A simple, robust test for choosing the level of fixed effects in linear panel data models

For the panel data case where cross-sectional units are nested within higher-level groups, and there are many such groups, we propose a test that allows one to determine whether controlling for fixed effects at the more aggregate level is sufficient. The alternative is that one should allow for fixed effects at the unit level. The regression-based test is simple to carry out, even for unbalanced panels. In addition, the test is easily made robust to arbitrary heteroskedasticity, serial correlation across time, and even cluster correlation at the group level. We also show how to modify the traditional Hausman test of a single coefficient to be fully robust to serial correlation and cluster correlation. The tests work well in terms of size and power in a small simulation study. We apply the test to choosing between a fixed effects analysis at the school district level and the disaggregated school level.