition of the indices that allows simple and similar geometric interpretations and easy numerical computation.

Inference for Generalized Gini Indices Using the Iterated-Bootstrap Method

Inference using the iterated-bootstrap method proposed by Hall is appealing for cases in which the percentile method needs to be used but the nominal level of a confidence interval has to be adjusted. One natural application is for generalized Gini indices of income inequality. When applying these theoretical inequality measures directly to sample data for the purpose of statistical inference, economists must come up with some measure of sampling variation. This is particularly the case when the index estimates are compared over time to infer information on the changes of social welfare and inequality. Although there are difficulties in the existing inferential procedures, a more intuitive approach is to use the iterated-bootstrap method.

U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures

U-statistics form a general class of statistics that have certain important features in common. This class arises as a generalization of the sample mean and the sample variance, and typically members of the class are asymptotically normal with good consistency properties. The class encompasses some widely used income inequality and poverty measures, in particular the variance, the Gini index, the poverty rate, the average poverty gap ratios, the Foster-Greer-Thorbecke index, and the Sen index and its modified form. This paper illustrates how these measures come together within the class of U-statistics, and thereby why U-statistics are useful in econometrics.

An empirical analysis of term premiums using significance tests for stochastic dominance

Abstract The economic significance of term premiums in real returns on US Treasury Bills is examined using recently developed tests for first- and second-order stochastic dominance. The tests place only general restrictions on the preferences of individuals and on the distribution of returns. The results indicate that the two-month real return is preferred to the one-month real return based on both dominance criteria. Other term premiums do not appear to be economically significant.

Statistical Inference for the Sen-Shorrocks-Thon Index of Poverty Intensity

The proposition of the modified Sen index (the SST index) for measuring poverty intensity represents an important advance in the literature of poverty measures. This index is useful in empirical research on income distribution and poverty because it satisfies a set of desirable properties while the Sen index and some other indices do not. This index is symmetric, monotonic, continuous, homogeneous of degree zero in incomes and the poverty line, and consistent with the transfer axiom. It also admits a useful geometric interpretation. Hence, there is a considerable interest on the part of economists to apply this measure to sample income data in order to draw valid statistical inference about poverty intensity. This paper examines the asymptotic distribution of the SST index estimator, and proposes a useful test for comparing two population SST indices over time or across states. This test can be used for evaluating the deprivation dominance relationship among income distributions.

Asymptotically distribution-free statistical test for generalized lorenz curves: An alternative approach

A generalized Lorenz (GL) curve differs from a Lorenz curve in that the former is a rescaled version of the latter. A GL curve represents the relationship between the average income computed from a cumulative percentage of the populations and the corresponding cumulative percentage. GL dominance is a useful criterion for ranking GL curves either for an economy over time or for a number of economies at one point in time. Relative to a dominated GL curve, a dominating GL curve indicates both that total income for the population is higher and that it is more equally distributed. Hence, it is obviously more desirable in a certain social sense. While sound statistical tests are essential for making statistical inference about GL dominance from sample GL curve estimates, the lack of suitable joint test procedure for GL dominance is an unsolved problem in income distribution literature. This paper aims at solving this problem and provides an illustrative empirical example to show how to apply this test procedure in empirical research.

An Anatomy of the Sen and Sen-Shorrocks-Thon Indices: Multiplicative Decomposability and its Subgroup Decompositions

This paper proposes a new and unified framework for the Sen and Sen-Shorrocks-Thon indices of poverty intensity, which shows an explicit connection between the two indices and the undelying social evaluation function. This paper also identifies the common multiplicative decomposition of the two indices. This allows simple and similar geometric interpretations, easy numerical computation, and common subgroup decompositions, which are useful to policy analysts but not possible prior to the multiplicative decomposition.

Determinants of the Decreasing Term Structure of Relative Yield Spreads for Taxable and Tax-Exempt Bonds

The empirical finding that the relative yield spread for taxable and tax-exempt bonds decreases across the term structure is usually attributed to tax differentials and/or arbitrage opportunities. Using monthly data, it is found that the decresing term structure of relative yield spreads is determined by the decreasing forward marginal tax rate; increasing default risk premium; increasing tax-timing option premium; and expected rate of inflation