Expectations of expansions for estimators in a dynamic panel data model: some results for weakly exogenous regressors

Abstract

Introduction In linear dynamic panel data models, the dependent variable (and hence also the lagged dependent regressor variable that makes the model dynamic) is determined by some linear function of present and past values of both the explanatory variables and the various stochastic error components. Since regression coefficient estimators are non-linear in all the regressor variables, the coefficient estimators are also non-linear in the stochastic error components in a linear dynamic panel data model. This non-linearity is the reason why the finite sample properties of inference methods for this type of model are very hard to establish. The actual probability distributions of estimators and test statistics are highly non-standard and usually they also depend on unknown values of nuisance parameters. Some knowledge on their actual shape and behavior can be obtained either experimentally by computer simulation or analytically by asymptotic approximations. For common model specifications the standard first-order asymptotic properties have been assessed for various estimation methods. Some methods are found to be inconsistent, but others are consistent and may even be asymptotically efficient for certain classes of models. However, from simulation studies it has often been found that first-order asymptotic properties do not always offer the right criterion for (dis)qualifying inference procedures as far as their finite sample properties are concerned; see for instance, Nerlove (1971), Arellano and Bond (1991), van den Doel and Kiviet (1995), and Kiviet (1995).

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