Essays on identification and semiparametric econometrics

Abstract

This dissertation is a collection of three independent essays in theoretical and applied econometrics. The first chapter analyzes dynamic games with continuous states and controls. There are two main contributions. First, we give conditions under which the payoff function is nonparametrically identified by the observed distribution of states and controls. The identification conditions are fairly general and can be expected to hold in many potential applications. The key identifying restrictions include that one of the partial derivatives of the payoff function is known and that there is some component of the state space that enters the policy function, but not the payoff function directly. The second contribution of the first chapter is to propose a two-step semiparametric estimator for the model. In the first step the transition densities and policy function are estimated nonparametrically. In the second step, the parameters of the payoff function are estimated from the optimality conditions of the model. We give high-level conditions on the first step nonparametric estimates for the parameter estimates to be consistent and parameters to be v/fn-asymptotically normal. Finally, we show that a kernel based estimator satisfies these conditions. The second chapter, which is coauthored with Liran Einav and Amy Finkelstein, analyzes the welfare cost of adverse selection in the U.K. annuity market. We develop a model of annuity contract choice and estimate it using data from the U.K. annuity market. The model allows for private information about mortality risk as well as heterogeneity in preferences over different contract options. We focus on the choice of length of guarantee among individuals who are required to buy annuities. The results suggest that asymmetric information along the guarantee margin reduces welfare relative to a first best symmetric information benchmark by about 2 percent of annuitized wealth. We also find that by requiring that individuals choose the longest guarantee period allowed, mandates could achieve the first-best allocation. The third chapter develops a test for the exogeneity assumptions of classical factor models based on the fixed interactive effects estimator of Bai (2005). The exact form of the test is given for simple linear models. Simulations are used to asses the test's performance. The application of the test to more complicated models is also considered. The test is applied to a model of education as an example.