Elsevier

Journal of Policy Modeling

Volume 23, Issue 8, November 2001, Pages 901-928
Journal of Policy Modeling

The volatility of the socially optimal level of investment

https://doi.org/10.1016/S0161-8938(01)00093-XGet rights and content

Abstract

In this paper, an annual series for the socially optimal level of investment from 1960–1961 to 1993–1994 for Australia is derived from a vintage production function and compared to the actual series for investment over the same period. The vintage production function can be expected to yield a smoother socially optimal investment series than that derived from a nonvintage, homogenous capital production function. Even so, the resulting series for socially optimal investment is much more volatile than the series for actual investment. Several alternative assumptions are tried in an attempt to further smooth the socially optimal investment series. These include smoothing the assumed values of the exogenous variables, modelling adjustment costs and delivery lags, and changing the form of the production function. While these approaches do succeed in smoothing the investment series, in order for the socially optimal investment series to be as smooth as the actual series the assumed values of the parameters must be quite unrealistic. In the conclusion, we suggest that, in the future research on the socially optimal level of investment, the role of liquidity constraints and of irreversible investment should be investigated.

Introduction

In public debate and discussion of macroeconomic performance, the level of investment is subject to frequent scrutiny and comment. Often concerns are raised that the level of investment is too low. Higher levels of investment are urged in the expectation that they will, by raising labour productivity, raise living standards. In spite of these concerns, economists have devoted little attention to calculating the socially optimal level of investment spending. It is true that there is a considerable literature on modelling the investment behaviour of privately optimising firms in an attempt to explain the pattern of actual investment (see Chirinko, 1993 for a survey). However, the privately optimal level of investment for the individual firm may be different from the socially optimal level. Some reasons for this are discussed in the conclusion.

In this paper, we develop and apply to Australia a method for calculating the socially optimal level of investment. This exercise is part of a broader project in which we are attempting to calculate the socially optimal level of aggregate saving and its socially optimal disposition between investment expenditure and the accumulation of foreign assets (see, e.g., Guest & McDonald, 1998, Guest & McDonald, 2001). Our calculations yield a series for the socially optimal level of investment, which has, compared with the series of the actual level of investment, a very high coefficient of variation.2 This is notwithstanding the use of a vintage putty–clay production function to calculate our series. Such a production function will yield a smoother series than a production function with homogeneous capital.

It seems, at first sight at least, unreasonable to argue for a socially optimal investment series with such a high level of volatility. Because of this, we investigate various ways in which the series can be smoothed. These include smoothing the exogenous variables, varying the elasticity of substitution between labour and capital, and introducing adjustment costs of investment. Even with the choice of reasonable degrees of smoothing using these techniques, we find that the series for the socially optimal level of investment spending is still very volatile compared with the series for the actual level of investment. This result is discussed in Section 5.

In a previous attempt to apply empirically the concept of the socially optimal level of investment, Abel, Mankiw, Summers, and Zeckhauser (1989) developed a criterion for determining whether an economy is dynamically efficient. However, while this criterion maximises social welfare, and, hence, investment is socially optimal, it assumes that the economy is in a steady state. An advantage of the approach in our paper is that it avoids steady state assumptions. For instance, interest rates and employment growth are allowed to vary over the planning horizon instead of setting these variables at constant long run levels. Hence, it is hoped that this flexibility makes the model more empirically useful.

Section snippets

Why a vintage model?

In neoclassical theory, the (nonvintage) production function is of the general form (Eq. (1)):Yj=AjF(Kj,Lj)where Yj, Kj, and Lj are the output, capital stock, and employment levels at time j, respectively. Aj is the efficiency parameter capturing disembodied technical progress. The early neoclassical model of investment was developed by Jorgenson (1963). It assumes perfect competition and determines the optimal capital stock at the level of the firm by assuming either that output is exogenously

Determining the socially optimal level of investment

Using the form of the vintage production function derived in Section 2, in this section, a series for the socially optimal level of investment for Australia for the period 1960–1961 to 1993–1994 is derived from the intertemporal optimising problem outlined in Appendix A (see also Guest & McDonald, 1998). The model is characterised by a representative agent who maximises utility and borrows or lends in a perfect world capital market. To generate a base case, assume a Cobb–Douglas form for F( ).

Volatility in the socially optimal investment series

The series for socially optimal investment from 1961 to 1994 is calculated using Eq. (7) with the values for the parameters and the exogenous variables described above. In Fig. 3, this series is compared to the series for actual investment, where both series are expressed as a proportion of GDP. The socially optimal series is obviously much more volatile than the series for actual investment. We measure volatility as the degree of relative dispersion around the mean, given by the coefficient of

Conclusion

This paper compares, for Australia, the volatility of the socially optimal series of investment with the volatility of the actual series. Various series of the socially optimal level of investment are constructed. These series are considerably more volatile than the actual investment series. In constructing the socially optimal series from a vintage production function, several factors, which may smooth the series, are considered. These are: (i) a constant rate of employment growth; (ii) a

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