Tuesday, March 17, 2015

Today's little epiphany

The worst possible case of omitted variable bias in estimating the causal effect of Z on Y would be if Z had no direct causal effect on Y whatsoever, but was highly correlated with Y entirely because of Z's correlation with some other confounding variable X that causes Y. Then the regression coefficient on Z would be nothing but omitted variable bias! But what if you changed your mind and decided you were actually more interested in the causal effect of X on Y? Then Z, of course, would be a perfect instrumental variable!

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