Customs data reveal the heterogeneity and granularity of relationships among buyers and sellers, showing how more exports to a destination break down into more firms selling there and more buyers per exporter. We develop a quantitative general equilibrium model of firm‐to‐firm matching that builds on this insight to separate the roles of iceberg costs and matching frictions in gravity. In the cross section, we find matching frictions as important as iceberg costs in impeding trade, and more sensitive to distance. Because domestic and imported intermediates compete directly with labor in performing production tasks, our model also fits the heterogeneity of labor shares across French producers. Applying the framework to the 2004 expansion of the European Union, reduced iceberg costs and reduced matching frictions contributed equally to the increase in French exports to the new members. While workers benefited overall, those competing most directly with imports gained less, even losing in some countries entering the EU.
We consider a dynamic buyer–seller interaction. Instead of the buyer's valuation, it is the frequency with which he needs to trade that is the buyer's private information. The difference matters. With commitment, full surplus extraction is possible, for instance via limited‐time offers. Without commitment, ratcheting is mitigated, as not buying is not necessarily a sign of strength. Because time is informative, the seller learns and may adjust her behavior over time. When finding a suitable alternative seller is easy, she starts with a pooling offer before permanently switching to a screening offer. When finding a suitable alternative seller takes time, she starts with a pooling offer before occasionally experimenting with separating offers.
This paper explores the impact of information design on the auctioneer's revenue in the U.S. offshore oil/gas lease auctions where, post‐auction, the winner decides whether to explore the auctioned tract and must pay the government a royalty on its production value. I first document that there is a positive correlation between the exploration rate and publicly observed losing bids. This suggests that the winning bidder uses the rivals' bids to infer their private information about the tract's potential. I then characterize the equilibrium bidding strategy when the auctioneer designs and commits to how to reveal information on losing bids to the winning bidder. Counterfactual exercises reveal that alternative bid disclosure policies significantly improve auctioneer revenue.
The U.S. Supreme Court's 2010 decision in Citizens United v. Federal Election Commission deregulated campaign finance, enabling the rise of a new political action committee (the Super PAC) with broad freedom to raise and spend money. This led to an unprecedented surge in spending in primary and general elections. To evaluate the impact of Super PACs, I estimate a multistage model of political competition using data from U.S. Congressional elections between 2010 and 2020. I find that Super PAC spending by both sides prompts offsetting responses, resulting in limited net equilibrium effects. However, by amplifying the role of donors, Super PACs still have the potential to reshape the electoral landscape.
Evidence from the laboratory and the field has uncovered both underreaction and overreaction to new information. We provide new experimental evidence on the underlying mechanisms of under‐ and overreaction by comparing how people make inferences and revise forecasts in the same information environment. Participants underreact to signals when inferring about underlying states, but overreact to the same signals when revising forecasts about future outcomes—a phenomenon we term “the inference‐forecast gap.” We show that this gap is largely driven by different simplifying heuristics used in the two tasks. Additional treatments suggest that the choice of heuristics is affected by the similarity between statistics in the information environment and the statistic elicited by the belief‐updating problem.
Tirole (1985) studied an overlapping generations model with capital accumulation and showed that the emergence of asset bubbles solves the capital over-accumulation problem. His Proposition 1(c) claims that if the dividend growth rate is above the bubbleless interest rate (the steady-state interest rate in the economy without the asset) but below the population growth rate, then bubbles are necessary in the sense that there exists no bubbleless equilibrium but there exists a unique bubbly equilibrium. We show that this result (as stated) is incorrect by presenting an example economy that satisfies all assumptions of Proposition 1(c) but its unique equilibrium is bubbleless. We also restore Proposition 1(c) under the additional assumptions that initial capital is sufficiently large and dividends are sufficiently small. We show through examples that these conditions are essential.
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.
We investigate how formularies used by pharmacy benefit managers (PBMs) affect equilibrium manufacturer rebates for branded drugs through tiering and exclusion. We develop a theoretical model of multidimensional contracting in which a PBM negotiates with drug manufacturers over menus of formulary-contingent rebates and chooses a formulary. We then estimate consumer demand responses to tier placement for statins using claims data from Princeton University, a large employer contracting with a single PBM to offer prescription drug coverage to its employees. Combining the theoretical model with demand estimates and observed list prices, we quantify how allowing for differential tier placement and exclusion affect equilibrium rebates. Our predictions are consistent with available aggregate rebate data, and we find that allowing a PBM to place branded drugs on preferred- and non-preferred tiers can substantially increase negotiated rebate payments.
Apprenticeships play a key role in enabling successful school-to-work transitions in many countries, but in the presence of imperfect information, the specificity of this type of training may entail important costs for those working outside their training fields. I study this issue in one of the most prominent training settings, the German apprenticeship system. Using administrative data and a broad occupational classification, I find that 40% of individuals work in occupations different from their training. I estimate the cost of mismatch using vacancy instruments and extend methodological approaches in high-dimensional selection settings. Lacking training in one's occupation entails an average wage penalty of 14%, the equivalent of two years of work experience. The penalty increases with the task distance between training and occupation. My findings suggest that retraining is crucial to mitigate the adverse consequences from imperfect information in specialized training settings.
