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Monetary policy shocks and long-term interest rates.

When monetary policymakers act, what happens to bond yields? There are good theoretical reasons why shorter-term bond yields should be affected by monetary policy. Open market operations of the Federal Reserve System have an immediate effect on the federal funds rate, which is the interest rate charged for overnight interbank loans. Since short-term borrowing (such as a one-month loan) acts as a reasonably close substitute for overnight borrowing, an increase in the federal funds rate should be accompanied by an increase in other short-term interest rates. However, it is less clear why monetary policy should have a significant effect on five-, ten-, and 15-year bond yields. It seems doubtful that five-year loans are close substitutes for overnight borrowing. Yet, casual observation suggests that monetary policy actions are associated with changes in long-term bond yields.

Consider the bond market debacle of 1994. Publications ranging from Barron's to the Los Angeles Times argue that 1994 was the worst year for the bond market since the 1920s. In figure 1, we display the one-year holding period returns for zero-coupon bonds of four years, six years, and ten years in maturity.(1) (The vertical lines toward the right-hand side of each panel indicate January 1994.) If we exclude the volatile period from 1979-82 (when the Federal Reserve experimented with direct targeting of monetary aggregates), the one-year cumulative losses in late 1994 were among the worst of the postwar period. This collapse of bond prices took its toll on well-known bond investors: Michael Steinhart's hedge fund sustained losses of 30.5 percent in 1994, George Soros's fell 4.6 percent, and Julian Robertson's fell 8.7 percent - all coming off very strong performances in 1993.

At the same time, 1994 was a period of concerted monetary tightening. After a period during which the federal funds rate was exceptionally low and stable, the Federal Open Market Committee (FOMC) raised the funds rate rapidly. As shown in figure 2, the 18 months from mid-1992 through the end of 1993 were characterized by a federal funds rate near 3 percent, with very little variability. This period more closely resembles the mid-1960s than the more volatile 1970s and 1980s. From February 1994 through February 1995, the FOMC doubled its target for the funds rate from 3 percent to 6 percent in seven increments. Figure 2 shows that this sort of monetary tightening is hardly unusual (even excluding the 1979-82 period, when the federal funds rate was not the monetary policy instrument). Nonetheless, the congruence of these two events (the rapid tightening of monetary policy and the precipitous rise in long-term bond yields) led some to assert that the collapse in the bond market was policy induced. For example, the Wall Street Journal of December 13, 1995 graphically describes February 1994 as the month "when the Fed began raising short-term interest rates and set off the year's bond-market slaughter."

In this article, we will look at the relationship between monetary policy and long rates during the postwar period, and then apply what we learn to the extraordinary events of 1994. To examine how a monetary policy action (such as an increase in the federal funds rate) affects the yields of bonds with differing maturities, we must confront the problem of causality. For example, suppose we find that a tightening of monetary policy is associated with higher long-term bond yields. Can we then infer that tighter monetary policy causes higher yields? Not necessarily. It is generally believed that the FOMC tends to tighten monetary policy when there are indicators of future inflation. It is also believed that expectations of higher inflation tend to increase current bond yields. The positive correlation between tighter money and higher yields could be evidence that the Fed causes yields to increase when it tightens money, or it could be evidence that both the Fed action and the higher yields are jointly caused by forecasts of higher inflation.(2)

To help us disentangle the various possible directions of causality, we use a framework developed by Lawrence Christiano, Martin Eichenbaum, and Charles Evans in a series of working papers published by the Federal Reserve Bank of Chicago.(3) In the Christiano-Eichenbaum-Evans (CEE) framework, a clear distinction is made between the monetary authority's feedback rule and an exogenous monetary policy shock. The feedback rule relates policymakers' actions to the state of the economy.(4) In the example of the preceding paragraph, the "normal" reaction of the Fed to an increase in inflation expectations would be incorporated into the feedback rule. The exogenous monetary policy shock is defined as the deviation of actual policy from the feedback rule. We refer to these policy shocks as "exogenous" because, by construction, they do not respond in any systematic way to the economic variables that are included in the feedback rule. (If certain realizations of these variables systematically implied a higher-than-average or lower-than-average policy shock, then the rule is incompletely specified: Any systematic linkage between the policy-shock component and the feedback-rule component should have been loaded into the feedback rule in the first place.)

We measure monetary policy by the level of the federal funds rate. We use the CEE framework to decompose changes in the funds rate into the feedback-rule component and the policy-shock component, and we ask how bond yields respond to an exogenous monetary policy shock. By focusing on the policy-shock component, we resolve the problem of ambiguous causality: Since the policy shock is exogenous by construction, causality can only flow from the policy shock to the bond yields (and to the other variables in the economy). However, this resolution is not without cost: We cannot ask how a change in the structure of the feedback rule itself would affect the behavior of long-term bond yields. The problem is that all observed economic relations are conditional on the particular feedback rule in place. [This is an application of the celebrated Lucas (1976) critique.]

