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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?
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  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.

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  • $\begingroup$ I think you are confusing validity, efficiency, and consistency. Serial correlation only affects the efficiency of the estimator, not its consistency. Also, to the best of my knowledge, estimators are not "valid". Test statistics can be valid or invalid, depending on whether the conditions hold or not. If they do, the test statistic does distribute as the theoretical distribution, and thus, comparing the test statistics with a critical values from that theoretical distribution is valid. $\endgroup$ – luchonacho Apr 20 '17 at 9:25
  • $\begingroup$ We are not talking about consistency or efficiency but about the validity of tests using standard errors computed in ordinary ways. Obviously, I should have been more specific and say "the t statistic using the ordinary standard error does not have the t distribution under the null hypothesis." From the way Neta_1990 wrote the question, I thought he/she would understand the sentence that way. $\endgroup$ – chan1142 Apr 20 '17 at 9:44

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