Re: sample adjustments

On Tue, 19 Feb 2008, Paul Chaney wrote:

> Hello everyone. I have been running the program to determine whether my
> observations are in the 'convex hull' or not. I have two samples of
> clients of auditors (2,000 clients of large auditors and 225 clients of
> small auditors). I intend to compute counterfactuals for auditor
> pricing. I determine that 41% of the clients of small auditors and 21%
> of the clients of large auditor are in the convex hull. I have the
> following questions.
>
> 1. Should I repeat my entire analysis using only observation contained
> in the convex hull or should I only compute counterfactuals for
> observations within the convex hull? (Or will counterfactuals just not
> be appropriate?)

you get to decide what is appropriate.  a counterfactual outside the 
convex hull is probably more model dependent and less secure than one 
inside and near the data.  so if there are lots of counterfactuals outside 
then that's a good warning sign.

>
> 2. Our primary competition for our paper uses propensity score matching
> with common support. Can anyone tell me the advantages and disadvantages
> of propensity score versus the convex hull solution?

it depends on how they compute 'common support'.  one way would be to use 
the convex hull.  probably they are computing the pscore and looking at 2 
overlapping histograms.  that is not so different from the convex hull, 
if the pscore is a good summary of X.  but there is no theorem that says 
the pscore will be a good summary for any empirical data unfortunately, so