To explore the consequences of a change in the feedback rule, one would have to specify a model of the bond market at the level of investor preferences, monetary policy objectives, technological constraints, and market structure. We do not attempt this potentially useful but extremely difficult modeling task in this article.

Once we determine the response of bond yields to an exogenous monetary policy shock, we can look at the events of 1994 through this lens: (1) To what extent was the monetary tightening in 1994 an application of the FOMC's prevailing feedback rule, and to what extent did it reflect exogenous shocks to monetary policy?; and (2) To what extent did policy shocks affect long-term bond yields during this period? In particular, if there were no policy shocks (that is, if the monetary authority had followed the feedback rule exactly), would the increase in bond yields have been substantially reduced?

Below, we describe the CEE framework and how it is used to investigate the behavior of long-term bond yields. We then detail the average response of bond yields to exogenous monetary policy shocks. Our analysis indicates that these policy shocks have a substantial impact only on short-term bond yields; the impact on maturities longer than three years is quite small, and the impact on maturities longer than 15 years is insignificant. We consider two theoretical explanations for these results: the expectations hypothesis of the term structure and the Fisher hypothesis that movements in long-term bond yields reflect changes in expected inflation. We find that the response of long yields to exogenous monetary policy shocks closely follows the predictions of the expectations hypothesis, while the Fisher hypothesis explains very little. We then apply our methodology to the 1994 period.

A framework for analyzing the effects of monetary policy on bond yields

The model we use for exploring the effects of monetary policy shocks is the version of the CEE framework with monthly data discussed in Christiano, Eichenbaum, and Evans (1994b, section 5). We include four types of variables in our model. The first is the monetary policy instrument. We assume that this policy instrument is the federal funds rate. Christiano, Eichenbaum, and Evans (1994b) also explore the use of nonborrowed reserves as an alternative policy instrument. They obtain stronger results with the federal funds rate, but their results are fairly robust to the choice of instrument. The second type of variable is contemporaneous inputs to the feedback rule. We assume that this feedback rule incorporates contemporaneous values of the log of nonagricultural employment, as measured by the establishment survey (EM), the log of the price level, as measured by the personal consumption expenditure deflator (PCED), and the change in an index of sensitive materials prices (CHGSMP).(5) We use EM as a monthly indicator of real economic activity. We measure the price level by PCED, rather than by the consumer price index (CPI), because the CPI is a fixed-weight deflator. Christiano, Eichenbaum, and Evans (1994b) discuss certain anomalous patterns that emerge when a fixed-weight deflator is used to gauge the price level.(6) These patterns are less of a problem when a variable-weight measure of consumer prices, such as PCED, is used. Finally, the CHGSMP series is a good predictor of future inflationary pressure. Some such predictor must be included if we are to construct a plausible representation of the Fed's feedback rule.

The third type of variable we include is the yield on a zero-coupon bond with T periods to maturity ([Y.sup.T]); we rotate, one at a time, through maturities from one month to 29 years.(7) We use yields on zero-coupon bonds to avoid complications associated with coupon payments. The yields from 1947 to 1991 are monthly data taken from J. Huston McCulloch and Heon-Chul Kwon (1993).(8) For the period 1991 through 1995, we use yields on Treasury STRIPS quoted in the Wall Street Journal for the first business day of each month. Finally, we include additional explanatory variables for long-term yields. In this category of variables, we use the log of nonborrowed reserves (NBR) and the log of total reserves (TR). We use these variables as measures of the demand for credit in the economy. In particular, the amount of nonborrowed reserves that must be injected or withdrawn to achieve a given federal funds target is determined by the price elasticity of demand for reserves. By including total reserves as well as nonborrowed reserves, we measure the component of reserve demand that is accommodated through the discount window.(9)

The resulting model includes seven individual variables: EM, PCED, CHGSMP, FF, NBR, TR, and [Y.sup.T]. We assume that the monetary policymakers' feedback rule is a linear function of (1) contemporaneous values of [EM.sub.t], [PCED.sub.t], and [CHGSMP.sub.t], and (2) lagged values of all variables in the economy. That is, the Federal Reserve sets policy based on current economic activity (as measured by [EM.sub.t]) and price movements (as measured by [PCED.sub.t] and [CHGSMP.sub.t]), as well as the entire history of the economy. The policy decision, in turn, has a contemporaneous effect on reserves and bond yields and affects the future realizations of all variables in the economy. Some argument could be made for including interest rates in the feedback rule, but there is statistical and economic justification for modeling the influence in the other direction. Cook and Hahn (1989) find that even on a daily basis there is little evidence of systematic movements in interest rates prior to an announcement of a change in the federal funds rate, while there are systematic movements after such an announcement.

