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Re: st: coefficient explanation

From   John Antonakis <>
Subject   Re: st: coefficient explanation
Date   Sat, 15 Jun 2013 10:25:10 +0200

Hi Kayla:

If you work through Equations 2 to 5c of the following article (there is nothing more than just simple algebra in there), you will better understand what you are seeing. How you estimate change will also depend on beta2 and gamma1:

Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (2010). On making causal claims: A review and recommendations. The Leadership Quarterly, 21(6). 1086-1120.

Also, you may benefit from looking at the following podcase, titled "Endogeneity: An inconvenient truth"


P.S. there is also a prequel article that explains the clay pigeon problem here in more detail:

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 15.06.2013 05:41, Kayla Bridge wrote:
> Dear all,
> The model I am working with now is:
> y=beta1*x1+beta2*x2+u   (here, beta1 is significant)
> However, I realize the correlation between y and x1 is due to some other factor which is not present in the model. Therefore, I add this critical variable that can best proxy for this factor, x3, in the model. Now the model is y=beta1*x1+beta2*x2+beta3*x3+u. In this case, beta1 should weaken when x3 is present. But my question is: beta1 should have smaller magnitude than before but still significant or beta1 should be insignificant when x3 is added? If beta1 is still significant but with smaller value when x3 is added, can I say x3 is a critical value which is ignored before or correlation between y and x1 is weakened?
> Any suggestion is appreciated.
> Best,
> Kayla
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