Cemmap Working Paper (CWP04/17)

Likelihood inference and the role of initial conditions for the dynamic panel data model

Date: 20 January 2017
Publisher: The IFS
JEL classification: C12, C30
DOI: 10.1920/wp.cem.2017.0417

Lancaster (2002) proposes an estimator for the dynamic panel data model with homoskedastic errors and zero initial conditions. In this paper, we show this estimator is invariant to orthogonal transformations, but is inefficient because it ignores additional information available in the data. The zero initial condition is trivially satis fied by subtracting initial observations from the data. We show that di fferencing out the data further erodes efficiency compared to drawing inference conditional on the rst observations. Finally, we compare the conditional method with standard random eff ects approaches for unobserved data. Standard approaches implicitly rely on normal approximations, which may not be reliable when unobserved data is very skewed with some mass at zero values. For example, panel data on fi rms naturally depend on the fi rst period in which the fi rm enters on a new state. It seems unreasonable then to assume that the process determining unobserved data is known or stationary. We can instead make inference on structural parameters by conditioning on the initial observations.