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

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 satisfied by subtracting initial observations from the data. We show that differencing out the data further erodes efficiency compared to drawing inference conditional on the first observations. Finally, we compare the conditional method with standard random effects 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 firms naturally depend on the first period in which the firm 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.