Re: RE: st: Robust Standard Errors in Paneldatasets

[Stas Kolenikov <skolenik@gmail.com>]

On Tue, Oct 26, 2010 at 11:16 AM, Amy Dunbar
<Amy.Dunbar@business.uconn.edu> wrote:
> Obviously I am still missing a critical point.  Could you help understand your point about time dummies not correcting for cross-sectional correlation?

Imagine that you have a canvas with threads running vertically and
horizontally. The ones running from top to bottom are time series for
a given panel; the ones running across are the cross-sections at a
given point in time. Let us represent correlations in the data set by
a color; say the vertical correlations over time are blue, and the
horizontal cluster correlations are red. If the values next to one
another are closely related, you have a strong color, and if there
isn't much relation between the adjacent observations, it is white.
Thus the whole canvas will look like kinda purple, with some spots
having stronger blue hues, and others having stronger red hues, and
yet others being somewhat faded. Your goal is, obviously, to make
everything look white, or at least gray, which is our standard i.i.d.
of the errors assumption.

Your time dummies act pretty much like a bleach... not quite a bleach
though as the dummies change the color into gray: you lose some
information (e.g., you cannot estimate variables that vary with time,
but constant across firms). You apply them to your data set, and you
pretty much get rid of the vertical blue threads making them gray
threads. What happens to the horizontal threads? Well, nothing; the
bleach only works in one direction.

Your cluster corrections works more like a color filter. You don't
kill a color, but you learn to ignore it. So to the remaining
reddish-brownish picture, you apply the "ignore red" color filter. As
all color filters, it will make the picture a little darker, so you
lose some accuracy in estimation, and your confidence intervals have
bad coverage in small samples. But at least the picture looks kinda
dark-gray now, and you hope that your standard errors are not affected
too badly by any remaining correlations.

-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.

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