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...

When procurement contracts are incomplete, they are frequently changed after the contract is awarded to the lowest bidder. This results in a final cost that differs from the initial price, and may involve significant transaction costs due to renegotiation. We propose a stylized model of bidding...