This paper reconciles the asymptotic disagreement between Bayesian and frequentist inference in set-identified models by adopting a multiple-prior (robust) Bayesian approach. We propose new tools for Bayesian inference in set-identified models and show that they have a well-defined posterior interpretation in finite samples and are asymptotically valid from the frequentist perspective. The main idea

We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original

We develop a model of international tariff negotiations to study the design of the institutional rules of the GATT/WTO. A key principle of the GATT/WTO is its most-favored-nation (MFN) requirement of nondiscrimination, a principle that has long been criticized for inviting free-riding behavior. We embed a multisector model of international trade into a model of interconnected bilateral negotiations

We study preferences estimated from finite choice experiments and provide sufficient conditions for convergence to a unique underlying “true” preference. Our conditions are weak and, therefore, valid in a wide range of economic environments. We develop applications to expected utility theory, choice over consumption bundles, and menu choice. Our framework unifies the revealed preference tradition with

Policymakers frequently use price regulations as a response to inequality in the markets they control. In this paper, we examine the optimal structure of such policies from the perspective of mechanism design. We study a buyer-seller market in which agents have private information about both their valuations for an indivisible object and their marginal utilities for money. The planner seeks a mechanism

We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisher's Z-transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing

We study the impact of manipulating the attention of a decision-maker who learns sequentially about a number of items before making a choice. Under natural assumptions on the decision-maker's strategy, directing attention toward one item increases its likelihood of being chosen regardless of its value. This result applies when the decision-maker can reject all items in favor of an outside option with

We characterize the relationship between the distributions of two variables linked by a structural model. We then show that, in models of heterogeneous firms in monopolistic competition, this relationship implies a new demand function that we call “CREMR” (Constant Revenue Elasticity of Marginal Revenue). This demand function is the only one that is consistent with productivity and sales distributions

Applied macroeconomists often compute confidence intervals for impulse responses using local projections, that is, direct linear regressions of future outcomes on current covariates. This paper proves that local projection inference robustly handles two issues that commonly arise in applications: highly persistent data and the estimation of impulse responses at long horizons. We consider local projections

We introduce a generalization of the popular local-to-unity model of time series persistence by allowing for p autoregressive (AR) roots and p − 1 moving average (MA) roots close to unity. This generalized local-to-unity model, GLTU(p), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA(p,p − 1) process on the unit interval. Our main theoretical result establishes

We estimate the distribution of television advertising elasticities and the distribution of the advertising return on investment (ROI) for a large number of products in many categories. Our results reveal substantially smaller advertising elasticities compared to the results documented in the literature, as well as a sizable percentage of statistically insignificant or negative estimates. The results

A ruler who does not identify with a social group, whether on religious, ethnic, cultural, or socioeconomic grounds, is confronted with a trade-off between taking advantage of the out-group population's eagerness to maintain its identity and inducing it to “comply” (conversion, quitting, exodus, or any other way to accommodate the ruler's own identity). This paper first nests economists' extraction

Present bias is the inclination to prefer a smaller present reward to a larger later reward, but reversing this preference when both rewards are equally delayed. Such behavior violates stationarity of temporal choices, and hence exponential discounting. This paper provides a weakening of the stationarity axiom that can accommodate present-biased choice reversals. We call this new behavioral postulate

Asymptotic justification of the bootstrap often takes the form of weak convergence of the bootstrap distribution to some limit distribution. Theoretical literature recognized that the weak convergence does not imply consistency of the bootstrap second moment or the bootstrap variance as an estimator of the asymptotic variance, but such concern is not always reflected in the applied practice. We bridge

This paper presents a continuous-time model of sovereign debt. In it, a relatively impatient sovereign government's hidden type switches back and forth between a commitment type, which cannot default, and an opportunistic type, which can, and where we assume outside lenders have particular beliefs regarding how a commitment type should borrow for any given level of debt and bond price. In any Markov

In their analysis of strategic information transmission, Vincent Crawford and Joel Sobel (1982) showed the existence of partition equilibria (Theorem 1). Although the theorem itself is correct, the proof contains some incorrect statements. We present a counter-example and provide a correct version of the proof.

