In this paper we analyze an aggregative general equilibriiri model in which the use of money is motivated by a cash-in-advance constraint, applied to purchases of a subset of consumption goods. The system is subject to both real and nxnetary shocks, which are economy-wide and observed by all. We develop methods for verifying the existence of, characterizing, and explicitly calculating equilibria. A main result of the analysis is that current money growth affects the current real allocation only insofar as it affects expectations about future money growth, i.e., only through its value as a signal.
The local power of test statistics is analyzed by considering sequences of data-generating processes (DGPs) that approach the null hypothesis without necessarily satisfying the alternative. The three classical test statistics-LR, Wald, and LM-are shown to tend asymptot ically to the same random variable under all such sequences. The powe r of these statistics depends on the null, the alternative, and the sequence of DGPs in a geometrically intuitive way. This implies that, for any statistic that is asymptotically chi-squared under the null, there exists an "implicit alternative hypothesis" against which that statistic will have highest power.
A basic tool of modern econometrics is a uniform law of large numbers (LLN). It is a primary ingredient used in proving consistency and asymptotic normality of parametric and nonparametric estimators in nonlinear econometric models. Thus, in a well-known review article, Burguete, Gallant, and Sousa [8, p. 162] introduce a uniform LLN with the statement: following theorem is the result upon which the asymptotic theory of nonlinear econometrics rests. So pervasive is the use of uniform LLNs, that numerous authors appeal to an unspecified generic uniform LLN. Others appeal to some specific result. The purpose of this paper is to provide a generic uniform LLN that is sufficiently general to incorporate most applications of uniform LLNs in the nonlinear econometrics literature. In summary, the paper presents a result that can be used to turn state of the art pointwise LLNs into uniform LLNs over compact sets, with the addition of a single smoothness condition -- either a Lipschitz condition or a derivative condition. The latter is particularly easy to verify, and is implied by common assumptions used to prove asymptotic normality of estimators. Thus, the additional condition is not particularly restrictive. In contrast to other uniform LLNs that appear in the literature, the one given here allows the full range of heterogeneity of summands (i.e., non-identical distributions), and temporal dependence, that is available with pointwise LLNs.
In recent years, preferences without transitive indifference have been much discussed in consumer theory.Surprisingly, we can show that their singleton valued choice functions turn out to be indistinguishable from those of classical transitive preferences.Let 2: be a preference relation on any set X, with choice function h.We prove that J: is reflexive, total, and semitransitive (or pseudotransitive) if and only if h satisfies the Strong Axiom of Revealed Preference.It follows that choice behavior generated by classical transitive preferences is indistinguishable from that generated by the more general preferences discussed in [2J, [3J, [4J, and [10J.INTRANSITIVE INDIFFERENCE AND REVEALED PREFERENCEl by
On introduit et on etudie une condition comportementale significative sur les fonctions d'utilite pour les richesses qui signifie qu'une loterie indesirable ne peut jamais etre rendue desirable par la presence d'une loterie indesirable independante
The purpose of this paper is to investigate testable implications of equilibrium asset pricing models. We derive a general representation for asset prices that displays the role of conditioning information. This representation is then used to examine restrictions implied by asset pricing models on the unconditional moments of asset payoffs and prices. In particular, we analyze the effect of information omission on the mean-variance frontier of one-period returns on portfolios of securities. Also, we deduce an information extension of equilibrium pricing functions that is useful in deriving restrictions on the unconditional moments of payoffs and prices.
OVER THE LAST DECADE the problem of measurement errors in the independent variables of a regression equation has attracted renewed interest among econometricians. In the fifties and sixties, the problem was considered to be more or less hopeless due to its inherent underidentification (e.g., Theil (1971)). Apart from instrumental variables, the most frequently cited textbook solution was Wald's method of grouping (Wald (1940)). Recent insight into the properties of the method of grouping can be interpreted as making this method worthless in most practical cases (Pakes (1982)). Since about 1970, new approaches to the problem have been explored, basically along three lines, viz. embedding the error-ridden equation into a set of multiple equations (e.g., Zellner (1970), Goldberger (1972)), into a set of simultaneous equations (e.g., Hsiao (1976), Geraci (1976)), and using the dynamics of the equation, if present (e.g., Maravall and Aigner (1977)). In view of the underidentification of the basic model, it is clear that all these methods invoke additional information of some kind. If this information takes the form of exact or stochastic knowledge of certain parameters in the model, the construction of consistent estimators is fairly straightforward (e.g. Fuller (1980), Kapteyn and Wansbeek (1984)). For an overview of the state of the art, see Aigner et al. (1984). An approach somewhat orthogonal to the ones described above has been to take the model as it is and to use prior ideas about the size of the measurement errors to diagnose how serious the probem is. Examples are Blomqvist (1972), Hodges and Moore (1972), and Davies and Hutton (1975). Leamer (1983) starts from the opposite direction by asking how serious the measurement error problem has to be in order to render the data useless for inference, that is to say, when measurement error is large enough to make it impossible to put bounds on regression parameters. In an empirical example, he shows that even very small measurement errors in some explanatory variables would open up the possibility of perfectly collinear explanatory variables and hence make the data useless for statistical inference (at least without additional prior information). The most systematic analysis of the information loss caused by measurement error is due to Klepper and Leamer (1984). They start out by invoking a minimal amount of prior information and then ask the question under what conditions it is still possible to make some inferences regarding the vector of unknown regression parameters p. In the special case where the measurement errors are assumed uncorrelated and the k + 1 estimates of ,3, obtained by regressing each of the k +1 variables involved (i.e. the one dependent variable and the k independent variables) on the remaining k variables, are all in the same orthant, one can bound the ML estimates of p. In that case, the convex hull of the k + 1 regressions contains all possible ML estimates and any point in the hull is a possible ML estimate. If the k + 1 regressions are not all in the same orthant then the set of ML estimates is unbounded. In that case Klepper and Leamer (1984) introduce extra prior information which allows them to bound the set of maximum likelihood estimates. The prior information comes in two forms. Firstly, a researcher is supposed to be able to specify a maximum value of R2 if all exogenous variables were measured accurately. It is shown that if this maximum is low enough, one can again bound the set of ML estimates by a convex hull. Secondly, if