Knowledge that Transforms

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. The k ‐player consensual dynamic delivers a probabilistic ranking of a game's equilibria, and via a varying k , facilitates estimation of such games. Applying the model to adolescents' smoking suggests that: (a) the response of the friendship network to changes in tobacco price amplifies the intended effect of price changes on smoking, (b) racial desegregation of high schools decreases the overall smoking prevalence, (c) peer effect complementarities are substantially stronger between smokers compared to between nonsmokers.

Quantile factor models (QFM) represent a new class of factor models for high‐dimensional panel data. Unlike approximate factor models (AFM), which only extract mean factors, QFM also allow unobserved factors to shift other relevant parts of the distributions of observables. We propose a quantile regression approach, labeled Quantile Factor Analysis (QFA), to consistently estimate all the quantile‐dependent factors and loadings. Their asymptotic distributions are established using a kernel‐smoothed version of the QFA estimators. Two consistent model selection criteria, based on information criteria and rank minimization, are developed to determine the number of factors at each quantile. QFA estimation remains valid even when the idiosyncratic errors exhibit heavy‐tailed distributions. An empirical application illustrates the usefulness of QFA by highlighting the role of extra factors in the forecasts of U.S. GDP growth and inflation rates using a large set of predictors.

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 of asymmetric costs of upsizing and downsizing the capital stock. We compute these two sufficient statistics using data on the size and frequency of investment of Chilean plants. The empirical values indicate significant effects of aggregate productivity shocks and favor investment models with a strong downsizing rigidity and random opportunities for free adjustments.

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.

We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they are simply two dimension reduction techniques with common estimand but different finite‐sample properties. (ii) VAR‐based structural identification—including short‐run, long‐run, or sign restrictions—can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under noninvertibility. (iv) Linear VARs are as robust to nonlinearities as linear LPs.

This paper develops a general framework to study how misinterpreting information impacts learning. Our main result is a simple criterion to characterize long‐run beliefs based on the underlying form of misspecification. We present this characterization in the context of social learning, then highlight how it applies to other learning environments, including individual learning. A key contribution is that our characterization applies to settings with model heterogeneity and provides conditions for entrenched disagreement. Our characterization can be used to determine whether a representative agent approach is valid in the face of heterogeneity, study how differing levels of bias or unawareness of others' biases impact learning, and explore whether the impact of a bias is sensitive to parametric specification or the source of information. This unified framework synthesizes insights gleaned from previously studied forms of misspecification and provides novel insights in specific applications, as we demonstrate in settings with partisan bias, overreaction, naive learning, and level‐k reasoning.

We often make high stakes choices based on complex information that we have no way to verify. Careful Bayesian reasoning—assessing every reason why a claim could be false or misleading—is not feasible, so we necessarily act on faith: we trust certain sources and treat claims as if they were direct observations of payoff relevant events. This creates a challenge when trusted sources conflict: Practically speaking, is there a principled way to update beliefs in response to contradictory claims? I propose a model of belief formation along with several updating axioms. An impossibility theorem shows there is no obvious best answer, while a representation theorem delineates the boundary of what is possible.

Are the highest sample realizations selected from a larger presample more or less informative than the same amount of random data? Developing multivariate accuracy for interval dominance ordered preferences, we show that sample selection always benefits (or always harms) a decision maker if the reverse hazard rate of the data distribution is log‐supermodular (or log‐submodular), as in location experiments with normal noise. We find nonpathological conditions under which the information contained in the winning bids of a symmetric auction decreases in the number of bidders. Exploiting extreme value theory, we quantify the limit amount of information revealed when the presample size (number of bidders) goes to infinity. In a model of equilibrium persuasion with costly information, we derive implications for the optimal design of selected experiments when selection is made by an examinee, a biased researcher, or contending sides with the peremptory challenge right to eliminate a number of jurors.

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.

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.