Re: st: mediation in constant coefficients panel regression

[Stas Kolenikov <skolenik@gmail.com>]

On Wed, May 19, 2010 at 9:20 AM, Sarita Koen <sarita_verslagen@yahoo.com> wrote:
> Dear statalist users,
>
> Currently I am testing for mediation in a constant coefficients panel regression.
>
> I will run three panel regressions with xtgls following Baron and Kenny
> (1986):
> (1). Regress the two mediators on the independent var
> (2). Regress the outcome var on the independent var
> (3). Regress the outcome var on both the independent var and two mediators
>
> and compare the coefficients.
>
> A previous thread discusses measuring the strength and significance of the mediation effect through an adjusted Sobel test with panel data.
> http://www.stata.com/statalist/archive/2010-05/msg00599.html
>
> Are there any further recommendations or additional literature I can take into consideration? Thank you.

I personally have always been puzzled by Baron and Kenny
recommendations (it would be great if you gave the full reference, so
that we don't look like two secret agents using code language :)).
There is no legal way to test the equality of the independent variable
coefficients in (2) and (3), although of course you can assess whether
the coefficients of the mediators are zeroes, and the coefficient of
the independent variable is zero in (3).

To me, since you are dealing with a system of regression equations,
you should estimate it with -reg3-. The (econometric) literature on
simultaneous equations has already been there for at least twenty
years before Baron & Kenny's paper, and it is VERY unfortunate that
they were not familiar with it. It does deal properly with the
measurement errors in mediators, one of the biggest problems in the
whole Baron-Kenny approach.

Also, I don't know how the Baron-Kenny framework can be extended to
the panel data models. In each of the regressions, you add a random
effect term, so in the end you have a multilevel model with three
random effects (one for each dependent variable). You should estimate
such model with -gllamm- or -xtmixed- (if you can trick the latter
into admitting three random effects; I don't know how to do that,
frankly). Otherwise, your estimation procedure is not internally
consistent.

-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.
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