The estimation of censored probit models can result in an estimated correlation between the disturbances approaching [plus]1.0 or -1.0 when most of the observations are selected into the sample and the outcomes are unequally distributed. Outcomes of 0 can induce an estimated correlation of -1.0, and outcomes of 1 can induce an estimated correlation of [plus]1.0. This paper analyzes the population problem, derives corresponding sample conditions, proposes a solution to the problem, and offers a computer program. Copyright 1996 by MIT Press.

This note presents tests of the specification of univariate and bivariate ordered probit. The test is sensitive to deviations from either normality or the exogeneity of the explanatory variables. As an example, the ownership of dogs and televisions, both sources of time-intensive entertainment, is studied. The specification for dogs is not rejected, the specification for televisions is rejected at the 2.0% level, and the specification of both together is rejected at the 1.3% level.

The Black/Scholes model gives the price of an option as a function of the true variance rate of the underlying stock and other parameters. Because the true variance rate is unobservable, an estimate of the variance rate is used in empirical tests. But, because the Black/Scholes formula is non-linear in the variance, option price estimates using an estimated variance are biased, even if the variance estimate itself is unbiased. This paper develops an unbiased estimator of the Black/Scholes formula from a Taylor series expansion of the formula and the properties of the pdf of the estimated variance.

A PROBLEM OF ESTIMATION that has long confronted many economists is the difficulty of estimating the parameters of equations with limited dependent variables on cross-section time-series (i.e., panel) data. While there are widely available packaged computer programs for estimating either (a) cross-section probit and Tobit models or (b) simple permanent-transitory, random-effects panel models with continuous dependent variables, there are no available computationally feasible methods of combining these two models. This is because the likelihood function that arises in such a combined model contains multivariate normal integrals whose evaluation is quite difficult, if not impossible, with conventional approximation methods. There is a widespread feeling among those working in the area that one possible method of evaluation, the use of quadrature techniques, is in principle possible but is in practice computationally too burdensome to consider (e.g., Albright et al. [2, p. 13]; Hausman and Wise [6, p. 12]). In this note we point out that this is true only of standard quadrature techniques such as trapezoidal integration or its improved variants; Gaussian quadrature, on the other hand, is extremely efficient and is well within the bounds of computational feasibility on modern computers. In what follows, we state the nature of the integrals that need to be evaluated, provide a brief exposition of Gaussian quadrature, and provide a numerical illustration of its use in

J. S. Butler, Kathryn H. Anderson, Richard V. Burkhauser, Work and Health after Retirement: A Competing Risks Model with Semiparametric Unobserved Heterogeneity, The Review of Economics and Statistics, Vol. 71, No. 1 (Feb., 1989), pp. 46-53

Measurement error may be an important source of bias in studies using self-reported health indicators to explain work behavior. As a test of measurement error, the tetrachoric correlation coefficient is used to examine the relationship between two alternative measures of arthritis, a standard self-reported measure and a simulated clinical measure. While the two measures are highly correlated, measurement error is found. Regression analysis demonstrates that it varies systematically across different socioeconomic groups. In particular, individuals who are not working tend to report their health incorrectly, perhaps owing to social pressure to justify not having a job. Coauthors are Richard V. Burkhauser, Jean M. Mitchell, and Theodore P. Pincus. Copyright 1987 by MIT Press.