On the fixed-effects vector decomposition

Breusch, Trevor and Ward, Michael B and Nguyen, Hoa and Kompas, Tom (2010): On the fixed-effects vector decomposition.

Abstract

This paper analyses the properties of the fixed-effects vector decomposition estimator, an emerging and popular technique for estimating time-invariant variables in panel data models with unit 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 which 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 are incorrect. (5) We recommend an alternative shrinkage estimator that has superior risk properties to the decomposition estimator, unless the endogeneity problem is known to be small or no relevant instruments exist.

• Item Type: MPRA Paper
• Language: English
• Keywords: panel data models; fixed-effects vector decomposition; instrumental variables; inconsistent estimator; incorrect standard errors; improved shrinkage estimator
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C23 - Panel Data Models ; Spatio-temporal Models; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C33 - Panel Data Models ; Spatio-temporal Models

References

Baltagi, B., G. Bresson, and A. Pirotte (2003). Fixed effects, random effects or Hausman–Taylor? A pretest estimator. Economics Letters 79 (3), 361–369.

Belke, A. and J. Spies (2008). Enlarging the EMU to the east: What effects on trade? Empirica 35 (4), 369–89.

Bound, J., D. Jaeger, and R. Baker (1995). Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. Journal of the American Statistical Association 90 (430), 443–50.

Breusch, T., G. Mizon, and P. Schmidt (1989). Efficient estimation using panel data.Econometrica 57 (3), 695–700.

Caporale, G., C. Rault, R. Sova, and A. Sova (2009). On the bilateral trade effects of free trade agreements between the EU-15 and the CEEC-4 countries. Review of World Economics 145 (2), 189–206.

Davidson, R. and J. G. MacKinnon (1993). Estimation and Inference in Econometrics. Oxford University Press.

Feldstein, M. (1974). Errors in variables: A consistent estimator with smaller MSE in finite samples. Journal of the American Statistical Association 69 (348), 990–96.

Green, E. and W. Strawderman (1991). A James-Stein type estimator for combining unbiased and possibly biased estimators. Journal of the American Statistical Association 86 (416), 1001–06.

Han, C. and P. Schmidt (2001). The asymptotic distribution of the instrumental variable estimators when the instruments are not correlated with the regressors. Economics Letters 74 (1), 61–66.

Hausman, J. and W. Taylor (1981). Panel data and unobservable individual effects. Econometrica 49 (6), 1377–98.

Hoeting, J., D. Madigan, A. Raftery, and C. Volinsky (1999). Bayesian model averaging: A tutorial. Statistical Science 14 (4), 382–401.

James, W. and C. Stein (1961). Estimation with quadratic loss. In J. Neyman (Ed.), Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1, pp. 361–79. University of California Press.

Kazimi, C. and D. Brownstone (1999). Bootstrap confidence bands for shrinkage estimators. Journal of Econometrics 90 (1), 99–127.

Krogstrup, S. and S. W¨alti (2008). Do fiscal rules cause budgetary outcomes? Public Choice 136 (1), 123–138.

Mittelhammer, R. and G. Judge (2005). Combining estimators to improve structural model estimation and inference under quadratic loss. Journal of Econometrics 128 (1), 1–29.

Mitze, T. (2009). Endogeneity in panel data models with time-varying and time-fixed regressors: to IV or not IV? Ruhr Economic Paper No. 83.

Mundlak, Y. (1978). On the pooling of time series and cross section data. Econometrica 46 (1), 69–85.

Plümper, T. and V. Troeger (2007a). Efficient estimation of time-invariant and rarely changing variables in finite sample panel analyses with unit fixed effects. Political Analysis 15 (2), 124–39.

Plümper, T. and V. Troeger (2007b). xtfevd.ado version 2.00 beta. Accessed from http://www.polsci.org/pluemper/xtfevd.ado.

Wong, K. (1997). Effects on inference of pretesting the exogeneity of a regressor. Economics Letters 56 (3), 267–71.

Wooldridge, J. M. (2002). Econometric Analysis of Cross Section and Panel Data. The MIT Press.