Identification and estimation of microeconometric models

This thesis studies the identification of discrete choice models, the use of sampling schemes in the finite sample analysis of instrumental variables (IV) estimators, and the estimation of panel data with cross-sectional dependence, which are at the forefront of modern econometrics. These topics, which are extremely closely linked, correspond to three critical steps in econometric research. In fact, the identification analysis is always the primary concern when determining the conditions under which the population of interest can logically be deducted from the information contained in the economic data before estimation procedures are proposed for conducting inference, whilst sampling schemes need to be considered when designing numerical experiments which will ultimately support analytical results. Chapter 1 provides an introduction to the background of identification, sampling schemes in IV estimation and panel data models with factor structures. In addition, we also outline the structure of this thesis. Chapter 2 then reviews and summarizes the existing literature in relevant areas. Chapter 3 revisits the identification problem of the binary response model studied by Chamberlain (2010) from a partial identification perspective. When the support of the predictor variables is bounded, Chamberlain (2010) showed that point identification of this model fails if the distribution of the disturbance is not logistic. Under his setup, we calculate the identified sets for some commonly used non-logistic distributions, adopting a constructive algorithm inspired by Honoré and Tamer (2006). These calculations suggest that Chamberlain's (2010) model restricts the identified sets to be very small in these cases, meaning that the failure of point identification of this model may not be important in practice. Moreover, we find that the extent of the identified sets may be determined by the configuration of the support of the predictor variables and the distribution function form of the disturbance. In particular, we examine the effects of distribution forms of the disturbance on the magnitude of the identified sets by studying the relevant convex hulls defined by Chamberlain (2010) from a geometric point of view. The exact distributions of the classical IV estimators have traditionally been studied based on a sampling scheme in which exogenous variables are kept fixed (e.g., Phillips (1983), and references therein). However, Kiviet and Niemczyk (2007), Kiviet and Niemczyk (2012) and Kiviet (2013) suggested that the existing results indicating disconcerting properties (e.g. bimodality) of the exact IV distributions may be fundamentally influenced by the use of this sampling scheme for the exogenous variables. In Chapter 4, we investigate their claims further in finite samples, focusing on the OLS, two-stage least squares (TSLS) and limited information maximum likelihood (LIML) estimators of the interest parameters in a structural equation model. The exact distributions of these estimators, conditional on the exogenous variables, are compared with their marginal distributions, and evidence is presented to show that the marginal and conditional distributions display the same properties, including bimodality, even for small sample sizes. Thus, the exact IV distributions exhibit the same finite sample properties under alternative sampling schemes. Chapter 5 considers a structural equations model with endogeneity (c.f. Schmidt (1976)) and cross-sectional dependence captured by factor structures. We consider a short term microeconomic panel where T is fixed, with the cross-sectional dependence being captured by various heterogeneous factor structures. The properties of the IV estimators, especially TSLS and LIML, are then investigated in this context. We show that the classical TSLS and LIML estimators are not consistent, due to cross-sectional dependence, and analyze potential remedies to regain this consistency. The transformation suggested by Peng (2013) proves to be an efficient candidate for dealing with cross-sectional dependence, in terms of various factor structures examined in this chapter.