Observed Contracts and Unobserved Selection: Essays in Applied Microeconomics

Abstract

This dissertation comprises three chapters on topics in applied microeconomics. The first chapter documents a novel vertical market contract dataset and several stylized facts. Typically, vertical market contracts are considered trade secrets. Until 2016, West Virginia made hospital–insurer contracts public records. Chapter 1 documents that in West Virginia, smaller insurers formed longer-lived contracts with faster price growth, so that the prices smaller insurers paid at any given time were higher than the most immediate prices at the time of negotiation. I then document that contract formation was staggered, making contract timing subtle. I argue that these observations call for a model of bargaining that recognizes contracts can be formed at different times.The second chapter proposes an empirical model of vertical market bargaining with contracts of heterogeneous length. Researchers studying vertical markets generally assume contracts are short-lived, but Chapter 1 documents that contracts can remain in place for multiple years. I extend standard vertical market models to accommodate forward-looking bargaining over multiperiod contracts, and I prove the extension uniquely controls the growth of relevant bargaining states. I use the model to consider the effect of a one-percentage-point annual increase in Medicare payments on private insurer contracts that negotiate prices as a fixed markup over Medicare. I find that after nine years, private insurer spending would increase by 1.319%, which extrapolates nationally to $4.98 billion. A myopic model lacking forward-looking offsets would overestimate the effect of the Medicare reimbursement reform by $2.35 billion. The third chapter, co-authored with Kevin Guo, studies causal inference in the presence of unobserved confounders. The chapter introduces a robust sensitivity analysis for inverse propensity weighting (IPW). We provide new partial identification results for Tan (2006)’s marginal sensitivity model. Our bound characterization yields a tractable estimator that converges to the sharp bounds under plausible conditions and converges to valid bounds under mild conditions. Our proposal is a refinement of the influential sensitivity analysis by Zhao, Small, and Bhattacharya (2019), which we show gives bounds that are too wide even asymptotically.