Evidence from the laboratory and the field has uncovered both underreaction and overreaction to new information. We provide new experimental evidence on the underlying mechanisms of under‐ and overreaction by comparing how people make inferences and revise forecasts in the same information environment. Participants underreact to signals when inferring about underlying states, but overreact to the same signals when revising forecasts about future outcomes—a phenomenon we term “the inference‐forecast gap.” We show that this gap is largely driven by different simplifying heuristics used in the two tasks. Additional treatments suggest that the choice of heuristics is affected by the similarity between statistics in the information environment and the statistic elicited by the belief‐updating problem.

We study deep neural networks and their use in semiparametric inference. We establish novel nonasymptotic high probability bounds for deep feedforward neural nets. These deliver rates of convergence that are sufficiently fast (in some cases minimax optimal) to allow us to establish valid second‐step inference after first‐step estimation with deep learning, a result also new to the literature. Our nonasymptotic high probability bounds, and the subsequent semiparametric inference, treat the current standard architecture: fully connected feedforward neural networks (multilayer perceptrons), with the now‐common rectified linear unit activation function, unbounded weights, and a depth explicitly diverging with the sample size. We discuss other architectures as well, including fixed‐width, very deep networks. We establish the nonasymptotic bounds for these deep nets for a general class of nonparametric regression‐type loss functions, which includes as special cases least squares, logistic regression, and other generalized linear models. We then apply our theory to develop semiparametric inference, focusing on causal parameters for concreteness, and demonstrate the effectiveness of deep learning with an empirical application to direct mail marketing.

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.

A seller and a buyer bargain over the terms of trade for an object. The seller receives a perfect signal that determines the value of the object to both players, whereas the buyer remains uninformed. We analyze the infinite-horizon bargaining game in which the buyer makes all the offers. When the static incentive constraints permit first-best efficiency, then under some regularity conditions the outcome of the sequential bargaining game becomes arbitrarily efficient as bargaining frictions vanish. When the static incentive constraints preclude first-best efficiency, the limiting bargaining outcome is not second-best efficient and may even perform worse than the outcome from the one-period bargaining game. With frequent buyer offers, the outcome is then characterized by recurring bursts of high probability of agreement, followed by long periods of delay in which the probability of agreement is negligible.

This paper proposes a class of optimal tests for the constancy of parameters in random coefficients models. Our testing procedure covers the class of Hamilton's models, where the parameters vary according to an unobservable Markov chain, but also applies to nonlinear models where the random coefficients need not be Markov. We show that the contiguous alternatives converge to the null hypothesis at a rate that is slower than the standard rate. Therefore, standard approaches do not apply. We use Bartlett-type identities for the construction of the test statistics. This has several desirable properties. First, it only requires estimating the model under the null hypothesis where the parameters are constant. Second, the proposed test is asymptotically optimal in the sense that it maximizes a weighted power function. We derive the asymptotic distribution of our test under the null and local alternatives. Asymptotically valid bootstrap critical values are also proposed.

An agent has access to multiple information sources, each modeled as a Brownian motion whose drift provides information about a different component of an unknown Gaussian state. Information is acquired continuously—where the agent chooses both which sources to sample from, and also how to allocate attention across them—until an endogenously chosen time, at which point a decision is taken. We demonstrate conditions on the agent's prior belief under which it is possible to exactly characterize the optimal information acquisition strategy. We then apply this characterization to derive new results regarding: (1) endogenous information acquisition for binary choice, (2) the dynamic consequences of attention manipulation, and (3) strategic information provision by biased news sources.