Hypothesis Testing and the Demand for Capital Goods

Abstract

ONE of basic facts of life confronting econometric researchers is that in order to test any hypothesis it is necessary to assume validity of other assumptions which cannot be tested. An important part of art of practical econometrics is knowing how much to include in maintained hypothesis; if too much is assumed there may be little or nothing left to test, while if too little is assumed it may be impossible to reach any conclusions, or else analysis may become hopelessly complex. In a recent article in this Review 1 Robert Eisner and M. I. Nadiri have examined critically one of essential maintained hypotheses used by Dale W. Jorgenson, James A. Stephenson, Robert E. Hall, and Calvin D. Siebert in a substantial body of empirical research on demand for capital goods.2 This assumption maintains that long-run partial elasticity of flow of capital services, stock of capital, flow of gross investment demand, or flow of net investment, with respect to price of output (p) divided by price of capital services (c) should be unity. By respecifying Jorgenson's model in a logarithmic form, Eisner and Nadiri have produced tests of hypothesis that long-run price elasticity of demand for capital stock is unity. Not only do they find that estimated elasticity with respect to (p/c) is significantly less than one, but all of their preferred point estimates of this parameter are less than 0.16 and in some cases do not differ significantly from zero. The first of seven conclusions summarized by Eisner and Nadiri is that the role of relative prices, critical element in approach, is not confirmed. I In principle, Eisner-Nadiri goal of relaxing and testing crucial maintained hypotheses is a laudable one. Their conclusions, if they can be sustained, have far-reaching implications. If their estimated elasticities are correct, then fiscal and monetary policy-makers have little, if any, direct influence on investment expenditures. A cautious to importance of Eisner-Nadiri conclusions would seem justified, however, in view of fact that others have also undertaken task of critically examining maintained hypotheses in Jorgenson model. While none of other critics of Jorgenson has defended precise manner in which he has specified his model, without exception results have been favorable to essence of neoclassical approach to investment functions assumption that relative prices do matter.4 The next section of this paper is essentially an exercise in detective work aimed at finding out why Eisner and Nadiri obtained results contrary to body of other research. The analytical method used is to carry goal of Eisner and Nadiri relaxing and testing maintained hypothesisone step further. The maintained hypothesis I relax and test involves assumption of serially independent errors.5 * Support for this research was provided under contract DACA31-67-C-0141, U.S. Army Corps of Engineers, for Office of Emergency Planning, and by National Science Foundation and Ford Foundation through grants to Cowles Foundation for Research in Economics. I am very grateful to Professors Robert Eisner, Robert J. Gordon, David Grether, Dale Jorgenson, Franco Modigliani, and Marc Nerlove and to members of Workshop in Econometrics and Mathematical Economics of University of Chicago, for criticisms of earlier versions of this paper, and to Petter Frenger for extremely helpful research assistance. '[7]. Eisner's criticisms have been amplified in [5] and [6]. 2This body of research includes [12] [13] [16] [17] [19] [20] [21] [22]. 3[7], p. 380. 'See [2] [3] [4] [9]. Some of this evidence is discussed briefly in section III below. The evidence on demand for factors other than capital, and on direct estimation of CES production functions, is also relevant, at least indirectly. See [23] for discussion of this evidence. 'As I note below, stochastic assumption I make that errors are a first order autoregressive process -is only one step more general than that used by Eisner and Nadiri. I do not wish to imply that this stochastic assumption is anything more than a minimal improvement; only reasons for not using other types of assumption was my desire to minimize computational problems.