We estimate this linear feedback rule as part of a vector autoregression (VAR) system. Formally, the system consists of seven equations. Each equation in the system takes one of the seven variables to be its dependent variable. For each equation, the independent variables are lagged values of all seven variables. The feedback rule consists of the fitted equation for FF, plus a linear combination of the residuals from the equations for EM, PCED, and CHGSMP. The exogenous monetary policy shock is that portion of the residual in the FF equation that is not correlated with this estimated feedback rule. The technical appendix to this article describes in detail how we set up and estimate this VAR, and how we use the VAR to infer the exogenous policy-shock component of FF.

In addition to the exogenous monetary policy shock, our model incorporates exogenous shocks to the other six variables. That is, there are a total of seven shock processes that act as the fundamental exogenous driving processes in the economy. These exogenous processes are transformations of the residuals from our seven VAR regressions. In particular, the exogenous shocks are serially uncorrelated, and are constructed to be mutually uncorrelated. (The technical appendix describes how we can isolate the effects of these seven exogenous processes.) Unexpected movement in any variable in the economy must be attributable to the effect of one or more of these exogenous processes. Below, we investigate how much of the unexpected movement in FF and [Y.sup.T] can be attributed to the exogenous shocks to each of the seven variables in the model.

The response of bond yields to exogenous monetary policy shocks

Figure 3 plots the estimated responses of bond yields to a one-standard-deviation exogenous monetary policy shock. This corresponds to an increase in the federal funds rate of approximately 50 basis points.(10) We display the responses for bond maturities of one month, six months, one year, three years, ten years, and 15 years. The colored lines delineate 95 percent confidence interval bands.(11) The plots trace the responses over 24 months.

A 50-basis-point federal funds shock increases the one-month rate by approximately 30 basis points in the period when the shock occurs. This response is highly significant statistically. The one-month rate continues to climb in the following period, and then falls, with the effect of the shock completely attenuated after 21 months. The six-month and one-year rates display qualitatively similar response patterns, although the magnitude of the response decreases for the longer-term bonds. When we move to longer-term bonds, the initial effect diminishes substantially as maturity increases: The initial response of the three-year bond is only 12 basis points, and the responses of the ten- and 15-year bonds are each less than 5 basis points. According to the point estimates, the response of the longer-term bonds appears more persistent than that of the shorter-term bonds. However, this apparent persistence is not statistically significant: The initial response for the ten- and 15-year bonds is barely significant; the response to a federal funds shock of all bonds longer than 15 years is insignificant at the 5 percent marginal significance level. For all maturities, the response is insignificant by one year. Interestingly, these results are roughly comparable to Cook and Hahn's (1989) estimates of the effects on interest rates of a publicly announced change in the federal funds rate. They find that in response to a 100-basis-point increase, short rates rise about 50 basis points, while long rates rise about 10 basis points.

The results are straightforward: There is a significant and relatively large effect on the short rates, with a decreasing, less significant effect at longer maturities. The effect on the term structure can perhaps be seen more easily by plotting the effect of a contractionary shock on the yield curve. The black line in figure 4 is the average yield curve from 1990 through 1995, for maturities up to five years. The remaining lines show our point estimates for the response of the yield curve to a one-standard-deviation exogenous monetary policy shock after one month, six months, one year, and two years. To illustrate the qualitative patterns more clearly over a wider range of maturities, figure 5 displays a similar plot for a five-standard-deviation monetary shock, with maturities up to 29 years. These plots clearly show that the impact on the term structure is a rise in shorter rates, with the effect diminishing as maturities increase. In other words, a monetary policy shock raises the level, flattens the slope, and decreases the curvature of the yield curve.

Why do monetary policy shocks affect yields? What generates the observed response in yields of different maturities to a monetary policy shock? We consider two well-known hypotheses: the expectations hypothesis, which states that the long yield is an average of expected future short yields, and a version of the Fisher hypothesis, which states that changes in long yields are largely determined by changes in expected inflation.

The expectations hypothesis

The expectations hypothesis can be written

[Mathematical Expression Omitted].

