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Re: st: Logit and the Clustered Bootstrap


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Logit and the Clustered Bootstrap
Date   Mon, 31 Aug 2009 12:58:55 -0400

Stas et al.--
I agree, but note that the bias due to estimating incidental
parameters when including a set of dummies in a logit model is
probably not too large, perhaps order 1/T so not too big a deal if you
have many years per state (T large relative to N), though you would
have to do a simulation for your particular set-up.  See e.g. recent
threads http://www.stata.com/statalist/archive/2007-10/msg01008.html
and http://www.stata.com/statalist/archive/2007-10/msg00926.html and
http://www.stata.com/statalist/archive/2007-10/msg00935.html

Also, there are solutions other than clogit/xtlogit including a
bias-corrected estimator (subtract off the first-order bias term as
discussed in e.g.
http://www.jstor.org/stable/2336755
but then you get higher variance, so maybe higher MSE) or a
kernel-based method, as discussed in
http://www.jstor.org/stable/2951556
and the many papers that cite that paper.

See also
http://www.econ.brown.edu/~tl/papers/IncidentalParameters1948.pdf
http://www.cemfi.es/~arellano/arellano-hahn-paper2006.pdf

On Mon, Aug 31, 2009 at 11:47 AM, Stas Kolenikov<skolenik@gmail.com> wrote:
> On top of the mechanical problems discussed by Austin and Jeff, I
> would like to remind that logit with dummy variables is not the same
> as conditional logit (although on most occasions the results that are
> quite similar). Conditional logit truly excludes the panel effects out
> of estimation, so Stata's bootstrap won't have any problems like
> "Oops... I dropped this variable because of multicollinearity... WHAT
> HAVE I JUST DONE? I CANNOT ESTIMATE THIS PARAMETER ANYMORE!!!" (shown
> as "x" in the -bootstrap- output when a useful option -dots- is
> specified). Logit with dummy variables is... well, it is a logit with
> dummy variables. It is not a panel data command. -xtlogit-, to my
> understanding, is identical to -clogit-. In your context, it only
> estimates one parameter (the slope of the January temperature), so it
> does not run into identification problems.
>
> Furthermore, there should be little difference of the bootstrap
> standard errors from -logit ..., cluster(division)-. If there is a big
> difference between the standard errors obtained from
> linearization/-cluster- option calculation, on one hand, and
> -bootstrap-, on the other, I won't trust either of them. The two types
> of standard errors work under pretty much the same assumptions
> (whatever warrants the asymptotic normality of the estimates as the
> number of clusters goes to infinity), so if they are wildly different,
> then those assumptions are likely not met (or you have not set up your
> bootstrap right).
>
> On Thu, Aug 27, 2009 at 4:53 PM, L S<lts40301@gmail.com> wrote:
>> I am trying to perform a clustered bootstrap in which I also include
>> fixed effects for the variable serving as the cluster identifier.  For
>> cross-sectional data on individuals in different states, I would like
>> to do a bootstrap that clusters by state, but also includes state
>> fixed effects.

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