The large literature on vertical market bargaining assumes contracts last for one period, but actual hospital-insurer contracts last for multiple years and are negotiated as a multiple of a benchmark price that changes over time. I study dynamic regulations to those benchmark prices by extending the existing period-by-period vertical market bargaining model to allow for contracts to be formed at different times.

We propose a meta-learner for conditional average treatment effect (CATE) bounds that can efficiently learn sharp bounds.

We provide sharp bounds for an existing sensitivity analysis that are valid under minimal conditions and sharp with only a consistent quantile regression estimate.

We extend Dorn and Guo (2022)’s characterization of bounds for Tan’s marginal sensitivity model to considerably more general assumptions and estimands.

We propose semiparametric average treatment effect (ATE) bounds estimators with novel robustness properties: double sharpness and double validity. Accept with major revisions at JASA.

We show that the Augmented IPW estimator’s simple t-statistics can remain well-calibrated even when strict overlap fails and there are many propensities near zero.