Multiplicative Panel Data Models without the Strict Exogeneity Assumption

This paper considers estimation of multiplicative, unobserved components panel
data models without imposing a strict exogeneity assumption on the conditioning
variables. The method of moments estimators proposed have significant robustness
properties. They require only a conditional mean assumption and apply to models
with lagged dependent variables and to finite distributed lag models with arbitrary
feedback from the explained to future values of the explanatory variables. The model
is particularly suited to nonnegative explained variables, including count variables,
continuously distributed nonnegative outcomes, and even binary variables. The general
model can also be applied to certain nonlinear Euler equations.
1. INTRODUCTION
In this paper, I extend Chamberlain's (1992a) method for estimating a class of
nonlinear, multiplicative panel data models without the strict exogeneity assumption.
The results reported here originated in Wooldridge (1991b) and were obtained
independently of Chamberlain (1992a).
I extend Chamberlain's research along two useful dimensions. First, rather
than restrict attention to an exponential regression function, I allow for a general
conditional mean function. Among other things, this allows for binary choice
models with multiplicative unobserved effects, as shown in Section 4. Furthermore,
I explicitly allow for models containing parametric nonlinear transformations
of the endogenous variables. This makes the approach applicable to Euler
equations with unobserved effects. An example is given in Section 4.