Equation 1 says that the long yield, [Mathematical Expression Omitted], on a T-period zero-coupon bond is the average of expected future yields on one-period bonds over the next T periods, plus a time-invariant term premium, [TP.sup.T]. The expectations hypothesis is attractive, because it implies that changes in forward interest rates should provide unbiased forecasts of changes in future spot rates. Unfortunately, tests of equation 1 using postwar U.S. data tend to decisively reject the hypothesis. For example, the equation implies that changes in the term spread [Mathematical Expression Omitted] should predict future yield changes [Mathematical Expression Omitted]. That is, in the following regression

[Mathematical Expression Omitted]

the slope coefficient b should equal unity. Campbell and Shiller (1991) show that, for numerous data samples and numerous maturities T, this slope coefficient is significantly negative. McCallum (1994) suggests that the Campbell-Shiller regressions may be problematic econometrically in the presence of activist monetary policy. If the term premium [TP.sup.T] displays only a small degree of time variation (so the expectations hypothesis holds approximately), but the monetary authority observes and responds to this time variation in [TP.sup.T], then [e.sub.t + 1] may be correlated with [Mathematical Expression Omitted]. This could bias the slope coefficient b downward. McCallum gives examples where the resulting bias is sufficient to explain the Campbell-Shiller results.

In our impulse response functions, the expectations hypothesis would predict that the one-step-ahead response of [Mathematical Expression Omitted] should equal the average of the first T-period-ahead responses of the short rate [Mathematical Expression Omitted]. The Campbell-Shiller results suggest that the expectations hypothesis may perform poorly as an explanation of our impulse responses. On the other hand, our framework may not be vulnerable to McCallum's critique, since we model monetary policy explicitly. If the variables entering the feedback rule include those variables that shift the term premium, then our regressions will not display the McCallum bias.

In figure 6, we display the difference between the first-step response of [Mathematical Expression Omitted] and the average of the first T-step responses of [Mathematical Expression Omitted], for T ranging from two months through 15 years. (The methodology used to construct the confidence intervals is described in the technical appendix.) According to this figure, the expectations hypothesis does a good job of explaining the impulse-response patterns. For all maturities, the difference between the first-period response of the long bond and the response predicted by the expectations hypothesis is less than 6 basis points, and is insignificant at the 5 percent marginal significance level.

The Fisher hypothesis

There is a school of thought that a good deal of the variation in very long-term bond yields is due to changes in expected inflation. An extreme version of this idea is the Fisher hypothesis, which asserts that the nominal bond yield [Mathematical Expression Omitted] should move, one for one, with changes in inflation expected over the life of the bond (that is, over the next T periods.)(12) Under this hypothesis, the only reason a monetary shock should affect long yields is because of its effect on the expected future price level: The first-period response of [Mathematical Expression Omitted] should equal the T-period-ahead response of the price level [PCED.sub.t].

There is substantial evidence against a literal one-to-one relationship between changes in expected inflation and changes in shorter-term interest rates.(13) However, it is not implausible that fluctuations in expected inflation are reflected, at least in part, in longer-term bond yields. To investigate this idea within our framework, we ask how much of the response of long yields to a monetary shock can be explained by the corresponding response in expected inflation. That portion of the response that cannot be tied to expected inflation would be attributable to liquidity effects, of the type described in Christiano and Eichenbaum (1992).

We assume that the impulse response of the price level is a good proxy, under rational expectations, for expected inflation following a shock in monetary policy. In figure 7, we display the response of our measure of the price level, PCED, to a one-standard-deviation contractionary shock to monetary policy. In figure 8, we display the difference between the first-step response of [Mathematical Expression Omitted] and the T-step-ahead response of [PCED.sub.t], divided by T in years, for maturities T ranging from two months through fifteen years. Unlike the expectations hypothesis, the Fisher hypothesis offers little explanation for our impulse responses. For all maturities, the difference between the first-period response of the bond yields and the response predicted by the Fisher hypothesis is significantly different from zero. Furthermore, the point estimates of these differences are fairly large, between 10 and 20 basis points. To see the source of this failure, compare figure 7 with figure 3. Figure 7 displays the response of the price level PCED to a one-standard-deviation monetary policy shock, along with the 95 percent confidence intervals. Initially, a monetary contraction is followed by a small (barely significant) rise in the price level.(14) The price level eventually falls in response to a monetary policy shock. Under the Fisher hypothesis, this would imply a negative response of the longer-maturity yields to a monetary contraction. However, the estimated response of all yields to the monetary policy shock is positive. We find essentially no evidence that the response of long yields to an exogenous monetary shock is due to that shock's effect on expectations of future inflation.

In summary, we find that a contractionary exogenous shock to monetary policy has a strong upward impact on the one-month rate. One-month loans are a partial substitute for overnight borrowing, so it would be surprising if the one-month rate did not respond strongly to an increase in the federal funds rate. The impact of a shock to monetary policy on longer-bond yields declines with maturity, with this decline well explained by the expectations hypothesis. That is, the declining impact of a monetary policy shock on longer-maturity yields tracks the rate at which the response of the one-month yield attenuates. We find no evidence of an excessive response of long yields to monetary innovations. At the same time, changes in expected inflation do not appear to account for the observed responses.

