We investigate estimation and inference of the (local) average treatment effect parameter when a binary instrumental variable is generated by a randomized or conditionally randomized experiment. Under i.i.d. sampling, we show that adding covariates and their interactions with the instrument will...

We derive the asymptotic distribution of the parameters of the \citet{blp} (BLP) model in a many markets setting which takes into account simulation noise under the assumption of overlapping simulation draws. We show that as long as the number of simulation draws $R$ and the number of markets...

This paper provides a numerical derivative based Delta method that complements the recent work by Fang and Santos (2014) and also generalizes a previous insight by Song (2014). We show that for an appropriately chosen sequence of step sizes, the numerical derivative based Delta method provides...

This paper studies inference on finite population average and local average treatment effects under limited overlap, meaning some strata have a small proportion of treated or untreated units. We model limited overlap in an asymptotic framework sending the propensity score to zero (or one) with...

This paper proposes a numerical bootstrap method that is consistent in many cases where the standard bootstrap is known to fail and where the m-out-of-n bootstrap and subsampling have been the most commonly used inference approaches. We provide asymptotic analysis under both fixed and drifting...