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.

Common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors

“…This applies to bootstrapped based corrections, as well as the analytical corrections based on asymptotic bias formulae such as the one derived by Kiviet and Phillips (1993). The development of analytical or bootstrapped bias correction procedures for dynamic panel data models with a multifactor error structure is beyond the scope of the present paper and deserve separate investigations of their own.…”

“…Hsiao, Pesaran, and Tahmiscioglu (1999) investigate bias-corrected mean group estimation, where Kiviet and Phillips (1993) bias correction is applied to the individual estimates of short-run coe¢ cients. Hsiao, Pesaran, and Tahmiscioglu (1999) propose also a Hierarchical…”

“…8 Pesaran and Zhao (1999) investigate bias correction methods in estimating long-run coe¢ cients and consider, in particular, two analytical corrections based on an approximation of the asymptotic bias of long-run coe¢ cients, a bootstrap bias-corrected estimator, and a "naive" bias-corrected panel estimator computed from bias-corrected short-run coe¢ cients (using a result derived by Kiviet and Phillips, 1993).…”

Jackknife estimation of stationary autoregressive models

“…Theorem 1 of Kiviet and Phillips (1993) provides a general expression for the bias ofβ to O(n −1 ) in a model that can contain a set of regressors in addition to a constant and trend. As an aid to simulation economy it can be shown thatβ is invariant to the values of α, γ and the variance of t provided that…”

Bartlett Correction in the Stable Ar(1) Model With Intercept and Trend

“…Hence, for this range, the finite-sample problems in the model with trend are expected to be more server than in the model without trend. Using Theorem 1 of Kiviet and Phillips (1993), the estimation bias of the AR(1) coefficient estimator can be shown to…”