# Econometrica July 2018 is now online

Submitted by mbz3@nyu.edu on Wed, 2018-08-15 16:06**TABLE OF CONTENTS** Volume 86, Issue 4 (July 2018)

**Articles**

**Strategic Trading in Informationally Complex Environments**

Nicolas S. Lambert, Michael Ostrovsky, Mikhail Panov

We study trading behavior and the properties of prices in informationally complex markets. Our model is based on the single‐period version of the linear‐normal framework of Kyle (1985). We allow for essentially arbitrary correlations among the random variables involved in the model: the value of the traded asset, the signals of strategic traders and competitive market makers, and the demand from liquidity traders. We show that there always exists a unique linear equilibrium, characterize it analytically, and illustrate its properties with a number of applications. We then use this characterization to study the informational efficiency of prices as the number of strategic traders becomes large. If liquidity demand is positively correlated (or uncorrelated) with the asset value, then prices in large markets aggregate all available information. If liquidity demand is negatively correlated with the asset value, then prices in large markets aggregate all information except that contained in liquidity demand.

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**Unrealistic Expectations and Misguided Learning**

Paul Heidhues, Botond Kőszegi, Philipp Strack

We explore the learning process and behavior of an individual with unrealistically high expectations (overconfidence) when outcomes also depend on an external fundamental that affects the optimal action. Moving beyond existing results in the literature, we show that the agent's beliefs regarding the fundamental converge under weak conditions. Furthermore, we identify a broad class of situations in which “learning” about the fundamental is self‐defeating: it leads the individual systematically away from the correct belief and toward lower performance. Due to his overconfidence, the agent—even if initially correct—becomes too pessimistic about the fundamental. As he adjusts his behavior in response, he lowers outcomes and hence becomes even more pessimistic about the fundamental, perpetuating the misdirected learning. The greater is the loss from choosing a suboptimal action, the *further* the agent's action ends up from optimal. We partially characterize environments in which self‐defeating learning occurs, and show that the decisionmaker learns to take the optimal action if, and in a sense only if, a specific *non*‐identifiability condition is satisfied. In contrast to an overconfident agent, an underconfident agent's misdirected learning is self‐limiting and therefore not very harmful. We argue that the decision situations in question are common in economic settings, including delegation, organizational, effort, and public‐policy choices.

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**Learning and Type Compatibility in Signaling Games**

Drew Fudenberg, Kevin He

Which equilibria will arise in signaling games depends on how the receiver interprets deviations from the path of play. We develop a micro‐foundation for these off‐path beliefs, and an associated equilibrium refinement, in a model where equilibrium arises through non‐equilibrium learning by populations of patient and long‐lived senders and receivers. In our model, young senders are uncertain about the prevailing distribution of play, so they rationally send out‐of‐equilibrium signals as experiments to learn about the behavior of the population of receivers. Differences in the payoff functions of the types of senders generate different incentives for these experiments. Using the Gittins index (Gittins (1979)), we characterize which sender types use each signal more often, leading to a constraint on the receiver's off‐path beliefs based on “type compatibility” and hence a learning‐based equilibrium selection.

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**Consumer Search and Price Competition**

Michael Choi, Anovia Yifan Dai, Kyungmin Kim

We consider an oligopoly model in which consumers engage in sequential search based on partial product information and advertised prices. By applying Weitzman's (1979) optimal sequential search solution, we derive a simple static condition that fully summarizes consumers' shopping outcomes and translates the pricing game among the sellers into a familiar discrete‐choice problem. Exploiting the discrete‐choice reformulation, we provide sufficient conditions that guarantee the existence and uniqueness of market equilibrium and analyze the effects of preference diversity and search frictions on market prices. Among other things, we show that a reduction in search costs raises market prices.

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**The Implementation Duality**

Georg Nöldeke, Larry Samuelson

Conjugate duality relationships are pervasive in matching and implementation problems and provide much of the structure essential for characterizing stable matches and implementable allocations in models with quasilinear (or transferable) utility. In the absence of quasilinearity, a more abstract duality relationship, known as a Galois connection, takes the role of (generalized) conjugate duality. While weaker, this duality relationship still induces substantial structure. We show that this structure can be used to extend existing results for, and gain new insights into, adverse‐selection principal‐agent problems and two‐sided matching problems without quasilinearity.

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**On Multiple Discount Rates**

Christopher P. Chambers, Federico Echenique

We study the problem of resolving conflicting discount rates via a social choice approach. We introduce several axioms, seeking to capture the tension between allowing for intergenerational comparisons of utility, and imposing intergenerational fairness. Depending on which axioms are judged appropriate, we are led to one of several conclusions: a *utilitarian*, *maxmin*, or a *multi‐utilitarian* rule, whereby a utility stream is judged by the worst in a set of utilitarian weighting schemes across discount rates.

