# Econometrica Volume 89, Issue 4 (July 2021) is now online

Submitted by mbz3@nyu.edu on Wed, 2021-07-21 15:51Volume 89, Issue 4 (July 2021) has just been published. The full content of the journal is accessible at

https://www.econometricsociety.org/publications/econometrica/browse

## Articles

**Frontmatter of Econometrica Vol. 89 Iss. 4**

**Robust Bayesian Inference for Set-Identified Models**

Raffaella Giacomini, Toru Kitagawa

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 is to construct a prior class that removes the source of the disagreement: the need to specify an unrevisable prior for the structural parameter given the reduced‐form parameter. The corresponding class of posteriors can be summarized by reporting the ‘posterior lower and upper probabilities’ of a given event and/or the ‘set of posterior means’ and the associated ‘robust credible region’. We show that the set of posterior means is a consistent estimator of the true identified set and the robust credible region has the correct frequentist asymptotic coverage for the true identified set if it is convex. Otherwise, the method provides posterior inference about the convex hull of the identified set. For impulse‐response analysis in set‐identified Structural Vector Autoregressions, the new tools can be used to overcome or quantify the sensitivity of standard Bayesian inference to the choice of an unrevisable prior.

Read More

**Extreme Points and Majorization: Economic Applications**

Andreas Kleiner, Benny Moldovanu, Philipp Strack

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 function *f* and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of an extreme point in each interval where it is constant. We apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.

Read More

**Quantitative Analysis of Multiparty Tariff Negotiations**

Kyle Bagwell, Robert W. Staiger, Ali Yurukoglu

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 over tariffs and assess the value of the MFN principle. Using 1990 trade flows and tariff outcomes from the Uruguay Round of GATT/WTO negotiations, we estimate the model and use it to simulate what would happen if the MFN requirement were abandoned and countries negotiated over discriminatory tariffs. We find that if tariff bargaining in the Uruguay Round had proceeded without the MFN requirement, it would have wiped out the world real income gains that MFN tariff bargaining in the Uruguay Round produced and would have instead led to a small reduction in world real income relative to the 1990 status quo.

Read More

**Recovering Preferences from Finite Data**

Christopher P. Chambers, Federico Echenique, Nicolas S. Lambert

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 models that allow for errors.

Read More

**Redistribution Through Markets**

Piotr Dworczak, Scott Duke Kominers, Mohammad Akbarpour

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 that maximizes agents' total utilities, subject to incentive and market‐clearing constraints. We uncover the constrained Pareto frontier by identifying the optimal trade‐off between allocative efficiency and redistribution. We find that competitive‐equilibrium allocation is not always optimal. Instead, when there is inequality across sides of the market, the optimal design uses a tax‐like mechanism, introducing a wedge between the buyer and seller prices, and redistributing the resulting surplus to the poorer side of the market via lump‐sum payments. When there is significant same‐side inequality that can be uncovered by market behavior, it may be optimal to impose price controls even though doing so induces rationing.

Read More

**A New Parametrization of Correlation Matrices**

Ilya Archakov, Peter Reinhard Hansen

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 the unique *n* × *n* correlation matrix from any vector in is provided, and we derive its numerical complexity.

Read More

**Attention Please!**

Olivier Gossner, Jakub Steiner, Colin Stewart

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 known value; if no outside option is available, the direction of the effect of manipulation depends on the value of the item. A similar result applies to manipulation of choices in bandit problems.

Read More

**Sales and Markup Dispersion: Theory and Empirics**

Monika Mrázová, J. Peter Neary, Mathieu Parenti

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 having the same form (whether Pareto, lognormal, or Fréchet) in the cross section, and it is necessary and sufficient for Gibrat's Law to hold over time. Among the applications we consider, we use our methodology to characterize misallocation across firms; we derive the distribution of markups implied by any assumptions on demand and productivity; and we show empirically that CREMR‐based markup distributions provide an excellent parsimonious fit to Indian firm‐level data, which in turn allows us to calculate the proportion of firms that are of suboptimal size in the market equilibrium.

