Now assume that $$ and $w_0$ are correlated and assume that $w_0=a++lon$ where a and $$ are fixed parameters and $lon$ is a residual independent from $$ with mean zero.

$.$ Show that the naive comparison of the wages of treated and untreated absent an experiment would no longer identify a treatment parameter. Discuss the sign of the bias depending on $.$

$.$ Show that comparing group $Z=1$ with group $Z=0$ identifies the same treatment parameter as before.