Centering and Reference Groups for Estimates of Fixed Effects: Modifications to Felsdvreg

Abstract

Availability of large, multilevel longitudinal databases in various fields including labor economics (with workers and firms observed over time) and education research (with students and teachers observed over time) has increased the application of panel-data models with multiple levels of fixed-effects. Existing software routines for fitting fixed-effects models were not designed for applications in which the primary interest is obtaining estimates of any of the fixed-effects parameters. Such routines typically report estimates of fixed effects relative to arbitrary holdout units. Contrasts to holdout units are not ideal in cases where the fixed-effects parameters are of interest because they can change capriciously, they do not correspond to the structural parameters that are typically of interest, and they are inappropriate for empirical Bayes (shrinkage) estimation. We develop an improved parameterization of fixed-effects models using sum-to-zero constraints that provides estimates of fixed effects relative to mean effects within well-defined reference groups (e.g., all firms of a given type or all teachers of a given grade) and provides standard errors for those estimates that are appropriate for shrinkage estimation. We implement our parameterization in a Stata routine called felsdvregdm by modifying the felsdvreg routine designed for fitting high-dimensional fixed-effects models. We demonstrate our routine with an example dataset from the Florida Education Data Warehouse.