Monetary policy and bond yields in 1994

We use the results from the model to examine the behavior of monetary policy and the bond markets in 1994. Taking the VAR estimates as given, we decompose the movement of the federal funds rate and bond yields into the following: (1) the expected path, given information known in December 1993; (2) the unexpected movement attributable to the exogenous monetary policy shocks; and (3) the unexpected movement attributable to exogenous shocks to the other variables in the economy.

We first look at the determinants of the federal funds rate. Panel A of figure 9 shows the decomposition of the federal funds rate when the VAR includes the one-month yield. Panel B shows the analogous decomposition when the VAR includes the six-month yield.(15) For both models, the expected path for the federal funds rate is flat. In contrast, the actual federal funds rate rises approximately 300 basis points from January 1994 through April 1995.

What accounts for this dramatic, unexpected tightening of monetary policy? By construction, the only sources of unexpected movements in the monetary policy are the exogenous policy shocks, and the effect of other economic shocks acting through the feedback rule. Figure 9 shows the relative importance of these two components. According to panel A of figure 9, the policy shocks account for virtually none of the unexpected run-up in the federal funds rate. Panel B of figure 9 indicates the exogenous policy shocks actually pull the federal funds rate below the expected path. It follows, therefore, that the increase in the federal funds rate must be due to the workings of the feedback rule. In particular, figure 9 indicates that most of the movement in the federal funds rate above the baseline forecast represents a response of the feedback rule to unexpected increases in sensitive materials prices. In both panels of figure 9, the line giving the path of the federal funds rate that would have obtained if all shocks other than shocks to CHGSMP were set equal to zero is very close to the path actually observed.

Recall that lagged values of the bond yield enter the feedback rule for monetary policy. Figure 9 documents the effect of shocks to the bond yield on the path of the federal funds rate. With the one-month bond (panel A of the figure), the exogenous shocks to the one-month yield have a rather small effect on the funds rate. When the six-month yield is used (panel B), the exogenous shocks in the bond yield do tend to push the funds rate above the expected path, but this effect is largely offset by the estimated exogenous monetary policy shocks.(16) The contributions from the inputs to the monetary policy rule other than the bond yield and CHGSMP are relatively small, so they are not plotted in figure 9.

Our analysis indicates that the rise in the federal funds rate during 1994 and the first few months of 1995 was largely a mechanical response of the feedback rule to an increased threat of inflation. In our model, the monetary authority incorporates the series CHGSMP as a warning indicator of potential inflationary pressures. In 1994, this series took a pronounced and unexpected upswing. In figure 10, we display the actual CHGSMP series, along with the expected path of the series conditional on December 1993 information. Note that the growth rate in sensitive materials prices increases from 0.5 percent to 2.5 percent over the year, while the expected path does not even rise above 1 percent. Note that the line displaying the path the series would have taken if all shocks except the own-shocks to the CHGSMP series were set to zero closely tracks the actual series, implying that virtually all of this increase is attributable to the exogenous shocks to the CHGSMP series itself.

Were the increases in bond yields in 1994 and 1995 predictable? If not, why not? Figure 11 shows the historical decompositions for the one- and six-month yields, as well as the one-, three-, ten-, and 15-year yields. In all cases, the expected paths for the yields conditional on December 1993 information are flat. In contrast, all of these yields increased substantially during 1994. The increases range from approximately 300 basis points for the one-month yield to approximately 180 basis points for the 15-year yield. However, virtually none of this increase can be attributed to exogenous monetary policy shocks. In figure 11, we plot the path of each yield that would have obtained if the feedback rule were followed strictly. (That is, if the exogenous monetary shocks were all set equal to zero.) For each bond, the path is virtually unchanged.

We can use our VAR model to explain the deviation of the bond yields from their expected paths. While some of these unexpected yield changes are a result of exogenous shocks to changes in sensitive materials prices (and, to a lesser degree, the remaining series in the model), for the most part, the unexpected movement in long bond yields is caused by exogenous shocks to the bond yields themselves. This is shown in figure 12. In each panel, the line tracing the path the bond yield would have taken if all shocks other than the own-shock to the yield itself were set to zero closely follows the movement in the bond yield. We interpret the exogenous shocks to the bond yields as shocks to financial markets that are unrelated to real economic activity (as measured by the employment variable [EM.sub.t]), price changes, or monetary policy. The only other exogenous shock series that had a major impact on long-bond yields during this period is the shock to the change in sensitive materials prices. Our interpretation of the results in figure 12 is that the collapse in bond prices during 1994 was due, in part, to early warning signs of future inflation. However, this extraordinary movement in bond prices was largely due to factors that are unrelated to the economic or policy variables included in our model.

