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Re: RE: st: Robust Standard Errors in Paneldatasets

 From Christopher Baum <[email protected]> To <[email protected]> Subject Re: RE: st: Robust Standard Errors in Paneldatasets Date Thu, 28 Oct 2010 09:22:49 -0400

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Amy wrote

> Obviously I am still missing a critical point.  Could you help understand your point about time dummies not correcting for cross-sectional correlation?

Note what happens to the cross-sectional correlation of errors when time dummies are introduced:

. webuse grunfeld,clear

. drop if company>3
(140 observations deleted)

. qui xtreg invest mvalue, fe

. predict double epsfe, e

. preserve

. keep epsfe year company

. qui reshape wide epsfe, i(year) j(company)

. // contemporaneous correlations between firm errors, straight FE
. corr epsfe*
(obs=20)

|   epsfe1   epsfe2   epsfe3
-------------+---------------------------
epsfe1 |   1.0000
epsfe2 |   0.6410   1.0000
epsfe3 |   0.4171   0.5185   1.0000

. restore

. qui xtreg invest mvalue i.year, fe

. predict double epsfet, e

. preserve

. keep epsfet year company

. qui reshape wide epsfet, i(year) j(company)

. // contemporaneous correlations between firm errors, two-way FE
. corr epsfet*
(obs=20)

|  epsfet1  epsfet2  epsfet3
-------------+---------------------------
epsfet1 |   1.0000
epsfet2 |  -0.7047   1.0000
epsfet3 |  -0.8402   0.2073   1.0000

When time dummies are added to the individual fixed effects, the correlations change considerably, but they are not driven to zero. As Stas' Clorox analogy suggests, that is hardly surprising. A fixed effect of either sort merely imposes the constraint that the errors for each unit (firm or time period) sum to zero (just as in standard regression the sum of residuals is zero in the presence of a constant term). Adding or subtracting a constant to the errors that belong to time period t cannot drive their correlation to zero. If you only have two firms, the correlation will be driven to -1, but that is just because the error for firm 1 at time t must be equal and opposite to the error for firm 2 at time t in that case. With even three firms in the sample, as above, one can no longer predict what will happen to the correlation across firms.

Kit

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html

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