There is a growing literature on direct and indirect effects Langche
mentions. Robins and Greenland (1992), Pearl (2001), and Robins (2003)
are the key references in that literature, but there are many more that
came out in the last year or two. It can be shown that under some (rather
strong!) assumptions you can identify indirect and direct effects by
conditioning on the post-treatment variable that lies on the causal path
between the treatment and the outcome variables. This literature has a
direct connection with the social science literature on causal mediation
analysis (e.g., Baron and Kenny 1986), which is based on path analysis and
structural equation modeling. Among political scientists, Adam Glynn
presented an interesting paper on this topic at the last year's polmeth.
Luke Keele, Teppei Yamamoto, and I have a working paper that proposes an
alternative identifying assumption and developes a new sensitivity
analysis. It's available from my website if you are interested.
Best,
Kosuke
---------------------------------------------------------
Kosuke Imai Office: Corwin Hall 041
Assistant Professor Phone: 609-258-6601
Department of Politics eFax: 973-556-1929
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Princeton, NJ 08544-1012 http://imai.princeton.edu/
---------------------------------------------------------
On Sun, 8 Feb 2009, Langche Zeng wrote:
> Carlos: controlling for variables that are consequences of a regressor will
> by definition bias the *total* effects of the regressor. Whether it is the
> right thing to do for getting at the *direct* effects depends on the
> underlying causal graph. e.g., if the relationship is Y<--X-->Z-->Y,
> controling for Z would severe an indirect path from X to Y and allow the
> estimation of direct effects; but if the graph is instead X-->Z<--U-->Y,
> where U is unobserved, then controling for Z would open the path between X
> and Y and create a spurious correlation between them when X actually has no
> effects whatsoever on Y (see Judea Pearl's book, "Causality", Cambridge,
> 2000.) If Z confounds the relationship between X and Y (e.g., when Z is a
> common cause of X and Y), not controling for Z will lead to omitted variable
> bias. So yes question is what is the underlying causal structure and how to
> learn about it from observational data. there is a large literature on causal
> structure discovery. Algorithms can be constraints based (checking
> independence conditions) or metric scoring (e.g. Bayesian learning, scoring
> posterior probabilities of candidate structures.) The Pearl 2000 book and
> Spirtes et al.'s 2000 book: "Causation, Prediction and Search" provide some
> good foundational references. Not a trivial issue by any means.
>
> Best regards,
> Langche
>
> On Sun, 8 Feb 2009, Carlos Rodriguez wrote:
>
>> Dear list participants,
>>
>> I would appreciate clarifications on this point: Controlling for
>> variables that are consequences of another regressor in the main
>> regression (i.e., overcontrolling) is said to lead to bias (right?).
>> I wonder, if that is so, how can we tell (assuming theory and common
>> sense do not help) if a right-hand side variable is a consequence of
>> another included regressor or just hihgly correlated with it? If it's
>> just correlated with that other explanatory variable and correlated
>> with the dependent variable and we excluded it, it would lead to
>> ommited variable bias, right? So how to tell? When can we safely
>> leave out a variable so as not to "overcontrol" and not risk ommited
>> variable bias?
>>
>> Finally, If we wanted to test (causal) mechanims, would it be fine to
>> include such a regressor that is a consequence of another?
>>
>> thanks!
>> carlos
>>
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