Knowledge that Transforms

[The estimation and testing of a singular equation system in the context of a general dynamic specification is considered. In an application to factor demand equations, hypotheses suggested by economic theory are expressed in terms of the long run structure of the system under alternative dynamic specifications. Variations in the dynamic specification are found to have a significant impact upon the inferences that can be made about the long run structure.]

The paper derives and compares the local power of three different methods of testing non-nested regression models that are available in the literature. It shows that the asymptotic power of the orthodox F test against local alternatives is strictly less than that of Cox's non-nested test or the J test recently proposed by Davidson and MacKinnon [5], unless the number of non-overlapping variables of the alternative hypothesis over the null hypothesis is unity, in which case all three tests are shown to be asymptotically equivalent. The final section of the paper gives results of Monte Carlo experiments designed to check the validity of the theoretical findings of the paper and also to shed light on the small sample properties of the Cox test and the orthodox test.

We consider the market value of excess demand as a measure of disequilibrium. We show that, in a fixed exchange economy, there exist approximate equilibria whose measures of disequilibrium depend only on the endowments and not on the preferences. A related bound on the norm of excess demand, depending on the endowments and the approximate equilibrium price, is also obtained. We show the existence of allocations which are nearly competitive, as measured by the largest proportion of demand given up at the allocation by any trader. We use these results to obtain, for very general sequences of exchange economies, allocations giving all traders bundles close in norm to their demands. This result includes a 0(l1/n) rate of convergence in the case of uniformly bounded endowments.

[In the classical linear regression model the conflict between the W, LR, and LM tests is due to the tests not having the correct significance level. This paper shows that the probability of conflict can be substantial when the three tests are based on the asymptotic chi-square critical value. For this model some computable correction factors for the chi-square critical values are examined, including those derived from a second-order Edgeworth approximation to the exact distributions. It is shown that the probability of conflict between the Edgeworth size-corrected tests is of no practical importance over a wide range of conditions.]

[There are many infinite horizon optimal problems in economic models. In such problems, the transversality condition may not be verified, as shown by Halkin'sexample. But we prove another property: the maximum of the Hamiltonian converges to zero when time goes to infinity. And, if along the optimal trajectory, after some time, changes of speed (by controls) in all directions at a given level are possible, then the transversality condition is verified. Examples show that the additional property proved here (i) allows exclusion of nonoptimal trajectories which verify the usual necessary conditions in an infinite horizon; (ii) is a result directly useful in some economic studies.]

This paper considers the possibility of static and dynamic speculation when traders have rational expectations. Its central theme is that, unless traders have different priors or are able to obtain insurance in the market, speculation relies on inconsistent plans, and thus is ruled out by rational expectations. Its main contribution lies in the integration of the rational expectations equilibrium concept into a model of dynamic asset trading and in the study of the speculation created by potential capital gains. Price bubbles and their martingale properties are examined. It is argued that price bubbles rely on the myopia of traders and that they disappear if traders adopt a truly dynamic maximizing behavior.