Knowledge that Transforms

The authors study repeated games in which players observe a public outcome that imperfectly signals the actions played. They provide conditions guaranteeing that any feasible, individually rational payoff vector of the stage game can arise as a perfect equilibrium of the repeated game with sufficiently little discounting. The central condition requires that there exist action profiles with the property that, for any two players, no two deviations--one by either player--give rise to the same probability distribution over public outcomes. The results apply to principal-agent, partnership, oligopoly, and mechanism-design models, and to one-shot games with transferable utilities. Copyright 1994 by The Econometric Society.

This paper establishes a correspondence in large samples between classical hypothesis tests and Bayesian posterior odds tests for models without trends. More specifically, tests of point null hypotheses and one- or two-sided alternatives are considered (where nuisance parameters may be present under both hypotheses). It is shown that, for certain priors, the Bayesian posterior odds test is equivalent in large samples to classical Wald, Lagrange multiplier, and likelihood ratio tests for some significance level and vice versa. The priors considered under the alternative hypothesis are taken to shrink to the null hypothesis at rate n[superscript -1/2] as the sample size n increases. Copyright 1994 by The Econometric Society.

"This paper describes and analyzes movements of older men among labor force states [in the United States] using quarterly observations derived from the Retirement History Survey (RHS)." The results indicate "substantial undercounts in the biannual data, indicating that the prevalence of labor force movements at older ages has been underestimated previously.... The results show that labor force dynamics at older ages are important, including duration and spell occurrence dependence, and work experience effects. These effects are robust to nonparametric controls for unobserved heterogeneity. The estimates indicate that social security benefits have strong effects on the timing of labor force transitions at older ages, but that changes in social security benefit levels over time have not contributed much to the trend toward earlier labor force exit."

The Theorem of Gittins and Jones (1974) is, perhaps, the single most powerful result in the literature on Bandit problems. This result establishes that in independent-armed Bandit problems with geometric discounting over an infinite horizon, all optimal strategies may be obtained by solving a family of simple optimal stopping problems that associate with each arm an index known as the dynamic allocation index or, more popularly, as the Gittins index. Importantly, the Gittins index of an arm depends solely on the characteristics of that arm and the rate of discounting, and is otherwise completely independent of the problem under consideration. These features simplify significantly the task of characterizing optimal strategies in this class of problems.

'No trade' theorems have shown that new information will not lead to trade when agents share the same prior beliefs. This paper explores the structure of no trade theorems with heterogeneous prior beliefs. It is shown how different notions of efficiency under asymmetric information--ex ante, interim, ex post--are related to agents' prior beliefs as well as incentive compatible and public versions of those efficiency concepts. These efficiency results are used to characterize necessary and sufficient conditions on agents' beliefs for no trade theorems in different trading environments. Copyright 1994 by The Econometric Society.

Suppose that the authors are interested in the distribution of a set of characteristics over a population. They study a precise sense in which this distribution can be said to be polarized and provide a theory of measurement. Polarization, as conceptualized here, is closely related to the generation of social tensions, to the possibilities of revolution and revolt, and to the existence of social unrest in general. The authors take special care to distinguish their theory from the theory of inequality measurement. They derive measures of polarization that are easily applicable to distributions of characteristics such as income and wealth. Copyright 1994 by The Econometric Society.

Many alternative theories have been proposed to explain violations of expected utility (EU) theory observed in experiments. Several recent studies test some of these alternative theories against each other. Formal tests used to judge the theories usually count the number of responses consistent with the theory, ignoring systematic variation in responses that are inconsistent. We develop a maximum-likelihood estimation method which uses all the information in the data, creates test statistics that can be aggregated across studies, and enables one to judge the predictive utility-the fit and parsimony-of utility theories. Analyses of 23 data sets, using several thousand choices, suggest a menu of theories which sacrifice the least parsimony for the biggest improvement in fit. The menu is: mixed fanning, prospect theory, EU, and expected value. Which theories are best is highly sensitive to whether gambles in a pair have the same support (EU fits better) or not (EU fits poorly). Our method may have application to other domains in which various theories predict different subsets of choices (e.g., refinements of Nash equilibrium in noncooperative games).

This paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null. For example, the results apply to tests of structural change with unknown changepoint. The testing problem considered is nonstandard and the classical asymptotic optimality results for the Lagrange multiplier, Wald, and likelihood ratio do not apply. A weighted average power criterion is used here to generate optimal tests. This criterion is similar to that used by A. Wald (1943) to obtain the classical asymptotic optimality properties of Wald tests in 'regular' testing problems. Copyright 1994 by The Econometric Society.

A number of generalizations of the expected utility preference functional are estimated using experimentally generated data involving 100 pairwise choice questions repeated on two separate occasions. Likelihood ratio tests are conducted to investigate the statistical superiority of the various generalizations and the Akaike information criterion is used to distinguish between them. The economic superiority of the various generalizations is also explored and the paper concludes that, for many subjects, the superiority of several of the generalizations is not established. Copyright 1994 by The Econometric Society.

[Many researchers have employed ARCH models to estimate conditional variances and covariances. How successfully can ARCH models carry out this estimation when they are misspecified? This paper employs continuous record asymptotics to approximate the distribution of the measurement error. This allows us to (a) compare the efficiency of various ARCH models, (b) characterize the impact of different kinds of misspecification (e.g., "fat-tailed" errors, misspecified conditional means) on efficiency, and (c) characterize asymptotically optimal ARCH conditional variance estimates. We apply our results to derive optimal ARCH filters for three diffusion models, and to examine in detail the filtering properties of GARCH(1, 1), AR(1) EGARCH, and the model of Taylor (1986) and Schwert (1989).]