Read More

**Local Projection Inference is Simpler and More Robust Than You Think**

José Luis Montiel Olea, Mikkel Plagborg‐Møller

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 that control for lags of the variables in the regression. We show that lag‐augmented local projections with normal critical values are asymptotically valid uniformly over (i) both stationary and non‐stationary data, and also over (ii) a wide range of response horizons. Moreover, lag augmentation obviates the need to correct standard errors for serial correlation in the regression residuals. Hence, local projection inference is arguably both simpler than previously thought and more robust than standard autoregressive inference, whose validity is known to depend sensitively on the persistence of the data and on the length of the horizon.

Read More

**Generalized Local-to-Unity Models**

Liyu Dou, Ulrich K. Müller

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 the richness of this model class, in the sense that it can well approximate a large class of processes with stationary Gaussian limits that are not entirely distinct from the unit root benchmark. We show that Campbell and Yogo's (2006) popular inference method for predictive regressions fails to control size in the GLTU(2) model with empirically plausible parameter values, and we propose a limited‐information Bayesian framework for inference in the GLTU(*p*) model and apply it to quantify the uncertainty about the half‐life of deviations from purchasing power parity.

Read More

**TV Advertising Effectiveness and Profitability: Generalizable Results from 288 Brands**

Bradley T. Shapiro, Günter J. Hitsch, Anna E. Tuchman

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 are robust to functional form assumptions and are not driven by insufficient statistical power or measurement error. The ROI analysis shows negative ROIs at the margin for more than 80% of brands, implying over‐investment in advertising by most firms. Further, the overall ROI of the observed advertising schedule is only positive for one third of all brands.

Read More

**Taxing Identity: Theory and Evidence from Early Islam**

Mohamed Saleh, Jean Tirole

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 model, in which rulers are revenue‐maximizers, within a more general identity‐based model, in which rulers care also about inducing people to lose their identity, both in a static and an evolving environment. This paper then constructs novel data sources to test the implications of both models in the context of Egypt's conversion to Islam between 641 and 1170. The evidence supports the identity‐based model.

Read More

**Present Bias**

Anujit Chakraborty

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 *Weak Present Bias* and characterize the general class of utility functions that is consistent with it. We show that present‐biased preferences can be represented as those of a decision maker who makes her choices according to conservative present‐equivalents, in the face of uncertainty about future tastes.

Read More

**Bootstrap Standard Error Estimates and Inference**

Jinyong Hahn, Zhipeng Liao

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 the gap between the theory and practice by showing that such common bootstrap based standard error in fact leads to a potentially conservative inference.

Read More

**Reputation and Sovereign Default**

Manuel Amador, Christopher Phelan

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 equilibrium, the opportunistic type mimics the commitment type when borrowing, revealing its type only by defaulting on its debt at random times. The equilibrium features a “graduation date”: a finite amount of time since the last default, after which time reputation reaches its highest level and is unaffected by not defaulting. Before such date, not defaulting always increases the country's reputation. For countries that have recently defaulted, bond prices and the total amount of debt are increasing functions of the amount of time since the country's last default. For countries that have not recently defaulted (i.e., those that have graduated), bond prices are constant.

Read More

**Submission of Manuscripts to the Econometric Society Monograph Series**

**ONLINE ONLY CORRIGENDUM:**

**Corrigendum to Crawford and Sobel (1982) “Strategic Information Transmission”**

Haruki Kono, Michihiro Kandori

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.

Read More

**Corrigendum to Capital Investment in “Assortative Matching With Large Firms”**

Jan Eeckhout, Philipp Kircher, Cristina Lafuente, Gabriele Macci

**Comment on “Efficient Resource Allocation on the Basis of Priorities”**

Yusuke Narita

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.

Read More

**Corrigendum to “Maximality in the Farsighted Stable Set”**

Jonathan Newton

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.

Read More