Re: st: 2SLS and Instrumental Variables

 From Richard Williams <[email protected]> To [email protected] Subject Re: st: 2SLS and Instrumental Variables Date Fri, 10 Dec 2004 14:09:31 -0500

```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.

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