That is, the interest rate on the long-term bond must equal the average of the mterest rates on short-term bonds over its lifetime.

In this example, since there is no uncertainty, rationality alone implies that the term structure is determined by the path that short-term interest rates wiU take. With uncertainty, under plausible assumptions expectations concerning future short-term rates continue to play an important role in the determination of the term structure. A typical formulation is

where Et denotes expectations as of period f. With uncertainty, the strategies of buying a single n-period bond and a sequence of 1-period bonds generally involve different risks. Thus rationality does not imply that the expected returns on the two strategies must be equal. This is reflected by the inclusion of 6, the term premium to holding the long-term bond, in (9.6).

The expectations theory of the term structure is the hypothesis that changes in the term structure are determined by changes in expectations of future interest rates (rather than by changes in the term premium). Typically, though not always, the expectations are assumed to be rational.

As described at the end of Section 9.2, even if prices are not completely flexible, a permanent increase in money growth eventually increases the short-term nominal interest rate permanently. Thus even if short-term rates faU for some period, (9.5) implies that interest rates for sufficiently long maturities (that is, for sufficiently large n) immediately rise. Thus our analysis imphes that a monetary expansion is likely to reduce short-term rates but increase long-term ones.

Empirical Application: The Response of the Term Structure to Changes in the Federal Reserves Federal-Funds-Rate Target

In many periods, the Federal Reserve has had a target level of a particular interest rate, the Federal funds rate, and has implemented monetary policy through discrete changes in that target. The Federal funds rate is the interest rate that banks charge each other on one-day loans of reserves; thus it is a very short-term rate. Because changes in the Federal Reserves target are discrete, it is usually clear what the target is and when it changes. Cook and Hahn (1989) use this fact to investigate the impact that monetary pohcy has

See Sliiller (1990) for an overview of the study of the term structure.

on interest rates on bonds of different maturities. They focus on the period 1974-1979, which was a time when the Federal Reserve was targeting the funds rate.

Cook and Hahn begin by compiling a record of the changes in the Federal Reserves target over this period. They examine both the records of the Federal Reserve Bank of New York (which implemented the changes) and the reports of the changes in the Wall Street Joumal. They find that the Jour-naVs reports are almost always correct; thus it is reasonable to think of the changes in the target reported by the Joumal as publicly observed.

As Cook and Hahn describe, the actual Federal funds rate moves closely with the Federal Reserves target. Moreover, it is highly implausible that the Federal Reserve is changing the target in response to factors that would have moved the funds rate in the absence of the policy changes. For example, it is unlikely that, absent the Federal Reserves actions, the funds rate would move by discrete amounts. In addition, there is often a lag of several days between the Federal Reserves decision to change the target and the actual change; thus arguing that the Federal Reserve is responding to forces that would have moved the funds rate in any event requires arguing that the Federal Reserve has advance knowledge of those forces.

The close link between the actual funds rate and the Federal Reserves target thus provides strong evidence that monetary policy affects short-term interest rates. As Cook and Hahn describe, earlier investigations of this issue mainly regressed changes in interest rates over periods of a month or a quarter on changes in the money supply over those periods; the regressions produced no clear evidence of the Federal Reserves ability to influence interest rates. The reason appears to be that the regressions are complicated by the same types of issues that complicate the money-output regressions discussed in Section 5.6: the money supply is not determined solely by the Federal Reserve, the Federal Reserve adjusts pohcy in response to information about the economy, and so on.

Cook and Hahn then examine the impact of changes in the Federal Reserves target on longer-term interest rates. Specifically, they estimate regressions of the form

AR = b\ + bl AFFt + ui, (9.7)

where AR} is the change in the nominal interest rate on a bond of maturity i on day f, and AFF, is the change in the target Federal funds rate on that day.

Cook and Hahn find, contrary to the predictions of the analysis in the first part of this section, that increases in the Federal-funds-rate target raise nominal interest rates at all horizons. An increase in the target of 100 basis points (that is, one percentage point) is associated with increases in the 3-month interest rate of 55 basis points (with a standard error of 6.8 basis points), in the 1-year rate of 50 basis points (5.2), in the 5-year rate of 21 basis points (3.2), and the 20-year rate of 10 basis points (1.8).

This explanation also implies that contractionan monetary policy can raise the short-term nommal rate without increasing the real rate.

The idea that contractionary monetary policy should immediately lower long-term nominal interest rates is intuitive: contractionary policy is likely to raise real interest rates only briefly and is likely to lower inflation over the longer term. Yet, as Cook and Hahns results show, the evidence does not support this prediction.

There are at least four possible explanations of this anomaly. First, the response of the real rate to monetary policy may be so persistent, and the response of inflation so slow, that the real-interest-rate effect dominates the expected-inflation effect even at fairly long horizons. Second, the Federal Reserve may be changing policy on the basis of information that it has, and that market participants do not have, concerning future inflation. If this is correct, when market participants observe a shift to tighter pohcy, they revise up their estimates of future inflation, and so long-term rates rise. Third, the behavior of the money supply may be sufficiently complicated that lower current money growth is on average associated with higher rather than lower money growth in the future (Barro, 1989).And finally, rational expectations of future short-term rates may not be the main determinant of the response of long-term rates to changes in monetary policy. For example, term premia may change systematically, or market participants may form their expectations partly on the basis of rules of thumb. Some support for this possibility is provided by the fact that the rational-expectations theory of the term structure does not seem to fit the data particularly well (see, for example, Mankiw and Miron, 1986). Whether it fails as a description of how longer-term rates react to changes in monetary policy is an open question, however.

9.4 The Dynamic Inconsistency of Low-Inflation Monetary Policy

Our analysis thus far suggests that money growth is the key determinant of inflation. Thus to understand what causes high inflation, we need to understand what causes high money growth. For the major industrialized countries, where government revenue from money creation does not appear important, the leading candidate is the existence of a perceived output-inflation tradeoff. If policymakers believe that aggregate demand movements affect real output, they may increase the money supply to try to push output above its normal level. Or, if they are faced with inflation that they believe is too high, they may be reluctant to undergo a recession to reduce it.

Any theory of how an output-inflation tradeoff can lead to inflation must confront the fact that there is no tradeoff in the long run. Since average inflation has no effect on average output, it might seem that the existence