Estimation in the presence of unobserved fixed factors: consistency or efficiency?
The recent literature examining the impact of strategic factors on business performance suggests the use of estimation methods that control for unobserved fixed firm factors. This recommendation is driven by the consideration of unbiasedness as the exclusive criterion for estimator selection, even though this may lead to inefficient estimators resulting in the inability to detect significant effects. The concern for unbiasedness is also reflected in instrumental estimation. The selection of instruments is typically focuses on the independence assumption of instruments and error term at the expense of the explanatory power of instruments. In this study, the authors examine the implications of making the statistical tradeoffs between the bias and the variance of estimators by considering the mean square error as the criterion for estimator selection. More specifically, they identify three measures that determine the selection of the estimator among the consistent but potentially inefficient fixed-effects estimator, the inconsistent but efficient random-effects estimators, and IV-estimation: (i) the within cross-sections variance relative to total sample variance of the independent variable, (ii) the correlation between the firm specific factor and the independent variable, and (iii) the quality of the instrumental variable. Through analytical evaluations of the estimators and extensive Monte-Carlo simulations, the authors determine conditions for selecting the appropriate estimator. Because the correlation between firm specific effects and the independent variables are unknown, they use simulation data and take advantage of the structural constraints imposed on this correlation to predict that correlation based on measurable factors. They illustrate the value of the methodology by applying these criteria to the study of the effect of market share on profitability. They demonstrate that, using the PIMS data, the key determinants are within a range where the fixed-effects model is not necessarily best in terms of MSE and they conclude that, if one is willing to trade off some bias for efficiency, the evidence tends to corroborate earlier work for a significant market share impact on firm performance.
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