This paper describes a semiparametric estimator for binary response models in which there may be arbitrary heteroskedasticity of unknown form. The estimator is obtained by maximizing a smoothed version of the objective function of C. Manski's maximum score estimator. The smoothing procedure is similar to that used in kernel nonparametric density estimation. The resulting estimator's rate of convergence in probability is the fastest possible under the assumptions that are made. The centered, normalized estimator is asymptotically normally distributed. Methods are given for consistently estimating the parameters of the limiting distribution and for selecting the bandwidth required by the smoothing procedure. Copyright 1992 by The Econometric Society.
In this paper, it is shown that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term. This identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term. The estimator is shown to be strongly consistent, and a two step procedure for its calculation is developed. The paper also includes examples of economic models that satisfy the conditions that are necessary to apply the results.
This paper introduces a semiparametric estimation method for Polychotomous Choice models. The method does not require a parametric structure for the systematic subutility of observable exogenous variables. The distribution of the random terms is assumed to be known up to a finite-dimensional parameter vector. In contrast, previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified. The systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory. The estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent. A computational technique to calculate the estimators is developed. Copyright 1991 by The Econometric Society.
[Differing opinions about the specification of econometric relationships often lead to a situation in which there are competing non-nested models. This paper is concerned with the problem of testing such models. It is first assumed that tests are based upon instrumental variable estimates (so that the models can be alternative versions of an equation in a system). The tests so derived are then specialized to the case in which ordinary least squares is an appropriate estimator.]
This paper examines some implications of the observation that the same Lagrange multiplier test is sometimes appropriate for quite different alternative hypotheses. A characterization of the class of such alternatives is developed which suggests a simple approach to testing for misspecification, and the consequences for finite sample power properties are examined by Monte Carlo experiments.
This paper builds a formal theory of consumer behavior under imperfect information when goods are described by multiple characteristics which vary in their degree of "observability." An optimal strategy for the consumer is shown to exist. In general, this strategy is shown to involve both inspection (sampling to observe general characteristics of goods) and evaluation (consumption of goods to observe specific characteristics). Comparative statics of the optimal strategy are also analyzed.
[There has been increasing concern recently over the use of the simple first order Markov form to model error autocorrelation in regression analysis. The consequence of misspecifying the error model will be especially serious when the regressors include lagged values of the dependent variable. The purpose of this paper is to develop Lagrange multiplier tests of the assumed error model against specified ARMA alternatives. It is shown that all of the tests can be regarded as asymptotic tests of the significance of a coefficient of determination, and a table is provided which gives details of two general tests and several special cases.]