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st: Direct and indirect effects for logit models


From   Fardad Zand <fardad.zand@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Direct and indirect effects for logit models
Date   Sat, 22 Aug 2009 17:42:13 +0200

Dear Lister,

I'm doing a research to distinguish and compare the direct and
indirect effects of enterprise systems (such as erp, scm, crm, etc.)
on firm performance using a firm-level dataset. I'm using conditional
logit (clogit) to control for market-specific fixed-effects in my
sample; you can think of a market as sector X in country Y. This is
seemingly a preferred approach than adding (a lot of) separate sector
and country dummies into the model; the method is described by
Chamberlain (1980).

Now the main issue is indeed to rigorously separate the direct and
indirect effects of enterprise systems adoption on firm performance.
Performance is measured as a dummy variable indicating if the firm has
been profitable or not or alternatively if it has experienced revenue
growth or not. The enterprise systems adoption is measured through
separate dummy variables for different applications such ERP, SCM,
CRM, etc. indicating if the firm uses a specific application or not.
For comparative purposes, these adoption variables shall be considered
simultaneously in the model.

In addition to the direct effect of these systems on firm performance,
their impact is also mediated through product and process innovation,
which are measured as separate dummies indicating if the firm has had
product and/or process innovation. So, ignoring the coefficients and
error terms, for simplicity, the available equations can be shown as:

1- ln(odds(performance)) = erp + scm + crm + control
2- ln(odds(product_innov)) = erp + scm + crm + control
3- ln(odds(process_innov)) = erp + scm + crm + control

The “control” is a vector of control variables including several dummy
and continuous variables to control for size, IT maturity, etc.

At this stage, I started to look into the literature (and there is
plenty of them in different fields :-((() and found several references
to implement my model specification in STATA; I’m really confused
which method is relevant/applicable and which not:

A. As a simple approach, I can run model (1) and separately another
model which has extra innovation variables as explanatory variables
(i.e. ln(odds(performance)) = product_innov + process_innov + erp +
scm + crm + control) to compare the direct and indirect effects. If
I’m right, the difference between the estimated coefficients of
interest (i.e. erp, scm and crm) between the two models indicates the
indirect effect.

B. I can use SEM to simultaneously estimate the set of three Eq. (1),
(2) and (3); however, I don't know exactly how I can do SEM for
non-linear models in STATA and further how the direct and indirect
effects should be calculated afterwards.

C. I can use a pseudo-2SLS method, in which I first run (2) and (3)
and then insert the predicted values of product and process innovation
as extra explanatory variables into (1); this is similar to approach
A, except that predicted values of innovation variables are used
rather than their actual 0/1 values. I still don’t know if the
prediction procedure indeed generates valid predicts in the range
[0,1].

D. As an alternative of method C, I can add an additional regressor to
(2) and (3) when predicting innovation outcomes. The percentage of
highly-educated employees can serve as a good instrument here. This
way, the set of control variables includes this additional variable in
(2) and (3) but not in (1).

E. I can use the IVE-GMM method for log-linear models; I know it
exists in STATA 11 but honestly don't know how to use it or if it
serves my objectives. I’m also not aware of any additional assumptions
required for this method.

F. I can use the -ldecomp command in STATA but seemingly it doesn't
allow for multiple direct variables to be considered. For me it is
important to have erp, scm and crm at the same time in the model to
compare their relative impacts on the performance outcome.

G. There is also the -fairlie method; I'm not familiar with it and
also don't know exactly how it differs from -ldecomp or similar
commands.


All in all, I'm really puzzled :-(( don't know what method(s) are the
favorable ones in terms of practical interpretations, consistency of
results and estimation efficiency.

I thought, you might be able to provide me with any guideline, advice
or recommendation, concerning your expertise and experience, as I'm
not an econometrician per se.

I know this is a very long email and would take a lot of your time to
read and perhaps reflect on; however, I should have explained what
happened to me within the past weeks. Nevertheless, I really
appreciate your help and support.

Many thanks indeed,
Fardad

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