Conclusion

In this chapter, we have analyzed the impact of money and the growth rate of the money supply in optimizing models of economic growth. Initially we analyzed the role of money in a representative household model, in which money enters the utility function of the representative household.

In growth models with money, one can analyze the determination of both real and nominal variables (such as the price level, inflation, and nominal interest rates) and examine the dynamic impact of the growth rate of the money supply. This is a major advantage of monetary over real models.

In the representative household model, the growth rate of the money supply has virtually no real effects, apart from reducing the demand for real money balances, because money does not pay interest. The balanced growth path of all other real variables is independent of the growth rate of the money supply, which only affects inflation, nominal interest rates, and the demand for real money balances by households. This result is known as the superneutrality of money.

In an OLG model, the growth rate of the money supply has real effects, as it has a different impact on the holdings of real money balances and on the level of consumption of different generations. When the growth rate of the money supply increases, older generations, which hold higher real money balances, pay a higher inflation tax than do younger generations. Therefore, current aggregate consumption falls, and savings increase. This leads to a higher accumulation of capital and a transition to a balanced growth path with higher capital per efficiency unit of labor. However, dynamic simulations suggest that these deviations from the superneutrality of money are quantitatively small for plausible parameter values.

The differences in the effects of the growth rate of the money supply between the two categories of models are due to the same reasons that government debt has real effects in OLG models, while it does not in a representative household model.

As is the case with the effects of government debt, the quantitative significance of the effects of the growth rate of the money supply on real variables is small in OLG models with competitive capital markets. This is because they depend on the product of two quantitatively small parameters: the rate of growth of population and the pure rate of time preference.

Both representative household and OLG models imply that the growth rate of the money supply mainly affects long-run inflation and nominal interest rates; it has quantitatively insignificant effects on per capita real output, consumption, and the capital stock. The only real variable that is affected significantly is the stock of real money balances, which depends negatively on the nominal interest rate. These conclusions are in accordance with the predictions of the two-period intertemporal model with money (analyzed in chapter 2). They are also in accordance with the evidence on the effects of the rate of monetary growth across countries discussed in chapter 1 (see figures 1.12 and 1.13). There it was shown that, although a very strong empirical association exists between monetary growth and inflation, the association between monetary and real growth is insignificant.

1. The approach to the derivation of money demand in the continuous time models of this chapter is the so-called money in the utility function approach. It is based on the assumption that real money balances yield utility due to their liquidity services and was first utilized in macroeconomics by Patinkin [1956]. This approach contrasts with an alternative one, used in chapter 2, called cash in advance. The cash in advance approach emphasizes the role of money as a means of payments, which reduces transaction costs, eliminating the need for a double coincidence of wants between buyers and sellers (Clower [1967]). As shown by Feenstra [1986], both approaches are functionally equivalent. We compare the two approaches in chapter 12, which has a fuller treatment of alternative partial and general equilibrium approaches to money demand and the money market.

2. The literature on money and economic growth originated with Tobin [1965]. Sidrauski [1967] first used a representative household model to demonstrate the superneutrality of money (i.e., that the rate of growth rate of the money supply does not affect the path of real variables on the adjustment path or the balanced growth). The literature has since expanded exponentially. Weil [1987b, 1991] analyzed the role of money in an OLG model and demonstrated that the superneutrality of money does not apply in such models.

3. See Fisher [1896] or Fisher [1930], chapter 2.

4. This approach to the welfare costs of inflation, developed by Bailey [1956] and extended by Friedman [1969], treats real money balances as a consumption good and inflation as a tax on real balances. Fischer [1981] and Lucas [1981] find the cost of inflation to be relatively low, between 0.3–0.5% of GDP. Lucas [2000] revised his estimate upward, to slightly less than 1% of GDP. The cost is low but not insignificant, and it appears to rise significantly for high-inflation economies. We shall return to this issue in chapter 12, when we discuss alternative approaches to the demand for money and the macroeconomics of high inflation and hyperinflation.

5. Logarithmic preferences are assumed, because this allows us to obtain exact aggregation. It implies little loss of generality.

6. See chapter 5 on how aggregation takes place in the Blanchard-Weil model.

7. See Weil [1987b, 1991].