Re: st: coefficient explanation

[John Antonakis <John.Antonakis@unil.ch>]

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. 
http://www.hec.unil.ch/jantonakis/Causal_Claims.pdf

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

http://www.youtube.com/watch?v=dLuTjoYmfXs

HTH,
John.

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. 
http://www.hec.unil.ch/jantonakis/Causality_and_endogeneity_final.pdf

__________________________________________

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 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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