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**Dynamic Mixture-Averse Preferences**

Todd Sarver

To study intertemporal decisions under risk, we develop a new recursive model of non‐expected‐utility preferences. The main axiom of our analysis is called mixture aversion, as it captures a dislike of probabilistic mixtures of lotteries. Our representation for mixture‐averse preferences can be interpreted as if an individual optimally selects her risk attitude from some feasible set. We describe some useful parametric examples of our representation and provide comparative statics that tightly link decreases in risk aversion to larger sets of feasible risk attitudes. We then present several applications of the model. In an insurance problem, mixture‐averse preferences can produce a marginal willingness to pay for insurance coverage that increases in the level of existing coverage. In investment decisions, our model can generate endogenous heterogeneity in equilibrium stock market participation, even when consumers have identical preferences. Finally, we demonstrate that our model can address the Rabin paradox even in the presence of reasonable levels of background risk.

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**Risk Preferences and the Macroeconomic Announcement Premium**

Hengjie Ai, Ravi Bansal

This paper develops a revealed preference theory for the equity premium around macroeconomic announcements. Stock returns realized around pre‐scheduled macroeconomic announcements, such as the employment report and the FOMC statements, account for 55% of the market equity premium. We provide a characterization theorem for the set of intertemporal preferences that generates a nonnegative announcement premium. Our theory establishes that the announcement premium identifies a significant deviation from time‐separable expected utility and provides asset‐market‐based evidence for a large class of non‐expected utility models. We also provide conditions under which asset prices may rise prior to some macroeconomic announcements and exhibit a pre‐announcement drift.

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**Activism, Strategic Trading, and Liquidity**

Kerry Back, Pierre Collin‐Dufresne, Vyacheslav Fos, Tao Li, Alexander Ljungqvist

We analyze dynamic trading by an activist investor who can expend costly effort to affect firm value. We obtain the equilibrium in closed form for a general activism technology, including both binary and continuous outcomes. Variation in parameters can produce either positive or negative relations between market liquidity and economic efficiency, depending on the activism technology and model parameters. Two results that contrast with the previous literature are that (a) the relationship between market liquidity and economic efficiency is independent of the activist's initial stake for a broad set of activism technologies, and (b) an increase in noise trading can reduce market liquidity because it increases uncertainty about the activist's trades (the activist trades in the opposite direction of noise traders) and thereby increases information asymmetry about the activist's intentions.

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**Alternative Asymptotics for Cointegration Tests in Large VARs**

Alexei Onatski, Chen Wang

Johansen's (1988,1991) likelihood ratio test for cointegration rank of a vector autoregression (VAR) depends only on the squared sample canonical correlations between current changes and past levels of a simple transformation of the data. We study the asymptotic behavior of the empirical distribution of those squared canonical correlations when the number of observations and the dimensionality of the VAR diverge to infinity simultaneously and proportionally. We find that the distribution weakly converges to the so‐called *Wachter distribution*. This finding provides a theoretical explanation for the observed tendency of Johansen's test to find “spurious cointegration.”

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**A One Covariate at a Time, Multiple Testing Approach to Variable Selection in High-Dimensional Linear Regression Models**

A. Chudik, G. Kapetanios, M. Hashem Pesaran

This paper provides an alternative approach to penalized regression for model selection in the context of high‐dimensional linear regressions where the number of covariates is large, often much larger than the number of available observations. We consider the statistical significance of individual covariates one at a time, while taking full account of the multiple testing nature of the inferential problem involved. We refer to the proposed method as One Covariate at a Time Multiple Testing (OCMT) procedure, and use ideas from the multiple testing literature to control the probability of selecting the approximating model, the false positive rate, and the false discovery rate. OCMT is easy to interpret, relates to classical statistical analysis, is valid under general assumptions, is faster to compute, and performs well in small samples. The usefulness of OCMT is also illustrated by an empirical application to forecasting U.S. output growth and inflation.

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**Uncertainty Shocks in a Model of Effective Demand: Comment**

Oliver de Groot, Alexander W. Richter, Nathaniel A. Throckmorton

Basu and Bundick, 2017 showed an intertemporal preference volatility shock has meaningful effects on real activity in a New Keynesian model with Epstein and Zin, 1991 preferences. We show that when the distributional weights on current and future utility in the Epstein–Zin time aggregator do not sum to 1, there is an asymptote in the responses to such a shock with unit intertemporal elasticity of substitution. In the Basu–Bundick model, the intertemporal elasticity of substitution is set near unity and the preference shock only hits current utility, so the sum of the weights differs from 1. We show that when we restrict the weights to sum to 1, the asymptote disappears and preference volatility shocks no longer have large effects. We examine several different calibrations and preferences as potential resolutions with varying degrees of success.

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**Uncertainty Shocks in a Model of Effective Demand: Reply**

Susanto Basu, Brent Bundick

de Groot, Richter, and Throckmorton, 2018 argue that the model in Basu and Bundick, 2017 can match the empirical evidence only because the model assumes an asymptote in the economy's response to an uncertainty shock. In this Reply, we provide new results showing that our model's ability to match the data does not rely either on assuming preferences that imply an asymptote nor on a particular value of the intertemporal elasticity of substitution. We demonstrate that shifting to preferences that are not vulnerable to the Comment's critique does not change our previous conclusions about the propagation of uncertainty shocks to macroeconomic outcomes.

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