Yoel Haitovsky

Lottomania and other anomalies in the market for lotto

Abstract This research is concerned with the determination of the demand for “lotto” in Israel. While an important focus of our research is upon the effects on the demand for lotto of ticket pricing and jackpot announcements, we also investigate several empirical phenomena that are apparently inconsistent with expected utility theory. These include an effect we call “lottomania” which is induced by rollover, and “prize fatigue” when the jackpot does not increase. Another aberration from expected utility theory is that the underlying odds of winning have no measurable effect on sales.

Bayesian identifiability and misclassification in multinomial data

The authors consider the Bayesian analysis of multinomial data in the presence of misclassi- fication. Misclassification of the multinomial cell entries leads to problems of identifiability which are categorized into two types. The first type, referred to as the permutation-type nonidentifiab ilities, may be handled with constraints that are suggested by the structure of the problem. Problems of identifiab ility of the second type are addressed with informative prior information via Dirichlet distributions. Computations are carried out using a Gibbs sampling algorithm.

The market for housing in Israel

Abstract Using data for 1974–1990 we estimate an econometric model of the Israeli housing market. Novel features of the model include the treatment of the starts–completions nexus, the implications of capital market imperfections for both building contractors and households, and the effects of public sector housing construction on the dynamics of the housing market. We find that the price elasticity of demand for housing is small, as is the supply elasticity. This implies that shocks to the housing market continue to affect housing prices and new building for many years.

Conditional resampling for misclassified multinomial data with applications to sampling inspection

A conditional resampling methodology is proposed for improving the estimators of multinomial classification probabilities in the presence of a fallible classifier. The (unbiased) estimator requires knowledge of the misclassification error rates, which are obtained by resampling from the initial sample and applying an infallible classifier. Tenenbeins “double sampling” methodology resamples randomly from the initial sample. We show that substantial gains in efficiency are obtainable if, instead of simple random resampling, different resampling rates are allowed for the fallibly determined classes in the initial sample. In most situations, this resampling methodology is neither more difficult nor more expensive than the double sampling methodology. A very promising area of application of the proposed methodology is sampling inspection in quality control, where products can either be classified quickly by inspectors or by a more thorough, perhaps destructive, inspection.

Optimal design for double sampling with continuous outcomes

We provide a method for finding the optimal double sampling plan for estimating the mean value of a continuous outcome. It is assumed that the fallible and true outcome data are related by a simple linear regression model. The design parameters are the total sample size, N, and the number of doubly sampled units n. We show that under certain conditions the efficiency gains, relative to standard sampling plans are considerable.

Generalized ridge regression, least squares with stochastic prior information, and Bayesian estimators

The ridge estimator of the usual linear model is generalized by the introduction of an a priori vector r and an associated positive semidefinite matrix S. It is then shown that the generalized ridge estimator can be justified in two ways: (a) by the minimization of the residual sum of squares subject to a constraint on the length, in the metric S, of the vector of differences between r and the estimated linear model coefficients, (b) by incorporating prior knowledge, r playing the role of the vector of means and S proportional to the precision matrix. Both a Bayesian and an Aitken generalized least squares frameworks are used for the latter. The properties of the new estimator are derived and compared to the ordinary least squares estimator. The new method is illustrated with different assumptions on the form of the S matrix.

Double Sampling Designs in Multivariate Linear Models with Missing Variables

We provide a method for finding the optimal double sampling plan for estimating the mean value of a continuous outcome. It is assumed that the fallible and true outcome data are related by a multivariate linear regression model where only some of the explanatory variables are sampled. Conditions under which double sampling is preferred over standard sampling plans are determined. An application of the method to a well-known data set on air pollution is presented.