We consider linear predictor definitions of noncausality or strict exogeneity and show that it is restrictive to assert that there exists a time-invariant latent variable c such that x is strictly exogenous conditional on c. A restriction of this sort is necessary to justify standard techniques for controlling for unobserved individual effects. There is a parallel analysis for multivariate probit models, but now the distributional assumption for the individual effects is restrictive. This restriction can be avoided by using a conditional likelihood analysis in a logit model. Some of these ideas are illustrated by estimating union wage effects for a sample of Young Men in the National Longitudinal Survey. The results indicate that the lags and leads could have been generated just by an unobserved individual effect, which gives some support for analysis of covariance-type estimates. These estimates indicate a substantial omitted variable bias. We also present estimates of a model of female labor force participation, focusing on the relationship between participation and fertility. Unlike the wage example, there is evidence against conditional strict exogeneity; if we ignore this evidence, the probit and logit approaches give conflicting results.
Chamberlain, Gary. "Multivariate Regression Models For Panel Data," Journal of Econometrics, 1982, v18(1), 5-46.
Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics, in: Z. Grilichesâ€ & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier.