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. Forthcoming in: Political Analysis

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

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