Conclusions

We find that there is a substantial response of one-month bond yields to an exogenous monetary policy shock, which dies out monotonically in about 20 months. Longer-term bond yields respond more or less as predicted by the expectations hypothesis: the initial month's response of a T-month bond's yield is approximately equal to the average of the first T months' response of the one-month bond. This pattern implies that longer-term bond yields have much weaker responses to an exogenous monetary shock. While these results are intuitive, they stand in sharp contrast to claims that long-bond yields react excessively to monetary policy innovations. We find no evidence that monetary policy shocks have any detectable effect on long-term bond yields.

When we apply these results to the dramatic events of 1994, we find no deviations from the general pattern. The substantial increase in long-term bond yields in 1994 cannot be attributed to exogenous monetary policy shocks. Indeed, the only evidence that might be interpreted as relating monetary policy to movements in long yields is the impact of sensitive materials prices on both the federal funds rate and long yields. This could be evidence that increases in sensitive materials prices affected monetary policy through the feedback rule, and that this component of monetary policy might have had some impact on long yields. However, it is also possible that the change in sensitive materials prices affected long bond yields directly, rather than indirectly through the policy rule. For the reasons described in the introduction, there is no way we can disentangle these two pathways without a structural model.

TECHNICAL APPENDIX

To isolate exogenous monetary policy shocks, we use the vector autoregression (VAR) procedure developed by Christiano, Eichenbaum, and Evans (1994a, 1994b). Let [Z.sub.t] denote the 7 x 1 vector of all variables in the model at date t. This vector includes the federal funds rate, which we assume is the monetary policy instrument, all inputs into the feedback rule, the long-bond yield being studied, and measures of nonborrowed reserves and total reserves. The order of the variables is:

A1) [Z.sub.t] = ([EM.sub.t], [PCED.sub.t], [CHGSMP.sub.t], [FF.sub.t], [NBR.sub.t], [TR.sub.t], [[Y.sub.t].sup.T])[prime].

We assume that (Z.sup.t) follows a sixth-order VAR:

A2) [Z.sub.t] = [A.sub.0] + [A.sub.1][Z.sub.t-1] + [A.sub.2][Z.sub.t-2] + ... + [A.sub.6][Z.sub.t-6] + [[Mu].sub.t],

where [A.sub.i] = 0,1, ... , 6 are 7 x 7 coefficient matrices, and the 7 x 1 disturbance vector [u.sub.t] is serially uncorrelated. We assume that the fundamental exogenous process that drives the economy is a 7 x 1 vector process {[[Epsilon].sub.t]} of serially uncorrelated shocks, with a covariance matrix equal to the identity matrix. The VAR disturbance vector [u.sub.t] is a linear function of a vector [[Epsilon].sub.t] of underlying economic shocks, as follows:

A3) [u.sub.t] = C [[Epsilon].sub.t],

where the 7 x 7 matrix C is the unique lower-triangular decomposition of the covariance matrix of [u.sub.t]:

A4) CC[prime] = E[[u.sub.t][u.sub.t][prime]].

This structure implies that the jth element of [u.sub.t] is correlated with the first j elements of [[Epsilon].sub.t], but is orthogonal to the remaining elements of [[Epsilon].sub.t].

In setting policy, the Federal Reserve both reacts to the economy and affects the economy; we use the VAR structure to capture these cross-directional relationships. We assume that the feedback rule can be written as a linear function [Psi] defined over a vector [[Omega].sub.t] of variables observed at or before date t. That is, if we let [FF.sub.t] denote the federal funds rate, then monetary policy is completely described by:

A5) [FF.sub.t] = [Psi]([[Omega].sub.t]) + [c.sub.4,4][[Epsilon].sub.4t],

where [[Epsilon].sub.4t] is the fourth element of the fundamental shock vector [[Epsilon].sub.t], and [c.sub.4,4] is the (4,4)th element of the matrix C. (Recall that [FF.sub.t] is the fourth element of [Z.sub.t].) In equation A5, [Psi]([[Omega].sub.t]) is the feedback-rule component of monetary policy, and [c.sub.4,4][[Epsilon].sub.4t] is the exogenous monetary policy shock. Since [[Epsilon].sub.4t] has unit variance, [c.sub.4,4] is the standard deviation of this policy shock. Following Christiano, Eichenbaum, and Evans (1994), we model [[Omega].sub.t] as containing lagged values (dated t - 1 and earlier) of all variables in the model, as well as time t values of those variables the monetary authority looks at contemporaneously in setting policy. In accordance with the assumptions of the feedback rule, an exogenous shock [[Epsilon].sub.4t] to monetary policy cannot contemporaneously affect time t values of the elements of [[Omega].sub.t]. However, lagged values of [[Epsilon].sub.4t] can affect the variables in [[Omega].sub.t].

