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Can monetary policy influence long-term interest rates? It depends.

I. INTRODUCTION

A stated goal of U.S. monetary policy is to maintain full employment in the U.S. economy. (1) To do so, however, means the Federal Reserve must be capable of stabilizing aggregate demand, particularly the historically volatile category of investment spending. As this form of spending is highly sensitive to long-term interest rates, one implication of the full employment goal for U.S. monetary policy is that the Federal Reserve should be able to influence long-term interest rates. An important question, then, is whether U.S. monetary policy actually has any meaningful influence over long-term interest rates. A number of studies in recent years have examined this question, but have come to different conclusions. Some studies show monetary policy has a sizeable and statistically significant effect on long-term interest rates, whereas others show the opposite. The uncertainty created by this lack of consensus makes it difficult for the Federal Reserve to determine its impact on long-term interest rates.

It is our objective in this paper to shed new empirical light on this murky relationship between monetary policy and long-term interest rates. We do so by looking at monetary policy innovations to the monetary base in an estimated vector autoregression (VAR) to see how monetary policy shocks impact the entire term structure of U.S. Treasury interest rates. (2) Other studies that have used VARs to examine this relationship have relied on innovations to the federal funds rate as their measure of monetary policy shocks (Berument and Froyen 2006; Berument and Froyen 2009; Edelberg and Marshall 1996; Evans and Marshall 1998). This approach has become problematic as the federal funds rate has grown to be more predictable in recent times and thus less capable of generating monetary policy surprises in estimated VARs. Our approach does not have this problem. Our study also has richer results than found in previous studies because we identify shocks to the money multiplier and real money demand in addition to the policy shock to the monetary base. This allows us to examine the effect of all three monetary shocks on long-term interest rates. A final improvement that our study brings to this literature is that it uses long-run identifying restrictions. Previous studies rely on short-run contemporaneous restrictions that constrain the short-run dynamics of the VAR. Our long-run restrictions avoid this issue while at the same time imposing long-run monetary neutrality on the monetary shocks. For these reasons our study provides a fresh take on the relationship between monetary policy and long-term interest rates. Using this approach, we find that contrary to what the previous VAR studies show, the Federal Reserve can meaningfully influence the entire term structure of interest rates. We also find, however, that Federal Reserve can do so only if it maintains its inflation-fighting credibility.

The rest of the paper proceeds as follows. First, we review previous findings on this issue and use them to help motivate our study. Second, we outline the empirical methods we use to estimate the relationship between monetary policy shocks and long-term interest rates. Third, we discuss our data and construction of endogenous variables. Fourth, we report our findings and examine how the results change over sub-periods. Fifth, the robustness of our findings are checked by examining how important the Faust and Leeper (1997) critique is to our identification strategy. Finally, we conclude by discussing the implications for monetary policy.

II. PREVIOUS FINDINGS MOTIVATING THIS STUDY

Over the past decade there has been a spate of studies on the relationship between monetary policy and long-term interest rates. The methods and findings from this empirical research can be grouped into two categories. On one hand there have been a number of studies using single-equation models with daily data that find unanticipated changes in the federal funds rate can have a statistically significant and sizeable effect on long-term interest rates (Beechey 2007; Berument and Froyen 2009; Cochrane and Piazzesi 2002; Ellingsten and Soderstrom 2003; Ellingsen, Soderstrom, and Masseng 2004; Gurkaynak, Sack, and Swanson 2005; Kuttner 2001; Poole et al. 2002). On the other hand, a number of studies using VARs with weekly or monthly data find that structural shocks to the federal funds rates do not have a large effect on long-term interest rates and sometimes this effect is statistically insignificant. Moreover, what little effect federal funds rate innovations do have on long-term interest rates begins to disappear after 1979 (Berument and Froyen 2006; Berument and Froyen 2009; Edelberg and Marshall 1996; Evans and Marshall 1998; McMillin 2001). These two groups of studies, therefore, come to different conclusions on monetary policy's influence on long-term interest rates.

