Knowledge that Transforms

When a continuous time model is estimated from its non-recursive discrete approximation, the presence of identities and exogenous variables in the system does not preclude the use of standard procedures. However, if we wish to use the exact discrete model for estimation purposes, the treatment of identities and exogenous variables is not so straightforward. It is found that the procedure based on the exact discrete model is unlikely to be affected by the presence of identities, but when exogenous variables occur in the system some sort of approximation is usually necessary before the model can be estimated with discrete data. An approximate model is constructed to deal with the latter case and the asymptotic properties of estimators derived from this model are investigated. UNDER CERTAIN CONDITIONS, a stochastic model represented by a system of continuously distributed lags can be regarded as the solution of a system,of linear stochastic differential equations. Two general approaches are available if we wish to estimate the parameters of such a system by conventional methods and with discrete data.2 The first approach (see [1 and 2]) is to take a discrete approximation to the model and estimate the approximate model by standard methods. The second approach makes use of the discrete model which is known to correspond to the continuous time model in the sense that observations at equidistant points in time that are generated by the latter system also satisfy the former. The main advantage of the second approach is that no specification error is involved, so that it is possible in some cases to obtain consistent and asymptotically efficient estimators of the parameters in the model. In addition to the arguments of asymptotic theory, the results of a previous study [8] have given some recommendation to the second approach on the basis of small sampling performance. However, the model used in the sampling experiment of this study was relatively simple and it is the aim of the present paper to discuss the use of the second approach in more complicated models. The complications with which we will be concerned are the presence of identities and exogenous variables; both these complications may be expected to occur in more realistic economic, models. Before the procedure is viable when there are identities in the model, we must ascertain whether the disturbance in the exact discrete model has a non-singular

[This paper investigates various properties of a two-sector putty-clay model in which physical durability of capital as well as its economic lifetime is a choice variable. Our model adopts Wicksell-Åkerman's hypothesis that the production of capital goods of greater durability can be accomplished only by incurring greater costs per unit of capital produced. Thus it is a synthesis of Wicksell's durability and putty-clay models. The case in which all capital goods are infinitely durable and are scrapped solely by obsolescence (i.e., pure obsolescence case) will appear as a special case of our model.]

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.]