"We show that the well-known numerical equivalence between two-stage least squares (2SLS) and the classic control function (CF) estimator raises an interesting and unrecognized puzzle. The classic CF approach maintains that the regression error is mean independent of the instruments conditional...

"We develop an estimator for the parameters of a utility function that has interactions between the unobserved demand error and observed factors including price. We show that the Berry (1994)/Berry, Levinsohn, and Pakes (1995) inversion and contraction can still be used to recover the mean...