Econometrica Volume 90, Issue 2 (March 2022) is now online

Volume 90, Issue 2 (March 2022) has just been published.  The full content of the journal is accessible at



Frontmatter of Econometrica Vol. 90 Iss. 2

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Unwilling to Train?—Firm Responses to the Colombian Apprenticeship Regulation
Santiago Caicedo, Miguel Espinosa, Arthur Seibold

We study firm responses to a large‐scale change in apprenticeship regulation in Colombia. The reform requires firms to train, setting apprentice quotas that vary discontinuously in firm size. We document strong heterogeneity in responses across sectors, where firms in sectors with high skill requirements tend to avoid training apprentices, while firms in low‐skill sectors seek apprentices. Guided by these reduced‐form findings, we structurally estimate firms' training costs. Especially in high‐skill sectors, many firms face large training costs, limiting their willingness to train apprentices. Yet, we find substantial overall benefits of expanding apprenticeship training, in particular when the supply of trained workers increases in general equilibrium. Finally, we show that counterfactual policies taking into account heterogeneity across sectors can deliver similar benefits from training while inducing less distortions in the firm‐size distribution and in the allocation of resources across sectors.
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Model and Predictive Uncertainty: A Foundation for Smooth Ambiguity Preferences
Tommaso Denti, Luciano Pomatto

Smooth ambiguity preferences (Klibanoff, Marinacci, and Mukerji (2005)) describe a decision maker who evaluates each act f according to the twofold expectation defined by a utility function u, an ambiguity index ϕ, and a belief μ over a set of probabilities. We provide an axiomatic foundation for the representation, taking as a primitive a preference over Anscombe–Aumann acts. We study a special case where is a subjective statistical model that is point identified, that is, the decision maker believes that the true law can be recovered empirically. Our main axiom is a joint weakening of Savage's sure‐thing principle and Anscombe–Aumann's mixture independence. In addition, we show that the parameters of the representation can be uniquely recovered from preferences, thereby making operational the separation between ambiguity attitude and perception, a hallmark feature of the smooth ambiguity representation.
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Optimal Discounting
Jawwad Noor, Norio Takeoka

The agent is modeled as a current self that optimally incurs a cognitive cost of empathizing with future selves. The model unifies well‐known experimental and empirical findings in intertemporal choice and enriches the multiple selves model with a notion of self‐control. The defining feature of the model is magnitude‐decreasing impatience: greater patience toward larger rewards. Two behavioral definitions of magnitude‐decreasing impatience are provided and the model is characterized under each of them.
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Discretizing Unobserved Heterogeneity
Stéphane Bonhomme, Thibaut Lamadon, Elena Manresa

We study discrete panel data methods where unobserved heterogeneity is revealed in a first step, in environments where population heterogeneity is not discrete. We focus on twostep grouped fixedeffects (GFE) estimators, where individuals are first classified into groups using kmeans clustering, and the model is then estimated allowing for group‐specific heterogeneity. Our framework relies on two key properties: heterogeneity is a function—possibly nonlinear and time‐varying—of a low‐dimensional continuous latent type, and informative moments are available for classification. We illustrate the method in a model of wages and labor market participation, and in a probit model with time‐varying heterogeneity. We derive asymptotic expansions of two‐step GFE estimators as the number of groups grows with the two dimensions of the panel. We propose a data‐driven rule for the number of groups, and discuss bias reduction and inference.
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Optimal Taxation and R&D Policies
Ufuk Akcigit, Douglas Hanley, Stefanie Stantcheva

We study the optimal design of corporate taxation and R&D policies as a dynamic mechanism design problem with spillovers. Firms have heterogeneous research productivity, and that research productivity is private information. There are non‐internalized technological spillovers across firms, but the asymmetric information prevents the government from correcting them in the first best way. We highlight that key parameters for the optimal policies are (i) the relative complementarities between observable R&D investments, unobservable R&D inputs, and firm research productivity, (ii) the dispersion and persistence of firms' research productivities, and (iii) the magnitude of technological spillovers across firms. We estimate our model using firm‐level data matched to patent data and quantify the optimal policies. In the data, high research productivity firms get disproportionately higher returns to R&D investments than lower productivity firms. Very simple innovation policies, such as linear corporate taxes combined with a nonlinear R&D subsidy—which provides lower marginal subsidies at higher R&D levels—can do almost as well as the unrestricted optimal policies. Our formulas and theoretical and numerical methods are more broadly applicable to the provision of firm incentives in dynamic settings with asymmetric information and spillovers, and to firm taxation more generally.
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Macro-Finance Decoupling: Robust Evaluations of Macro Asset Pricing Models
Xu Cheng, Winston Wei Dou, Zhipeng Liao

This paper shows that robust inference under weak identification is important to the evaluation of many influential macro asset pricing models, including (time‐varying) rare‐disaster risk models and long‐run risk models. Building on recent developments in the conditional inference literature, we provide a novel conditional specification test by simulating the critical value conditional on a sufficient statistic. This sufficient statistic can be intuitively interpreted as a measure capturing the macroeconomic information decoupled from the underlying content of asset pricing theories. Macro‐finance decoupling is an effective way to improve the power of the specification test when asset pricing theories are difficult to refute because of a severe imbalance in the information content about the key model parameters between macroeconomic moment restrictions and asset pricing cross‐equation restrictions. We apply the proposed conditional specification test to the evaluation of a time‐varying rare‐disaster risk model and the construction of robust model uncertainty sets.
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Optimal Decision Rules for Weak GMM
Isaiah Andrews, Anna Mikusheva

