Random effects panel model with serial correlation

[Sarah McKenzie]

Does clustering robust standard errors in a random effects panel data model automatically solve the problem of serial correlation and heteroskedasticity?

[Weiwen Ng]

Does clustering robust standard errors in a random effects panel data model automatically solve the problem of serial correlation and heteroskedasticity?

I don't think that clustered SEs will solve the problem of residual serial correlation, but I have no real experience with that. I will say two things. One, note that I said residual serial correlation; you're already using a person-specific random intercept (presumably), and that already models some of what might otherwise be seen as serial correlation.

Two, if you read the -mixed- manual's examples 7 and 8, you will find that there are ways to explicitly model various residual error structures, e.g. the default independence structure, autoregressive, moving average, toeplitz, etc. You can test various structures versus independence using a likelihood ratio test.

Among applied statisticians in health services research, I haven't yet encountered papers using any of these residual structures. That doesn't mean it's not justified to explore the question or to use such a structure if it's justified.

[Sarah McKenzie]

Sorry I don't really understand what you mean. Is there anyone else who knows whether clustering robust standard errors in a random effects panel data model solves the problem of serial correlation and/or heteroskedasticity?

[Sebastian Kripfganz]

You did not precisely define what "problem" of serial correlation / heteroskedasticity you are having in mind. If all regressors are strictly exogenous, then neither serial correlation nor heteroskedasticity turn the RE-GLS estimator inconsistent. However, the RE-GLS estimator will no longer be an efficient estimator and it is not even a priori clear whether it will be more efficient than the pooled OLS estimator. Clustering standard errors does not solve this problem because the estimator itself is not affected by the clustering. Clustering standard errors can only solve the problem that the variance-covariance matrix of the estimator would otherwise not be consistently estimated which would result in size distortions of hypothesis tests.

Weiwen Ng pointed out some alternatives. If you model the structure of the serial correlation and then use an estimator that accounts for it, you could get both an efficient estimator and consistent standard errors, assuming that your model is correct. In addition to the previous recommendations, another alternative might be to consider a dynamic random-effects model with a lagged dependent variable to account for the serial correlation. This could be estimated for example with a random-effects ML estimator:
XTDPDQML: new Stata command for quasi-maximum likelihood estimation of linear dynamic panel models

[Weiwen Ng]

Sorry I don't really understand what you mean. Is there anyone else who knows whether clustering robust standard errors in a random effects panel data model solves the problem of serial correlation and/or heteroskedasticity?

I'll try to simplify. The mixed model structure by itself will correct for what might otherwise show up as serial correlation. It's frequently used in randomized trials of drugs, where we measure some baseline value, then again at 3 months, then again at 6 months. The people whose blood pressure starts high will likely tend to have high blood pressure at 3 months. A random intercept model (perhaps with a random slope) is one way to model that.

If you do in fact have serial autocorrelation beyond what a model with a random intercept models explicitly, then you can accommodate that in a mixed model by saying that OK, maybe the residuals have an autoregressive structure. Read the examples I linked or the documentation that Sebastian linked. But again, your mixed model is already accommodating some of that issue. It may not be necessary to modify the model, but you can read the documentation and decide for yourself.

[Sarah McKenzie]

Thank you!