Essays on the identification and estimation of econometric models

This dissertation includes three essays on the identification and estimation of econometric models.The first essay presents a novel approach to inference in models where the partially identified parameter is defined by a set of conditional moment inequalities with continuous covariates. This class of models covers many economic applications, including treatment response models and regression with missing or interval outcome data. I propose inference procedure that is based on the distance between the set of conditional moment functions and the cone of non-positive (or non-negative) functions. If a researcher is reluctant to impose any assumptions about the shape of conditional moment functions except certain smoothness conditions, I offer a method that relies on bootstrapping of the simultaneous lower confidence bands for nonparametric estimators of conditional moments. In general, this inference procedure may lead to a conservative coverage. However, I show that under a particular set of shape restrictions on conditional moment functions one can construct confidence sets based on a Gaussian asymptotic approximation that is relatively easy to implement and attains accurate coverage in small samples. I conduct Monte Carlo simulations to illustrate both procedures.The second essay extends the two-step estimator of the additive nonparametric model with a known link function proposed in Horowitz and Mammen (2004) to cover the additive models with multiplicative interaction terms. I find the same rate of convergence (n2/5) for estimators of both the univariate additive part and the multiplicative interaction part. I show that this convergence rate does not depend on the dimension of the vector of covariates.The third essay proposes a moments-based approach to the identification and estimation of panel data quantile regression (QR) models with fixed effects when the number of time periods T is small. When the covariates have discrete support, the QR model is identified if fixed effects have pure location shift effect. In this case I propose an estimator that is based on the sequence of certain moments estimators. Finally, I show that if the covariates are continuously distributed, then the QR model is identified even when fixed effects are allowed to be different for different quantiles.