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RE: st: Interaction Variables as Instruments

From   Cameron McIntosh <>
Subject   RE: st: Interaction Variables as Instruments
Date   Fri, 20 Jan 2012 18:11:10 -0500


Is this a wage differential analysis? At first glance, your instrumenting seems confusing and strikes me as overkill (and you have a 3-way interaction m*x*z_1?), but for now I'll let others chime in on that...

I think you may want to see this paper:

Overton, R.C. (2001). Moderated multiple regression for interactions involving categorical variables: a statistical control for heterogeneous variance across two groups. Psychological Methods, 6(3), 218-233.

and also look into Blinder-Oaxaca decompositions, as these will help you quantify intergroup gaps and the degree to which given predictors are responsible for those gaps:

Jann, B. (2008). The Blinder–Oaxaca decomposition for linear regression models. The Stata Journal, 8(4), 453-479.

Jann, B. (May 6, 2008). OAXACA: Stata module to compute the Blinder-Oaxaca decomposition.

Elder, T.E., Goddeeris, J.H., & Haider, S.J. (2010). Unexplained gaps and Oaxaca–Blinder decompositions. Labour Economics, 17, 284–290.

Emamian, M.H., Zeraati, H., Majdzadeh, R., Shariati, M., Hashemi, H., & Fotouhi, A. (2011). The Gap of Visual Impairment Between Economic Groups in Shahroud, Iran: A Blinder-Oaxaca Decomposition. American Journal of Epidemiology, 173, 1463-1467.
Ñopo, H. (2008). An extension of the Blinder–Oaxaca decomposition to a continuum of comparison groups. Economics Letters, 100(2), 292-296.
Heinrichs, J., & Kennedy, P. (2007). A computational trick for calculating the Blinder-Oaxaca decomposition and its standard error. Economics Bulletin, 3(66), 1-7.


> Date: Fri, 20 Jan 2012 10:58:23 -0500
> Subject: st: Interaction Variables as Instruments
> From:
> To:
> Dear statalist,
> I am having some programming trouble with 2SLS and would appreciate any help :)
> I want to estimate a 2 stage least squares model.  The goal is to
> estimate the relationship between x and y.  x is not exogenous.
> Consider 2 groups (e.g. men and women), represented by z_1.  Consider
> a policy that affects one group relative to the other, represented by
> z_2.  The first stage is therefore:
> x = constant + a*z_1 + b*z_2 + c*z_1*z_2 + e
> I am not sure what the second-stage should be and how to implement it
> in Stata. Would the second stage be
> y = constant + k*x + u, instrument x with the z_1, z_2, and z_1*z_2
> y = constant + k*x + l*z_1 + u, instrument x with z_2 and z_1*z_2
> y = constant + k*x + l*z_1 + m*x*z_1 + u, instrument x and x*z_1 with
> z_2 and z_1*z_2
> I am having difficulty because z_1 is not the exogenous source of variation.
> The goal is to say that the gap between group 1 (e.g. men) and group 2
> (e.g. women) with regards to y has narrowed because of a reduction in
> the corresponding gap in x, and the reduction in the gap in x is the
> result of exogenous policy z_2.
> Any help would be very much appreciated :)
> *
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