We cast the problem of communicating scientific uncertainty as one of reporting a posterior distribution on an unknown parameter to an audience of Bayesian decision‐makers. We establish novel bounds on the audience's regret when the analyst reports an approximation to a posterior that the audience treats as exact. Under a palatable restriction on the audience's decision problems, the bounds take an especially convenient form. Under a further restriction on the audience's priors, a bootstrap distribution can be used as a stand‐in posterior. We propose a practical recipe for checking whether a conventional statistical report (say, a normal parameterized by a point estimate and standard error) is a good approximation, and for improving the report if it is not. We illustrate our proposals using the articles in the 2021 American Economic Review that use a bootstrap for inference.

Biopharmaceuticals advance health and economic growth. Unlike central bargaining abroad, the United States uses private firms, pharmacy benefit managers (PBMs), to manage medicine access and spending. Yet, PBMs' roles in advancing efficiency are understudied. Ho and Lee model PBMs' use of tiered formularies, lists of covered medicines, without the use of proprietary data on the price concessions drug makers offer for preferred placement. They find PBMs' use of tiered formularies generate significant payor savings through competition. Complementing Ho and Lee, Feng and Maini (2024) model how patient demand inertia limits PBMs' ability to extract price concessions from drug makers which consequently erodes the efficacy gains of PBM formularies. Conti, Frandsen, Powell, and Rebitzer (2021) model formulary auctions where PBM size drives payor savings, but also spurs endogenously set high list prices, reducing patient access. Future economic research should focus on PBM market entry and vertical integration, pharmacy steering, and effects on innovation.

Internal labor markets are increasingly important for matching workers to jobs within organizations. We present evidence from a randomized trial that compares matching workers to jobs using the deferred acceptance (DA) algorithm to the traditional manager‐directed matching process. Our setting is the U.S. Army's internal labor market, which matches over 14,000 officers to units annually. We find that DA reduces administrative burden and increases match quality as measured by reduced justified envy, increased truthful preference reporting, and officers' and units' preferences over their matches. The overall impact of DA on officer retention and performance in the two years after officers started their new jobs is limited by strategic preference coordination between officers and units. However, DA leads to significant improvements in officer retention and promotions in markets with inexperienced managers. Our findings suggest that cross‐market communication between agents in internal labor markets can attenuate the benefits of strategyproof matching algorithms.