Knowledge that Transforms

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or, equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are nonseparable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median-bias-corrected estimator of such bounds as a by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of “penultimate” Gaussian processes. These penultimate processes are generally not weakly convergent, and thus are non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.

This paper extends the subjective expected utility model of decision making under uncertainty to include incomplete beliefs and tastes. The main results are two axiomatizations of the multiprior expected multiutility representations of preference relations under uncertainty. The paper also introduces new axiomatizations of Knightian uncertainty and the expected multiutility model with complete beliefs.

This paper develops a new theory of fluctuations—one that helps accommodate the notions of “animal spirits” and “market sentiment” in unique-equilibrium, rational-expectations, macroeconomic models. To this goal, we limit the communication that is embedded in a neoclassical economy by allowing trading to be random and decentralized. We then show that the business cycle may be driven by a certain type of extrinsic shocks which we call sentiments. These shocks formalize shifts in expectations of economic activity without shifts in the underlying preferences and technologies; they are akin to sunspots, but operate in unique-equilibrium models. We further show how communication may help propagate these shocks in a way that resembles the spread of fads and rumors and that gives rise to boom-and-bust phenomena. We finally illustrate the quantitative potential of our insights within a variant of the RBC model.

We investigate the testable implications of the theory of stable matchings. We provide a characterization of the matchings that are rationalizable as stable matchings when agents' preferences are unobserved. The characterization is a simple nonparametric test for stability, in the tradition of revealed preference tests. We also characterize the observed stable matchings when monetary transfers are allowed and the stable matchings that are best for one side of the market: extremal stable matchings. We find that the theory of extremal stable matchings is observationally equivalent to requiring that there be a unique stable matching or that the matching be consistent with unrestricted monetary transfers.

We study the role of incomplete information and outside options in determining bargaining postures and surplus division in repeated bargaining between a long-run player and a sequence of short-run players. The outside option is not only a disagreement point but reveals information privately held by the long-run player. In equilibrium, the uninformed short-run players' offers do not always respond to changes in reputation and the informed long-run player's payoffs are discontinuous. The long-run player invokes inefficient random outside options repeatedly in order to build reputation to a level where the subsequent short-run players succumb to his extraction of a larger payoff, but he also runs the risk of losing reputation and relinquishing bargaining power. We investigate equilibrium properties when the discount factor goes to 1 and when the informativeness of outside option diffuses. In both cases, bargaining outcomes become more inefficient and the limit reputation building probabilities are interior.

What preferences will prevail in a society of rational individuals when preference evolution is driven by the resulting payoffs? We show that when individuals' preferences are their private information, a convex combination of selfishness and morality stands out as evolutionarily stable. We call individuals with such preferences homo moralis. At one end of the spectrum is homo oeconomicus, who acts so as to maximize his or her own payoff. At the opposite end is homo kantiensis, who does what would be “the right thing to do,” in terms of payoffs, if all others would do likewise. We show that the stable degree of morality—the weight placed on the moral goal—is determined by the degree of assortativity in the process whereby individuals are matched to interact.

Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article, we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either of these scenarios, we derive joint functional central limit theorems and bootstrap validity results for regression-based estimators of the status quo and counterfactual outcome distributions. These results allow us to construct simultaneous confidence sets for function-valued effects of the counterfactual changes, including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals. These confidence sets can be used to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general counterfactual changes and covers the main regression methods including classical, quantile, duration, and distribution regressions. We illustrate the results with an empirical application to wage decompositions using data for the United States. As a part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution. We show that distribution regression encompasses the Cox duration regression and represents a useful alternative to quantile regression. We establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals.

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private types. We prove that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus. The short proof is based on an extension of an elegant result due to Gutmann, Kemperman, Reeds, and Shepp (1991). We also show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed or when the equivalence concept is strengthened to apply to interim expected allocations.

We study European banks' demand for short-term funds (liquidity) during the summer 2007 subprime market crisis. We use bidding data from the European Central Bank's auctions for one-week loans, their main channel of monetary policy implementation. Our analysis provides a high-frequency, disaggregated perspective on the 2007 crisis, which was previously studied through comparisons of collateralized and uncollateralized interbank money market rates which do not capture the heterogeneous impact of the crisis on individual banks. Through a model of bidding, we show that banks' bids reflect their cost of obtaining short-term funds elsewhere (e.g., in the interbank market) as well as a strategic response to other bidders. The strategic response is empirically important: while a naïve interpretation of the raw bidding data may suggest that virtually all banks suffered an increase in the cost of short-term funding, we find that, for about one third of the banks, the change in bidding behavior was simply a strategic response. We also find considerable heterogeneity in the short-term funding costs among banks: for over one third of the bidders, funding costs increased by more than 20 basis points, and funding costs vary widely with respect to the country-of-origin. The funding costs we estimate using bidding data are also predictive of market- and accounting-based measures of bank performance, reinforcing the usefulness of “revealed preference” information contained in bids.

Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time-homogeneity conditions that are like “time is randomly assigned” or “time is an instrument.” Partial-identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed-effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. Bounds for overall effects in static and dynamic models are given. The dynamic bounds provide a partial-identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. The impact of T, the number of time periods, is shown by deriving shrinkage rates for the identified set as T grows. We also consider semiparametric, discrete-choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds. Computationally convenient methods for semiparametric models are presented. We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. We give empirical illustrations.