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Re: st: Modeling simultaneity

From   "Pavlos C. Symeou" <>
To, John Antonakis <>
Subject   Re: st: Modeling simultaneity
Date   Thu, 07 Feb 2013 15:14:41 +0200

Dear John,

thank you for this. Do the procedures you suggest below have respective commands for panel data structures? In this context, I suppose I could use the lags of my endogenous variables as their instruments.

Best wishes,


On Τρίτη, 5 Φεβρουάριος 2013 8:08:39 μμ, John Antonakis wrote:

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

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.

[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



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
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305

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.


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