Knowledge that Transforms

This paper extends the revelation principle to environments in which the mechanism designer cannot fully commit to the outcome induced by the mechanism. We show that he may optimally use a direct mechanism under which truthful revelation is an optimal strategy for the agent. In contrast with the conventional revelation principle, however, the agent may not use this strategy with probability one. Our results apply to contracting problems between a principal and a single agent. By reducing such problems to well-defined programming problems they provide a basic tool for studying imperfect commitment.

It is widely known that when there are errors with a moving-average root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We consider a class of Modified Information Criteria (MIC) with a penalty factor that is sample dependent. It takes into account the fact that the bias in the sum of the autoregressive coefficients is highly dependent on k and adapts to the type of deterministic components present. We use a local asymptotic framework in which the moving-average root is local to −1 to document how the MIC performs better in selecting appropriate values of k. In Monte-Carlo experiments, the MIC is found to yield huge size improvements to the DFGLS and the feasible point optimal PT test developed in Elliott, Rothenberg, and Stock (1996). We also extend the M tests developed in Perron and Ng (1996) to allow for GLS detrending of the data. The MIC along with GLS detrended data yield a set of tests with desirable size and power properties.

Potential games are games with potential functions.Technically, the potential function defines a refinement concept.We provide justification for this refinement concept using the notion of robustness of equilibria.A Nash equilibrium of a complete information game is said to be robust if every incomplete information game where payoffs are almost always given by the complete information game has an equilibrium which generates behavior close to the Nash equilibrium.We show that Nash equilibria that maximize potential functions are generically robust.

generous referee; remaining errors are my own. The exact finite sample distribution for the two-stage least square estimator has been derived for quite general situations (see Phillips (1983) for a survey of the literature). Unfortunately, these general expressions do not lend themselves to easy interpretations. Consequently, a number of authors have looked at special cases to illustrate some of the problems that can arise when using asymptotic distribution results for finite samples. Two such special cases of note are: 1) The totally unidentified case, where the population covariance between the instruments and the endogenous variable is zero; 2) The very weakly correlated case (first stage R2 much less than the inverse of the sample size) with one equation and one endogenous regressor. Nelson and Startz ’ (1990a&b) pioneered the study of the very weakly correlated case. Their work dramatized the substantial differences that can arise between the exact distribution of the IV estimator and the asymptotic distribution. They argue that: 1) the IV estimate will be concentrated around a value more biased than the plim of the OLS estimate and the ratio of the two biases falls as the correlation between the endogenous variable and

Laboratory and field studies of time preference find that discount rates are much greater in the short-run than in the long-run. Hyperbolic discount functions capture this property. This paper solves the decision problem of a hyperbolic consumer who faces stochastic income and a borrowing constraint. The paper uses the bounded variation calculus to derive the Hyperbolic Euler Relation, a natural generalization of the standard Exponential Euler Relation. The Hyperbolic Euler Relation implies that consumers act as if they have endogenous rates of time preference that rise and fall with the future marginal propensity to consume (e.g., discount rates that endogenously range from 5% to 41% for the example discussed in the paper).

We consider discriminatory and uniform price auctions for multiple identical units of a good. Players have private values, possibly asymmetrically distributed and for multiple units. Our setting allows for aggregate uncertainty about demand and supply. In this setting, equilibria generally will be inefficient. Despite this, we show that such auctions become arbitrarily close to efficient if they are "large, " and use this to derive an asymptotic characterization of revenue and bidding behavior.

UNIT ROOT TESTING has been developed through numerous papers since the work of Ž. Dickey and Fuller 1979 . The idea is to test the hypothesis that the differences of an observed time series do not depend on its levels, or in other words, the levels of the time series have a unit root that can be removed by differencing. While it is in general possible to have multiple unit roots, only the hypothesis of exactly one unit root is considered Ž. here. The available tests therefore hinge on two assumptions: i the levels of the time Ž. series have exactly one unit root which can be removed by differencing, and ii the remaining characteristic roots of the time series are stationary roots. In this paper it is proved that for the likelihood ratio test and a number of other likelihood based statistics Ž. Ž . the assumption ii is redundant whereas i is necessary. It is also shown that for some tests that are not likelihood based it is indeed necessary to assume that the differences have stationary roots. The consequences of the result are perhaps best understood from the implications of Ž. condition i . For autoregressive models of order two or higher, that condition is not satisfied in the entire parameter space and the asymptotic distribution of the likelihood ratio test for a unit root depends on unknown nuisance parameters. In this situation the test statistic is not pivotal; hence the test is not similar, and this complicates the testing. Ž. For non-likelihood based tests the necessity of condition ii implies an additional similarity problem. The practitioner is therefore faced with a trade off between likelihood based tests with fewer similarity problems and other tests that may have other advantageous properties. There are thus two empirical implications of the result. First, when analyzing time series with stationary roots that have modulus close to one so that Ž. condition ii is nearly violated, then the likelihood based tests are preferable and other tests should be used cautiously. Secondly, if explosive roots are found in an application, most of the statistical analysis is actually valid and should not necessarily be disregarded because of the presence of explosive roots. Section 2 presents a Gaussian autoregressive model along with its statistical analysis Ž. and the result showing that condition ii is redundant for likelihood based tests. Robustness with respect to innovations that are martingale difference is also discussed. The results of Section 2 are given for a model without deterministic trends. In Section 3 these are generalized to models with deterministic terms. The mathematical proofs Ž. following in two Appendices are based on the work of Lai and Wei 1983 and Chan and Ž. Wei 1988 .

This paper considers testing problems where several of the standard regularity conditions fail to hold. We consider the case where (i) parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and (ii) there may be a nuisance parameter that appears under the alternative hypothesis, but not under the null. The paper establishes the asymptotic null and local alternative distributions of quasi-likelihood ratio, rescaled quasi-likelihood ratio, Wald, and score tests in this case. The results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models. Examples treated in the paper are: (i) tests of the null hypothesis of no conditional heteroskedasticity in a GARCH(1, 1) regression model and (ii) tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with (possibly) correlated random coefficients.

In expected utility theory, risk attitudes are modeled entirely in terms of utility. In the rank-dependent theories, a new dimension is added: chance attitude, modeled in terms of nonadditive measures or nonlinear probability transformations that are independent of utility. Most empirical studies of chance attitude assume probabilities given and adopt parametric fitting for estimating the probability transformation. Only a few qualitative conditions have been proposed or tested as yet, usually quasi-concavity or quasi-convexity in the case of given probabilities. This paper presents a general method of studying qualitative properties of chance attitude such as optimism, pessimism, and the "inverse-S shape" pattern, both for risk and for uncertainty. These qualitative properties can be characterized by permitting appropriate, relatively simple, violations of the sure-thing principle. In particular, this paper solves a hitherto open problem: the preference axiomatization of convex ("pessimistic" or "uncertainty averse") nonadditive measures under uncertainty. The axioms of this paper preserve the central feature of rank-dependent theories, i.e. the separation of chance attitude and utility.