These contrary findings in the literature were recently examined by Berument and Froyen (2009). They conclude that unanticipated changes in monetary policy can meaningfully influence long-term interest rates but note that this relationship is hard to find with VARs because innovations to the federal funds rates in these models may not fully isolate "surprises" in monetary policy. They contend that this problem became particularly pronounced after 1979 as policy actions by the Federal Reserve became more predictable as a result of its increased transparency and gradualism in changing the target federal funds rate. The findings of Lange et al. (2003) and Poole (2005) support this interpretation.

One implication of this understanding is that as changes in the target federal funds rate became more predictable, changes in the monetary base may have become less predictable. Because the Federal Reserve can only independently target a price (i.e., the federal funds rate) or a quantity (i.e., the monetary base) but not both, it is possible that the Federal Reserve's increased transparency and gradualism in changing the target federal funds rate came at the expense of greater variation in the monetary base. If so, it presents a previously unexploited source of variation in a monetary policy instrument that could be used to better estimate the underlying monetary policy shocks. Although it should not matter in a properly specified model whether one uses the federal funds rate or the monetary base to estimate monetary policy shocks, the VAR studies cited above indicate that it does matter. It makes sense then to assess the relationship between monetary policy and long-term interest rates from a fresh perspective by examining estimated monetary policy shocks to the monetary base. Doing so could provide a way to salvage the link between monetary policy shocks and long-term interest rates in VARs after 1979.

One issue, however, with using innovations to the monetary base as a measure of monetary policy shocks is that for most of the period in question the Federal Reserve used the federal funds rate as its operating instrument. Thus, for a given target federal funds rate, movement in the monetary base could be reflecting the Federal Reserve's response to changes in the demand for bank reserves rather than a monetary policy shock. What is needed, then, is to capture only those changes in the monetary base that are truly exogenous. In terms of an interest rate target this means identifying those movements in the monetary base that supported unexpected changes to the target federal funds rate. One way to isolate such policy shocks to the monetary base is to first identify and control for those shocks that cause changes in the demand for bank reserves. Such demand shocks include shocks to the demand for currency (which indirectly affect the demand for bank reserves) and shocks to the demand for bank reserves. Also, real money demand (i.e., velocity) shocks could affect the monetary base if such changes in broad money demand are accommodated by the Federal Reserve. After controlling for these demand shocks (and foreign demand for U.S. currency as noted below), the remaining unexplained variation in the monetary base should be the monetary policy shock.

We follow this approach in our study by identifying a money-multiplier shock that captures unexpected changes to demand for currency and the demand for reserves, a real money demand shock, and a monetary policy-induced shock to the monetary base. (3) These three monetary shocks are identified by imposing long-run restrictions such that none of these monetary shocks can have a permanent effect on any real economic variable. (4) In short, we impose long-run monetary neutrality restrictions on the monetary shocks, an approach consistent with standard macroeconomic theory. Later in the paper, we show that the impulse response functions (IRFs) created by these shocks are consistent with what standard macroeconomic theory predicts they should be. These results indicate that this approach properly identifies the three monetary shocks. It is also worth noting that identifying monetary policy shocks this way is robust to the monetary authorities' choice of operating instrument. As mentioned earlier, this approach can identify monetary policy shocks when the operating instrument is an interest rate by controlling for demand shocks. On the other hand, if the monetary authorities target the monetary base itself then this approach would obviously work too given it isolates monetary policy shocks to the monetary base. Either way, this identification approach works because it looks to the unexplained, nondemand driven variation in the instrument over which the Federal Reserve has direct control--the monetary base.

There are, however, two other issues to address when using innovations to the monetary base as a measure of monetary policy shocks. The first one is that the U.S. dollar continues to serve as the main reserve currency for the world. (5) As a consequence, there is a sizeable portion of the monetary base that is held abroad by foreigners. According to the Federal Reserve's flow of funds data, the portion of the monetary base held abroad prior to the economic crisis was about a third of the total amount. (6) Several studies have shown that accounting for these foreign holdings of the monetary base can significantly increase the predictive power of the monetary base for real output and inflation in the United States (Aksoy and Piskorski 2005, 2006; Nelson 2002). Given these findings and our use of innovations to the monetary base as a measure of monetary policy, it is important to control for this influence. We do so in our VAR using the flow of funds data on foreign holdings of the monetary base.

