Expected value maximizing sequential search rules can be expressed in terms of reservation values. In search with learning the reservation value at any stage of the search is unknown until that stage is reached. Thus calculating ex ante (and subsequent) probabilities of search duration and the offer accepted is difficult if these probabilities are expressed in terms of reservation values. This paper shows, for a wide class of learning procedures, how re-expressing these probabilities in terms of fixed points allows their direct calculation and, thereby, calculation of the expected value of adaptive search. Examples and comparative statics results are presented.
This paper derives the exact finite sample distribution of the two-stage generalized least squares (GLS) estimator in a multivariate linear model with general linear parameter restrictions. This includes the seemingly unrelated regression (SUR) model as a special case and generalizes presently known exact results for the latter system. The usual classical assumptions are made concerning nonrandom exogenous variables and normally distributed errors. The theoretical results of this paper are made possible by the author's development of a matrix fractional calculus. This operator calculus is the main theoretical tool of the paper and may be used to solve a wide range of other unsolved problems in econometric distribution theory. IN THE EARLY 1960's Zellner [10] developed a two-stage GLS estimator for the coefficients in a linear multivariate system that is now popularly known as the SUR model. This two-stage procedure has since been used in many empirical applications. GLS also forms the basis of other commonly used estimators both in linear models with heteroscedastic or autocorrelated errors and in simultaneous equation systems where it leads to three stage least squares (3SLS). In spite of extensive research and perhaps surprisingly in view of the popularity of GLS methods in empirical work, the exact finite sample distribution of the SUR estimator is known only in highly specialized cases. These cases effectively restrict attention to two equation systems and models with orthogonal regressors [2]. Existing distribution theory is even more limited in the case of other commonly used GLS estimators, such as the two-stage estimator in linear models with heteroscedastic errors. Here, only low order moment formulae are known and then only in the simplest two sample setting. The research underlying the present paper is motivated by the deficiencies outlined above. Our initial object of study was the exact distribution of the SUR estimator in the general case. But the methods we have developed open the way to an exact distribution theory for econometric estimators in a much wider setting than the SUR model. The present paper will derive the exact finite sample distribution of the two-stage GLS estimator in the multivariate linear model subject to general linear parameter restrictions. This generalizes all presently known distribution theory for the SUR model itself. Two important specializations of our results will be illustrated in detail: the unrestricted multivariate linear model; and the Zellner model with pairwise orthogonal regressors. The analytical results reported here are made possible by the introduction of a fractional matrix calculus. This calculus is developed in terms of the action of
This paper reexamines both monthly and quarterly U.S. postwar data to investigate if the observed comovements between money, real interestrates, prices and output are compatible with the money-real interest-output link suggested by existing monetary theories of output, which include both Keynesian and equilibrium models.The major empirical findings are these;1) In both monthly and quarterly data, we cannot reject the hypothesis that the ex ante real rate is exogenous, or Granger-causally prior in the context of a four-variable system which contains money, prices, nominal interest rates and industrial production.2) In quarterly data, there is significantly more information con-tained in either the levels of expected inflation or the innovationof this variable for predicting future output, given current and lagged output, than in any other variable examined (money, actualinflation, nominal interest rates, or ex ante real rates). The effect of an inflation innovation on future output is unambiguously negative. The first result casts strong doubt on the empirical importance of existing monetary theories of output, which imply that money should have a causal role on the ex ante real rates. The second result would appear incompatible with most demand driven models of output.In light of these results, we propose an alternative structural model which can account for the major dynamic interactions among the variables.This model has two central features: i) output is unaffected by money supply;and ii) the money supply process is motivated by short-run price stability.
[The existence of a positive balanced growth solution for the discrete dynamic input-output (IO) model is studied. Previous work in the area invariable assumed unrealistic restrictions on the matrices A or B, such as regularity or irreducibility. In our work these restrictions are not imposed. We find that in the realistic case of reducible A, a balanced growth solution exists if each sector depends on all others for either its current account or its capital inputs. If this condition is not satisfied a balanced growth solution may still exist. Conditions for its existence relate the overall growth rate to the growth rates which groups of sectors would have if they were isolated from the rest of the economy.]