This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equations in the spirit of Firth (1993). In particular, this paper compares the stochastic expansions of the analytically-bias-corrected estimator and the alternative estimator and...

It is well known that efficient estimation of average treatment effects can be obtained by the method of inverse propensity score weighting, using the estimated propensity score, even when the true one is known. When the true propensity score is unknown but parametric, it is conjectured from the...

"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...