This document corrects an error in Eeckhout and Kircher (2018) in the sign of an underived condition for positive assortative matching (PAM thereafter) within those extensions that allows for generic capital investment: It occurs in the applications of the main theory to The skill premium with generic capital investment and The misallocation debate; see page 104. This note provides the correct condition

This note points out that the proof of Theorem 1, the main theorem, in Ergin (2002) needs two corrections. We provide two counterexamples to Ergin's (2002) proof and show that the theorem holds as it is by providing an alternative proof.

Lemma 1 of Ray and Vohra (2019) is false as stated, but holds under alternative conditions which are consistent with the ideas of coalitional sovereignty that motivate the cited paper.

We develop a tractable general equilibrium framework in which firms are large and have market power with respect to both products and labor, and in which a firm's decisions are affected by its ownership structure. We characterize the Cournot–Walras equilibrium of an economy where each firm maximizes a share‐weighted average of shareholder utilities—rendering the equilibrium independent of price normalization

We study how an agent learns from endogenous data when their prior belief is misspecified. We show that only uniform Berk–Nash equilibria can be long‐run outcomes, and that all uniformly strict Berk–Nash equilibria have an arbitrarily high probability of being the long‐run outcome for some initial beliefs. When the agent believes the outcome distribution is exogenous, every uniformly strict Berk–Nash

We characterize optimal asset management contracts in a classic portfolio‐investment setting. When the agent has access to hidden savings, his incentives to misbehave depend on his precautionary saving motive. The contract dynamically distorts the agent's access to capital to manipulate his precautionary saving motive and reduce incentives for misbehavior. We provide a sufficient condition for the

We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional mean of the outcome variable, we derive estimators and confidence intervals (CIs) that are optimal in finite samples when the regression errors are normal with known

In response to a change, individuals may choose to follow the responses of their friends or, alternatively, to change their friends. To model these decisions, consider a game where players choose their behaviors and friendships. In equilibrium, players internalize the need for consensus in forming friendships and choose their optimal strategies on subsets of k players—a form of bounded rationality

We reconsider the microeconomic foundations of financial economics. Motivated by the importance of Knightian uncertainty in markets, we present a model that does not carry any probabilistic structure ex ante, yet is based on a common order. We derive the fundamental equivalence of economic viability of asset prices and absence of arbitrage. We also obtain a modified version of the fundamental theorem

How does an economy's capital respond to aggregate productivity shocks when firms make lumpy investments? We show that capital's transitional dynamics are structurally linked to two steady‐state moments: the dispersion of capital to productivity ratios—an indicator of capital misallocation—and the covariance of capital to productivity ratios with the time elapsed since their last adjustment—an indicator

A finite number of vertically differentiated firms simultaneously compete for and screen agents with private information about their payoffs. In equilibrium, higher firms serve higher types. Each firm distorts the allocation downward from the efficient level on types below a threshold, but upward above. While payoffs in this game are neither quasi‐concave nor continuous, if firms are sufficiently differentiated

A profit‐maximizing seller has a single unit of a good to sell. The bidders have a pure common value that is drawn from a distribution that is commonly known. The seller does not know the bidders' beliefs about the value and thinks that beliefs are designed adversarially by Nature to minimize profit. We construct a strong maxmin solution to this joint mechanism design and information design problem

How much capital should financial intermediaries hold? We propose a general equilibrium model with a financial sector that makes risky long‐term loans to firms, funded by deposits from savers. Government guarantees create a role for bank capital regulation. The model captures the sharp and persistent drop in macro‐economic aggregates and credit provision as well as the sharp change in credit spreads

This paper develops inference methods for the iterated overidentified Generalized Method of Moments (GMM) estimator. We provide conditions for the existence of the iterated estimator and an asymptotic distribution theory, which allows for mild misspecification. Moment misspecification causes bias in conventional GMM variance estimators, which can lead to severely oversized hypothesis tests. We show

What should researchers do when their baseline model is falsified? We recommend reporting the set of parameters that are consistent with minimally nonfalsified models. We call this the falsification adaptive set (FAS). This set generalizes the standard baseline estimand to account for possible falsification. Importantly, it does not require the researcher to select or calibrate sensitivity parameters