Essays on Nonparametric Identication

In Chapter 1, I extend the techniques in Li and Vuong (1998), Schennach (2004a), and Bonhomme and Robin (2010) to identify nonparametric distributions of unobserved variables in a system of linear equations with more unobserved variables than outcome variables and with subsets of statistically dependent unobserved variables. I construct estimators of the distributions of unobserved variables and derive their uniform convergence rates. In Chapter 2, I develop a method for identification and estimation of coefficients in a linear regression model with measurement error in all the variables. The method is extended to identification in a system of linear equations in which only some of the coefficients on the unobserved variables are known. The estimator uses an assumption that is testable in the data and is in the class of Extremum estimators. The asymptotic distribution of the estimator is derived. In Chapter 3, I identify the nonparametric joint distribution of random coefficients in a linear panel data regression model. The distributions of the coefficients can depend on covariates, coefficients can be statistically dependent or equal in distribution, and there can be more coefficients than the fixed number of time periods. I construct estimators from the identification proofs. In finite sample simulations all the estimators have tight confidence bands around their theoretical counterparts