Applied econometric research frequently encounters the diﬀiculty that estimation of the parameters of interest is complex owing to the presence of incidental parameters. It is tempting therefore to try to circumvent the diﬀiculties by proceeding in two stages. In the ﬁrst, some estimates are made of the incidental parameters. In the second, these estimates are treated as though they were population values, leading to a large reduction in the dimension of the unknown parameter space, possibly even down to that of the parameters of interest only. The properties of such a staged process (particularly as they relate to issues arising from the consistency and eﬀiciency of the estimator and the provision of reliable inference), applications involving the presence of current and future anticipations, an alternative estimator, and diagnostic tests are all discussed in this paper.
Pagan, Adrian, "Two Stage and Related Estimators and Their Applications" (1985). Cowles Foundation Discussion Papers. 982.