time

time

time

/ )

time

FIGURE 9.3 The effects of an increase in money growth

of real balances demanded falls discontinuously. Since M does not change discontinuously, it follows thai P must jump up at the time of the change. This information is summarized in the remaining panels of Figure 9.3.

This analysis has two messages. First, the change in inflation resulting from the change in money growth is reflected one-for-one in the nominal interest rate. The hypothesis that inflation affects the nominal rate

In addition to the path of P described here, there may also be bubble paths that satisfy (9.4). Along these paths, P rises at an increasing rate, thereby causing w" to be rising and the quantity of real balances demanded to be faUing. See, for example. Problem 2.20 and Blanchard and Fischer (1989, Chapter 5, Secnon 3).

The Case of Incomplete Price Flexibility

In the preceding analysis, an increase in money growth increases nominal interest rates. In practice, however, the immediate effect of a monetary expansion is to lower short-term nominal rates. This negative effect of monetary expansions on nominal rates is known as the liquidity effect.

The conventional explanation of the liquidity effect is that monetary expansions reduce real rates. If prices are not completely flexible, an increase in the money stock raises output, which requires a decline in the real interest rate; in terms of the IS-LM framework of Chapter 5, the LM curve shifts to the right along the downward-sloping /5" curve. If the decline in

This analysis raises the question of why expected inflation falls when the money supply is exploding. We return to this issue in Section 9.7.

one-for-one is known as the Fisher effect; it follows from the Fisher identity and the assumption that inflation does not affect the real rate.

Second, a higher growth rate of the nominal money stock reduces the real money stock. The rise in money growth increases expected inflation, thereby increasing the nominal interest rate. This increase in the opportunity cost of holding money reduces the quantity of real balances that individuals want to hold. Thus equilibrium requires that P rises more than M does. That is, there must be a period when inflation exceeds the rate of money growth. In our model, this occurs al the moment that money growth increases. In models where prices are not completely flexible or individuals cannot adjust their real money holdings costlessly, in contrast, it occurs over a longer period.

A corollary is that a reduction in inflation can be accompanied by a temporary period of unusually high money growth. Rather than taking the path of the money stock as fixed, consider the problem of choosing the path of the money stock to yield some desired path of the price level. Specifically, suppose that policymakers want to reduce inflation and that they do not want the price level to change discontinuously. What path of M is needed to do this? The decline in inflation will reduce expected inflation, and thus lower the nominal interest rate and raise the quantity of real balances demanded. Writing the money market equilibrium condition as M = , Y), it follows that-since Y) increases discontinuously and P does not jump- M must jump up. Of course, to keep inflation low, the money stock must then grow slowly from this higher level.

Thus, the monetary policy that is consistent with a permanent drop in inflation is a sudden upward jump in the money supply, followed by low growth. And, in fact, the clearest examples of dechnes in inflation-the ends of hyperinflations-are accompanied by spurts of very high money growth that continue for a time after prices have stabilized (Sargent, 1982)."*

9.3 Monetary Policy and the Term Structure of Interest Rates

In many situations, we are interested in the behavior not just of short-term interest rates, but also of long-term rates. To understand how monetary policy affects long-term rates, we must consider the relationship between short-term and long-term rates. The relationship among interest rates over different horizons is known as the term structure of interest rates, and the standard theory of that relationship is known as the expectations theory of the term structure. This section describes this theory and considers its implications for the effects of monetary policy.

The Expectations Theory of the Term Structure

Consider the problem of an investor deciding how to invest a dollar over the next n periods; assume for simplicity that there is no uncertainty about future interest rates. Suppose firsl the investor puts the dollar in an n -period zero-coupon bond (that is, a bond whose entire payoff comes after n periods). If the bond has a continuously compounded return of i" per period, the investor has exp(n/f") dollars after n periods. Now consider what happens if he or she puts the dollar into a sequence of 1-period bonds paying continuously compounded rates of return of „ i over the n

periods. In this case, he or she ends up with exp(Zf! -i- i+ + n i) doUars.

Equilibrium requires that investors are willing to hold both 1-period and n -period bonds. Thus the returns on the investors two strategies must be the same. This requires

See Problem 9.2. In addition, if inflation is completely unresponsive to monetary policy for any interval of time, then expectations of inflation over that interval do not rise; thus in this case short-term nominal rates necessarily fall.

the real rate is large enough, it more than offsets the effect of the increase in expected inflation.

If prices are fully flexible in the long run, then the real rate eventually retums to normal following a shift to higher money growth. Thus if the real-rate effect dominates the expected-inflation effect in the short mn, the shift depresses the nominal rate in the short run but increases it in the long run. As Friedman (1969) pointed out, this appears to provide an accurate description of the effects of monetary policy in practice. The Federal Reserves expansionary policies in the late 1960s, for example, seem to have lowered nominal rates for several years, but, by generating inflation, to have raised them over the longer term.