Assume the following regression: Y=b0 + b1*D + b2*X + b3*X*D where D=1
if X>tresholdX and D=0 otherwise. This division poses no problems.
However, it is of interest also to divide the sample by the dependent
variable Y and see if there are any differences between coefficients
estimated for the (non-random) sample above a certain treshold for the
dependent variable Y>threshold and below. Simply truncating the sample
at the treshold level would induce the familiar sample truncation bias
and the results would be biased in predicted regressions.
Has anyone come accross a similar problem in their applications or know
a paper that deals with this?
