| This thesis is concerned with the estimation of a particular class of econometric models, which we call incomplete econometric models. The defining characteristic of these models is that they do not necessarily predict a unique value for the dependent variable, given the explanatory variables. In the first chapter, we study a bivariate simultaneous discrete response model. This model describes the equilibria of a two person discrete game. Previous work has avoided the problem of multiple equilibria inherent in this model. We analyze it in the presence of multiple equilibria. We show that the model contains enough information to allow us to identify the unknown values of parameters of interest and to obtain a well-defined, consistent, and root-n normal estimator of those parameters. Moreover, by exploiting the presence of multiplicity, we are able to obtain a sharper estimator than the existing methods do. In the second chapter, we examine another example of an incomplete econometric model, a binary regression where the only information we know about the value of a particular regressor is that it falls within a particular interval. Using weak assumptions on the distribution of the unobserved random terms, we propose a procedure to estimate the model. We then show that the estimator is consistent. To illustrate our findings, we present an empirical case-study using the Health and Retirement Survey. In the third chapter, we estimate nonlinear models when one of the explanatory variables is measured with error. Previous studies have assumed the existence of double measurements or of validation data sets. Instead, we use weak distributional assumptions to identify the error process. Using deconvolution methods, we obtain a consistent estimator of the density of the unknown true regressor. Then, we obtain a root-n consistent estimator of the unknown parameters of the model. |
