Econometric inference involving discrete indicator functions

This thesis contains four essays on two topics in econometric theory in which inference involving discrete-valued indicator functions is concerned. On the fi…rst topic, I study structural dynamic discrete choice models in which the indicator represents the outcome of a discrete choice made by a forward looking economic agent as a function of utility and other structural objects. The choice is based on an explicitly postulated structural dynamic discrete Markov decision process. An attempt to infer the underlying structural parameters that generates the observed data runs into identifi…cation problems, particularly under nonparameteric and semiparameteric speci…fications. I analyse these problems in Chapter 1 and present new identifi…cation results. In Chapter 2, I propose a semiparametric estimator for the estimation of a …finite horizon structural dynamic discrete choice model. My estimator is constructed based on simultaneous estimation using the method of sieves. I provide and verify sufficient conditions for my structural model to show that the proposed sieve estimator is consistent. On the second topic, I study the use of discrete-valued indicator functions to represent restrictions of one or more inequalities in underlying econometric parameters. I exploit such representation in designing practically applicable procedures of testing econometric restrictions involving multiple inequalities. The method proposed in this thesis is to chain the several hypothesized inequalities on underlying estimable econometric parameters using discrete indicator functions. I then smooth these functions to overcome the distribution problems of discrete functions of continuous variates. Based on this idea, I propose two new methods of testing multiple inequalities restrictions. The linear normal-based chaining method is proposed in Chapter 3 and the quadratic chi-square based chaining method is provided in Chapter 4 as another alternative. Asymptotic properties of both methods are studied and Monte Carlo simulations are also carried out to assess their fi…nite sample performance.