[FIGURE 1 OMITTED]

The second and final issue in estimating the effect of policy-driven monetary base shocks is that there have been regime shifts in monetary policy. One such shift in the systematic part of monetary policy began in October 1979 when newly appointed Federal Reserve Chairman Paul Volker began aggressively pursuing price stability (Lindsey et al. 2005). Several studies find that since this time U.S. monetary policy has systematically responded to inflationary pressures in a manner that has led to increasingly well-anchored inflation expectations (Biovin and Giannoni 2006; Clarida et al. 2000; Leduc et al. 2007; Stock and Watson 2007; Taylor 1999). As shown by Levin and Taylor (2009), the 15 years or so prior to October 1979 on the other hand were times when the Federal Reserve failed to systematically keep inflation in check and, as a result, inflationary expectations took off. This development can be seen in Figure 1 which shows 1-year expected CPI inflation forecast from the biannual Livingston Survey. (7)

The shaded area in the figure shows the 15-year period when the great unmooring of inflation expectations took place. After this time, the figure shows inflationary expectations becoming increasingly well anchored. The Federal Reserve, then, regained inflation-fighting credibility in the post-October 1979 period after losing it during the previous 15 years (Huh and Lansing 1998; Thorbeke and Zhang 2009). (8) One potential implication of this fact is that a change in the stance of monetary policy may have been interpreted differently by the market based on the time period. For example, a sudden easing of monetary policy is more likely to have been interpreted as inflationary in the 1965-1979 period given the Federal Reserve's lack of inflation-fighting credibility at the time. On the other hand, a similar move by the Federal Reserve in the post-October 1979 period is likely to have been interpreted in a more benign manner such as the Fed responding to expected disinflationary pressures. In the former case, inflationary expectations would increase and offset to some extent the liquidity effect on current and expected future short-term interest rates. Under the expectations hypothesis, then, long-term interest rates in this case may barely budge. In the latter case, however, inflationary expectations could actually drop--if the easing of monetary policy is interpreted as a response to disinflationary pressures--and reinforce the liquidity effect on current and expected future short-term interest rates. Here, long-term interest rates would be more responsive to monetary policy easing. This reasoning suggests that the VAR should be estimated separately for the pre-October 1979 period and the post-October 1979 period as well as for the entire sample period. In this paper, therefore, we estimate VARs over all three periods.

III. EMPIRICAL METHODS

As mentioned earlier, we use a VAR with long-run monetary neutrality to estimate the effect of monetary policy shocks upon long-term interest rates. This is implemented by imposing long-run identifying restrictions on money supply shocks, an approach first introduced by Blanchard and Quah (1989) and subsequently applied to many studies examining the effects of monetary policy. (9) In addition to its theoretical motivations of long-run monetary neutrality, this approach has the virtue of leaving the short-run dynamics of the VAR unconstrained. (10) Formally, this approach starts with an autoregressive structural model of the form

(1) [A.sub.0][x.sub.t] = [A.sub.1] [x.sub.t-1] + ... [A.sub.p] [x.sub.t-p] + [u.sub.t],

where [x.sub.t] is the vector of endogenous variables, [A.sub.0], ..., [A.sub.p] are n x n structural parameters matrices, and [u.sub.t] is a n x 1 vector of uncorrelated structural shocks that are assumed to be multivariate normal with mean zero and unit variance. The vector of endogenous variables is defined as [x.sub.t] = ([y.sub.t], [sp.sub.t][l.sub.tt], [st.sub.t], [m.sub.t], [mm.sub.t], [B.sub.t], [c.sub.t])', where [y.sub.t] is real output, [sp.sub.t] is the spread on corporate yields, [lt.sub.t] is a long-term nominal interest rate, [st.sub.t] is the short-term policy interest rate or the federal funds rate, mt is real money balances, [mm.sub.t] is the money multiplier, [B.sub.t] is the monetary base, and [c.sub.t] is a commodity price index. Here [mm.sub.t] = [M.sub.t]/[B.sub.t], where Mt is a monetary aggregate, while mt = [M.sub.t]/[P.sub.t], with [P.sub.t] being the price level. Since Bt x [mm.sub.t] = [M.sub.t] and ([B.sub.t] x [mm.sub.t])/[m.sub.t] = [P.sub.t], the money supply and the price level also are implicitly in the VAR. We use this fact later to extract the money supply and price level responses to structural shocks without having to explicitly estimate them. Corporate yield spreads are included in the VAR to control for default risk on long-term interest rates, while commodity prices are included as they may serve as a harbinger of future inflation. (11)

