Paul D. Thistle

Asymptotically Distribution-Free Statistical Inference for Generalized Lorenz Curves

This paper provides asymtotically distribution-free statistical inference procedures for generalized Lorenz curves. Given appropriate measures of income and the income recipient unit are chosen appropriately, the tests allow consensually valid statements regarding social welfare to be made from sample data on the basis of sound inferential procedures. More generally, the results presented here can be applied to test for second degree stochastic dominance. Copyright 1989 by MIT Press.

Time Series, Homicide, and the Deterrent Effect of Capital Punishment*

Erlich [5; 6] presents regression results showing that the U.S. time-series data supports the deterrent effect of capital punishment (the deterrence hypothesis). Other researchers [9; 10; 16] criticize Erlichs findings on a number of grounds-including the possibility of simultaneity bias, and the sensitivity of the results to the choice of sample period, control variables, and functional form. Layson [11] extends Erlichs U.S. sample to the 1936-1977 period and, taking account of these criticisms, concludes that the U.S. time-series evidence provides robust support for the deterrence hypothesis. This paper contributes to the debate on the deterrence hypothesis by analyzing the time-series properties of the homicide rate; the U.S. homicide rate is a nonstationary time series. It is well known that the use of nonstationary series in regression analysis leads to inconsistent coefficient estimators, biases estimators of coefficient standard errors toward zero, and invalidates standard statistical-inference procedures [2; 8; 13; 14; 15; 17; 18]. Nonstationarity may be due to a linear trend (trend nonstationarity) or may be a property of the underlying stochastic process (difference nonstationarity). If the time series is difference nonstationary then use of a linear trend does not correct these problems and may be misleading [13; 14; 15]. We explicitly test for the source of the nonstationarity of the homicide rate, difference or trend nonstationarity, using the tests recently developed by Dickey and Fuller [3; 4; 7]. We find that the homicide rate is difference nonstationary. This implies that the data must be first differenced to achieve stationarity, and that use of a linear trend (as in [5; 6; 9; 10; 11; 16]) is inappropriate. The regression results obtained using the first-differenced, stationary data do not provide robust support for a deterrence effect of capital punishment.

The Formation of Mutual Insurers in Markets with Adverse Selection

The size distribution of mutual property-liability insurers has a larger proportion of relatively small companies than the size distribution of stock property-liability insurers. Small mutuals are unlikely to offer risk-sharing advantages over conventional insurance, so these firms must offer their members other advantages. This article develops a theoretical model showing that these mutuals may offer advantages over conventional insurance in addressing problems of adverse selection. When adverse selection exists, conventional insurers may coexist with small mutuals. Small mutuals may be strictly preferred by low-risk individuals. The size of the mutuals is limited by asymmetric information problems.

Negative Moments, Risk Aversion, and Stochastic Dominance

A simple moment-ordering condition is shown to be necessary for stochastic dominance. Closely related results on generalizations of the geometric and harmonic means are also provided. An ordering of the moment-generating functions is shown to be necessary and sufficient for stochastic dominance. The results have a straightforward and useful interpretation in terms of constant relative and absolute risk aversion utility functions. These results are used to provide necessary and sufficient conditions for optimality of distributions on an important class of utility functions.

Explaining Interstate Variation in Income Inequality

This paper investigates interstate variation in income inequality. By avoiding inequality indices and focusing directly on the Lorenz curve, the authors provide a more general explanation of the differences in inequality. They find that mean family income, the standard deviation of years of schooling, per capita educational expenditure, and property income are robust predictors of inequality. Of particular interest is their finding that, ceteris paribus, higher per capita education expenditures tend to be associated with states that have income inequality which is greater than the U.S. average. Copyright 1992 by MIT Press.

Rank dominance and international comparisons of income distributions

Abstract The rank dominance criterion for comparing income distributions assumes the Pareto principle, anonymity, and population size invariance. This paper applies rank dominance to compare international income distributions. Empirically, rank dominance is a powerful tool for ordering income distributions. Our results suggest that much of the power of generalized Lorenz dominance is due to efficiency preference, and equity preference adds only marginally to the ability to order income distributions.

The Property/Liability Insurance Cycle: A Comparison of Alternative Models

The objective of this paper is to compare alternative models of insurance pricing as theories of the property-liability underwriting cycle. The existing literature has focused on comparing two models, the financial pricing and capacity constraint models. However, these are not the only relevant models. We show that six alternative models imply the same general form of the pricing equation. We apply the model to data on stock property-liability insurers for the period 1935–1997. We find that the actuarial model and the capacity constraint hypothesis are the only theoretical models that are consistent with the data.

Rates and Race: An Analysis of Racial Disparities in Mortgage Rates

Abstract We use a model based on the 1991–2001 American Housing Survey to determine whether differences in mortgage rates among whites, blacks, and Hispanics are due to differences in the property and loan characteristics of the borrowers themselves or to racial differences in how those characteristics are priced into rates. We separate loans into major market categories and present decompositions to assess the differences and distinguish between them. Very little information on mortgage pricing has been generally available to researchers, and the literature that discusses what information there is has not used a scheme that allows rate differences to be classified by characteristics and pricing. We find that significant differentials are more likely in the conventional mortgage market. The largest occur among blacks, who pay a much higher annual percentage rate than whites for both purchases and refinancing. For government‐insured loans, Hispanics do slightly better than whites.

Convergence and Divergence of Regional Income Distributions and Welfare

Regional income distributions are analyzed and tested for convergence and divergence in the 1970s. The methodology is the same as that recently used to show the almost complete convergence of the South and non-South. This paper disaggregates the non-South into major regions consisting of the West, Midwest, and Northeast. Tests for rank dominance reveal surprising results. Income distributions in the major regions of the non-South were equivalent in 1969, and the South was uniformly dominated. Fundamental changes in the 1970s resulted in the West rank dominating the Midwest, which dominated the South, which in turn dominated the Northeast. Copyright 1994 by MIT Press.

The Average Tax Burden and the Welfare Implications of Global Tax Progressivity

The measurement of global tax progressivity has been extensively debated over the last decade. We find that the debate stems from a failure to fully recognize the role of the average tax burden. We demonstrate that, once the effect of the average tax burden is controlled for, the two major approaches to global progressivity measurement, which have been long thought to be fundamentally different, must rank tax systems the same way. We show that valid welfare inferences can be drawn from global progressivity comparisons only under these same conditions.