"Semiparametric Estimation and Inference in Partially Identified Econometric Models"

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The econometrics literature has made substantial progress on estimation and inference methods for economic models, in which the parameter of interest is identified as a set. Yet, little is known about their properties when such partially identified models contain both finite and infinite dimensional parameters. Semiparametric models have been used widely in various empirical studies to make predictions and to conduct policy evaluations. They combine tractable parametric specification on key features of an economic model with flexible nonparametric restrictions on the rest. The main objective of this project is to expand the scope of semiparametric inference to major classes of partially identified econometric models. A particular focus will be placed on the theory of semiparametric efficiency. Recently, Kaido and Santos (2011) proposed an asymptotic efficiency concept for an important subset of partially identified models: the class of models defined by convex moment inequalities. The proposed research aims to expand the scope of this framework by studying other major classes of semiparametric partially identified models. Specifically two topics are considered.The first topic is on semiparametric regression models with an interval-censored variable. Interval censoring occurs frequently in micro-level data. The goal is to estimate a parameter that captures the marginal impacts of covariates on an interval-valued outcome variable without assuming any specific functional form of the regression function. The weighted average derivative of the regression function is one of such parameters. Although this parameter is not point identified in the presence of interval censoring, this approach may characterize its identified set. The researchers plan to study asymptotically efficient estimation of this set. The proposed efficient set-valued estimator will be useful for conducting empirical studies with survey data such as the Health and Retirement Study (HRS).The second topic studies efficient estimation of parameters indexed by a nuisance parameter. Many econometric models contain such parameters. Entry game models, for example, that are used to study various industries, contain structural parameters that could be fully recovered when the equilibrium selection rule were known. By varying the selection rule, the identified set can be equivalently viewed as a function of it. This project aims to to extend the efficiency concept developed in Kaido and Santos (2011) to study efficient estimation of this type of identified sets. Successful developments of inference methods for this class of models will be useful for conducting policy evaluations efficiently while allowing partial identification and flexible semiparametric specification.