Knowledge that Transforms

This paper introduces the model confidence set (MCS) and applies it to the selection of models. A MCS is a set of models that is constructed such that it will contain the best model with a given level of confidence. The MCS is in this sense analogous to a confidence interval for a parameter. The MCS acknowledges the limitations of the data, such that uninformative data yield a MCS with many models, whereas informative data yield a MCS with only a few models. The MCS procedure does not assume that a particular model is the true model; in fact, the MCS procedure can be used to compare more general objects, beyond the comparison of models. We apply the MCS procedure to two empirical problems. First, we revisit the inflation forecasting problem posed by Stock and Watson (1999), and compute the MCS for their set of inflation forecasts. Second, we compare a number of Taylor rule regressions and determine the MCS of the best regression in terms of in-sample likelihood criteria.

We propose a new and flexible nonparametric framework for estimating the jump tails of Itô semimartingale processes. The approach is based on a relatively simple-to-implement set of estimating equations associated with the compensator for the jump measure, or its intensity, that only utilizes the weak assumption of regular variation in the jump tails, along with in-fill asymptotic arguments for directly estimating the “large” jumps. The procedure assumes that the large-sized jumps are identically distributed, but otherwise allows for very general dynamic dependencies in jump occurrences, and, importantly, does not restrict the behavior of the “small” jumps or the continuous part of the process and the temporal variation in the stochastic volatility. On implementing the new estimation procedure with actual high-frequency data for the S&P 500 aggregate market portfolio, we find strong evidence for richer and more complex dynamic dependencies in the jump tails than hitherto entertained in the literature.

This paper axiomatizes the robust control criterion of multiplier preferences introduced by Hansen and Sargent (2001). The axiomatization relates multiplier preferences to other classes of preferences studied in decision theory, in particular, the variational preferences recently introduced by Maccheroni, Marinacci, and Rustichini (2006a). This paper also establishes a link between the parameters of the multiplier criterion and the observable behavior of the agent. This link enables measurement of the parameters on the basis of observable choice data and provides a useful tool for applications.

This paper examines repeated implementation of a social choice function (SCF) with infinitely lived agents whose preferences are determined randomly in each period. An SCF is repeatedly implementable in Nash equilibrium if there exists a sequence of (possibly history-dependent) mechanisms such that its Nash equilibrium set is nonempty and every equilibrium outcome path results in the desired social choice at every possible history of past play and realizations of uncertainty. We show, with minor qualifications, that in the complete information environment an SCF is repeatedly implementable in Nash equilibrium if and only if it is efficient. We also discuss several extensions of our analysis.

In this paper, we introduce the extended method of moments (XMM) estimator. This estimator accommodates a more general set of moment restrictions than the standard generalized method of moments (GMM) estimator. More specifically, the XMM differs from the GMM in that it can handle not only uniform conditional moment restrictions (i.e., valid for any value of the conditioning variable), but also local conditional moment restrictions valid for a given fixed value of the conditioning variable. The local conditional moment restrictions are of special relevance in derivative pricing to reconstruct the pricing operator on a given day by using the information in a few cross sections of observed traded derivative prices and a time series of underlying asset returns. The estimated derivative prices are consistent for a large time series dimension, but a fixed number of cross sectionally observed derivative prices. The asymptotic properties of the XMM estimator are nonstandard, since the combination of uniform and local conditional moment restrictions induces different rates of convergence (parametric and nonparametric) for the parameters.

We study the effects of deliberation on collective decisions. In a series of experiments, we vary groups' preference distributions (between common and conflicting interests) and the institutions by which decisions are reached (simple majority, two-thirds majority, and unanimity). Without deliberation, different institutions generate significantly different outcomes, tracking the theoretical comparative statics. Deliberation, however, significantly diminishes institutional differences and uniformly improves efficiency. Furthermore, communication protocols exhibit an array of stable attributes: messages are public, consistently reveal private information, provide a good predictor for ultimate group choices, and follow particular (endogenous) sequencing.

A finite number of sellers (n) compete in schedules to supply an elastic demand. The cost of each seller is random, with common and private value components, and the seller receives a private signal about it. A Bayesian supply function equilibrium is characterized: The equilibrium is privately revealing and the incentives to rely on private signals are preserved. Supply functions are steeper with higher correlation among the cost parameters. For high (positive) correlation, supply functions are downward sloping, price is above the Cournot level, and as we approach the common value case, price tends to the collusive level. As correlation becomes maximally negative, we approach the competitive outcome. With positive correlation, private information coupled with strategic behavior induces additional distortionary market power above full information levels. Efficiency can be restored with appropriate subsidy schemes or with a precise enough public signal about the common value component. As the market grows large with the number of sellers, the equilibrium becomes price-taking, bid shading is on the order of 1/n, and the order of magnitude of welfare losses is 1/n2. The results extend to inelastic demand, demand uncertainty, and demand schedule competition. A range of applications in product and financial markets is presented.

We provide a pure Nash equilibrium existence theorem for games with discontinuous payoffs whose hypotheses are in a number of ways weaker than those of the theorem of Reny (1999). In comparison with Reny's argument, our proof is brief. Our result subsumes a prior existence result of Reny (1999) that is not covered by his theorem. We use the main result to prove the existence of pure Nash equilibrium in a class of finite games in which agents' pure strategies are subsets of a given set, and in turn use this to prove the existence of stable configurations for games, similar to those used by Schelling (1971, 1972) to study residential segregation, in which agents choose locations.

This paper provides an empirical analysis of the effects of employer-provided health insurance, Medicare, and Social Security on retirement behavior. Using data from the Health and Retirement Study, we estimate a dynamic programming model of retirement that accounts for both saving and uncertain medical expenses. Our results suggest that Medicare is important for understanding retirement behavior, and that uncertainty and saving are both important for understanding the labor supply responses to Medicare. Half the value placed by a typical worker on his employer-provided health insurance is the value of reduced medical expense risk. Raising the Medicare eligibility age from 65 to 67 leads individuals to work an additional 0.074 years over ages 60–69. In comparison, eliminating 2 years worth of Social Security benefits increases years of work by 0.076 years.

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to 1 for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players') equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period's state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.