# Research Discussion Paper – RDP 8004 Money, Inflation and Economic Growth: Conditions for Superneutrality

September 1980

## Abstract

The key question addressed by the literature on money and growth is whether or not changes in the rate of monetary expansion have real effects on the growth path of the economy. This question is usually phrased in terms of the superneutrality of money. Superneutrality is distinguished from the more commonly used term of neutrality by the former's reference to monetary growth rates, as distinct from one-shot changes in the money stock; superneutrality is thus a dynamic concept of neutrality.

Superneutrality has also appeared in the literature in the guise of the natural rate of interest. The idea of a natural rate of return on capital, determined solely by real factors and thereby invariant to monetary behaviour is an attractive concept. The proposition is usual attributed to Wicksell although its recent popularization owes much to Friedman's influential 1968 Presidential address.

The early contributions to the literature, based on descriptive analysis, unanimously rejected superneutrality. They argued that money and capital are substitutes in the eyes of portfolio holders. A change in the rate of monetary expansion chnages the rate of inflation and thus the rate of return on real money balances. In principle this should set in motion a complex interaction of income and substitution effects which would alter the equilbrium of the economy. This view was largely overthrown by Sidrauski who put forward a model based on explicit optimization in which the real economy was invariant to the rate of monetary expansion. The accepted interpretation of his model is that far-sighted individuals “see through” the veil of money, and choose a pattern of behaviour that will set the economy on an optimal real expansion path. Sidrauski's work appeared at the same time that Friedman was expounding his views on the natural rate of interest, and between them they have dominated thinking on this topic for a decade or more.

Recently, however, several economists have expressed doubts about some of Sidrauski's assumptions. The main objective of this paper is to determine whether Sidrauski's results depend on unrealistically restrictive assumptions, and if so, whether anything can be said about the likely direction of any real effects associated with a change in the monetary growth rate.

The essence of Sidrauski's model is utility-maximization over time by an immortal household. The household has preferences over consumption in each period and real money balances. The apparent weak links in his model are: (i) the infinite horizon of the individuals involved (ii) the assumption that all individuals are identical and have the same rate of time discount (iii) the assumption that the individuals like consumption in all periods equally except for the use of the time discount rate to weight current consumption higher than future consumption (iv) the assumption that the production process is independent of money balances held by firms and (v) the assumption that money yields a return to the individual that varies with the amount held.

Using an overlapping-generations framework in which individuals live for a finite length of time, but are still linked to the future by concern for their children it is possible to replicate Sidrauski's superneutrality result. The advantage of this approach is that, unlike Sidrauski's original model, the overlapping generations model allows a much wider range of alternative assumptions. Indeed, it is shown that superneutrality requires all five of the assumptions listed above. Superneutrality has little to do with the long-sightedness of Sidrauski's household. It is more accurately described as a technical accident of combining certain types of assumptions. When any one of these assumptions is abandoned, monetary growth has real effects.

What are these real effects? From the assumptions listed above it should be apparent that superneutrality requires two types of restrictions on the productive process and on the behaviour of individual consumers. Real effects can be generated by relaxing either of these two sides of the model. In general the effects will be an indeterminate mixture of income and substitution effects. There are, however, two cases in which an unambiguous outcome can be predicted.

The first, due to Dornbusch and Frenkel arises when we relax the production side of the model to allow money to affect production directly as an input. In this case, an increase in the monetary growth rate will decrease the real growth rate of output provided cross-effects are positive (that is, an increase in the price of one good increases the demand for all other goods) and own-effects are dominant (that is, the demand (supply) for each good responds more to movements in its own price than it does to movements in the prices of other goods). The essence of this result is that since money and capital are usually hypothesised to be complementary inputs in production, a decrease in the rate of return on money will lead to a reduction in the use of money and, through complementarity, a reduction in the use of capital. The second arises when we relax the restrictions on the consumer (e.g. assumptions (i)-(iii), and (v) above). In this case an increase in the rate of monetary growth will increase the real rate of growth of output if money is held at the margin purely for its properties as an asset. If this is the case, the financial returns on money and capital will be forced into alignment. A decrease in the rate of return on money will decrease the rate of return on capital thereby implying a higher capital-labour ratio.