This paper studies optimal decision rules, including estimators and tests, for weakly identified GMM models. We derive the limit experiment for weakly identified GMM, and propose a theoretically‐motivated class of priors which give rise to quasi‐Bayes decision rules as a limiting case. Together with results in the previous literature, this establishes desirable properties for the quasi‐Bayes approach regardless of model identification status, and we recommend quasi‐Bayes for settings where identification is a concern. We further propose weighted average power‐optimal identification‐robust frequentist tests and confidence sets, and prove a Bernstein‐von Mises‐type result for the quasi‐Bayes posterior under weak identification.
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Global Banks and Systemic Debt Crises
Juan M. Morelli, Pablo Ottonello, Diego J. Perez

We study the role of global financial intermediaries in international lending. We construct a model of the world economy, in which heterogeneous borrowers issue risky securities purchased by financial intermediaries. Aggregate shocks transmit internationally through financial intermediaries' net worth. The strength of this transmission is governed by the degree of frictions intermediaries face in financing their risky investments. We provide direct empirical evidence on this mechanism showing that around Lehman Brothers' bankruptcy, emerging‐market bonds held by more distressed global banks experienced larger price contractions. A quantitative analysis of the model shows that global financial intermediaries play a relevant role in driving borrowing‐cost and consumption fluctuations in emerging‐market economies, during both debt crises and regular business cycles. The portfolio of financial intermediaries and the distribution of bond holdings in the world economy are key to determine aggregate dynamics.
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Range-Dependent Attribute Weighting in Consumer Choice: An Experimental Test
Jason Somerville

This paper investigates whether the range of an attribute's outcomes in the choice set alters its relative importance. I derive distinguishing predictions of two prominent theories of range‐dependent attribute weighting: the focusing model of Kőszegi and Szeidl (2013) and the relative thinking model of Bushong, Rabin, and Schwartzstein (2021). I test these predictions in a laboratory experiment in which I vary the prices of high‐ and low‐quality variants of multiple products. The data provide clear evidence of choice‐set dependence consistent with relative thinking: price increases that expand the range of prices in the choice set lead to more purchases. Structural estimates imply economically meaningful effect sizes: the average participant was willing to pay around 17% more when a seemingly irrelevant option is added to their choice set.
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The Welfare Effects of Dynamic Pricing: Evidence from Airline Markets
Kevin R. Williams

Airfares fluctuate due to demand shocks and intertemporal variation in willingness to pay. I estimate a model of dynamic airline pricing accounting for both sources of price adjustments using flight‐level data. I use the model estimates to evaluate the welfare effects of dynamic airline pricing. Relative to uniform pricing, dynamic pricing benefits early‐arriving, leisure consumers at the expense of late‐arriving, business travelers. Although dynamic pricing ensures seat availability for business travelers, these consumers are then charged higher prices. When aggregated over markets, welfare is higher under dynamic pricing than under uniform pricing. The direction of the welfare effect at the market level depends on whether dynamic price adjustments are mainly driven by demand shocks or by changes in the overall demand elasticity.
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Are Medical Care Prices Still Declining? A Re-examination Based on Cost-effectiveness Studies
Abe Dunn, Anne Hall, Seidu Dauda

More than two decades ago, a well‐known study on heart attack treatments provided evidence suggesting that, when appropriately adjusted for quality, medical care prices were actually declining (Cutler, McClellan, Newhouse, and Remler (1998)). Our paper revisits this subject by leveraging estimates from more than 8000 cost‐effectiveness studies across a broad range of conditions and treatments. We find large quality‐adjusted price declines associated with treatment innovations. To incorporate these quality‐adjusted indexes into an aggregate measure of inflation, we combine an unadjusted medical‐care price index, quality‐adjusted price indexes from treatment innovations, and proxies for the diffusion rate of new technologies. In contrast to official statistics that suggest medical care prices increased by 0.53 percent per year relative to economy‐wide inflation from 2000 to 2017, we find that quality‐adjusted medical care prices declined by 1.33 percent per year over the same period.
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Detecting p-Hacking
Graham Elliott, Nikolay Kudrin, Kaspar Wüthrich

We theoretically analyze the problem of testing for p‐hacking based on distributions of p‐values across multiple studies. We provide general results for when such distributions have testable restrictions (are non‐increasing) under the null of no p‐hacking. We find novel additional testable restrictions for p‐values based on t‐tests. Specifically, the shape of the power functions results in both complete monotonicity as well as bounds on the distribution of p‐values. These testable restrictions result in more powerful tests for the null hypothesis of no p‐hacking. When there is also publication bias, our tests are joint tests for p‐hacking and publication bias. A reanalysis of two prominent data sets shows the usefulness of our new tests.
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Multivariate Rational Inattention
Jianjun Miao, Jieran Wu, Eric R. Young

We study optimal control problems in the multivariate linear‐quadratic‐Gaussian framework under rational inattention. We propose a three‐step procedure to solve this problem using semidefinite programming and derive the optimal signal structure without strong prior restrictions. We analyze both the transition dynamics of the optimal posterior covariance matrix and its steady state. We characterize the optimal information structure for some special cases and develop numerical algorithms for general cases. Applying our methods to solve three multivariate economic models, we obtain some results qualitatively different from the literature.
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Forthcoming Papers

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2021 Election of Fellows to the Econometric Society

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Backmatter of Econometrica Vol. 90 Iss. 2

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Publication Date: 
Monday, March 21, 2022