Nonparametric estimation in case of endogenous selection

Abstract

This paper addresses the problem of estimation of a nonparametric regression function from selectively observed data when selection is endogenous. Our approach relies on independence between covariates and selection conditionally on potential outcomes. Endogeneity of regressors is also allowed for. In both cases, consistent two-step estimation procedures are proposed and their rates of convergence are derived. Also pointwise asymptotic distribution of the estimators is established. In addition, we propose a nonparametric specification test to check the validity of our independence assumption. Finite sample properties are illustrated in a Monte Carlo simulation study and an empirical illustration.

Early child development and parents' labor supply

“…Parental selection into the labor market is driven by their potential income given the development status of their child and parental background characteristics. We therefore follow Breunig et al (2018) and d'Haultfoeuille (2010) and assume that there exists a variable H , which is independent of the parental reservation wage once we control for our covariates X , our early child development index C , and potential income Y . More formally, we assume…”

“…Here, we need to assume that the handedness of a child is not correlated with unobserved determinants of parental hours worked. In our empirical strategy, we also account for the potential endogenous labor force participation decision of parents applying a novel approach (Breunig, Mammen, & Simoni, 2018; d'Haultfoeuille, 2010).…”

Semiparametric Correction for Endogenous Truncation Bias With Vox Populi-Based Participation Decision

“…The aforementioned joint density function consists of two components: a Copula function 51 characterizing the disturbances' dependence structure and two marginal distribution functions F ξ1 and F ξ2 for the substantive equation and selection equation, respectively. In order to verify our model's performance in the presence of random disturbances' distribution functions which are not restricted to the family of symmetric and unimodal distribution functions, each one of these two disturbances is marginally distributed according to a mixture of three different distribution functions: (i) a normal distribution function with expectation and standard deviation parameters (µ, σ a ), denoted by N (µ, σ 2 a ); (ii) a normal distribution function with expectation and standard deviation parameters (−µ, σ b ), denoted by N (−µ, σ 2 b ); (iii) a gamma distribution function with scale and shape parameters (µϕ, ϕ), denoted by Γ Gamma (µϕ, ϕ) 52 . This mixture distribution function is defined as:…”

“…Unlike the Monte Carlo simulations in[52] for censored sample selection models implemented by using normally distributed disturbances, we consider a truncated sample selection model characterized by non-normally distributed disturbances.VOLUME 4, 2016 …”

“…According to Sklar's Theorem[53], any continuous joint distribution function can be characterized by a set of marginal distribution functions and a joint distribution function determining the dependence structure which is referred to as a Copula function 52. The scale and shape parameters implies that the expectation and standard deviation parameters are (µ, µ/ϕ) 53.…”