Knowledge that Transforms

THIS PAPER IS A THEORETICAL examination of the stochastic behavior of equilibrium asset prices in a one-good, pure exchange economy with identical consumers. The single good in this economy is (costlessly) produced in a number of different productive units; an asset is a claim to all or part of the output of one of these units. Productivity in each unit fluctuates stochastically through time, so that equilibrium asset prices will fluctuate as well. Our objective will be to understand the relationship between these exogenously determined productivity changes and market determined movements in asset prices. Most of our attention will be focused on the derivation and application of a functional equation in the vector of equilibrium asset prices, which is solved for price as a function of the physical state of the economy. This equation is a generalization of the Martingale property of stochastic price sequences, which serves in practice as the defining characteristic of market efficiency, as that term is used by Fama [7] and others. The model thus serves as a simple context for examining the conditions under which a price series' failure to possess the Martingale property can be viewed as evidence of non-competitive or irrational behavior. The analysis is conducted under the assumption that, in Fama's terms, prices fully reflect all available an hypothesis which Muth [13] had earlier termed rationality of expectations. As Muth made clear, this hypothesis (like utility maximization) is not behavioral: it does not describe the way agents think about their environment, how they learn, process information, and so forth. It is rather a property likely to be (approximately) possessed by the outcome of this unspecified process of learning and adapting. One would feel more comfortable, then, with rational expectations equilibria if these equilibria were accompanied by some form of stability theory which illuminated the forces which move an economy toward equilibrium. The present paper also offers a convenient context for discussing this issue. The conclusions of this paper with respect to the Martingale property precisely replicate those reached earlier by LeRoy (in [10] and [11]), and not surprisingly, since the economic reasoning in [10] and the present paper is the same. The

Darius J. Conger, John M. Campbell, Jr., Simultaneity in the Birth Rate Equation: The Effects of Eduction, Labor Force Participation, Income and Health, Econometrica, Vol. 46, No. 3 (May, 1978), pp. 631-641

[Green and Laffont have characterized certain appealing dominant-strategy revelation mechanisms as precisely the mechanisms introduced by Groves, but they have established the characterization only for unstructured sets of public alternatives: if the set has some natural structure, their proof generally requires that pathological preferences be admissible. It is shown here that the same characterization holds on sets in R extasciicircumn, even when only nice preferences are admitted; this greatly extends the usefulness of the characterization.]

[A set of standard dynamic disaggregated price equations are estimated to examine the relationship between changes in input prices and output prices. The equations perform satisfactorily by conventional criteria; however, when disaggregated by frequency, it is found that the high and low frequency components appear to satisfy different models. The differences are generally significant suggesting that the model is misspecified and that another lag distribution should be used. In particular, the sum of the lag coefficients for labor inputs is substantially larger when estimated with the low frequency component than the high. Therefore, such a price equation estimated during a regime of continued wage inflation would exhibit a much larger long run output price elasticity with respect to wages, than would one estimated during a period of stable or randomly fluctuating wages.]

to prepare and allow a large number of options. The program can be run in batch mode or interactively at a computer terminal. Computer core storage is dynamically allocated so that large problems are only limited by the size of the machine. SHAZAM is designed to grow so that new algorithms and procedures can easily be added by any programmer familiar with the internal structure of the program. Features of SHAZAM include ordinary least squares, two-stage least squares, seemingly unrelated regressions and iterative estimation of seemingly unrelated regressions, threestage least squares and iterative three-stage least squares, models with first and second order autocorrelated disturbances, estimation of Box-Cox [1] type nonlinear functional forms, principal components and factor analysis, regression on principal components, ridge regression, regressions by matrix decompositions, random number generatign for Monte Carlo samples, forecasting, and plotting. Any set of linear restrictions or hypothesis tests can be used in the estimation. A wide variety of output statistics are available with each procedure. The autocorrelation section of SHAZAM is rather extensive and includes maximum likelihood or least squares estimation by a grid search or iterative Cochrane-Orcutt [2] procedure and inclusion or deletion of initial observations, exact and higher-order DurbinWatson [4] type tests, tests based on Golub's [6] uncorrelated residuals, Dhrymes [3, p. 199] corrections for lagged dependent variables, Savin-White [7] corrections for missing observations in a time series, Savin-White [8] type simultaneous testing for functional form and autocorrelation, and forecasting using Goldberger's [5] best linear unbiased predictor. A SHAZAM user's manual [9], which is also machine readable, is available from the author on request.