There is quite a bit of recent literature on this. Most of it probably
advises against doing mediation analysis at all unless you meet criteria
such as sequential ignorability (laid out by Imai et al). See, for example:

   - Bullock, John G., and Shang E. Ha. 2011. Mediation Analysis is Harder
   Than it Looks. In Cambridge Handbook of Experimental Political Science, ed.
   James N. Druckman, Donald P. Green, James H. Kuklinski, and Arthur Lupia.
   New York: Cambridge University Press.
   - Bullock, John G., Donald P. Green, and Shang E. Ha. 2010. Yes, But
   What’s the Mechanism? (Don’t Expect an Easy Answer). Journal of Personality
   and Social Psychology 98 (April): 550-58.
   - Fiedler, Klaus, Malte Schott, and Thorsten Meiser. 2011. “What
   Mediation Analysis Can (Not) Do.” Journal of Experimental Social
   Psychology. doi:10.1016/j.jesp.2011.05.007.
   http://dx.doi.org/10.1016/j.jesp.2011.05.007.
   - Green, Donald P., Shang E. Ha, and John G. Bullock. 2009. “Enough
   Already about `Black Box’ Experiments: Studying Mediation is More Difficult
   than Most Scholars Suppose.” The ANNALS of the American Academy of
   Political and Social Science 628 (March) (January): 200-208.
   - Imai, Kosuke, Luke Keele, Dustin Tingley, and Teppei Yamamoto. 2011.
   “Unpacking the Black Box: Learning about Causal Mechanisms from
   Experimental and Observational Studies.” American Political Science Review
   105 (4) (November 10): 765-789.
   http://imai.princeton.edu/talk/files/ISM10.pdf.
   - Imai, Kosuke, and Teppei Yamamoto. 2011. "Identification and
   Sensitivity Analysis for Multiple Causal Mechanisms: Revisiting Evidence
   from Framing Experiments."
   - MacKinnon, David P., Amanda J. Fairchild, and Matthew S. Fritz. 2007.
   “Mediation Analysis.” Annual review of psychology 58 (January): 593-614.
   doi:10.1146/annurev.psych.58.110405.085542.
   http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2819368&tool=pmcentrez&rendertype=abstract
   .
   - Spencer, Steven J., Mark P. Zanna, and Geoffrey T Fong. 2005.
   “Establishing a Causal Chain: Why Experiments Are Often More Effective than
   Mediational Analyses in Examining Psychological Processes.” Journal of
   Personality and Social Psychology 89 (6) (December): 845-51.
   doi:10.1037/0022-3514.89.6.845.
   http://www.ncbi.nlm.nih.gov/pubmed/16393019.



On Sat, Feb 18, 2012 at 3:47 PM, Salehyan, Idean <[log in to unmask]> wrote:

> Hi All,
>
> I'm trying to get a handle on measuring direct and indirect effects of a
> variable, but with variables that may be endogenous.
>
> Here is the basic set-up.  I have three variables, X, Y, and M, where X is
> the independent variable, Y is the dependent variable, and M is a mediator.
>  I want to estimate how much of a direct effect X has an Y as well as how
> much of the effect works through M.
>
> I know that:
> 1) X is a significant predictor of Y (X-->Y)
> 2) M is a significant predictor of Y (M-->Y)
> 3) X is a significant predictor of M (X-->M)
> 4) in a single regression, X and M are both significant predictors of Y
>
> I've looked at the Sobel test and know that M is partially mediating the
> X-->Y relationship.  However, the problem is that M and Y are clearly
> endogenous.  I can't use X as an instrument, since it doesn't meet the
> exclusion criterion (note that M and X are both significant in a single
> equation).
>
> Is there a good way of determining the direct and indirect effect of X on
> Y, knowing that M is endogenous?
>
> Thanks!
>
> Idean
>
>
>
> _____________________________
> Idean Salehyan, PhD
> Associate Professor of Political Science
> University of North Texas
> 1155 Union Circle #305340
> Denton, TX. 76203
>
> [log in to unmask]
> www.cas.unt.edu/~idean
>
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-- 
Thomas J. Leeper

PhD Candidate, ABD
Coordinator, Undergraduate Research Participation Pool
Department of Political Science
Northwestern University
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