On the Fixed-Effects Vector Decomposition

This paper analyzes the properties of the fixed-effects vector decomposition estimator, an emerging and popular technique for estimating time-invariant variables in panel data models with group effects. This estimator was initially motivated on heuristic grounds, and advocated on the strength of favorable Monte Carlo results, but with no formal analysis. We show that the three-stage procedure of this decomposition is equivalent to a standard instrumental variables approach, for a specific set of instruments. The instrumental variables representation facilitates the present formal analysis that finds: (1) The estimator reproduces exactly classical fixed-effects estimates for time-varying variables. (2) The standard errors recommended for this estimator are too small for both time-varying and time-invariant variables. (3) The estimator is inconsistent when the time-invariant variables are endogenous. (4) The reported sampling properties in the original Monte Carlo evidence do not account for presence of a group effect. (5) The decomposition estimator has higher risk than existing shrinkage approaches, unless the endogeneity problem is known to be small or no relevant instruments exist.

[1]  Signe Krogstrup,et al.  Do fiscal rules cause budgetary outcomes? , 2008 .

[2]  C. Stein,et al.  Estimation with Quadratic Loss , 1992 .

[3]  J. Hausman.  Specification tests in econometrics , 1978 .

[4]  J. MacKinnon,et al.  Estimation and inference in econometrics , 1994 .

[5]  Christophe Rault,et al.  On the bilateral trade effects of free trade agreements between the EU-15 and the CEEC-4 countries , 2008, SSRN Electronic Journal.

[6]  B. Efron.  Better Bootstrap Confidence Intervals , 1987 .

[7]  Michael P. Murray.  Avoiding Invalid Instruments and Coping with Weak Instruments , 2006 .

[8]  G. Judge,et al.  Combining estimators to improve structural model estimation and inference under quadratic loss , 2005 .

[9]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[10]  Jerry A. Hausman,et al.  Panel Data and Unobservable Individual Effects , 1981 .

[11]  Badi H. Baltagi,et al.  Fixed effects, random effects or Hausman–Taylor?: A pretest estimator , 2003 .

[12]  David A. Jaeger,et al.  Problems with Instrumental Variables Estimation when the Correlation between the Instruments and the Endogenous Explanatory Variable is Weak , 1995 .

[13]  William E. Strawderman,et al.  A James-Stein Type Estimator for Combining Unbiased and Possibly Biased Estimators , 1991 .

[14]  Peter Schmidt,et al.  EFFICIENT ESTIMATION USING PANEL DATA , 1989 .

[15]  T. Mitze.  Endogeneity in Panel Data Models with Time-Varying and Time-Fixed Regressors: To IV or Not IV? , 2009 .

[16]  Y. Mundlak.  On the Pooling of Time Series and Cross Section Data , 1978 .

[17]  G. Judge,et al.  A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss , 2004 .

[18]  W. Greene,et al.  Fixed Effects Vector Decomposition: A Magical Solution to the Problem of Time-Invariant Variables in Fixed Effects Models? , 2011, Political Analysis.

[19]  Thomas Plümper,et al.  Efficient Estimation of Time-Invariant and Rarely Changing Variables in Finite Sample Panel Analyses with Unit Fixed Effects , 2007, Political Analysis.

[20]  D. Brownstone,et al.  Bootstrap confidence bands for shrinkage estimators , 1999 .

[21]  Jeffrey M. Woodbridge.  Econometric Analysis of Cross Section and Panel Data , 2002 .

[22]  Jonathan N. Katz,et al.  What To Do (and Not to Do) with Time-Series Cross-Section Data , 1995, American Political Science Review.

[23]  M. Feldstein,et al.  Errors in Variables: A Consistent Estimator with Smaller MSE in Finite Samples , 1974 .

[24]  T. Sawa.  The mean square error of a combined estimator and numerical comparison with the TSLS estimator , 1973 .

[25]  A. Belke,et al.  Enlarging the EMU to the east: what effects on trade? , 2007 .

[26]  Ka-fu Wong.  Effects on inference of pretesting the exogeneity of a regressor , 1997 .

[27]  P. Schmidt,et al.  The asymptotic distribution of the instrumental variable estimators when the instruments are not correlated with the regressors , 2001 .

[28]  Aman Ullah,et al.  Finite Sample Econometrics , 2004 .