We study the problem of a partisan gerrymanderer who assigns voters to equipopulous districts to maximize his party's expected seat share. The designer faces both aggregate, district‐level uncertainty (how many votes his party will receive) and idiosyncratic, voter‐level uncertainty (which voters will vote for his party). Segregate‐pair districting , where weaker districts contain one type of voter, while stronger districts contain two, is optimal for the gerrymanderer. The optimal form of segregate‐pair districting depends on the designer's popularity and the relative amounts of aggregate and idiosyncratic uncertainty. When idiosyncratic uncertainty dominates, a designer with majority support pairs all voters, while a designer with minority support segregates opposing voters and pairs more favorable voters; these plans resemble uniform districting and “packing‐and‐cracking,” respectively. When aggregate uncertainty dominates, the designer segregates moderate voters and pairs extreme voters; this “matching slices” plan has received some attention in the literature. Estimating the model using precinct‐level returns from recent U.S. House elections shows that, in practice, idiosyncratic uncertainty dominates. We discuss implications for redistricting reform, political polarization, and detecting gerrymandering. Methodologically, we exploit a formal connection between gerrymandering—partitioning voters into districts—and information design—partitioning states of the world into signals.

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.

Certain extremum estimators have asymptotic distributions that are non‐Gaussian, yet characterizable as the distribution of the arg max of a Gaussian process. This paper presents high‐level sufficient conditions under which such asymptotic distributions admit a continuous distribution function. The plausibility of the sufficient conditions is demonstrated by verifying them in three examples, namely, maximum score estimation, empirical risk minimization, and threshold regression estimation. In turn, the continuity result buttresses several recently proposed inference procedures whose validity seems to require a result of the kind established herein. A notable feature of the high‐level assumptions is that one of them is designed to enable us to employ the Cameron–Martin theorem. In a leading special case, the assumption in question is demonstrably weak and appears to be close to minimal

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

Macroeconomic outcomes depend on the distribution of markups across firms and over time, making firm‐level markup estimates key for macroeconomic analysis. Methods to obtain these estimates require data on the prices that firms charge. Firm‐level data with wide coverage, however, primarily come from financial statements, which lack information on prices. We use an analytical framework to show that trends in markups over time or the dispersion of markups across firms can still be well‐measured with such data. Measuring the average level of the markup does require pricing data, and we propose a consistent estimator for such settings. We validate the analytical results using simulations of a quantitative macroeconomic model and offer supporting evidence from firm‐level administrative production and pricing data. Our analysis supports the use of financial data to measure trends in aggregate markups.

A multi‐product monopolist faces a buyer who is privately informed about his valuations for the goods. As is well known, optimal mechanisms are in general complicated, while simple mechanisms—such as pure bundling or separate sales—can be far from optimal and do not admit clear‐cut comparisons. We show that this changes if the monopolist has sufficiently precise information about the buyer's valuations: Now, pure bundling always outperforms separate sales; moreover, there is a sense in which pure bundling performs essentially as well as the optimal mechanism. To formalize this, we characterize how fast the corresponding revenues converge to the first‐best revenue as the monopolist's information grows precise: Pure bundling achieves the same convergence rate to the first‐best as optimal mechanisms; in contrast, the convergence rate under separate sales is suboptimal.

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 (Müller (2016))—is indeed robust in the sense of Bergemann and Morris (2009).

We provide sufficient conditions for equilibrium existence in first‐price auctions with private values that accommodate non quasi‐linear utilities and value‐distributions that contain atoms and exhibit positive or negative correlation. These conditions show that equilibrium existence often turns on properties of a single statistic of the joint distribution of values, namely, the minimum value in the support of the high‐value distribution (the mHV). We also show that modifying the standard tie‐breaking rule only at the mHV is enough to guarantee equilibrium existence without our sufficient conditions. Our results also apply to Bertrand price competition when each firm's constant marginal cost is private information.

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

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