Knowledge that Transforms

A firm selects applicants to hire based on hard information, such as a test result, and soft information, such as a manager's evaluation of an interview. The contract that the firm offers to the manager can be thought of as a restriction on acceptance rates as a function of test results. I characterize optimal acceptance rate functions both when the firm knows the manager's mix of information and biases and when the firm is uncertain. These contracts may admit a simple implementation in which the manager can accept any set of applicants with a sufficiently high average test score.

Centralized markets reduce search for buyers and sellers. Their “thickness” increases the chance of order execution at nearly competitive prices. In spite of the incentives to consolidate, some markets, securities markets and on‐line advertising being the most notable, are fragmented into multiple trading venues. We argue that fragmentation is an inevitable feature of any centralized market except in special circumstances.

We compare sparse and dense representations of predictive models in macroeconomics, microeconomics, and finance. To deal with a large number of possible predictors, we specify a prior that allows for both variable selection and shrinkage. The posterior distribution does not typically concentrate on a single sparse model, but on a wide set of models that often include many predictors.

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.

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.

The location of individuals determines their job and schooling opportunities, amenities, and housing costs. We conceptualize the location choice of individuals as a decision to invest in a “location asset.” This asset has a current cost equal to the location's rent, and a future payoff through better job and schooling opportunities. As with any asset, savers in the location asset transfer resources into the future by going to expensive locations with high future returns. In contrast, borrowers transfer resources to the present by going to cheap locations that offer few other advantages. Holdings of the location asset depend on its comparison to other assets, with the distinction that the location asset is not subject to borrowing constraints. We propose a dynamic location model and derive an agent's mobility choices after experiencing income shocks. We document the investment dimension of location and confirm the core predictions of our theory using French individual panel data from tax returns.

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.

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mrow> <a:mi mathvariant="double-struck">R</a:mi> </a:mrow> <a:mrow> <a:mi>n</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>n</a:mi> <a:mo>−</a:mo> <a:mn>1</a:mn> <a:mo stretchy="false">)</a:mo> <a:mo stretchy="false">/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:msup> </a:math> is provided, and we derive its numerical complexity.

May's theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that grant voters identical roles. We show that a weakening of May's symmetry assumption allows for a far richer set of rules that still treat voters equally. We show that such rules can have minimal winning coalitions comprising a vanishing fraction of the population, but not less than the square root of the population size. Methodologically, we introduce techniques from group theory and illustrate their usefulness for the analysis of social choice questions.