We incorporate equation A5 into the VAR structure A2 through A3. Variables EM, PCED, and CHGSMP are the contemporaneous inputs to the monetary feedback rule. These are the only components of [[Omega].sub.t] that are not determined prior to date t. The variables in the model that are not contemporaneous inputs to monetary policy but which do affect the long-yield under study are NBR and TR. Finally, the last element of [Z.sub.t] is the long yield. With this structure, we can identify the right-hand side of equation A5 with the fourth equation in the VAR equation A2:[Psi]([[Omega].sub.t]) equals the fourth row of [A.sub.0] + [A.sub.1][Z.sub.t-1] + [A.sub.2][Z.sub.t-2] + ... + [A.sub.6][Z.sub.t-6], plus [summation of [c.sub.4i] [[Epsilon].sub.it]] where i=1 to 3 (where [c.sub.4i] denotes the (4, i)th element of matrix C, and [[Epsilon].sub.it] denotes the ith element of [[Epsilon].sub.t]). Note that [FF.sub.t] is correlated with the first four elements of [[Epsilon].sub.t] but is uncorrelated with the remaining elements of [[Epsilon].sub.t]. By construction, the shock [c.sub.4,4][[Epsilon].sub.4t] to monetary policy is uncorrelated with [[Omega].sub.t].

We estimate matrices [A.sub.i], i = 0,1, ... , 6 and C by ordinary least squares. The response of any variable in [Z.sub.t] to an impulse in any element of the fundamental shock vector [[Epsilon].sub.t] can then be computed by using equations A2 and A3.

The standard-error bands in figures 3, 7, and 8 are computed by taking 1,000 random draws from the asymptotic distribution of [A.sub.0], [A.sub.1], ... , [A.sub.6], C, and, for each draw, computing the statistic whose standard error is desired. The reported standard-error bands give the point estimate plus or minus 1.96 times the statistic's standard error across the 1,000 random draws.

To generate Monte Carlo standard-error bands in figure 6, our test of the expectations hypothesis, we must estimate an eight-variable VAR rather than the seven-variable VAR described in the text. The first six variables are unchanged; the last two variables are the one-month yield and the T-month yield, for T ranging from two months through 29 years. That is, the VARs now include EM, PCED, CHGSMP, FF, NBR, TR, [Y.sup.1], and [Y.sup.T], T [greater than] 1. Thus, 48 VARs were estimated, each with a different maturity's yield as the eighth variable. We use this modified VAR to calculate within a single model the difference between the first step response of [Mathematical Expression Omitted] and the average of the first T-period ahead responses of the one-month rate. The standard errors are then computed using 1,000 Monte Carlo draws, as described in the preceding paragraph. Note that the point estimate of the difference can also be estimated using the results from the seven variable VARs, which offers a good check of the eight-variable VAR method. The results are robust.

NOTES

1 We use zero-coupon bonds to avoid the ambiguous impact of coupons on bond-price fluctuations. In particular, the effect of interest rates on bond prices (and therefore on holding period returns) depends both on the bond's maturity and on its coupon rate. Two ten-year bonds with different coupon rates will respond differently to a given interest rate shock. The behavior of one-year holding period returns for coupon bonds with durations of four, six, and ten years would be approximated by the plots in figure 1.

2 A third direction of causality would be that an exogenous increase in yields induces a tight-money response by the Fed.

3 See Christiano, Eichenbaum, and Evans (1994a, 1994b), and Eichenbaum and Evans (1992).

4 Our use of the term "feedback rule" follows Christiano, Eichenbaum, and Evans (1994b). It should be clear, however, that the feedback rule is not a "law" and that there are no penalties for deviating from it. Rather, the feedback rule should be thought of as a set of quantitative relations that summarize the policymakers' normal response to economic developments.

5 The variable CHGSMP is constructed by the Bureau of Economic Analysis. It measures the change in a composite index based on two sensitive materials price series, the producer price index of 28 sensitive crude and intermediate materials and the spot market price index of industrial raw materials.

6 In particular, the price level displays a sustained rise following a monetary contraction.

7 In this study, [Y.sup.T] always denotes the continuously compounded yield to maturity. If [Y.sup.T] is the simple yield, then the continuously compounded yield is defined as log (1 + [y.sup.T]).

8 McCulloch and Kwon (1993) provide yields on zero-coupon bonds for maturities through 40 years, but because of significant missing data, only rates through 29 years are used in our analysis. There are rates for monthly maturities from one to 18 months, then quarterly to two years, then semiannually to three years, and then annually to 29 years. All rates are annual percentage returns on a continuously compounded basis and are derived from a tax-adjusted cubic spline discount function, as described in McCulloch (1975). A more detailed explanation can be found in McCulloch and Kwon (1993).

9 Other than the bond yields, all data are from the Federal Reserve's macroeconomic database. The series are monthly from 1959-95 and are seasonally adjusted where appropriate.

