Approximating the bias of the LSDV estimator for dynamic panel data models

It is well known that the LSDV estimator for dynamic panel data models is not consistent for N large and finite T. Nickell (1981) derives an expression for the inconsistency for N going to infinity, which is of order 1/T. Kiviet (1995) uses asymptotic expansion techniques to approximate the small sample bias of the LSDV estimator to also include terms of at most order 1/NT, thus offering a method to correct the LSDV estimator for samples where N is small or only moderately large. In Kiviet (1999) and Bun and Kiviet (2003) the bias expression is more accurate, including higher order terms. Monte Carlo evidence in Judson and Owen (1999) strongly supports the corrected LSDV estimator compared to more traditional GMM estimators when N is only moderately large. Bruno (2004) extends the bias approximation formulas in Bun and Kiviet (2003) to accommodate unbalanced panels with a strictly exogenous selection rule. This paper describes the Stata codes used in Bruno (2004) to compute the bias approximations and carry out the Monte Carlo experiment estimating the actual LSDV bias for various data generating processes. The analysis covers both balanced and unbalanced panels. It is found that the actual bias as estimated by Monte Carlo replications, besides following the same patterns as in Bun and Kiviet (2003), turns out non-increasing in the degree of unbalancedness. Moreover, the approximations are always accurate with a decreasing contribution to the actual bias of the higher order terms.