Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable

Abstract

The small sample bias of the least-squares coefficient estimator is examined in the dynamic multiple linear regression model with normally distributed whitenoise disturbances and an arbitrary number of regressors which are all exogenous except for the one-period lagged-dependent variable. We employ large sample (T → ∞) and small disturbance (σ → 0) asymptotic theory and derive and compare expressions to O(T⁻¹) and to O(σ²), respectively, for the bias in the least-squares coefficient vector. In some simulations and for an empirical example, we examine the mean (squared) error of these expressions and of corrected estimation procedures that yield estimates that are unbiased to O(T^−l) and to O(σ²), respectively. The large sample approach proves to be superior, easily applicable, and capable of generating more efficient and less biased estimators.