文档介绍：Recitation Notes 6
Konrad Menzel
October 22, 2006
1 Random Coefficient Models
Motivation
In the empirical literature on education and earnings, the main object of interest is the human capital
earnings function (HCEF)
2
Yi = α+ βSi + γ1Xi + γ2Xi + εi
Typically, IV estimates of the return to education are higher than OLS even though we’d thought that
OLS already suffered from an upward ability bias (for a summary of results from prominent studies, see
tables from Card’s handbook chapter on next page). There are several explanations for this empirical
regularity
1. OLS suffers from measurement error, IV does not
2. publication bias: a study by Ashenfelter and Harmon finds a positive correlation between the point
estimate and its sampling error across studies1
3. Card’s favorite story: instruments in the literature affect populations with relatively low levels of,
and therefore high returns to education
In this recitation, I am planning to elaborate a little on the last point.
Heterogeneous Treatment Effects
Assume you have data about a training program for unemployed workers, and you want to tell a policy
maker whether the program was essful so that the government should continue to finance it. Say, your
main e of interest is earnings six months after the training program, yi, and you know whether a
particular person particip