Estimation of transformation models, generalized bivariate probit models, and Box-Cox partially linear models: Three essays in microeconomics

The dissertation contains three chapters. Respectively, they cover the topics of transformation model with fixed effect, binary response model, and partially linear model. They are all within the scope of semiparametric estimation, but independent of each other.; The first chapter, entitled "Semiparametric Estimation of a Nonstationarity Panel Data transformation Model Under Symmetry"---As is well known, nonstationarity is a common phenomenon in applied research, but in transformation model estimation, most existing semiparametric procedures require the stationarity assumption and usually deal with cross sectional data. In this chapter we consider semiparametric estimation of a nonstationary transformation model with panel data, a semiparametric estimator is proposed under a symmetry condition, allowing for nonstationarity. Under some mild regularity conditions, its consistency and asymptotic normality established. A simulation study illustrates its usefulness by comparing our estimator with the estimator proposed by Abrevaya (1999).; The second chapter concerns a model that is an extension of the standard Bivariate binary choice model, consisting of two binary choice equations, with correlated disturbances. The title is "Estimating a Generalized Correlation Coefficient for a Generalized Bivariate Probit Model"---It is well known, by assuming normally distributed disturbances with possible correlation, the Bivariate probit model is the most widely used model in the family of bivariate choice model. However, economic theory usually does not give any guidance on the distribution of the error terms; any misspecification of the distribution may lead to inconsistent estimates and misleading inference. In this chapter, we consider semiparametric estimation of a generalized correlation coefficient in a generalized bivariate probit model which relaxed the restriction on the error terms. The generalized correlation coefficient provides a simple summary statistic measuring the relationship between the two binary decision processes. Our semiparametric estimation procedure consists of two steps, combining semiparametric estimators for univariate binary choice models with the method of maximum likelihood for the bivariate probit model with nonparametrically generated regressors. The estimator is shown to be consistent and asymptotically normal. We apply our estimator in some numerical studies and one empirical research to show its usefulness.; The third chapter is concerned with the estimation of a transformation model with partially linear structure, the title is "Semiparametric Estimation of the Box-Cox Regression Model With Partially Linear Structure"---The Box-Cox regression model has been commonly used in theoretical and applied econometrics, and it is one of the most important transformation models. However, most of the literature has been restricted to parametric models (e.g., Foster, Tian and Wei (2000)). But purely parametric models may cause inconsistent estimates and seriously misleading inferences when misspecified, while fully nonparametric modeling is associated both with greater robustness and lesser precision. To fill the gap in the literature, in this chapter, we adopt an intermediate strategy which employs semiparametric form ga0,Yi =X'ib0+h Wi+ui where a0 is the transformation parameter, g( a0 ,Y) is the Box-Cox transformation of Y. b is the slope coefficients, h(.) corresponds to the nonlinear part, and the distribution of the error term u is unspecified. We are mainly interested in the estimation of a0 and b0 . Under some regularity conditions, the consistency and asymptotic normality are established for our semiparametric estimator of ( a0,b0 ). A small Monte Carlo study indicates that our estimator performs satisfactorily.