Incidental parameters, initial conditions and sample size in statistical inference for dynamic panel data models

We use a quasi-likelihood function approach to clarify the role of initial values and the relative sample size of the cross-section dimension N and the time series dimension T on the asymptotic properties of estimators for dynamic panel data models with the presence of individual-specific effects. We show that a properly specified quasi-likelihood estimator (QMLE) that uses the Mundlak-Chamberlain approach to condition the unobserved effects and initial values on the observed strictly exogenous covariates is asymptotically unbiased if N goes to infinity whether T is fixed or goes to infinity. Monte Carlo studies are conducted to demonstrate the importance of properly treating initial values in getting valid statistical inference. The simulation results also suggest that to deal with the incidental parameters issues arising from the presence of individual-specific effects or initial values, following the Mundlak's (1978) suggestion to condition on the time series average of individual's observed regressors performs better than conditioning on each observed variable at all different time periods.