Summary
Bayesian non‐parametric estimates of Australian distributions of mental health scores are obtained to assess how the mental health status of the population has changed over time, and to ...compare the mental health status of female/male and Aboriginal/non‐Aboriginal population subgroups. First‐order and second‐order stochastic dominance are used to compare distributions, with results presented in terms of the posterior probability of dominance and the posterior probability of no dominance. If a criterion for dominance is satisfied, then, in terms of that criterion, the mental health status of the dominant population is superior to that of the dominated population. If neither distribution is dominant, then the mental health status of neither population is superior in the same sense. Our results suggest mental health has deteriorated in recent years, that males' mental health status is better than that of females, and that non‐Aboriginal health status is better than that of the Aboriginal population.
Income and Health Concentration in Australia Chotikapanich, Duangkamon; Creedy, John; Hopkins, Sandra
The Economic record,
September 2003, Letnik:
79, Številka:
246
Journal Article
Recenzirano
This paper measures the concentration of ill‐health among income groups in Australia using health survey data from 1989–90 (Australian Bureau of Statistics 1991) and 1995 (Australian Bureau of ...Statistics 1997), which contain responses on self‐assessed health status and gross personal income. The technique of direct standardisation is used to control for the influence on health status of gender and age. Comparisons of the concentration of ill‐health over time and between males and females and persons living in rural and urban areas are reported. For both surveys and all groups, we find that ill‐health is concentrated among lower income groups. Concentration measures of ill‐health are higher (in absolute terms) for men than for women. In all categories apart from women, the concentration measures fell between 1989–90 and 1995 surveys.
As indicators of social welfare, the incidence of inequality and poverty is of ongoing concern to policy makers and researchers alike. Of particular interest are the changes in inequality and poverty ...over time, which are typically assessed through the estimation of income distributions. From this, income inequality and poverty measures, along with their differences and standard errors, can be derived and compared. With panel data becoming more frequently used to make such comparisons, traditional methods which treat income distributions from different years independently and estimate them on a univariate basis, fail to capture the dependence inherent in a sample taken from a panel study. Consequently, parameter estimates are likely to be less efficient, and the standard errors for between-year differences in various inequality and poverty measures will be incorrect. This paper addresses the issue of sample dependence by suggesting a number of bivariate distributions, with Singh–Maddala or Dagum marginals, for a partially dependent sample of household income for two years. Specifically, the distributions considered are the bivariate Singh–Maddala distribution, proposed by Takahasi (1965), and bivariate distributions belonging to the copula class of multivariate distributions, which are an increasingly popular approach to modelling joint distributions. Each bivariate income distribution is estimated via full information maximum likelihood using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey for 2001 and 2005. Parameter estimates for each bivariate income distribution are used to obtain values for mean income and modal income, the Gini inequality coefficient and the headcount ratio poverty measure, along with their differences, enabling the assessment of changes in such measures over time. In addition, the standard errors of each summary measure and their differences, which are of particular interest in this analysis, are calculated using the delta method.
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 estimation techniques that have good properties when the error terms are independently and normally distributed. Observations on cumulative proportions are clearly neither independent nor normally distributed. This article proposes and applies a new methodology that recognizes the cumulative proportional nature of the Lorenz curve data by assuming that the income proportions are distributed as a Dirichlet distribution. Five Lorenz curve specifications are used to demonstrate the technique. Maximum likelihood estimates under the Dirichlet distribution assumption provide better fitting Lorenz curves than nonlinear least squares and another estimation technique that has appeared in the literature.
The conventional formula for estimating the extended Gini coefficient is a covariance formula provided by Lerman and Yitzhaki (1989). We suggest an alternative estimator, obtained by approximating ...the Lorenz curve by a series of linear segments. In a Monte Carlo experiment designed to assess the relative bias and efficiency of the two estimators, we find that, when using grouped data with 20 or fewer groups, our new estimator has less bias and lower mean squared error than the covariance estimator. When individual observations are used, or the number of groups is 30 or more, there is little or no difference in the performance of the two estimators.
This paper examines Bayesian methods of examining posterior distributions of inequality, concentration, tax progressivity and social welfare measures. Use is made of an explicit income distribution ...assumption and two alternative assumptions regarding the distribution of pre-tax mean incomes within each income group. The methods are applied to a simulated distribution of individual incomes and tax payments. It is possible to identify a minimum acceptable number of income classes to be used. The results suggest support for the use of group means in practical applications, particularly where large sample sizes are available.
The purpose of the present paper is to extend Flatau and Wood in five ways: 1. The methodological framework is expanded by taking into account post-housing equity conversion housing costs for owner ...occupiers. 2. The rates of poverty are estimated for the Australian population using survey data rather than simulating the impact of using the net comprehensive income measure for selected income units in a controlled environment. 3. The net comprehensive income measure to income inequality measurement is applied. 4. The analysis is extended beyond the simple head-count poverty measure into a broader range of income inequality and poverty measures - namely, the Foster poverty measures and the Gini inequality measure. 5. A series of formal hypothesis tests is conducted on whether there is a statistically significant difference in the rate of poverty and the degree of income inequality when a net comprehensive income measure is used in place of a cash disposable income measure. The key question posed in this context is whether the net comprehensive measure of income results in a significantly different picture of income inequality and poverty for Australia.
Beal’s (1995) method of estimating the value of Carnarvon Gorge for recreational use is re‐examined. When an inconsistency in her estimation procedure is corrected, the estimated value of Carnarvon ...Gorge for camping is found to be six times higher. The sensitivity of the estimate to the choice of functional form is examined, and standard errors and interval estimates for consumer surplus are provided. Comments are made about functional form choice and prediction in log‐log models.
PDF
