In this paper, the authors propose a simple procedure for testing the existence of common roots in lag polynomials. They first show, by using a generalized Bezout property, that this hypothesis can be put under a "mixed" form that is linear with respect to the auxiliary parameters and with respect to the initial parameters. It follows that the test procedures can be implemented only by using regressions packages. Copyright 1989 by The Econometric Society.
This paper deals with the problem of aggregation where the focus of the analysis is whether to predict aggregate variables using macro or micro equations. The GrunfeldGriliches prediction criterion for choosing between aggregate and disaggregate equations is generalized to allow for contemporaneous covariances between the disturbances of micro equations and the possibility of different parametric restrictions on the equations of the disaggregate model. A new test is proposed of the hypothesis of 'perfect aggregation' which tests the validity of aggregation either through coefficient equality or through the stability over time of the composition of the regressors across the micro units. The tools developed in the paper are then applied to employment demand functions for the UK economy disaggregated by 40 industries. Firstly a set of unrestricted log-linear dynamic specifications are estimated for the disaggregate equations and then linear parameter restrictions are imposed as appropriate. Corresponding unrestricted and restricted aggregate equations are estimated. Two different levels of aggregation are considered: aggregation over the 23 manufacturing industries and aggregation over all 40 industries of the economy. In both cases the hypothesis of perfect aggregation is firmly rejected. For the manufacturing industries the prediction criterion marginally favors the aggregate equation but over all industries the disaggregated equations are strongly preferred.
The authors study a differentiated industry in which two firms compete by offering intervals of qualities to heterogenous consumers. They establish conditions which, for perfect competition and monopoly, imply that different consumers choose different qualities. Under these conditions, they show existence and essential uniqueness of a price equilibrium. At all price equilibria in which both firms make a positive profit, discrimination of consumers is incomplete. The authors also discuss the choice of product lines, and show that the Chamberlinian incentive to differentiate its products from those of its competitor dominates for intermediate qualities. Copyright 1989 by The Econometric Society.
Let P be a real-valued function defined on the space of cooperative games with transferable utility, satisfying the following condition: In every game, the marginal contributions of all players (according to P) are efficient (i.e., add up to the worth of the grand coalition). It is proved that there exists just one such function P--called the potential--and moreover that the resulting payoff vector coincides with the Shapley value. The potential approach yields other characterizations for the value; in particular, in terms of a new internal consistency property. Further results deal with weighted values and with the nontransferable utility case. Copyright 1989 by The Econometric Society.
An act maps states of nature to outcomes: deterministic outcomes, as well as random outcomes, are included. Two acts f and g are comonotonic, by definition, if it never happens that f(s) > f(t) and g(t) > g(s) for some states of nature s and t. An axiom of comonotonic independence is introduced here. It weakens the von Neumann-Morgenstern axiom of independence as follows: If f > g and if f, g and h are comonotonic then $f + (1 - $)h > $g + (1 - $)h. If a nondegenerate, continuous, and monotonic (state independent) weak order over acts satisfies comonotonic independence, then it induces a unique non-(necessarily-) additive probability and a von Neumann-Morgenstern utility. Furthermore, one can compute the expected utility of an act with respect to the nonadditive probability, using the Choquet integral. This extension of the expected utility theory covers situations, such as the Ellsberg paradox, which are inconsistent with additive expected utility. The concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included. Copyright 1989 by The Econometric Society.(This abstract was borrowed from another version of this item.)
A new framework for games in continuous time is proposed. The continuous-time model conforms as closely as possible to the conventional discrete-time framework. Indeed, continuous time is viewed as "discrete time, but with a grid that is infinitely fine." The paper presents several examples illustrating the difficulties that arise in continuous-time game theory. Theorems relate the equilibria of continuous time games to the equilibria of approximating discrete time games. A variety of industrial organization applications are studied, yielding sharp predictions. Applications include continuously repeated games, preemption models, and patent races. Copyright 1989 by The Econometric Society.
We consider the null hypothesis that a time series has a unit root with possibly nonzero drift against the alternative that the process is «trend-stationary». The interest is that we allow under both the null and alternative hypotheses for the presence for a one-time change in the level or in the slope of the trend function. We show how standard tests of the unit root hypothesis against trend stationary alternatives cannot reject the unit root hypothesis if the true data generating mechanism is that of stationary fluctuations around a trend function which contains a one-time break
A general central limit theorem is proved for estimators defined by minimization of the length of a vector-valued, random criterion function. No smoothness assumptions are imposed on the criterion function in order that the results might apply to a broad class of simulation estimators. Complete analyses of two simulation estimators, one introduced by A. Pakes (1986) and the other by D. McFadden (1989), illustrate the application of the general theorems. These examples illustrate how simulation can be used to circumvent two computational problems that arise frequently in applied econometrics: evaluating intractable aggregation formulae and evaluating discrete response probabilities. Copyright 1989 by The Econometric Society.