Serial correlation and clustered correlation in FE and FD estimators

Economics Asked by Neta_1990 on May 9, 2021

I’m running a regression on panel data, one time with Fixed Effects and one time with First Differences. The estimators are really different (the FE estimator is statistically significant and the FD isn’t). While I’m running the regressions with the Clustered Standard Errors, it affects a lot the S.D of the FD estimator but not the S.D of the FE estimator. When I’m running Wooldridge test for serial correlation I get that there is no serial correlation. My questions:

  1. Is it possible to be within clustered correlation for the FD model but not for the FE?
  2. If there is no serial correlation, is it possible to be a within clustered correlation?

One Answer

  1. Yes. If the idiosyncratic error is iid, xtreg (FE) with no options (ordinary se) is valid, but the ordinary se for FD, reg d.(y x), is invalid because the differenced error is serially correlated.

  2. Yes, it is. It's cluster-robust, which means OK regardless of the presence of within-group correlation.

Answered by chan1142 on May 9, 2021

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