We apply a revealed preference approach to administrative data from Washington to show that constraints on work hours are widespread: Workers have limited discretion over hours at a given employer, and there is substantial mismatch of workers who prefer long hours to employers that provide short hours. Voluntary job transitions imply a ratio of the marginal rate of substitution of earnings for hours to the wage rate of 0.5-0.6 for prime-age workers. The average absolute deviation between observed and optimal hours is about 15%, and low-wage workers face particularly acute constraints on hours. On average, observed hours tend to be less than preferred levels, and workers would require a 12% higher wage with their current employer to be as well off as with an employer offering ideal hours. These findings suggest that hour constraints are an equilibrium feature of the labor market because long-hour jobs are costly to employers.
This paper studies how the risk of hold-up affects procurement. I use data on the universe of solar power auctions in India. The Indian context allows clean estimates of counterparty risk, because solar plants set up in the same states, by the same firms, are procured in auctions intermediated by either risky states themselves or the trusted central government. I find that the counterparty risk of an average state increases solar prices by 10%. This risk premium sharply reduces investment, because demand for green energy is elastic. Contract intermediation by the central government eliminates the counterparty risk premium.
In the context of one-to-one matching markets, we study myopic-farsighted stable sets, which are internally and externally stable when myopic agents consider immediate payoffs from their deviations, while farsighted agents anticipate counter-deviations and consider final payoffs. We constructively prove the existence of a (rational expectations) myopic-farsighted stable set, in which farsighted agents receive a single payoff while myopic agents may receive multiple payoffs. Our existence result extends to settings with enforcing coalitions of arbitrary size, yielding coalitional myopic-farsighted stable sets, and to settings where not all members of an enforcing coalition must strictly gain, yielding myopic-farsighted weakly stable sets. When all farsighted agents have unit demand, our results also extend to many-to-one matching markets. As a key corollary, we provide a foundation for the efficiency-adjusted deferred acceptance algorithm by showing that its outcome constitutes a singleton myopic-farsighted stable set when one side is farsighted and the other is myopic.
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.
This paper studies the economic effects of rural-urban migration on Brazilian cities. Using a shift-share IV design, we show that, over a decade, drought-induced immigration reduces informality, has no effect on unemployment, and increases the number of formal firms and jobs. Downward formal wage adjustments play a key role, as these long-run effects are weaker in regions with stronger wage rigidity. In the short run, when wage rigidity is strongest, we replicate the informality-increasing effects documented in the literature. We develop and estimate a model of firm dynamics and informality that rationalizes these results. The counterfactuals reveal that, in the short run, the informal sector absorbs the expanding labor force and acts as a "stepping-stone" to formality for firms and workers. In the long run, however, it reduces the aggregate benefits from immigration by allowing the least productive firms to survive.
Shrinkage methods are frequently used to improve the precision of least squares estimators of fixed effects. However, widely used shrinkage estimators guarantee improved precision only under strong distributional assumptions. I develop an estimator for the fixed effects that obtains the best possible mean squared error within a class of shrinkage estimators. This class includes conventional shrinkage estimators and the optimality does not require distributional assumptions. The estimator has an intuitive form and is easy to implement. Moreover, the fixed effects are allowed to vary with time and to be serially correlated, in which case the shrinkage optimally incorporates the underlying correlation structure. I also provide a method to forecast fixed effects one period ahead in this setting.
Studies on agricultural technology adoption often focus on one input, practice, or package, which is analytically useful, but may overlook the complexities involved with multidimensional learning needed for a lot of agricultural decisions. In Kenya, we study farmers' dynamic learning (from oneself and others) and adoption decisions over six seasons after randomly inviting them to participate in agronomic research trials, comparing different combinations of inputs during three consecutive seasons. As a response to the trials, adoption increases steadily despite the absence of positive profits multiple seasons after exposure to the trials. Know-how increases rapidly and faster for high skill farmers who experiment the most, at the cost of making new mistakes. The findings are consistent with a theoretical model with multidimensionality of input and practice decisions and differential learning from one's own experience by skills, where complementarities imply that adoption of an input requires finding how to re-optimize other dimensions, which adds to the cost of adoption.
In sequential games, the set of paths consistent with rationality and forward-induction reasoning may change nonmonotonically when adding transparent restrictions on players' beliefs. Yet, we prove that-in an incomplete-information environment-predictions become sharper when the restrictions only concern initial beliefs about types. Thus, strong rationalizability for games with payoff uncertainty characterizes the path predictions of forward-induction reasoning across all possible restrictions on players' hierarchies of exogenous beliefs. With this, we can solve an open problem: the implementation of social choice functions through sequential mechanisms under forward-induction reasoning-which considerably expands the realm of implementable functions compared with simultaneous mechanisms (M & uuml;ller (2016))-is indeed robust in the sense of Bergemann and Morris (2009).
This paper studies the labor market impacts of firm accommodation decisions after workplace disability and assesses implications for the design of firm subsidies. We leverage a workers' compensation (WC) program in Oregon that provides wage subsidies to firms for accommodating workers with workplace disabilities. Leveraging rich administrative data and a policy change to the wage subsidy, we show that accommodation rates respond to the subsidy rate and that receipt of accommodation leads to a significant increase in employment and earnings a year later. To explore welfare implications, we develop and estimate a frictional labor market model of accommodation as a form of human capital investment. Worker turnover and imperfect experience rating in WC lead to underaccommodation and inefficient labor market outcomes after workplace disability. Counterfactual simulations show that subsidizing accommodation not only improves long-run labor market outcomes of workers experiencing work-related disability but also yields welfare gains for most workers.
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.