Our approach closely follows that of Fackler and McMillin (1998) who argue that when using long-run identifying restrictions to get monetary neutrality, one must use shocks to the monetary base--rather than shocks to a monetary aggregate--to properly identify monetary policy shocks. As mentioned earlier, however, in order to identify policy-driven innovations to the monetary base one must control for changes in the monetary base originating from shocks to the money multiplier and real money demand. We do that by identifying all three monetary shocks using long-run restrictions. Consequently, structural shocks to the money multiplier, real money demand, and the monetary base can have no permanent effect on variables preceding them in the vector of endogenous variables. While it is apparent that the long-run monetary neutrality restrictions make sense for the real variables of [y.sub.t] and [sp.sub.t], they are also reasonable to apply to the two nominal interest rates, [lt.sub.t] and [st.sub.t], as these series mimic the behavior of the real interest rate in the long run. This is because a one-time monetary shock only affects the price level permanently but not inflation. Note that unlike other studies where innovations to the federal funds rate are considered the monetary policy shocks, this approach has the federal funds rate responding to monetary policy shocks arising from unexpected changes in the monetary base. This approach, then, has the virtue of measuring monetary policy shocks on the instrument over which the Federal Reserve has direct and complete control.

Given this framework, the structural autoregressive model in Equation (1) can be transformed into a structural moving average form so that the relationship between the endogenous variables and the structural shocks can be defined. The structural moving average model can be shown to be

(2) [y.sub.t] = ([D.sub.0] + [D.sub.1]L + [D.sub.2][L.sup.2] + ...)[u.sub.t] = D(L)[u.sub.t],

where [D.sub.0] = [A.sub.0.sup.-1], [D.sub.i] = [([A.sub.0.sup.-1] [A.sub.i]).sup.i] [A.sub.0.sup.-1], and L denotes the lag operator. The coefficient matrices in D(L) represent the dynamic multipliers of the structural shocks. As it stands, Equation (2) is still a structural model and cannot be estimated directly. Rather, a reduced-form version must be estimated and then identifying restrictions imposed to recover the structural model. The reduced form moving average can be expressed as follows:

(3) [y.sub.t] = (I + [C.sub.1]L + [C.sub.2][L.sup.2] + ...)[[epsilon].sub.t] = C(L)[[epsilon].sub.t].

There is a mapping between the reduced-form parameters in Equation (3) and the structural parameters in Equation (2) since et = Dour, C(L) = D(L)[D.sub.0.sup.-1], and E[[epsilon].sub.t][[epsilon].sub.t]' = [summation] = [D.sub.0][D.sub.0]. However, this mapping is not unique. Consequently, even though the reduced-form parameters C(L) and [SIGMA] are directly estimable, identifying restrictions need to be imposed to recover the structural shocks. As noted earlier, the identification scheme adopted here is to impose long-run monetary neutrality restrictions on shocks to the money multiplier, real money balances, and the monetary base. Given the ordering of variables in [x.sub.t], this requires taking the infinite-horizon sum of D(L), D(1), and imposing the following restrictions:

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Again, these restrictions mean that money supply shocks have a cumulative effect of zero on the real variables ordered above them in the VAR. Note that these restrictions are set up such that the monetary policy shocks to the monetary base have no permanent effect on the money multiplier. (12) Finally, shocks to the monetary base and to the money multiplier can have no permanent effect on real money balances while real money demand shocks can, restrictions consistent with long-run monetary neutrality. Although this approach leaves the model under-identified, it does fully identify real money demand, money multiplier, and monetary policy shocks. It is implemented by taking a Choleski decomposition of the long-run covariance matrix (Keating 1996). (13)

Using these long-run restrictions, the estimated VAR can be used to show the effect of exogenous shocks to real money demand, the money multiplier, and monetary policy on the endogenous variables through innovation accounting. Here, innovation accounting in the form of cumulative IRFs is used to show the typical cumulative dynamic response of an endogenous variable to the various monetary shocks. Then, the IRFs are used to show how the average treasury yield curve changed in response to the monetary policy shocks.