10 The precise magnitude of a one-standard-deviation shock depends on the particular model, as follows: one-month rate, 50-basis-point shock; six-month rate, 49-basis-point shock; one-year rate, 48-basis-point shock; three-year rate, 49-basis-point shock; ten-year rate, 53-basis-point shock; and 15-year rate, 53-basis-point shock.

11 Standard-error bands were calculated using the Monte Carlo procedure outlined in Christiano, Eichenbaum, and Evans (1994), with 1,000 Monte Carlo draws. The technical appendix describes this procedure in greater detail.

12 To our knowledge, Irving Fisher never made the assertion implied by the hypothesis bearing his name. Fisher did note that if two risk-free interest rates are denominated in terms of different numeraires, they could differ only by the difference between the rates-of-change in the value of the numeraire goods. To derive the "Fisher hypothesis," one must combine Fisher's insight with the strong hypothesis that the real risk-free rate is constant, or at least uncorrelated with the inflation rate.

13 See Marshall (1992) and the references therein.

14 This initial rise in the price level is somewhat counterintuitive. One explanation is that the Fed uses information to forecast inflation that we have not included in our model. Since monetary policy affects the price level with some delay, the initial effect of a monetary tightening is to provide information that the Fed is forecasting future inflation. If these forecasts are accurate, on average, the initial response of the price level will be to rise. See Eichenbaum (1992) and Sims (1992) for further discussion of this issue.

15 A decomposition of the monetary policy instrument when the one-month yield is included differs from the decomposition that includes the six-month yield because these are two distinct models of the monetary policy rule. We find that the decompositions with yields longer than six months have the same qualitative behavior as the decomposition using the six-month yield.

16 A similar pattern obtains for all maturities longer than six months. For these longer maturities, the shocks to the yield tend to pull the federal funds rate below the expected path after March 1995. However, the exogenous monetary policy shocks also offset this effect.

REFERENCES

Campbell, J.Y., and R.J. Shiller, "Yield spreads and interest rate movements: A bird's eye view," Review of Economic Studies, Vol. 58, No. 3, May 1991, pp. 495-514.

Christiano, L.J., and M. Eichenbaum, "Liquidity effects and the monetary transmission mechanism," American Economic Review, Vol. 82, No. 2, May 1992, pp. 346-53.

Christiano, L.J., M. Eichenbaum, and C. Evans, "The effects of monetary policy shocks: Evidence from the flow of funds," Federal Reserve Bank of Chicago, working paper, No. 94-2, 1994a.

-----, "Identification and the effects of monetary policy shocks," Federal Reserve Bank of Chicago, working paper, No. 94-7, 1994b.

Cook, T., and T. Hahn, "The effect of changes in the federal funds target on market interest rates in the 1970s," Journal of Monetary Economics, Vol. 24, No. 3, November 1989, pp. 331-351.

Eichenbaum, M., "Interpreting the macroeconomic time-series facts: The effects of monetary policy: Comments," European Economic Review, Vol. 36, No. 5, June 1992, pp. 1001-1011.

Eichenbaum, M., and C. Evans, "Some empirical evidence of the effects of monetary policy shocks on exchange rates," Federal Reserve Bank of Chicago, working paper, No. 92-32, 1992.

Federal Reserve Board of Governors, "INTQ database," various releases, online, Washington, DC: Federal Reserve Board of Governors, August 1995.

Lucas, R.E., "Econometric policy evaluation: A critique," in The Phillips Curve and Labor Markets, K. Brunner and A.H. Meltzer (eds.), Amsterdam: North-Holland, 1976, pp. 19-46.

Marshall, D., "Inflation and asset returns in a monetary economy," Journal of Finance, Vol. 47, No. 4, September 1992, pp. 1315-1342.

McCallum, B., "Monetary policy and the term structure of interest rates," National Bureau of Economic Research, working paper, No. 4938, 1994.

McCulloch, J.H., "The tax adjusted yield curve," Journal of Finance, Vol. 30, 1975, pp. 811-830.

McCulloch, J.H., and H. Kwon, "U.S. term structure data, 1947-1991," Ohio State University, working paper, No. 93-6, 1993.

Sims, C.A., "Interpreting the macroeconomic time-series facts: The effects of monetary policy," European Economic Review, Vol. 36, No. 5, June 1992, pp. 975-1000.

Wendy Edelberg is an associate economist and David Marshall is a senior economist at the Federal Reserve Bank of Chicago. The authors thank Charlie Evans for many useful discussions and for providing his VAR estimation code. They also thank John Cochrane and Kent Daniel for helpful comments and Jennifer Wilson for research assistance.
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Publication:Economic Perspectives
Date:Mar 1, 1996
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