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st: Robust standard errors in Panel Data


From   "Yvonne Capstick" <yvonnecapstick@hotmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Robust standard errors in Panel Data
Date   Tue, 15 Feb 2005 23:19:13 -0500

Hi,

I have a simple panel data model of the form:

return = a + b*monday + c*january

which I'm testing across multiple time periods and 5 countries. Through using Stata's "help" function and reading the FAQs, I've learned of the numerous options available to correct for the errors not being iid. The differences between some of these are clear, but I am not sure about all of the differences:

"xtreg return monday january, i(country) fe" will give me a fixed effects regression, equivalent to generating 5 dummy variables for each country and thus effectively allowing the intercept to vary by country. However, the standard errors generated assume the errors are iid.

"xtgls" allows for non-iid errors. E.g. "xtgls return monday january, p(c) c(p)" allows for heteroschedasticity and cross-sectional correlation across panels (countries in my example), in addition to panel-specific AR1 autocorrelation within each panel.

- How does xtgls differ from xtreg, re? The random effects model is often referred to as the FGLS estimator for panel data in textbooks.

"xtpcse" allows for heteroschedastic and contemporaneously correlated errors, and potentially also panel-specific AR1 autocorrelation within each panel. E.g. "xtpcse return monday january c(p)"

- How does this differ from the xtgls formulation above?

"xi : reg return monday january i.country, cluster(country)" allows for observations to be correlated within each panel, and heteroschedastic across panels, but independent across panels. It works best when you have many panels.

- How is this different from running: "xtgls return monday january, p(h) c(p)"?

I would like to err on the conservative side and "over-correct" for violations of iid. Please could you advise me on the best specification to use - I think it's "xtpcse return monday january c(p)", but I don't know how this differs from "xtgls return monday january, p(c) c(p)"

Finally, I would like to allow for the coefficient on "january" to differ across countries, but the coefficient on "monday" to remain constant (hence I still would like to use the panel data model).

I can do a simple OLS by xi : reg return monday i.country*january. However, what options are available to me to correct for errors not being iid? I can still do "cluster(country)" but this assumes errors are independent across panels. I can't seem to be able to accommodate panel-specific coefficients on any of the regressors within the xtgls or xtpcse framework. I would like to be able to correct for contemporaneously correlated errors across panels.

Thanks in advance for any help. Normally my problem is not knowing any appropriate function; here I have many alternatives available and am not sure how to choose between them.

Yvonne

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