Challenging Cassandra: Household and Per Capita Household Income Distribution in the October Household Surveys 1995-1999, Income and Expenditure Surveys 1995 & 2000, and the Labour Force Survey 2000

This paper examines household income inequality in the South African October Household Survey datasets between 1995 and 1999, the Labour Force Survey 2000, and the Income and Expenditure Surveys 1995 and 2000. The paper reflects both on changing patterns of income inequality in South Africa, and on the quality and comparability of the data employed. We employ several measures of income inequality, employing nominal income and expenditure data from South Africa over the 1995-2000 period. Results prove sensitive to the choice of welfare measure. Furthermore, results from income data and expenditure data provide contrasting results. On self-reported income data, our findings are that inequality measures increased over the 1995 - 2000 time period. While we do not attach much credence to the evidence for reasons attaching to data quality, there is nevertheless evidence suggesting that the general increase in inequality for the African race group also hides a decrease in inequality for the bottom 1/3 of the income distribution, and (more unambiguously) a widening of inequality for the middle 1/3 of the income distribution for Africans. There is also some evidence of a narrowing inequality amongst rich households for the population as a whole. This suggests that there is at least some evidence consistent with a successful redistribution of income from richest to poorest households, though this has not yet reversed the high aggregate level of inequality in South Africa. Evidence from inequality measures based on expenditure data reverse the findings based on self-reported income. Where there is evidence of an increase in inequality, in most instances this proves to be statistically insignificant. On some measures African as well as total population inequality has declined significantly, and for a number of racial groups inequality has remained unchanged. The central conclusion of the paper is therefore that there is much contradictory evidence that emerges from household level data on income inequality - suggesting that the choice of data set is non-trivial in drawing inference on income inequality in South Africa

Measuring Inequality Using Censored Data: A Multiple Imputation Approach

To measure income inequality with right censored (topcoded) data, we propose multiple imputation for censored observations using draws from Generalized Beta of the Second Kind distributions to provide partially synthetic datasets analyzed using complete data methods. Estimation and inference uses Reiter's (Survey Methodology 2003) formulae. Using Current Population Survey (CPS) internal data, we find few statistically significant differences in income inequality for pairs of years between 1995 and 2004. We also show that using CPS public use data with cell mean imputations may lead to incorrect inferences about inequality differences. Multiply-imputed public use data provide an intermediate solution.Income inequality, topcoding, partially synthetic data, CPS, current population survey, generalized beta of the second kind distribution

Measuring Inequality Using Censored Data: A Multiple Imputation Approach

To measure income inequality with right censored (topcoded) data, we propose multiple imputation for censored observations using draws from Generalized Beta of the Second Kind distributions to provide partially synthetic datasets analyzed using complete data methods. Estimation and inference uses Reiter’s (Survey Methodology 2003) formulae. Using Current Population Survey (CPS) internal data, we find few statistically significant differences in income inequality for pairs of years between 1995 and 2004. We also show that using CPS public use data with cell mean imputations may lead to incorrect inferences about inequality differences. Multiply-imputed public use data provide an intermediate solution.income inequality, topcoding, partially synthetic data, CPS, Current Population Survey, Generalized Beta of the Second Kind distribution

Measuring inequality using Censored data: A multiple imputation approach

To measure income inequality with right censored (topcoded) data, we propose multiple imputation for censored observations using draws from Generalized Beta of the Second Kind distributions to provide partially synthetic datasets analyzed using complete data methods. Estimation and inference uses Reiter’s (Survey Methodology 2003) formulae. Using Current Population Survey (CPS) internal data, we find few statistically significant differences in income inequality for pairs of years between 1995 and 2004. We also show that using CPS public use data with cell mean imputations may lead to incorrect inferences about inequality differences. Multiply-imputed public use data provide an intermediate solution.Income Inequality, Topcoding, Partially Synthetic Data, CPS, Current Population Survey, Generalized Beta of the Second Kind distribution

Inference on Income Distributions

This paper attempts to provide a synthetic view of varied techniques available for per- forming inference on income distributions. Two main approaches can be distinguished: one in which the object of interest is some index of income inequality or poverty, the other based on notions of stochastic dominance. From the statistical point of view, many techniques are common to both approaches, although of course some are specific to one of them. I assume throughout that inference about population quantities is to be based on a sample or samples, and, formally, all randomness is due to that of the sampling process. Inference can be either asymptotic or bootstrap-based. In principle, the bootstrap is an ideal tool, since in this paper I ignore issues of complex sampling schemes, and suppose that observations are IID. However both bootstrap inference, and, to a considerably greater extent, asymptotic inference can fall foul of difficulties associated with the heavy right-hand tails observed with many income distributions. I mention some recent attempts to circumvent these difficulties.Income distribution; delta method; asymptotic inference; bootstrap; influence function; empirical process

Estimating Lorenz Curves Using a Dirichlet Distribution

The Lorenz curve relates the cumulative proportion of income to the cumulative proportion of population. When a particular functional form of the Lorenz curve is specified it is typically estimated by linear or nonlinear least squares assuming that the error terms are independently and normally distributed. Observations on cumulative proportions are clearly neither independent nor normally distributed. This paper proposes and applies a new methodology which recognizes the cumulative proportional nature of the Lorenz curve data by assuming that the proportion of income is distributed as a Dirichlet distribution. Five Lorenz-curve specifications were used to demonstrate the technique. Once a likelihood function and the posterior probability density function for each specification are derived we can use maximum likelihood or Bayesian estimation to estimate the parameters. Maximum likelihood estimates and Bayesian posterior probability density functions for the Gini coefficient are also obtained for each Lorenz-curve specification.

Taste Asymmetries and Trade Patterns

We study trade patterns in a pure exchange economy where preferences are symmetric up to taste intensity parameters. In a 2-person, 2-good endowment economy, then all endowments in a particular Edgeworth box rectangle require trading out of that rectangle. Under strictly quasi-concave preferences, trade will occur away from a larger area of initial endowments. The identified area is larger still when preferences are homothetic and identical up to taste intensity parameters. Implications for the factor price equalization theorem are explored.

Consumption Inequality and Intra-Household Allocations

The current literature on consumption inequality treats all adults within the household equally, making the implicit assumption that all consumption inequality is between, not within, households. However, increased marital sorting on earnings and the subsequent rise in the share of women's income in the household may have important implications for consumption inequality measured at the individual level. We use an extension of the collective framework of Chiappori to estimate a rule for assigning resources to individual household members. We then construct a measure of individual level inequality by looking at implied changes in intra-household allocations and explore the implications of our framework for the measurement of individual level, versus household level, consumption inequality. Our analysis, which is based on households comprising one or two adults, suggests that the conventional approach of ignoring intra-household allocations underestimates the level of cross-sectional consumption inequality by 30% and overstates the trend by two-thirds. Our findings also indicate that increases in marital sorting on wages and hours worked can simultaneously explain virtually all of the decline in within household inequality and a substantial fraction of the rise in between household inequality in the UK since the 1970s.Collective Model, Consumption Inequality, Marital Sorting