I received an email from Tymon Słoczyński (Warsaw School of Economics), about a recent paper of his, titled, "New Evidence on Linear Regression and Treatment Effect Heterogeneity". Tymon wrote:
"I have recently written a new paper, which I believe that you might find interesting, given some of your blog posts that I have read.
This paper is available here (as an IZA DP No. 9491): http://ftp.iza.org/dp9491.pdf; or from my website: http://akson.sgh.waw.pl/~tslocz/Sloczynski_paper_regression.pdf.
This paper implicitly criticizes the standard approach in reduced-form applied microeconomics to use very simple linear models and estimate them using OLS (or 2SLS). I provide a new interpretation of the least squares estimand in the constant-effects linear regression model when the assumption of constant effects is violated (so there is, in fact, "treatment effect heterogeneity"). This new interpretation is very pessimistic: in particular, I prove that the weight that is being placed by OLS on the effect on each group ("treated" or "controls") is inversely related to the proportion of this group. This property might have severe consequences for applied work, and I demonstrate this via a replication of two recent papers from the American Economic Review."
Tymon's paper is, indeed, very interesting. I recommend that you read it. It should serve as a 'wake-up call' to some of our empirical micro. friends!