  This paper explores the identification and estimation of nonseparable panel
data models. We show that the structural function is nonparametrically
identified when it is strictly increasing in a scalar unobservable variable,
the conditional distributions of unobservable variables do not change over
time, and the joint support of explanatory variables satisfies some weak
assumptions. To identify the target parameters, existing studies assume that
the structural function does not change over time, and that there are
"stayers", namely individuals with the same regressor values in two time
periods. Our approach, by contrast, allows the structural function to depend on
the time period in an arbitrary manner and does not require the existence of
stayers. In estimation part of the paper, we consider parametric models and
develop an estimator that implements our identification results. We then show
the consistency and asymptotic normality of our estimator. Monte Carlo studies
indicate that our estimator performs well in finite samples. Finally, we extend
our identification results to models with discrete outcomes, and show that the
structural function is partially identified.
