Estimating panel data models in the presence of endogeneity and selection

Abstract

a b s t r a c tWe consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors. The tests are based on the fixed effects two-stage least squares estimator, thereby permitting arbitrary correlation between unobserved heterogeneity and explanatory variables. The first correction procedure is parametric and is valid under the assumption that the errors in the selection equation are normally distributed. The second procedure estimates the model parameters semiparametrically using series estimators. In the proposed testing and correction procedures, the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations. Because these methods allow for a rather flexible structure of the error variance and do not impose any nonstandard assumptions on the conditional distributions of explanatory variables, they provide a useful alternative to the existing approaches presented in the literature.

Temporary Contracts and Young Workers’ Job Satisfaction in Italy

“…In all models a battery of simple variable addition tests (see Semykina and Wooldridge 2010) never reject the null of zero correlation between and past or future realizations of the selection. More specifically, the selection rule is such that if individual i is in the sample at time t (has the employee status) and otherwise.…”

“…We estimated equation ( Testing for contemporaneous selection is more intricate. For example, implementing the twostep procedure suggested in Semykina and Wooldridge (2010) requires that we take care of the incidental truncation on a subset of right-hand-side variables, specifically the aspect satisfaction variables, the contract indicators and, in models 2 and 3, the interactions between the two groups of variables. In any event, this boils down to an unusually high number of potentially endogenous regressors, which should be matched by an equal number of nontruncated excluded instruments, a hard task in our sample.…”

Multiple Job Holding as a Strategy for Skills Diversification and Labour Market Mobility

“…In order to address the above issues, Wooldridge (1995) and Semykina and Wooldridge (2005) have proposed a suitable Conditional Maximum Likelihood (CML) estimation procedure. Specifically, following Mundlak (1978) and Chamberlain (1984) it is initially assumed that the correlation between ߟ and ‫ݖ‬ ௧ can be parameterized via a linear relationship, ߟ ൌ ‫ݖ‬ҧ ′ ߜ ߱ , where ߱ ݅݅݀ ܰሺ0, ߪ ఠ ଶ ሻ, ‫ܧ‬ሺ߱ ‫ݖ|‬ ௧ , ߝ ௧ ሻ ൌ 0 and ‫ݖ‬ҧ are the means over the sample period of all exogenous variables.…”

“…௧ = 1. The Wooldridge (1995) and Semykina and Wooldridge (2005) methodology is utilized again so that the estimation of equations (7) and (8) proceeds as follows 6 :…”

The effect of housework on wages in Germany: no impact at all

“…To assess whether our results are influenced by selectivity, we applied several two-step control function estimators: In our GSOEP sample we used the estimators proposed by To test our fourth hypothesis that daily routine housework activities have a stronger negative impact on wages as opposed to those activities that are more easily postponed, we distinguish two categories of housework. As hours spent on daily routine housework activities we define the sum of hours spent on "shopping", "washing, cooking, and cleaning", "childcare", and "care and support for persons in need of care", whereas the hours spent on re- Wooldridge (1995), which intuitively adds a sample selection correction term to the standard FE model, and by Semykina and Wooldridge (2010), which does the same in the IV FE model. In our GTUS sample, we made use of a standard Heckit and a Heckit IV model (for the latter, see Wooldridge 2010, pp.…”