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Re: st: Modeling simultaneity
From
John Antonakis <[email protected]>
To
[email protected]
Subject
Re: st: Modeling simultaneity
Date
Tue, 05 Feb 2013 19:08:39 +0100
Hi Pavlos:
You are estimating:
abs = b0 + b1Div + b2x1 + e
div = g0 + g1abs + g2x2 + u
perf = d0 + d1abs + d2div + w
Where x1 and x2 are instruments, and where cov(e,u; e,w; and u,w) are
estimated.
Note, the above system of equations is just identified. You have
5(5+1)/2 = 15 elements in the variance-covariance matrix and estimating:
1. Correlations between exogenous variables: 1
2. Correlations between disturbances: 3
3. Regressions coefficients: 6
4. Variances of exogenous variables: 2
5: Variances of endogenous variables: 3
Total parameters estimated: 15
Thus, your DF = 15-15 = 0. This model can be estimated, but because you
are not cannot overidentified you cannot determine whether the
constraints you make are tenable via a chi-square test of fit (i.e.,
Hansen-Sargan test). Thus, I would recommend to you to find at least
another instrument, x3 in the abs and/or div equation to be overidentified.
You can estimate this system of equations with reg3, as follows:
reg3 (abs div x1) (div abs x2) (perf abs div), 2sls
est store two
(if you are overidentified, you can test for this if download the user
command -overid- (from SSC)).
Note, I would first estimate this with 2sls to ensure that any
mispecification remains local. I would then rerun it with 3sls, which is
more efficient and compare that estimator with the first:
reg3 (abs div x1) (div abs x2) (perf abs div),
est store three
hausman two three
If they don't differ you can retain the 3sls estimator.
You can estimate this in sem too (with maximum likelihood), which will
give you more information on the estimated parameters (note to have an
instrumental variable estimator you must correlate disturbances of the
endogenous variables explicitly).
sem (abs <- div x1) (div<- abs x2) (perf y<- abs div),
covstructure(e._OEn, unstructured)
Or you can do the cov option explicitly:
sem (abs <- div x1) (div<- abs x2) (perf y<- abs div), cov(e.abs*e.div,
e.abs*e.perf, e.div*e.perf)
-sem- will give you an overidentification test (chi-square test on the
bottom of the table)
We discuss these issues in an applied manner here:
Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (2010). On
making causal claims: A review and recommendations. The Leadership
Quarterly, 21(6). 1086-1120.
http://www.hec.unil.ch/jantonakis/Causal_Claims.pdf
[If you wish, refer to the following “prequel” paper, which is really a
more basic introduction--and we explain overidentification explicitly]:
Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (submitted).
Causality and endogeneity: Problems and solutions. In D.V. Day (Ed.),
The Oxford Handbook of Leadership and Organizations.
http://www.hec.unil.ch/jantonakis/Causality_and_endogeneity_final.pdf
HTH,
John.
__________________________________________
John Antonakis
Professor of Organizational Behavior
Director, Ph.D. Program in Management
Faculty of Business and Economics
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis
Associate Editor
The Leadership Quarterly
__________________________________________
On 04.02.2013 15:03, Pavlos C. Symeou wrote:
Dear Statalisters,
I was wondering whether any of you can help me with this.
I have three variables: Absorptive capacity, Diversification, and
Performance. I am arguing that the first two are simultaneously
determined and they influence the third one.
Explicitly, I am arguing that the ability of the firm to understand
new knowledge (what is called Absorptive Capacity AC) influences the
direction of the firm's market diversification (DIV). However, once
the firm has diversified, it in turn influences the firm's ability to
understand new knowledge (AC). I want to empirically account for this
simultaneity when I try to examine the effect of AC and DIV on the
performance of the firm.
I can use instrumental variables to model the simultaneity, but I
don't know how to examine the final effects of AC and DIV on firm
performance while controlling for simultaneity.
I look forward to receiving your comments.
Best,
Pavlos
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