Researchers usually use Hausman test(1978) to select between random effects model and fixed effects model. Can we use same Hausman test to select between FE and BE or do we have any other test for that?
Two tests can help you fulfill the goal. First is to run a Hausman test of the fixed effect and random effect models. Second is to construct a seemingly unrelated regression model with the within estimator and the between estimator. Then run a Wald test of the coefficients. (When you think carefully of the difference between random effect mode and fixed effect model, you will figure out that what you want to achieve is similar to distinguishing between RE and FE.)