Knowledge that Transforms

Different concepts of noncausality for continuous time processes, using conditional independence and decomposition of semimartingales, are defined. As in the discrete-time setup, continuous time noncausality is a property concerned with the prediction horizon (global versus instantaneous noncausality) and the nature of the prediction (strong versus weak noncausality). Relations between the resulting continuous time noncausality concepts are then studied for the class of decomposable semimartingales for which, in general, the weak instantaneous noncausality does not imply the strong global noncausality. The paper then characterizes these different concepts in the case of counting processes and Markov processes.

The authors study collective choice of fiscal policy in 'federations.' Local policy redistributes across individuals and affects the probability of local shocks. Federal policy shares international risk but may induce local governments to enact policies that increase local risk. The resulting trade-off between risk-sharing and moral hazard is different under alternative fiscal constitutions because the constitutions create different incentives for policymakers and voters and give rise to different political equilibria. The authors specifically contrast vertically ordered systems, like the European Community, with horizontally ordered systems, like the United States. Under appropriate institutions, centralization of functions and power can mitigate the moral hazard problem.

Well-behaved infinite signaling games may have no sequential equilibria. The author proves that adding cheap talk to these games 'solves' the nonexistence problem: the limit of sequential equilibrium outcomes of finite approximating games is a sequential equilibrium outcome of the cheap-talk extension of the limit game. In addition, when the signaling space has no isolated points, any cheap-talk sequential equilibrium outcome can be approximated by a sequential [epsilon]-equilibrium of the game without cheap talk.

4 Celentani (1996) uses multiple types of short-run players to get around the problem of unobservable off-path behavior of the long-run player in repeated games with observable actions.His approach can be extended to short run players who live for more than one periodo

This paper considers hypothesis tests when the parameter space is restricted under the alternative hypothesis. Multivariate one-sided tests are a leading example. The likelihood ratio (LR) test is shown to be admissible and to maximize power against alternatives that are arbitrarily distant from the null hypothesis. Exact results are established first for Gaussian linear regression models with known variance. Asymptotic analogues are then established for dynamic nonlinear models.

This paper proposes three classes of consistent tests for serial correlation of the residuals from a linear dynamic regression model. The tests are obtained by comparing a kernel-based spectral density estimator and the null spectral density using three divergence measures. The null normal distributions are invariant whether the regressors include lagged dependent variables. Both asymptotic local and global power properties are investigated. G. Box and D. Pierce's (1970) test can be viewed as a test based on the truncated kernel; many other kernels deliver better power than Box and Pierce's test. A simulation study shows that the new tests have good power against weak and strong dependence.

Existence of equilibrium with incomplete markets is problematic because demand functions are typically not continuous. Discontinuities occur at prices for which a marketed asset suddenly becomes redundant. The authors show that this discontinuity disappears if they allow an agent in the economy to introduce a new asset when such redundancies occur. This enables them to prove generic existence with incomplete markets using a standard path-following argument. Moreover, the authors' approach suggests a simple algorithm for computing equilibria when markets are incomplete. They demonstrate this by computing equilibrium for a numerical example.

Many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses. This paper studies the asymptotic distribution theory for such tests. The asymptotic distributions of standard test statistics are described as functionals of chi-square processes. In general, the distributions depend upon a large number of unknown parameters. We show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters, and we show that this transformation can be easily approximated via simulation. The theory is applied to threshold models, with special attention given to the so-called self-exciting threshold autoregressive model. Monte Carlo methods are used to assess the finite sample distributions. The tests are applied to U.S. GNP growth rates, and we find that Potter's (1995) threshold effect in this series can be possibly explained by sampling variation.

We present a finite system of polynomial inequalities in unobservable variables and market data that observations on market prices, individual incomes and aggregate endowments must satisfy to be consistent with the equilibrium behavior of some pure trade economy. Quantifier elimination is used to derive testable propositions on finite data sets for the pure trade model.

This paper is organized as follows. In Section 2, we motivate and discuss the sequential testing approach. Section 3 discusses invariance principles of the past and present, and the CUSUM and fluctuation instability detectors. Section 4 contains some illustrative Monte Carlo experiments. A summary and concluding remarks are given in Section 5. Proofs are gathered into the Mathematical Appendix