A life cycle model of labor supply predicts the presence of an
unobserved individual effect (log marginal utility of wealth) in the labor
supply equation which is correlated with the observed explanatory variables,
leading to an omitted variables bias in the cross section. We examine the
sensitivity of parameter estimates to the presence of unobserved individual
effects, using both fixed- and random effect Tobit models. The estimated
effects of children are biased away from zero in the cross section. The
estimated intertemporal substitution elasticity ranges from 1.1 to 1.7. The
results are similar for both fixed and random effects models, and for models
using log leisure and hours of work as the dependent variable.

This paper presents estimates of the union wage effect while controlling for
person specific unmeasured variables which do not change over time (‘fixed
effects‘) as well as specification tests for the person effect models commonly in
use. a sample of men from the PSID, we find that controlling for a person effect
POSUH in estimates of the union wage effect on the order of 5-81, as opposed to 201
in the cross section. An omnibus test based on an unrestricted reduced form and an
instrumental variables test based on a differencing idea provide no evidence against
the conventional model. A third test, based on a comparison of those who enter and
leave union coverage, does provide evidence against the usual model.

Cross section estimates of the union wage effect are typically much
larger than estimates derived from within estimators using panel data. Two
competing explanations for this difference have been advanced. The first is
that the cross section estimates suffer from an omitted variables bias due to
a correlation between unobserved productivity and union status which biases
the cross section estimator upwards. The second is that measurement error
in union status is more severe in the changes than in the levels, imparting a
more severe downward bias to the panel estimator.
This paper derives a method of moments estimator which allows for
both effects, nested within the same model. The binary nature of the
explanatory variable is exploited to derive an estimating model which allows
simultaneous estimation of both the structural parameters of the model and
the parameters of the measurement error process. When the estimator is
applied to sample of men from the PSID we find that allowing for measurement
error does lead to a larger estimate of the union wage effect than the usual
within estimator, but that most of the difference between the cross section
and the panel estimates is not due to measurement error in the union
variable. Further, the estimates of the extent of measurement error are
close to those found in a validation study of the PSID.