Knowledge that Transforms

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.

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.

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.

We examine the effects of international trade in the presence of a set of domestic distortions giving rise to informality, a prevalent phenomenon in developing countries. In our quantitative model, the informal sector arises from burdensome taxes and regulations that are imperfectly enforced by the government. In equilibrium, smaller, less productive firms face fewer distortions than larger, more productive ones, potentially leading to substantial misallocation. We show that in settings with a large informal sector, the gains from trade are significantly amplified, as reductions in trade barriers imply a reallocation of resources from initially less distorted to more distorted firms. We confirm findings from earlier reduced‐form studies that the informal sector mitigates the impact of negative labor demand shocks on unemployment. Nonetheless, the informal sector can exacerbate the adverse real income effects of economic downturns, amplifying misallocation. Last, our research sheds light on the relationship between trade openness and cross‐firm wage inequality.

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.

Weak environmental regulation has global consequences. When domestic regulation fails, the international community can target emitters with trade policy. I develop a dynamic empirical framework for evaluating trade policy as a substitute for domestic regulation, and I apply the framework to the market for palm oil, a major driver of deforestation and global CO 2 emissions. Relative to business as usual, a domestic production tax of 50% reduces CO 2 emissions by 7.4 Gt from 1988 to 2016, amounting to 0.26 Gt annually. Coordinated, committed import tariffs of similar magnitude reduce emissions by 5.4 Gt over the same period. The cost of these import tariffs is only $15 per ton of CO 2 , even accounting for compensating transfers that recognize welfare losses for producing countries. Without coordination and commitment, import tariffs have more limited effects. Alternative policies include domestic export taxes, which are fiscally appealing independent of emission concerns, and a carbon border adjustment mechanism, which encourages domestic regulation.