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st: [Fwd: Endogeneity in Bivariate Probit]


From   mmolina@uniroma3.it
To   statalist@hsphsun2.harvard.edu
Subject   st: [Fwd: Endogeneity in Bivariate Probit]
Date   Sun, 9 Aug 2009 18:07:46 +0200 (CEST)

Thank you Cameron.
Mi model is:
y1* = alpha1 + betaY2* + e1
y2* = alpha2 + betaX + e2
where y1 (0,1) is innovation in product and y2 (0,1) is innovation in
process.
I supossed that both inlfuence each other and put them in a system. X
represent other factors such as foreign ownership, quality certification
and also two dummies (for 3) different sizes.
For two of the selected countries I received low Prob > chi(2) and for the
third, these results.

Likelihood-ratio test of rho = 0 :      chi2(1) = 2,1962
Prob > chi(2) = 0,1383

I was wondering if these results imply endogenity.
Best,
Alejandra


Hi Alejandra,

So if I understand your model specification correctly, it is along the
lines of some mediational model (let's say the underlying response variate
y2* is the mediator between some IV X and the ultimate outcome y1*):

y1* = alpha1 + betaX + betaY2* + e1
y2* = alpha2 + betaX + e2

Then you are asking if a test of cov(e1,e2) = 0 under the 'biprobit' is
equivalent to a Hausman test of endogeneity. Indeed, the Knapp and Seakes
(1998) paper is oft-cited in the bivariate probit context for this
purpose, but I am not 100% sure if it can be invoked in this case. (I
could be wrong). Mediational models bring in a number of issues about the
proper direction of causal flow among the variables in the system. Of
course, cov(e1,e2) = 0 is necessary for getting good overall empirical
model fit (implying, for example, that no common causes of y1* and y2* 
have been omitted), and thus unbiased estimates, but I don'[t know if this
automatically implies endogeneity in the sense that cov(y2*,e1) = 0
(unless X is being regarded as an instrument here), and I believe that
more is involved for convincingly demonstrating the properness of the
postulated causal chain. I would suggest having a look at:

James, L.R., Mulaik, S.A., & Brett, J.M. (2006). A tale of two methods.
Organizational Research Methods, 9(2), 233-244.

Further, quantifying the degree of mediation in probit (and logit) models
is more complicated than in the linear case:

MacKinnon, D.P., Lockwood, C.M., Brown C.H., Wang W., & Hoffman M. (2007).
The intermediate endpoint effect in logistic and probit regression.
Clinical Trials, 4(5), 499-513.

For more general readings on mediation see:

MacKinnon, D.P. (2008). Introduction to statistical mediation analysis.
Mahwah, NJ: Erlbaum.

MacKinnon, D. P., & Fairchild, A. J. (2009). Current directions in
mediation analysis. Current Directions in Psychological Science, 18,
16-20.

Hope this is helpful, and that I have understood the situation correctly.

Cam






-------------------------- Messaggio originale ---------------------------
Oggetto: Endogeneity in Bivariate Probit
Da:      mmolina@uniroma3.it
Data:    Dom, 9 Agosto 2009 1:51 am
A:       statalist@hsphsun2.harvard.edu
--------------------------------------------------------------------------

Dear Statalist,
I found on the Statist archive that Knapp and Seaks argue that a
likelihood-ratio test of the correlation coefficient of the residuals
(rho) can be used as an endogeneity test.
On the other hand I read that if "the second dependent variable, y2,
appears on the right-hand side of the first equation, this is a recursive,
simultaneous-equations model. Surprisingly, the endogenous nature of one
of the variables on the right-hand side of the first equation can be
ignored in formulating the log-likelihood" (Greene, 2002, pp.715).
I run my model for three countries and only in one case I obtained these
results:

Likelihood-ratio test of rho = 0 :      chi2(1) = 2,1962
Prob > chi(2) = 0,1383

Should I consider that y2 variable have passed the endogeneity test?
Thanks in advance and regards,
Alejandra Molina


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