Production functions and the measurement of technical change : with special reference to the agricultural processing industries

Abstract

The neoclasssical production function developed by Arrow, Chenery, Minhas and Solow, and subsequently called the Constant Elasticity of Substitution (CES) production function, has been extensively analysed in the economic literature. There is already a substantial volume of research devoted to both the theoretical and empirical aspects of the CES function.

This study is essentially a continuation of such empirical research. Detailed results will be presented of estimated parameters for the CES production function obtained from time series data on New Zealand manufacturing industries. In particular, estimates will be given of the elasticity of factor substitution, the rate of technical progress, and the bias of technology.

A review of the objections to the neoclassical production function, raised by the Cambridge economists, will not be undertaken in this study. The controversies surrounding the aggregate production function, and in particular the objections to the concept of a capital aggregate, have been adequately surveyed by Walters (1963) and Harcourt (1969).

This study will adopt the essentially pragmatic position of the Neoclassicists; to quote Solow:

I have never thought of the macro-economic production function as a rigorously justifiable concept. In my mind it is either an illuminating parable, or else a mere device for handling data, to be used so long as it gives good empirical results, and to be abandoned as soon as it does not, or as soon as something better comes along.

The possibility is explored in this study of an explicit form of the neoclassical production function, namely the CES formulation, as an 'illuminating parable' and a 'device for handling data'.

A number of studies on economic growth have employed the concept of the aggregate production function. The general conclusion has been that economic growth is more explainable in terms of technical progress than factor inputs as conventionally measured. Chapter 1 introduces the concept of the aggregate production function and discusses the role of technological change in economic growth.

Chapter 2 begins with an intuitive explanation of the effects of a changing technology, and then goes on to consider in detail the Diamond-McFadden theory. In essence, the theory states that there will generally be more than one production function consistent with a given set of discrete observations which comprise the data normally available on an industry. However, Arrow and Nerlove have shown that if we specify a priori that technological advance raises the efficiencies of capital and labour exponentially over time, then the production function can be uniquely identified. Some theoretical results from a recent paper by Sato and Beckmann are also considered in this chapter.

Chapters 3 and 4 discuss the CES production function in some detail, and a number of relationships capable of statistical estimation are derived. From these relationships estimates can be obtained of the elasticity of factor substitution, the rate of technical progress, the bias of technology, and the returns to scale parameter, Single-equation estimation of the production function parameters is proposed whilst fully recognising that estimation should generally be by simultaneous-equation techniques.

A systematic treatment of the general aggregation problem in CES production functions is developed in Chapter 5. Simple arithmetic summation of the micro-variables (the usual form taken by published industry data) is equivalent to specifying a priori that factor inputs are perfectly substitutable. The conclusion of this analysis is that the estimated production function parameters derived from industry data are likely to be devoid of any relationship with the underlying micro-parameters. The estimated production function parameters have meaning therefore only at a particular level of aggregation and at no other level.

The first section of Chapter 6 derives a procedure for obtaining an index of capital-in-general from the two distinct capital series available for New Zealand manufacturing industries. In the second section it is shown that, on the not unreasonable assumption that intermediate inputs are paid the value of their marginal products, a satisfactory index of net physical output is obtained by using the index of the industry's current dollar 'value added' deflated by the price index of the industry's final product.

In Chapter 7 the results of classical least-squares estimation of the CES production function parameters are presented for a number of New Zealand manufacturing industries. Discussion of the results and the conclusions to be drawn from this empirical study also appear in this chapter.