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RE: st: RE: How to perform a Wald test between the fixed effect...

From   Frank Barbera <>
To   "" <>
Subject   RE: st: RE: How to perform a Wald test between the fixed effect...
Date   Thu, 21 Feb 2013 17:29:43 +1000

First off, I'd like to thank Dave and John for their responses. 

John, your work on this issue has been very helpful in particular. And (when there's time) I'll be sure to read the Allison book which Dave has mentioned. With that said, I have already considered Mundlak's approach, but the issue of performing the Wald test within the fixed set-up remains (as this will be compared to the random and Mundlak estimates). 

With respect to my previous message, I've been playing with a toy dataset and noticed that if I -generate- the following id variables... 

	generate ffid = id*ff

	generate nfid = id*(1-ff)

which separates the id into two groups (ff and nf). To estimate the ai's...

	xi: regress y x i.ffid i.nfid, noconstant

which, unbeknownst to me, creates a dummy for each firm (coded as _Iffid_i, where i = {1...10} in my toy dataset. The fist 5 blong to ff while the last 5 belong to nf). Then for the restriction, Wald test of the average ai ff = average ai nf by...

	test ( _Iffid_1+_Iffid_2+ _Iffid_3+_Iffid_4+ _Iffid_5)/5 = (_Infid_6+ _Infid_7+_Infid_8+_Infid_9+_Infid_10)/5

	F(  1,     9) =    0.38
            	Prob > F =    0.5532

which seems to have worked (albiet there is no ff effect). Can anyone confirm if this procedure is correct? If so, how to do the final step for 3450 dummies? 

Sorry for the basic questions, but I'm completely new to Stata.

Frank Barbera

-----Original Message-----
From: [] On Behalf Of John Antonakis
Sent: Thursday, 21 February 2013 3:20 AM
Subject: Re: st: RE: How to perform a Wald test between the fixed effect...

Hi Frank:

See the following, with the basic explanations about the Mundlak procedure:

Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (2010). On making causal claims: A review and recommendations. The Leadership Quarterly, 21(6). 1086-1120.
(refer to the paper by Mundlak for technical explanations)

Try this (suppose you want to test for race):

webuse nlswork
xtset idcode
xtreg ln_w race age , fe r
est store fe

*notice race gets kicked out

bys idcode: egen mean_race = mean(race)

xtreg ln_w race age , re r
est store re

est tab fe re, se t

So, you can have your cake an eat it too. A fixed-effects estimator with time-invariant predictors.

So, basically, if you include the cluster means of all time-varying variables, and assuming that ff is exogenous, then you can interpret the coefficient of ff.



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 20.02.2013 17:57, Jacobs, David wrote:
> You might find Paul Allison's book in the paperback Sage series on methods (it has fixed-effects in the title) to be quite useful.  In it Allison outlines a way to estimate time-variant explanatory variables with fixed-effects combined with (or included in the same model) a random-effects estimate of one or more time-invariant explanatory variables.  Of course, the estimate of the coefficient on the time-invariant explanatory variable may suffer from omitted variable disturbances due to the absence of the automatic controls in the non-fixed-effects estimate, but a solution like this may be your only choice.
> I understand that I am not answering your exact question, but this quite different approach may nevertheless suffice.
> Dave Jacobs
> -----Original Message-----
> From: 
> [] On Behalf Of Frank 
> Barbera
> Sent: Wednesday, February 20, 2013 4:59 AM
> To:
> Subject: st: How to perform a Wald test between the fixed effect...
> Dear Stata users, I'm attempting to perform what appears to be a 
> relatively simple procedure in Sata, but due to my lack of experience 
> with the program, I'm having a really hard time. I'm using a panel to 
> estimate a the following standard fixed effects model
> (1)	yit = ai + bxit + eit.
> Where i are individual firms (3450 firms, coded as 'id') and t is time 
> (3 years, coded as 'time'). Each firm can further be classified as 
> belonging to a group (called 'ff') or not (I'll call these 'not ff'). 
> This is done by way of a dummy variable equating to 1 if the firm is 
> in the ff group and 0 otherwise. The problem is that ff is time 
> invariant, so its effect cannot be directly estimated in the model 
> (it's been absorbed into ai). Of course a random effect specification 
> would allow me to observe the ff effect on y, but the data violate the 
> assumption of no correlation between the unique errors and the 
> regressors, so the fixed effect model is preferred. I took a closer 
> look at the estimates for ai by way of the following command
> regress y x, noconstant
> and simply compared the average ai for firms in the ff category with those in the not ff category. I now wish to officially test if the average ai (for ff firms) = average ai (for not ff firms), or in other words if the ff effect is significant. A Wald coefficient test with the restriction that average ai (for ff firms) - average ai (for not ff firms) = 0 should do it, but since I estimated (1) using the option, I have no idea how to do this within (1). i.e. I do not wish to perform a fixed effect vector decomposition in multiple stages.
> Can anyone help?
> Frank Barbera
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