Knowledge that Transforms

Applications of capital theory refer to a world of changing population, institutional processes, technology, and innovation. For example, an investment decision may be affected by some expected repetitive patterns of circumstances or by some seemingly irreversible processes threatened by obsolescence or stagnation. One may assume the principle of an eventually diminishing net returns flow. It seems desirable to treat the marginal efficiency of capital in terms of an initial investment and a net returns flow that varies with time. For a variety of such time dependent net returns flows the treatment of the marginal efficiency of capital is simplified by the Laplace transform technique illustrated in this article.

In this paper, a 14-equation model of the United States potato industry is presented. Four of the equations contain endogenous variables lagged one time period. The solution to this system of first-order difference equations is presented to determine the system's stability. The stochastic stability is then investigated by obtaining estimates of the limiting variance-covariance matrix of endogenous variables. This matrix shows the cumulated effect of historical random shocks. This is followed by a similar study of the effect of erratic variation in exogenous variables. Next is a comparative static analysis, comparing actual values of variables with their stationary state values. The impact of the price support program on the industry is analyzed. Impact and stationary state multipliers are computed and short and long run effects of structural changes are evaluated. RELATIVELY LARGE fluctuations of prices and quantities have characterized the United States potato industry during the last three decades. These fluctuations have had a profound effect on growers' income, regional allocation of production, and the economic efficiency of the industry in general.2 The quantitative analysis of the stability properties of the United States potato industry and its stationary states under changing environmental conditions constitute the main objectives of the present study. In addition, the analysis is so designed as to focus on certain questions pertaining to the particular position maintained by California potato growers in the United States market. The method of analysis consists in formulating an econometric model of the United States potato market. Then, having estimated the parameters of the economic structure, a detailed analysis of the static and dynamic properties of the system is undertaken. The comparative static analysis seeks to evaluate equilibrium values of the endogenous variables both in the short and in the long run and to determine quantitatively the effects of conceivable variation in exogenous variables and certain parameters of the structural relations on these values.

According to Wold, information on some of the variables at time t cannot be used for prediction of the values of the remaining variables at t, in a simultaneous equation system. This, however, is not the case with his causal model. This paper considers the stochastic processes underlying the two models, uses the theory of canonical correlation to discuss Wold's criticism, and suggests the type of additional information necessary to remove these objections. It further shows how both these models are complementary to each other. IN A SERIES of papers, Wold [9, 10, 11, 12] has recently proposed a new type of econometric model, which he calls the implicit causal chain model. The main incentive for this model was an attempt to combine the advantages of Tinbergen's causal model with those of the simultaneous equation systems initiated by Haavelmo [3, 4]. This latter model, which has been studied in detail by the Cowles Commission, is also known as the system. Wold has raised some objections, mainly from the point of view of prediction, against the simultaneous equation system; and in order to remedy these, he relaxed some of the restrictions on the correlational properties of the residuals in the simultaneous equation system. In this paper, these two models are discussed from an angle which offers a possibility for reconciling them. It is shown how the merits of both systems can be utilized by effecting some synthesis of them with the help of the stochastic process underlying both models. Furthermore, by using canonical analysis, it is shown how both these models are complementary. It must, of course, be added that the prediction problem has been considered purely on the basis of the stochastic model assumed, and the possible applicability of different representations of such models, for example, in economic contexts, under wider conditions is not discussed. Wold has objected to interdependent models on grounds other than prediction, especially from the point of view of the interpretation of structural parameters as elasticities, etc. The present paper, however, will not deal with this aspect of the problem. Instead, it deals primarily with the stochastic processes underlying economic models, and the demand and supply model, considered in the next section, is only for illustration.