Knowledge that Transforms

THE CLASSIC PAPER by Grunfeld and Griliches [3] contains many instructive insights into question of circumstances under which an aggregate dependent variable may be forecasted more precisely with a model based on aggregate variables as opposed to an aggregate of forecasts from individual equations. The statistical model they employ is standard regression framework, a single at macro level and a set of seemingly unrelated regressions (to use Zellner's term) at level. Under assumptions of perfect model specification and nonstochastic regressors, a result of Theil's supports superiority of equations. It is Grunfeld and Griliches' main contention, however, that equations are likely to be more poorly specified than is macro equation. Perhaps, therefore, an aggregation will be realized in prediction of aggregate dependent variable by use of macro equation. While intuitively appealing, one soon finds that to articulate notion that micro equations are likely to be more poorly specified than is macro equation is difficult. Grunfeld and Griliches provide an illustration [3, pp. 7-9] that more than anything else points up elusive character of this notion. Recently, Orcutt, Watts, and Edwards [7] and Edwards and Orcutt [2] published papers that ostensibly support prediction from disaggregated data. Edwards and Orcutt note that a more basic difficulty with equations is that suitable data are scarce. Grunfeld and Griliches had earlier observed in passing that the poor quality of data may be another source of aggregation gain [3, p. 10]. It is precisely this consideration which we propose to examine in present paper. More particularly, we examine virtues of estimating or macro equations when independent variables in equations are observed with error, but corresponding aggregate variables have a smaller (or possibly no) observation error. There are many economic applications in which such offsetting errors may be plausibly hypothesized. For example, there may be some arbitrariness in classification of products (or industrial breakdown), so that while total sales figures for a given firm may be well established, their components may be subject to error. Alternatively, we may have common situation in which an aggregate figure is collected on a regular basis from a relatively complete sample, but components are calculated from benchmarks provided from a smaller or an older sample.

[This paper investigates the possibility of arriving at the mixed-strategy solution of a zero-sum two-person game through an iterative learning process. Learning takes place during repeated play of the game, in which the players have no direct knowledge of the payoff matrix but are allowed to record what happens during play. In this context, all members of a wide class of behaviorally plausible learning mechanisms are shown to be locally unstable for "almost all" zero-sum two-person games with mixed-strategy solutions.]

[An eight equation dynamic model of aggregate demand in the United Kingdom is estimated by a variety of methods which make different assumptions about, and provide different treatments of, the problems of simultaneity and serial correlation, the latter being both within and between equations. Although the system appears to perform quite well on conventional criteria, the alternative estimators reveal a number of misspecifications and demonstrate the sensitivity of the results to estimators choice. The paper also considers the methodological problems involved in estimating dynamic simultaneous equation models with possibly auto-correlated errors using seasonally unadjusted quarterly data.]

[This lecture surveys the history and recent resurgence of interest in models with errors in variables and substantive unobservable variables. Among several examples of such models, special attention is paid to a schooling-occupation-income achievement model in which identification and estimation are based on the variance-components structure (across families) of the unobserved individual ability variable.]

[A set of independent axioms are exhibited which characterize the price mechanism. The Debreu-Scarf limit theorem on the core of an economy and a category theory viewpoint are employed in the analysis.]

[This paper considers the application of various models of consumer demand to United Kingdom time series from 1900 to 1970. As well as testing the various forms of the "Rotterdam" model, reparametrization of that system is carried out in order to test the linear expenditure system and the direct addilog system on an exactly comparable basis. A further variant of the Rotterdam model is also introduced; this is intermediate between symmetry and additivity and allows for the calculation of all cross price elasticities from information on own price and income elasticities alone. The results of testing these models on a nine commodity model using maximum likelihood estimation are presented and discussed. Unlike most previous work, and in spite of some anomalous results, the United Kingdom experience seems broadly consistent with neoclassical demand theory. However, all restrictions more stringent than those directly implied by the theory are rejected, though it is maintained that these may still be of considerable practical significance in particular instances.]

[This paper presents a method for obtaining the large sample distribution of the mean deviation and related measures of income inequality.]

A nonparametric framework for deriving the asymptotic MSE-optimal predictor for a multiplicative model is presented. The resulting predictor is compared to several known competitors in a limited Monte Carlo experiment. RECENT PAPERS BY Zellner [10] and Teekens and Koerts [7] address themselves to the problem of minimum-MSE prediction in a Cobb-Douglas-type multiplicative model under a lognormal distribution assumption for the disturbance term. Each derives the finite sample predictor (which turns out to be a function of the familiar least-squares predictor) for the model based on the assumption that ?2, the variance of the lognormally distributed disturbance, is known. An approximately optimal finite sample predictor is then suggested, where an estimate of w2 is utilized. Under certain conditions the approximately optimal predictor poses a computational burden. Under others, the predictor is easily computed, but no longer are small sample properties guaranteed. Our purpose in this note is to present a general framework for deriving the asymptotically optimal-MSE predictor for this multiplicative model without the imposition of a distributional assumption at the outset. Not only does this exercise provide us with a convenient vehicle for discussing further the aforementioned contributions, it also yields a viable distribution-free predictor that may