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RE: RE: st: Robust Standard Errors in Paneldatasets

From   Amy Dunbar <[email protected]>
To   "[email protected]" <[email protected]>
Subject   RE: RE: st: Robust Standard Errors in Paneldatasets
Date   Thu, 28 Oct 2010 00:26:04 +0000

What a great analogy!  I'm going to forward your response on to my class.  Thank you, Stas.

-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Stas Kolenikov
Sent: Wednesday, October 27, 2010 8:18 PM
To: [email protected]
Subject: Re: RE: st: Robust Standard Errors in Paneldatasets

On Tue, Oct 26, 2010 at 11:16 AM, Amy Dunbar <[email protected]> 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 Small print: I use this email account for mailing lists only.

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