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I am currently working with a balanced time-series cross-section dataset (or a T dominant panel), consisting in 8 units (countries) and 32 observations (quarters) per unit. Thus, the dataset has 8 x 32 = 256 observations. The dependent variable is continuous and there are 5 regressors. I am estimating my model using Fixed Effects (in Stata, "xtreg, fe"), Random Effects (in Stata, "xtreg, re"), Beck and Katz Panel Corrected Standard Errors ("xtpcse") and GLS ("xtgls"). Since my data is not what Greene would called "well-behaved data" -it shows panel heteroskedasticity, serial correlation and contemporaneous correlation-, I am proecting the models against these issues. Thus, my first question is about how to control for time and unit unobserved heterogeneity with PCSE and GLS models. Or, in different words:

(a) Does it make sense to include time and unit dummies with PCSE and GLS models? Any reference supporting your statement will be appreciated. I have found some other people asking this out there, but no proper answer so far.

(b) Does it make sense to include a time trend and time dummies simultaneously in FE/RE/PCSE/GLS? I have found different answers to this question: ones arguing that it makes sense and some others arguing that it does not. Again, explanations with a minimal reference or link are welcome.

Thank you all!

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(a) PCSE just changes the estimated standard errors and can be used with time/unit dummies and/or time trends; in fact the inclusion of dummies and trends is not really related to the issue of how to get appropriate standard errors. So yes, it makes sense. PCSE were introduced by Beck and Katz 1995 and in fact the use of unit dummies and PCSE together is something like a standard in political science at least. GLS is a different way to estimate both the coefficients and the standard errors, and is also not really related to the model specification (dummies and trends). So you would also include dummies or trends based on substantive considerations, and then you might apply GLS if OLS leads to heteroskedasticity or serial correlation. However, and this is extensively discussed in Beck and Katz 1995, the (F)GLS procedure especially for your kind of data has really bad finite-sample behavior.

(b) Jeff Wooldrdige says: "No, it doesn't make sense to include a full set of time dummies along with any function of time. Putting in time dummies allows for any kind of trend, of which a linear trend is a special case." (You get a linear time trend if all the time dummies happen to haven the same estimate). The inclusion of time dummies is of course "conservative", in a sense, but could be more or less warranted depending on the question you try answer - essentially, do you think that units pick up the treatment because of unobserved stuff that changes over time, that this also influences the dependent variable, and that it somehow is common across units?

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  • $\begingroup$ Julian, may I conclude that: 1. I ignore FGLS (in Stata, "xtgls") because it has bad finite sample properties. 2. I can include time and unit dummies with XTPCSE. 3. I either include time dummies or a time trend of any form, but not both simultaneously. Let me ask you something else: if there is serial autocorrelation, a LDV is usually added with PCSE. However, including a LDV in the right hand side along with unit FE would generate bias, wouldn't it? What's better, then, XTPCSE with FE, with LDV or with both? $\endgroup$ – Héctor Jul 2 '16 at 13:58
  • $\begingroup$ Yes, in linear models with a LDV and unit fixed effects you get "Nickell" bias, but it diminishes as T grows, so should be fine with your data (also, it's part of the recommendation by Beck and Katz 1995). Note, however, that with a LDV you get short-term effects (the betas) and long-term effects (betas divided by 1 minus the coefficient of the LDV). The latter might be larger and more precisely estimated than the former. Usually it's instructive to estimate FE-only, LDV-only, and models with both (there's also a discussion of that in Mostly Harmless Econometrics). $\endgroup$ – Julian Schuessler Jul 2 '16 at 16:42

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