This paper presents a simple estimator of the shape parameter in a Weibull duration model with unobserved heterogeneity. The estimator is consistent and asymptotically normal under mild conditions, and a consistent estimator of the asymptotic variance is available. A Monte Carlo study indicates that the asymptotic distribution of the estimator provides a good approximation to the finite sample distribution. The estimation strategy can be extended to a model with regressors and to a log-logistic model with unobserved heterogeneity. The advantages of the estimator are that it is easy to calculate and that its asymptotic distribution can be derived.

IN NONLINEAR MODELS the power function is often approximated by asymptotic methods. The most common approach is to consider the asymptotic local power function. The local power function is monotonic and it has essentially the same shape as the power function in the classical normal linear regression model. However, the accuracy of the approximation can be poor at nonlocal alternatives. This note examines the exact powers of the Wald test in the case of a one parameter nonlinear regression model with normal errors. The model is based on the exponential response function f( x, O) = exp( Ox). The results show that the exact power function of the Wald statistic can be nonmonotonic. For selected designs the exact powers of the Wald test first increase and then eventually decline as the distance between the hypothesized and the true values of the parameter increases. The exponential structure appears in many nonlinear models; see Gallant (1975, 1987) and Bates and Watts (1988). This suggests that nonmonotonicity of the Wald test is a feature of a wide class of nonlinear models. Indeed, Nelson and Savin (1988) show that it arises in standard logit, probit, and Tobit models as well. The focus here on the nonlinear regression model is for expository convenience. While the existence of nonmonotonic power is not new, the surprising results are that this phenomenon occurs in very simple nonlinear models and that it can be quite severe. In such cases the asymptotic local power approximation provides a very poor guide to the performance of alternative tests.

This paper explores the robustness of the essential economic conclusions of the Roy model of self-selection and income inequality to relaxation of its normality assumptions. A log concave version of the model reproduces most of the main results. Log convex cases offer counterexamples. The authors show that in a Roy economy, random assignment is inegalitarian and Pareto inefficient. They consider nonparametric identifiability of latent skill distributions with cross-section and panel data. The authors' analysis proves nonparametric identifiability for the closely related competing risks model.

EMPIRICAL STUDIES OF TWO SIDED MATCHING have so far concentrated on markets in which certain kinds of market failures were addressed by resorting to centralized, deterministic matching procedures. Loosely speaking, the results of these studies are that those centralized procedures which achieved stable outcomes resolved the market failures, while those markets organized through procedures that yielded unstable outcomes continued to fail.2 So the market failures seem to be associated with instability of the outcomes. But many entry-level labor markets and other two-sided matching situations don't employ centralized matching procedures, and yet aren't observed to experience such failures. So we can conjecture that at least some of these markets may reach stable outcomes by means of decentralized decision making. And decentralized decision making in complex environments presumably introduces some randomness into what matchings are achieved. However, as far as we are aware, no nondeterministic models leading to stable outcomes have yet been studied. The present paper demonstrates that, starting from an arbitrary matching, the process of allowing randomly chosen blocking pairs to match will converge to a stable matching with probability one. (This resolves an open question raised by Knuth (1976), who showed that such a process may cycle.) Furthermore, every stable matching can arise