At 04:56 PM 12/10/2004 +0000, you wrote:
I'm not 100% sure I understand the questions but I will take a crack at it.
regress Y1 X1 X2 Z1-Z4 Y2res
How do I reconcile the two arguments below--
(a) Z1-Z4 should come out to be significant since if we substitute Z1-Z4
by Y2hat, Y2hat comes in significant VERSUS
Jointly significant, perhaps (not 100% sure), but not necessarily
individually significant.
(b) According to the theory behind IV, there should be no direct causal
impact of the instruments on Y1. So Z1-Z4 cannot explain Y1 and hence
should not be significant. Is this statement wrong?
Speaking generally -- variables which have 0 direct effect can nonetheless
have important indirect effects. So, if the model is specified correctly,
the estimated direct effects will be zero or thereabouts. BUT, if the
model is specified incorrectly, and you leave out the intermediate
variables, then the variables which really only have indirect effects can
have estimated direct effects that are statistically significant.
A simple example I do in class: Income is regressed on a dummy variable for
race, and the effect is highly significant. Income is then regressed on
race and education -- the effect of race then becomes
insignificant. Possible implication: the effect of race on income is
indirect -- race affects education and education affects income. When you
leave education out of the model the indirect effect of race gets
mis-estimated as a direct effect.
In your case, you seem to be saying that z1-z4 affect y2 which affects
y1. Leave y2 out of the model and the effects of z1-z4 could be
mis-estimated as non-zero.
Also according to (a) multicollinearity would explain why Z1-Z4 may not
come out significant individually but they are jointly significant. Im
wondering why multicollinearity shows up when we regress Y1 on Z1-Z4 and
not when we regress Y2 on Z1-Z4.
Strength of association is one possible explanation. Z1-Z4 may have
stronger effects on some variables than on others. The stronger the
relationship, the more likely you are to get significant results, even when
variables are collinear.
-------------------------------------------
Richard Williams, Associate Professor
OFFICE: (574)631-6668, (574)631-6463
FAX: (574)288-4373
HOME: (574)289-5227
EMAIL: [email protected]
WWW (personal): http://www.nd.edu/~rwilliam
WWW (department): http://www.nd.edu/~soc
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
