Knowledge that Transforms

The subject is retiming of lags in a system of linear difference equations. The issues are (i) the effect of retiming on stability and (ii) the effect of retiming on speed of adjustment. Regarding (i), a theorem due to Bear [1] is sharpened; and new conditions for stability to survive under a retiming of lags are obtained. Regarding (ii), the main results concern the effects of lag perturbations and spread perturbations on speed of adjustment in models with nonnegative coefficients.

A NUMBER OF ARTICLES have been written in recent as well as more distant times on the subject of limited dependent variables. This broad classification includes two particular special cases. First, the dependent variable has finite probability mass concentrated at some limit point-the so called Tobit model. This case is referred to as the censored model in the statistical literature. The second case is when the dependent variable simply has a limited range and follows a continuous density on this support-the truncated case. In this note we show that a fairly powerful technique for truncated normal distributions, first suggested over 70 years ago by Karl Pearson and Alice Lee [9], can be used in the place of more sophisticated iterative maximum likelihood or instrumental variables techniques. Approximations based upon least squares regressions can be generated which require only a calculator and the table produced here. The censored or limited variable case can also be treated in much the same way. Although the estimator is inconsistent, a consistent estimator based upon this general approach could probably be constructed. An example is given comparing this approximation with the results produced by least squares, maximum likelihood, and Amemiya's consistent estimator. The estimator suggested here compares very favorably with Amemiya's. In a more literary vein, Pearson and Lee should be given substantial credit for their work without detracting in any way from those who independently advanced the area without the benefit of reference to the rather obscure article by Pearson and Lee.2

This paper considers a problem faced by players who are involved in a sequence of games: not necessarily the same games, not necessarily with the same opponents, and not necessarily under conditions of complete information. The players are assumed to act in response to stationary Markovian hypotheses which they form about the actions of their opponents. Conditions are explored which require that these hypotheses be correct on average and that the players actions be optimal in response to their hypotheses.

Publisher Summary This chapter explains that the set of feasible net production points is convex if the underlying production functions are of the constant returns, no-joints-products type, and if there are no technological externalities. However, the upper boundary of the set, that is, the transformation surface, is not necessarily strictly concave; it may contain linear segments or, more generally, flats of dimension possibly greater than one. Recently, it has been shown that the degree of flatness is related to the rank of the matrix of primary factor inputs. It has been shown that if at any point P in the transformation surface, there are s industries active, then the surface contains an (s-r)-dimensional flat embracing P if and only if at P there are exactly r linearly independent vectors of primary-factor inputs. As corollary, if the number of primary factors is less than s, then P necessarily lies in a flat of dimension at least one.

[Normally the objective functions used in optimal growth theory either treat present generations more favorable than future ones or give an incomplete ranking of possible welfare distributions. The problem is the infinite horizon. In this paper we analyze the conditions under which it is possible to treat a countably infinite number of generations equally. The existence of equitable objective functions or preferences, giving a complete ranking of possible welfare distributions, is proved.]

PROFESSOR MORISHIMA [1, pp. 621-622] has interpreted his own Generalized Fundamental Marxian Theorem (GFMT) as an extension to the joint production case of the theorem stating that, for systems without joint production, a positive rate of exploitation is a necessary and sufficient condition for a positive rate of profit [2, pp. 63-68]. In fact the GFMT only establishes that a positive warranted rate of profit requires a positive rate of exploitation as defined by Morishima; it does not establish that the same holds for a positive equilibrium rate of profit. An example will now be presented which shows that in fact, under the same assumptions as for the GFMT, a zero rate of exploitation is not incompatible with a positive equilibrium rate of profit. Consider an economy where there is only one (constant returns to scale) technique, consisting of a single process, which jointly produces two goods, z and y, utilizing good z and labor L as inputs, in the following proportions: 2z®1L->4z81y

This paper considers the econometric problems raised by multi-market disequilibrium models. It uses a specification which is derived from general disequilibrium theory and, therefore, provides a first bridge between the economic theory approach and the econometric theory approach of disequilibrium. The model is piecewise linear; the problem of the existence of a reduced form, which is a crucial issue in nonlinear models, is solved. Limited information estimators as well as full information estimators are proposed; a simple numerical algorithm is given for the computation of a FIML estimator.

[This paper analyzes an intertemporal production-investment model of the firm, which includes as a special case the adjustment cost model. Properties of the optimal value function are related to properties of the quasi-profit function. An intertemporal analogue of Hotelling's Lemma is derived, which allows derivation of optimal investment demand equations from knowledge of the optimal value function alone. A simple example illustrates the main results.]

This paper is concerned with testing for causation, using the Granger definition, in a bivariate time-series context. It is argued that a sound and natural approach to such tests must rely primarily on the out-of-sample forecasting performance of models relating the original (non-prewhitened) series of interest. A specific technique of this sort is presented and employed to investigate the relation between aggregate advertising and aggregate consumption spending. The null hypothesis that advertising does not cause consumption cannot be rejected, but some evidence suggesting that consumption may cause advertising is presented.