Knowledge that Transforms

We formulate an order over constraint sets <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>A</mi> <mo>⊆</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>ℓ</mi> </mrow> </msup> </math>, called the parallelogram order , which guarantees that argmin p ⋅ x : x ∈ A increases in the product order as A increases in the parallelogram order, for any vector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>p</mi> <mo>∈</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>ℓ</mi> </mrow> </msup> </math>. Using this result, we characterize the utility/production functions that lead to normal demand as well as the closely related class of production functions with marginal costs that increase with factor prices. By generalizing the concept of supermodularity, we also characterize the class of production functions for which factors are complements. In the context of decision‐making under uncertainty, our new set order leads to natural generalizations of first‐order stochastic dominance in multi‐prior models.

In a setting of many‐to‐one two‐sided matching with nontransferable utilities, for example, college admissions, we study conditions under which preferences of both sides are identified with data on one single market. Regardless of whether the market is centralized or decentralized, assuming that the observed matching is stable, we show nonparametric identification of preferences of both sides under certain exclusion restrictions. To take our results to the data, we use Monte Carlo simulations to evaluate different estimators, including the ones that are directly constructed from the identification. We find that a parametric Bayesian approach with a Gibbs sampler works well in realistically sized problems. Finally, we illustrate our methodology in decentralized admissions to public and private schools in Chile and conduct a counterfactual analysis of an affirmative action policy.

We study the design of optimal mechanisms when the designer is uncertain both about the form of information held by the agents and also about which equilibrium will be played. The guarantee of a mechanism is its worst performance across all information structures and equilibria. The potential of an information structure is its best performance across all mechanisms and equilibria. We formulate a pair of linear programs, one of which is a lower bound on the maximum guarantee across all mechanisms, and the other of which is an upper bound on the minimum potential across all information structures. In applications to public expenditure, bilateral trade, and optimal auctions, we use the bounding programs to characterize guarantee‐maximizing mechanisms and potential‐minimizing information structures and show that the max guarantee is equal to the min potential.

This paper introduces and analyzes sequentially stable outcomes in extensive‐form games. An outcome ω is sequentially stable if, for any ε > 0 and any small enough perturbation of the players' behavior, there is an ε ‐perturbation of the players' payoffs and a corresponding equilibrium with outcome close to ω . Sequentially stable outcomes exist for all finite games and are outcomes of sequential equilibria. They are closely related to stable sets of equilibria and satisfy versions of forward induction, iterated strict equilibrium dominance, and invariance to simultaneous moves. In signaling games, sequentially stable outcomes pass the standard selection criteria, and when payoffs are generic, they coincide with outcomes of stable sets of equilibria.

We introduce Cautious Utility, a new model based on the idea that individuals are unsure of trade‐offs between goods and apply caution. The model yields an endowment effect, even when gains and losses are treated symmetrically. Moreover, it implies either loss aversion or loss neutrality for risk, but in a way unrelated to the endowment effect, and it captures the certainty effect, providing a novel unified explanation of all three phenomena. Cautious Utility can help organize empirical evidence, including some that directly contradicts leading alternatives.

We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test statistic is based on a modified leave‐one‐out sample analog of a quadratic distance between the restricted and unrestricted sieve two‐stage least squares estimators. We provide computationally simple, data‐driven choices of sieve tuning parameters and Bonferroni adjusted chi‐squared critical values. Our test adapts to the unknown smoothness of alternative functions in the presence of unknown degree of endogeneity and unknown strength of the instruments. It attains the adaptive minimax rate of testing in L 2 . That is, the sum of the supremum of type I error over the composite null and the supremum of type II error over nonparametric alternative models cannot be minimized by any other tests for NPIV models of unknown regularities. Confidence sets in L 2 are obtained by inverting the adaptive test. Simulations confirm that, across different strength of instruments and sample sizes, our adaptive test controls size and its finite‐sample power greatly exceeds existing non‐adaptive tests for monotonicity and parametric restrictions in NPIV models. Empirical applications to test for shape restrictions of differentiated products demand and of Engel curves are presented.

We study how long‐lived, rational agents learn in a social network. In every period, after observing the past actions of his neighbors, each agent receives a private signal, and chooses an action whose payoff depends only on the state. Since equilibrium actions depend on higher‐order beliefs, it is difficult to characterize behavior. Nevertheless, we show that regardless of the size and shape of the network, the utility function, and the patience of the agents, the speed of learning in any equilibrium is bounded from above by a constant that only depends on the private signal distribution.

When does society eventually learn the truth, or take the correct action, via observational learning? In a general model of sequential learning over social networks, we identify a simple condition for learning dubbed excludability . Excludability is a joint property of agents' preferences and their information. We develop two classes of preferences and information that jointly satisfy excludability: (i) for a one‐dimensional state, preferences with single‐crossing differences and a new informational condition, directionally unbounded beliefs; and (ii) for a multi‐dimensional state, intermediate preferences and subexponential location‐shift information. These applications exemplify that with multiple states, “unbounded beliefs” is not only unnecessary for learning, but incompatible with familiar informational structures like normal information. Unbounded beliefs demands that a single agent can identify the correct action. Excludability, on the other hand, only requires that a single agent must be able to displace any wrong action, even if she cannot take the correct action.

We ask how fiscal deficits are financed in environments with two key features: (i) nominal rigidity, and (ii) a violation of Ricardian equivalence due to finite lives or liquidity constraints. In such environments, deficits can contribute to their own financing through two channels: a boom in real economic activity, which expands the tax base; and a surge in inflation, which erodes the real value of nominal government debt. Our main theoretical result establishes that this mechanism becomes more potent as fiscal adjustment is delayed, leading to full self‐financing in the limit: if the monetary authority does not lean too heavily against the fiscal stimulus, then the government can run a deficit today, refrain from tax hikes or spending cuts in the future, and still see its debt converge back to its initial level. We further demonstrate that a significant degree of self‐financing is achievable when the theory is disciplined by empirical evidence on marginal propensities to consume, nominal rigidities, the monetary policy reaction, and the speed of fiscal adjustment.