Assessing presence of causal mediation with ivreg2

[David Quinn]

Hello,

I am trying to run a causal mediation analysis with an endogenous, dichotomous mediator using the user-written Stata module -ivreg2- (Baum, Schaffer, and Stillman 2010). I chose this module because of the endogeneity of the mediator (hence the need for 2sls), and I am using Stata 11. My dependent variable, treatment variable, and mediator variable are all dichotomous.

My equation is as follows:

ivreg2 y x1 x2 x3...x10 (m=z1 z2...z6), robust first

Where,
y = dependent variable
x1 = treatment variable (included instrument)
x2...x10 = control variables for outcome equation (included instruments)
m = mediator variable (endogenous mediator being instrumented)
z1...z6 = independent variables in mediator equation (excluded instruments)

I chose to report robust standard errors due to my outcome being dichotomous (and the associated violation of i.i.d.).

I am a bit confused by the output, particularly how to assess or test whether or not my mediator variable (m) mediates the effect of my treatment variable (x1) on the outcome. How do I test for and isolate the mediated effects of m on the relationship between x1 and y?

Also, it doesn't appear that bootstrapping is an available option with -ivreg2-. Is that correct? Since I'm working with non-linear relationships, that would seem to be more useful and appropriate than simply reporting robust standard errors.

Thanks in advance for any insight that you may have!

--David Quinn


References
Baum, C.F., Schaffer, M.E., Stillman, S. 2010. "ivreg2: Stata module for extended instrumental variables/2SLS, GMM and AC/HAC, LIML and k-class regression." http://ideas.repec.org/c/boc
/bocode/s425401.html

[David Quinn]

Following up on my previous message, I have done some additional investigation, both of the user-written -ivreg2- module (see reference above) (as well as Stata's native -ivregress- module) and my approach to setting up the equation. I think that my construction of the equation may be incorrect, but I remain confused about how -ivreg2- and -ivregress- can be used to test for and assess causal mediation.

Let me start by describing what I am trying to test. I have an observed treatment variable (x1) that I think has both a direct and indirect effect on my outcome variable (y), with the indirect effect occurring through an observed, endogenous mediator variable. The mediator is endogenous with respect to the treatment. I also have several observed, exogenous control variables that may affect the outcome variable (x2...x10), and several observed, exogenous control variables that may affect the mediator variable (z1...z6).

It is my understanding that when using -ivreg2- and -ivregress- to conduct a mediation analysis with an endogenous mediator, you instrument for the endogenous mediator. So, with that in mind, do I need to move the treatment variable (x1) into the Stage 1 equation? In other words, the Stage 1 equation would look like this: (m=x1 z1...z6). And it seems to me that I also need to keep the treatment in the Stage 2 equation since I am also trying to assess its direct effect on the outcome. Is that correct? How is one able to assess whether or not mediation is present, and if so, both the direct effect of the treatment (x1) on the outcome (y) and the indirect effect of the treatment (x1) through the endogenous mediator (m) on the outcome (y), using -ivreg2- or -ivregress-?

Also, is it the case that in order to avoid inconsistent estimation, I have to include all controls in both stages/equations, even if theoretically x2...x10 should only affect the outcome (Stage 2) and z1...z6 should only affect the mediator (Stage 1)?