Many outcomes of interest in economics are binary. For example, we may want to learn how employment status \(Y^*\) varies with demographics \(X\), where \(Y^*=1\) means “employed” and \(Y^*=0\) means unemployed or not in the labor force.

Pop Quiz: If \(D^*\) and \(D\) are binary random variables and \(D\) is a noisy measure of \(D^*\), is it possible for the measurement error \(W \equiv D - D^*\) to be classical?