Commitment is typically modelled by assigning to one of the players the ability to take an initial binding action. The weakness of this approach is that the fundamental question of who has the opportunity to commit cannot be addressed, as it is assumed. This paper presents a framework in which commitment power arises endogenously from the fundamentals of the model. We construct a finite dynamic game in which players are given the option to change their minds as often as they wish, but pay a switching cost if they do so. We show that for games with two players and two actions there is a unique subgame-perfect equilibrium with a simple structure. This equilibrium is independent of the order and timing of moves and is robust to other protocol specifications. Moreover, despite the perfect information nature of the model and the costly switches, strategic delays may arise in equilibrium. The flexibility of the model allows us to apply it to various environments. In particular, we study an entry deterrence situation. Its equilibrium is intuitive and illustrative of how commitment power is endogenously determined.

This paper investigates the effects of mandatory seat belt laws on driver behavior and traffic fatalities. Using a unique panel data set on seat belt usage in all U.S. jurisdictions, we analyze how such laws, by influencing seat belt use, affect the incidence of traffic fatalities. Allowing for the endogeneity of seat belt usage, we find that such usage decreases overall traffic fatalities. The magnitude of this effect, however, is significantly smaller than the estimate used by the National Highway Traffic Safety Administration. In addition, we do not find significant support for the compensating-behavior theory, which suggests that seat belt use also has an indirect adverse effect on fatalities by encouraging careless driving. Finally, we identify factors, especially the type of enforcement used, that make seat belt laws more effective in increasing seat belt usage.

We develop a structural econometric model to estimate risk preferences from data on deductible choices in auto insurance contracts. We account for adverse selection by modeling unobserved heterogeneity in both risk (claim rate) and risk aversion. We find large and skewed heterogeneity in risk attitudes. In addition, women are more risk averse than men, risk aversion exhibits a U-shape with respect to age, and proxies for income and wealth are positively associated with absolute risk aversion. Finally, unobserved heterogeneity in risk aversion is greater than that of risk, and, as we illustrate, has important implications for insurance pricing. (JEL D81, G22)

We study one benefit to firms of selling subscriptions: the prospect that consumers will continue to pay for subscriptions they no longer value. We use comprehensive data from a large payment card network to document that months during which cards are replaced, when active renewal is required, are associated with much higher rates of cancellation. Using two stylized models of consumer inertia—driven by inattention or switching costs—we estimate that these cancellation frictions roughly double seller revenues on average, holding fixed initial subscribers. We use the estimated models to explore the impact of possible regulatory remedies. (JEL D12, D18, L81, L88)

We study the demand response to non-linear price schedules using data on insurance contracts and prescription drug purchases in Medicare Part D. We exploit the kink in individuals' budget set created by the famous "donut hole," where insurance becomes discontinuously much less generous on the margin, to provide descriptive evidence of the drug purchase response to a price increase. We then specify and estimate a simple dynamic model of drug use that allows us to quantify the spending response along the entire non-linear budget set. We use the model for counterfactual analysis of the increase in spending from "filling" the donut hole, as will be required by 2020 under the Affordable Care Act. In our baseline model, which considers spending decisions within a single year, we estimate that "filling" the donut hole will increase annual drug spending by about $150, or about 8 percent. About one-quarter of this spending increase reflects "anticipatory" behavior, coming from beneficiaries whose spending prior to the policy change would leave them short of reaching the donut hole. We also present descriptive evidence of cross-year substitution of spending by individuals who reach the kink, which motivates a simple extension to our baseline model that allows - in a highly stylized way - for individuals to engage in such cross year substitution. Our estimates from this extension suggest that a large share of the $150 drug spending increase could be attributed to cross-year substitution, and the net increase could be as little as $45 per year.

We develop a stylized model that allows us to estimate a value-added measure for nursing homes ("SNFs") which accounts for patient selection both into and out of a SNF. We use the model, together with detailed data on the physical and mental health of about 6 million Medicare SNF patients between 2011 and 2016, to estimate the value added for about 14,000 distinct SNFs. We document substantial heterogeneity in value added. Nationwide, compared to a 10th percentile SNF, a 90th percentile SNF is able to discharge a patient at the same health level almost a week sooner, or one quarter of the median length of stay. Heterogeneity in value added within a market is almost as large as it is nationwide. Our results point to the potential for substantial gains through policies that encourage reallocation of patients to higher-quality SNFs within their market.

We study the design of provider incentives in the post-acute care setting - a high-stakes but under-studied segment of the healthcare system. We focus on long-term care hospitals (LTCHs) and the large (approximately $13,500) jump in Medicare payments they receive when a patient s stay reaches a threshold number of days. Discharges increase substantially after the threshold, with the marginal discharged patient in relatively better health. Despite the large financial incentives and behavioral response in a high mortality population, we are unable to detect any compelling evidence of an impact on patient mortality. To assess provider behavior under counterfactual payment schedules, we estimate a simple dynamic discrete choice model of LTCH discharge decisions. When we conservatively limit ourselves to alternative contracts that hold the LTCH harmless, we find that an alternative contract can generate Medicare savings of about $2,100 per admission, or about 5% of total payments. More aggressive payment reforms can generate substantially greater savings, but the accompanying reduction in LTCH profits has potential out-of-sample consequences. Our results highlight how improved financial incentives may be able to reduce healthcare spending, without negative consequences for industry profits or patient health.

We analyze subprime consumer lending and the role played by down payment requirements in screening high-risk borrowers and limiting defaults. To do this, we develop an empirical model of the demand for financed purchases that incorporates both adverse selection and repayment incentives. We estimate the model using detailed transaction-level data on subprime auto loans. We show how different elements of loan contracts affect the quality of the borrower pool and subsequent loan performance. We also evaluate the returns to credit scoring that allows sellers to customize financing terms to individual applicants. Our approach shows how standard econometric tools for analyzing demand and supply under imperfect competition extend to settings in which firms care about the identity of their customers and their postpurchase behavior.

Much of the extensive empirical literature on insurance markets has focused on whether adverse selection can be detected. Once detected, however, there has been little attempt to quantify its welfare cost or to assess whether and what potential government interventions may reduce these costs. To do so, we develop a model of annuity contract choice and estimate it using data from the U.K. annuity market. The model allows for private information about mortality risk as well as heterogeneity in preferences over different contract options. We focus on the choice of length of guarantee among individuals who are required to buy annuities. The results suggest that asymmetric information along the guarantee margin reduces welfare relative to a first-best symmetric information benchmark by about £127 million per year or about 2 percent of annuitized wealth. We also find that by requiring that individuals choose the longest guarantee period allowed, mandates could achieve the first-best allocation. However, we estimate that other mandated guarantee lengths would have detrimental effects on welfare. Since determining the optimal mandate is empirically difficult, our findings suggest that achieving welfare gains through mandatory social insurance may be harder in practice than simple theory may suggest.