On bias, inconsistency and efficiency of various estimators in dynamic panel data models

Abstract When a model for panel data includes lagged dependent explanatory variables, then the habitual estimation procedures are asymptotically valid only when the number of observations in the time dimension (T) gets large. Usually, however, such datasets have substantial sample size in the cross-section dimension (N), whereas T is often a single-digit number. Results on the asymptotic bias (N → ∞) in this situation have been published a decade ago, but, hence far, analytic small sample assessments of the actual bias have not been presented. Here we derive a formula for the bias of the Least-Squares Dummy Variable (LSDV) estimator which has a O(N −1 T − 3 2 ) approximation error. In a simulation study this is found to be remarkably accurate. Due to the small variance of the LSDV estimator, which is usually much smaller than the variance of consistent (Generalized) Method of Moments estimators, a very efficient procedure results when we remove the bias from the LSDV estimator. The simulations contain results for a particular operational corrected LSDV estimation procedure which in many situations proves to be (much) more efficient than various instrumental variable type estimators.

[1]  Peter Schmidt,et al.  Efficient estimation of models for dynamic panel data , 1995 .

[2]  Marc Nerlove,et al.  Pooling Cross-section and Time-series Data in the Estimation of a Dynamic Model , 1966 .

[3]  J. Kiviet,et al.  Neglected dynamics in panel data models; consequences and detection in finite samples* , 1995 .

[4]  Patrick Sevestre,et al.  The Econometrics of Panel Data , 1993 .

[5]  M. Arellano,et al.  A NOTE ON THE ANDERSON-HSIAO ESTIMATOR FOR PANEL DATA , 1989 .

[6]  Jan F. Kiviet,et al.  Bias Assessment and Reduction in Linear Error Correction Models , 1994 .

[7]  Cheng Hsiao,et al.  Benefits and limitations of panel data , 1985 .

[8]  Alok Bhargava,et al.  Estimating Dynamic Random Effects Models from Panel Data Covering Short Time Periods , 1983 .

[9]  N. Savin,et al.  Finite Sample Distributions of t and F Statistics in an AR(1) Model with Anexogenous Variable , 1987, Econometric Theory.

[10]  M. Nerlove,et al.  Biases in dynamic models with fixed effects , 1988 .

[11]  M. Arellano,et al.  Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations , 1991 .

[12]  Cheng Hsiao,et al.  Analysis of Panel Data , 1987 .

[13]  Stephen Nickell,et al.  Biases in Dynamic Models with Fixed Effects , 1981 .

[14]  Jan F. Kiviet,et al.  On the Rigour of Some Misspecification Tests for Modelling Dynamic Relationships , 1986 .

[15]  Badi H. Baltagi,et al.  A survey of recent theoretical developments in the econometrics of panel data , 1992 .

[16]  Marc Nerlove,et al.  Further evidence on the estimation of dynamic economic relations from a time series of cross-sections , 1971 .

[17]  Richard Blundell,et al.  Conditions initiales et estimation efficace dans les modéles dynamiques sur données de panel: une application au comportement d'investissement des entreprises , 1990 .

[18]  Cheng Hsiao,et al.  Formulation and estimation of dynamic models using panel data , 1982 .

[19]  W. Newey,et al.  Estimating vector autoregressions with panel data , 1988 .

[20]  Cheng Hsiao,et al.  Estimation of Dynamic Models with Error Components , 1981 .

[21]  J. Kiviet,et al.  Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable , 1993, Econometric Theory.

[22]  P. Sevestre,et al.  Propriétés de grands échantillons d'une classe d'estimateurs des modèles autorégressifs à erreurs composées , 1983 .

[23]  Patrick Sevestre,et al.  A note on autoregressive error components models , 1985 .

[24]  G. Maddala,et al.  THE USE OF VARIANCE COMPONENTS MODELS IN POOLING CROSS SECTION AND TIME SERIES DATA , 1971 .