No abstract

We discuss the semi-nonparametric approach of Gallant and Nychka (1987, Econometrica 55: 363-390), the semiparametric maximum likelihood approach of Klein and Spady (1993, Econometrica 61: 387-421), and a set of new Stata commands for semiparametric estimation of three binary-choice models. The first is a univariate model, while the second and the third are bivariate models without and with sample selection, respectively. The proposed estimators are √ n consistent and asymptotically normal for the model parameters of interest under weak assumptions on the distribution of the underlying error terms. Our Monte Carlo simulations suggest that the efficiency losses of the semi-nonparametric and the semiparametric maximum likelihood estimators relative to a maximum likelihood correctly specified estimator of a parametric probit are rather small. On the other hand, a comparison of these estimators in non-Gaussian designs suggests that semi-nonparametric and semiparametric maximum likelihood estimators substantially dominate the parametric probit maximum likelihood estimator.

Abstract.Model averaging has become a popular method of estimation, following increasing evidence that model selection and estimation should be treated as one joint procedure. Weightedaverage least squares (WALS) is a recent model-average approach, which takes an intermediate position between frequentist and Bayesian methods, allows a credible treatment of ignorance, and is extremely fast to compute. We review the theory of WALS and discuss extensions and applications.

We introduce two new Stata commands for the estimation of an ordered response model with sample selection. The opsel command uses a standard maximum-likelihood approach to fit a parametric specification of the model where errors are assumed to follow a bivariate Gaussian distribution. The snpopsel command uses the semi-nonparametric approach of Gallant and Nychka (1987, Econometrica 55: 363-390) to fit a semiparametric specification of the model where the bivariate density function of the errors is approximated by a Hermite polynomial expansion. The snpopsel command extends the set of Stata routines for semi-nonparametric estimation of discrete response models. Compared to the other semi-nonparametric estimators, our routine is relatively faster because it is programmed in Mata. In addition, we provide new postestimation routines to compute linear predictions, predicted probabilities, and marginal effects. These improvements are also extended to the set of semi-nonparametric Stata commands originally written by Stewart (2004,

In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares estimator developed by Magnus, Powell, and Prüfer (2010, Journal of Econometrics 154: 139-153). Unlike standard pretest estimators that are based on some preliminary diagnostic test, these model-averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Special emphasis is given to several practical issues that users are likely to face in applied work: equivariance to certain transformations of the explanatory variables, stability, accuracy, computing speed, and out-of-memory problems. Performances of our bma and wals commands are illustrated using simulated data and empirical applications from the literature on model-averaging estimation.