Optimal Shrinkage Estimation of Fixed Effects in Linear Panel Data Models
Abstract
Shrinkage methods are frequently used to improve the precision of least squares estimators of fixed effects. However, widely used shrinkage estimators guarantee improved precision only under strong distributional assumptions. I develop an estimator for the fixed effects that obtains the best possible mean squared error within a class of shrinkage estimators. This class includes conventional shrinkage estimators and the optimality does not require distributional assumptions. The estimator has an intuitive form and is easy to implement. Moreover, the fixed effects are allowed to vary with time and to be serially correlated, in which case the shrinkage optimally incorporates the underlying correlation structure. I also provide a method to forecast fixed effects one period ahead in this setting.
Fields of Study & Subjects
Spatial and Panel Data Analysis
Statistical Methods and Inference
Monetary Policy and Economic Impact
Publication details
- Journal / source
- Econometrica
- Publisher
- The Econometric Society
- Volume
- 94
- Issue
- 2
- Pages
- 663–677
- Publication date
- 1 January 2026
- Language
- EN