A buyer and seller bargain in continuous time over a good. Bargainers can be rational or committed to some fixed price. A rational buyer has a private value and outside option. If the set of buyer values and commitment types is rich and the probability of commitment vanishes, outcomes are partially consistent with the Coase conjecture: the seller chooses a price below the maximum of the lowest outside option and half the lowest value; the buyer immediately accepts or takes his outside option.
We analyze marital matching on income using an extremely rich Dutch data set containing all income tax files over seven years. We develop a novel methodology that directly extends previous contributions to allow for highly flexible matching patterns. Investigating all marriages that took place between 2013 and 2019, we find that marital patterns are particularly intriguing. While a majority of couples match assortatively, a small but significant minority display negative assortative matching. We also show that standard approaches, which consider all married couples using current incomes (as opposed to pre‐marriage incomes used in our approach), may generate misleading conclusions.
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.
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.
Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable and empirically rejected. This paper proposes to model the conditional distribution of the parameter given the standard errors as a flexibly parameterized location‐scale family of distributions, leading to a family of methods that we call close . The close framework unifies and generalizes several proposals under precision dependence. We argue that the most flexible member of the close family is a minimalist and computationally efficient default for accounting for precision dependence. We analyze this method and show that it is competitive in terms of the regret of subsequent decision rules. Empirically, using close leads to sizable gains for selecting high‐mobility Census tracts.
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.
Consider a repeated interaction where it is unknown which of various stage games will be played each period. This framework separates the basic logic of intertemporal incentives from the requirement that any given strategy profile yields a well‐defined payoff vector. A natural solution concept is ex post perfect equilibrium: strategies must form a subgame‐perfect equilibrium for any realization of the sequence of stage games. When there is one long‐run player and others are short‐run, and public randomization is available, we can adapt the standard recursive approach to determine the maximum feasible gap between reward and punishment for the long‐run player. This allows us to identify which actions can be played in equilibrium and, assuming perfect monitoring, to fully characterize what outcome paths can arise. With multiple long‐run players or no public randomization, the approach fails; a diagnostic of this failure is that optimal penal codes may no longer exist.
This paper studies how governments intervene in agricultural markets to reshape the economic consequences of climate extremes. We construct a global dataset of agricultural policies and extreme heat exposure by country and crop since 1980. Extreme heat shocks to domestic production lead to policies that assist consumers by lowering domestic food prices. This effect is persistent, primarily implemented via border policies, and stronger during election years. Shocks to foreign production induce the opposite response: policies that assist producers by raising prices. These findings can be rationalized by a model in which governments use agricultural policy to redistribute among domestic interest groups. Our estimates imply that policy responses shield domestic consumers, while exacerbating losses for domestic producers and foreign consumers. Policy responses have regressive consequences globally, disproportionately harming poor and heat‐exposed countries.
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.
We propose a novel optimal transport‐based version of the Generalized Method of Moment (GMM). Instead of handling overidentification by reweighting the data to satisfy the moment conditions (as in Generalized Empirical Likelihood methods), this method proceeds by allowing for errors in the variables of the least mean‐square magnitude necessary to simultaneously satisfy all moment conditions. This approach, based on the notions of optimal transport and Wasserstein metric, aims to address the problem of assigning a logical interpretation to GMM results even when overidentification tests reject the null, a situation that cannot always be avoided in applications. We illustrate the method by revisiting Duranton, Morrow and Turner's (2014) study of the relationship between a city's exports and the extent of its transportation infrastructure. Our results corroborate theirs under weaker assumptions and provide insight into the error structure of the variables.