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Re: st: Modeling simultaneity

From   John Antonakis <>
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.

[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.



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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