RDP 8501: Neoclassical Theory and Australian Business Investment: A Reappraisal 2. Neoclassical Investment Theory: Traditional Approach and Interpretation

U.R. Kohli and C.J. Ryan

August 1985

Neoclassical investment theory is mostly due to the work of Jorgenson.[4] Assuming cost minimisation, Jorgenson derives the desired stock of capital from a Cobb-Douglas production function:

Inline Equation is the desired stock of capital,[5] p is the price of output,. y is the level of output, wK is the rental price of capital[6] and α is the elasticity of output with respect to the capital stock.

Net investment is then assumed to be a distributed lag function of the change in the desired stock of capital, and gross investment can be obtained by adding replacement investment. The resulting equation has been estimated with Australian data on a number of occasions, but the results have generally been very poor. Our own estimates have proved to be no exception: we have been unable to detect a significant role for the relative price term (p/wK). On several occasions, this variable even entered the estimating equation with the wrong sign.[7] This result is of course inconsistent with the hypothesis of a Cobb-Douglas production function.

The poor performance of the neoclassical model is not only very disappointing, but it is also somewhat surprising. Indeed, there is ample empirical evidence, for Australia and elsewhere, supporting the hypothesis that capital and labour can be substituted for each other in production. It is rather odd, therefore, that the flexible accelerator model should out-perform the neoclassical model.[8] There are two possible explanations that come to mind. First, it could be that although the aggregate production function is neoclassical, it is not Cobb-Douglas. Actually, there is empirical evidence available for Australia pointing in this direction.[9] Second, and maybe more importantly, it could be that although the production function is neoclassical (whether Cobb-Douglas or not), the model has not been put to proper use. The neoclassical model, as set up by Jorgenson, predicts that a decrease in the relative rental price of capital will lead to an increase in the demand for capital services, and hence to increased investment. This proposition is only meaningful if the rental price of capital is exogenous, and if the stock of capital is endogenous. However, one can make a strong case that it is the reverse that is true in the aggregate. The stock of capital is given at any point in time, and under competitive conditions, the rental price of capital will tend to equal its marginal product. Hence, one can argue that the role of the production function is not to determine the demand for capital services, but rather to determine the equilibrium rental price of capital (Inline Equation):

where xK is the actual (beginning-of-period) capital stock. (2) can be viewed as an inverse demand for capital services. The actual rental price of capital can then be assumed to be a distributed lag function of Inline Equation. Estimation of the resulting equation, under alternative dynamic specifications, gives some very encouraging results.[10] In particular, the implied estimate of a is systematically found to be quite close to its theoretical value.

Investment affects the future values of the stock of capital, but the change in the capital stock cannot be deduced from the production function if the rental price of capital is endogenous. What then determines investment? One possible answer has been provided by Tobin (1969). According to Tobin, investment will take place whenever the shadow price of capital (Tobin's q) exceeds the market price of new investment goods (the price of output in Tobin's model). The shadow price of capital depends primarily on the demand for capital as an asset, which itself is likely to be a function of the rental price of capital. Thus, there is a link between the production function and the decision to invest, but it is much less direct than it is sometimes thought.

As noted previously, the 1970's were marked in Australia by a substantial increase in real wages, thus making the use of capital services relatively more attractive. The fact that investment did not increase, however, is not incompatible with the neoclassical model. On the contrary, properly applied neoclassical theory suggests that for given capital stock, an exogenous increase in real wages leads to a reduction in the real rental price of capital. This makes the ownership of capital less attractive, it decreases its shadow price, and, by the same token, it reduces incentives to produce and to install additional capital goods. Besides decreasing investment, the exogenous increase in real wages also tends to reduce output and employment, in the short run as well as in the long run. All three predictions are consistent with recent Australian history.

It seems at this stage that one possible way of proceeding is to formulate an investment function along the lines suggested by Tobin to complement (2). At the same time it would probably be worthwhile to relax the assumption of a Cobb-Douglas production function, i.e. (2) could be replaced by a more general formulation. One difficulty with Tobin's approach, however, is his assumption that the price of existing capital goods will tend to exceed the price of new capital goods. Tobin invokes the existence of adjustment and installation costs, but these costs are not accounted for by the model.

Tobin's approach, of course, is motivated by the desire to explain investment within the framework of a single-sector production model,[11] but it seems to us that it is preferable at this stage to relax the assumption of a single output. In what follows we therefore assume two outputs: investment goods and other (e.g. consumption) goods. At the same time we will also examine the question of the pricing of capital goods within a portfolio framework.

Footnotes

See Jorgenson (1963) and subsequent papers by the same author. [4]

Throughout the paper, we assume that capital services are proportional to the capital stock. The two concepts can be used interchangeably through appropriate choice of measurement units. [5]

Defined in the appendix. [6]

Typical of our results is the following equation based on a Koyck-lag structure: yI is gross investment, yIN is net investment, and xK is the beginning-of-period capital stock. The equation was estimated by OLS with quarterly data (seasonally adjusted) for the period 1963:I–1983:I. [7]

The flexible accelerator and the neoclassical models are sometimes viewed as competing models, but the only difference between them concerns the underlying production function: Leontief in the former, Cobb-Douglas in the latter. [8]

See Kohli (1983b). Eisner and Nadiri (1968) criticise Jorgenson for assuming that the elasticity of the desired capital stock with respect to its real rental price is unity. [9]

A sample of our results is provided by the following equation (a partial adjustment mechanism is assumed, and the equation is estimated in terms of first differences to facilitate comparison with the estimates reported in footnote 7): The equation appears to be well behaved. The fact that the speed of adjustment is greater than unity is somewhat odd, but need not be of great concern to us. The goodness of fit is rather low, but this is not surprising given that the dependent variable is a first difference. Moreover, the fit could undoubtedly be improved by relaxing the assumption of a Cobb-Douglas production function. Note that use of an inverse demand for capital function is made in RBA76 [Jonson et al. (1977)] to explain investment. [10]

Without ad hoc assumption of adjustment or installation costs, investment may be undetermined in a one-sector model. See Turnovsky (1977), for instance. [11]