Essays in identification and estimation of duration models and varying coefficient models

Chapter 1 studies the identification of a preemption game where the timing decisions are expressed as mixed hitting time (MHT). It considers a preemption game with private information, where agents choose optimal time to invest, with payoffs driven by Geometric Brownian Motion. The game delivers the optimal timing of investment based on a threshold rule that depends on both the observed covariates and the unobserved heterogeneity. The timing decision rules specify durations before the irreversible investment as the first time the Geometric Brownian Motion hits a heterogeneous threshold, which fits the MHT framework. As a result, identification strategies for MHT can be used for a first stage identification analysis of the model primitives. Estimation results are performed in a Monte Carlo simulation study. Chapter 2 studies the identification of a real options game similar to chapter 1, but with complete information. Because of the multiple equilibria problems associated with the complete information game, the point identification is only achieved for a duopoly case. This simple complete information game delivers two possible different kinds of equilibria, and we can separate the parameter space of unobserved investment cost accordingly for different equilibria. We also show the non-identification result for a three-player case in appendix B.4. Chapter 3 studies the estimation of a varying coefficient model without a complete data set. We use a nearest-matching method to combine two incomplete samples to get a complete data set. We demonstrate that the simple local linear estimator of the varying coefficient model using the combined sample is inconsistent and in general the convergence rate is slower than the parametric rate to its probability limit. We propose the biascorrected estimator and investigate the asymptotic properties. In particular, the bias-corrected estimator attains the parametric convergence rate if the number of matching variables is one. Monte Carlo simulation results are consistent with our findings.