Wednesday, April 05, 2006
Last night, some friends and I were wondering what effect the crazy variation in weather has on visiting pre-frosh. Some pre-frosh make their campus visits during 70 degree days where campus is abuzz -- people are happy, wearing fewer clothes, tossing the frisbee around, etc. . Other pre-frosh visit on miserable days like today -- people are dour, bundled-up, scurrying to escape the snow. We are curious to know what effect weather has on the number and composition of students who enroll. Do fewer students enroll? Do different types of students enroll? Harvard may not be the best place to look at this because it's yield is already so high, but it might have noticeable effects on students admitted to other schools.
It would be super cool if there were noticeable effects along the selectivity margin because then we might be able to estimate the returns to attending a more selective college. That is, if there are a significant number of students admitted to selective colleges who are more likely to attend a less selective college (e.g., their local public institution) when their pre-frosh visit is marred by bad weather, we could use weather during the pre-frosh weekend as an instrument for attending a more selective college.
Recall, an instrumental variable is something that is used to produce unbiased coefficient estimates when there are problems with omitted variables or simultaneity. It is a variable that is correlated with the regressor of interest (in this case attending a more selective college) but uncorrelated with the error term in the OLS specification (that is, it is only correlated with the outcome (Y) through its correlation with the regressor (X)).
If the effects discussed above are observed, then pre-frosh weather would work as an instrument. It would be correlated with attending a selective college, but, since the weather is random, it would be uncorrelated with the error term. As such, we could use it to produce unbiased estimates for the returns to attending a more selective college.
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