The elite school illusion

15 Dec, 2020 at 19:28 | Posted in Economics | 1 Comment

 

A great set of lectures — but yours truly still warns his students that regression-based averages is something we have reasons to be cautious about.

Suppose we want to estimate the average causal effect of a dummy variable (T) on an observed outcome variable (O). In a usual regression context one would apply an ordinary least squares estimator (OLS) in trying to get an unbiased and consistent estimate:

O = α + βT + ε,

where α is a constant intercept, β a constant ‘structural’ causal effect and ε an error term.

The problem here is that although we may get an estimate of the ‘true’ average causal effect, this may ‘mask’ important heterogeneous effects of a causal nature. Although we get the right answer of the average causal effect being 0, those who are ‘treated’ (T=1) may have causal effects equal to -100 and those ‘not treated’ (T=0) may have causal effects equal to 100. Contemplating being treated or not, most people would probably be interested in knowing about this underlying heterogeneity and would not consider the OLS average effect particularly enlightening.

The heterogeneity problem does not just turn up as an external validity problem when trying to ‘export’ regression results to different times or different target populations. It is also often an internal problem to the millions of OLS estimates that economists produce every year.

1 Comment

  1. Looking out the window of sanctity, too conserve purity of thought, and then amplify it with numerology of different ilks is not a proof of truth or fact, especially when reality observed is not static, for the observer or the observed depending on the ever changing environment.


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