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A1111
Title: Double-lasso estimation of Heckman's sample selection model Authors:  Masayuki Hirukawa - Ryukoku University (Japan) [presenting]
Di Liu - Stata Corp (United States)
Irina Murtazashvili - Drexel University (United States)
Artem Prokhorov - University of Sydney (Australia)
Abstract: Sample selection models that contain high-dimensional covariates in both the main and selection equations are investigated. The particular focus is on estimation and inference of a low-dimensional parameter of interest in the main equation. Taking econometric practices into account, we maintain the assumption of bivariate normality on the error terms in two equations and adopt the two-step estimation approach. A double-selection procedure based on $l_{1}$-penalized regression models is applied in each step. In the first step, we estimate the selection equation by tailoring the double-selection procedure for generalized linear models to the Probit model with many covariates. After obtaining an estimate of the inverse Mills ratio, we proceed to the second step, in which a double-selection procedure for linear regression models with many covariates is employed for the main equation. It is demonstrated that under the sparsity assumption, the estimator of the low-dimensional parameter in the main equation is $n^(1/2)$-consistent and asymptotically normal, where $n$ is the sample size. Monte Carlo simulations confirm attractive properties of the estimator, and an empirical application is considered.