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st: Selection bias or endogeneity with continuous treatment?


From   Lori Thompsen <lori.thompsen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Selection bias or endogeneity with continuous treatment?
Date   Mon, 28 Sep 2009 12:08:37 -0400

Hi Statalisters!

I'm hoping that someone can point me in the right direction here. I am
trying to assess the impact of advertising through two different
channels on the sales of products. The issue is that some of the
products are featured on one, both, or neither of the channels. I have
sales data for everything in my sample, so it doesn't seem like an
endogenous sample selection problem (which, after going through many
texts, might be addressed by propensity score matching or Heckman
two-step). Also, my "treatments" are not binary, but reflect the
number of promotions on each channel. Further complicating the problem
is that I don't really have any good observables that can explain why
some are selected for treatment, since I'm dealing with differentiated
products.

I've gone through the archives and found a post from 2007 on a similar
issue (st: treatreg with a continuous self-selected treatment) and the
FAQ on sample selection versus endogeneity. I also read Austin
Nichol's "Causal inference with observational data: Regression
discontinuity and related methods in Stata", which was tremendously
helpful. So it seems like in my case that selection occurs due to some
unobservable factor. Does this make it a problem of endogeneity
(omitted variable)? If I use panel data methods to control for the
unobserved characteristics, will that address the "selection" problem?

Also, for those products that aren't featured on one or both channels,
there are a lot of "missing observations" since they weren't
advertised on a particular channel. I replaced these observations with
zero because otherwise they would be dropped if I run a regression.
What is the difference between using these observations with zeros, or
just leaving them out altogether?

I've kind of hit a wall with this and could really use some advice.
Many thanks for any help!

Best,
Lori

-- 
Lori Thompsen
lori.thompsen@gmail.com
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