Some inverse and high dimensional problems in econometrics.

Summary A first work considers the identification and estimation of the binary choice model with random coefficients and its asymptotic study. A second work gives minimax lower bounds and presents an adaptive estimator. The third paper considers a binary treatment effect model when the selection model is a binary choice random coefficient model that relaxes the monotonicity assumption. We discuss the identification and estimation of marginals, a generalization of the marginal treatment effect and the joint law of counterfactuals, conditional on the vector of unobservables in the selection equation, as well as the treatment effect parameters. The fourth work deals with the identification of the joint distribution of ex-ante and ex-post earnings in a generalized Roy model with random coefficients and uncertainty. The fifth chapter obtains confidence regions for instrumental variable estimation of a high-dimensional linear model with endogenous regressors. The method is robust to identification, to very many weak instruments, to heteroskedasticity. We study the properties of the method when the structural model is not parsimonious and obtain model selection results. We present several extensions. The last work considers the estimation of confidence intervals for wealth inequality indicators from the 2004 wealth survey where the wealth components are intervals, and from tax data. They take into account the uncertainty on the data, the parameters, and the uncertainty related to sampling and total non-response.