IV. DATA

To see how monetary policy can influence long-term interest rates, we examine the monthly effect of monetary policy shocks across the term structure of U.S. Treasury interest rates for the period December 1964 to December 2007 as well as for the subperiods December 1964 to September 1979, October 1979 to December 2007. Our Treasury term structure includes interest rates for the following maturities: 3-month, 6-month, 1-year, 2-year, 3-year, 4-year, 5-year, 6-year, 7-year, and the 10-year. (14) The VAR is estimated separately for each of the interest rates in the Treasury term structure with each one filling the slot of [lt.sub.t] in the vector of endogenous variables. (15) The data for the Treasury securities with maturities 1-year or greater are the zero coupon yields from the Treasury yield curve database of Gurkaynak, Sack, and Wright (2006). (16) The 3-month and 6-month yields are the secondary market interest rates on 3-month and 6-month Treasury bills and come from the Fred database of the St. Louis Federal Reserve Bank.

The corporate bond yield spread is constructed by subtracting Moody's seasoned AAA corporate bond yield from its seasoned BAA corporate bond yield. Here, industrial production is used for output and money zero maturity (MZM) is used as the monetary aggregate. We adopt MZM because it, unlike other monetary aggregates, has been shown to have a stable money demand relationship (Teles and Zhou 2005). (17) Real money balances are constructed by dividing MZM by the CPI, while the money multiplier is constructed by dividing MZM by the monetary base. The federal funds rate is included as the short-term policy interest rate and the St. Louis Federal Reserve-adjusted monetary base is used as the instrument. (18) All of these variables are in seasonally adjusted form and also come from the Fred database. For commodity prices we use the Commodity Research Bureau's spot commodity price index.

Exogenous variables in each VAR equation includes a constant, dummies for the periods October 1999 to February 2000 and September 2001 to October 2001 to account for the large spikes in the monetary base at those times, and foreign holdings of the U.S. monetary base. Foreign holdings of the monetary base are constructed using the Federal Reserve's Flow of Funds data on U.S. currency held by the rest of the world found in Table L.204. This series is in a quarterly frequency but interpolated to a monthly frequency using the Denton (1971) method. This technique uses a higher frequency indicator series to interpolate a lower frequency series yet preserves the original lower frequency values. In this case, we use the actual U.S. monetary base to interpolate the quarterly foreign holdings of U.S. monetary base to a monthly frequency. To minimize any spurious relationships that may arise from the interpolation, we include the current period and three lags of foreign-held monetary base exogenously in the VAR. This way the foreign-held monetary base in the VAR spans an entire quarter--the original frequency of the series--and presumably captures its actual influence on the total U.S. monetary base. (19)

All variables are transformed into log form and first differenced--except for the interest rates and corporate yield spreads which are just first differenced--as standard unit root tests indicate nonstationarity in the levels of the variables. (20) The VARs are estimated using seven lags as the Ljung-Box Q test indicates that these lags are sufficient to whiten the residuals of any serial correlation.

V. EMPIRICAL RESULTS

Figure 2 reports the cumulative IRFs for all the variables--including the money supply and the price level--to a one standard deviation shock to real money demand, the money multiplier, and monetary policy in the VAR with the 10-year Treasury interest rate for the entire sample period of December 1964 to December 2007. The solid line shows the cumulative IRE point estimate while the dotted lines show simulated two standard error bands. (21) The IRF for the interest rates and corporate yield spread can be interpreted as showing the dynamic change to these variables in terms of basis points. For the other variables, the IRFs can be seen as the percent change to their level.

Figure 2 shows that across all monetary shocks the economic variables respond in a manner consistent with macroeconomic theory. First note that the positive real money demand shock leads to a temporary decline in industrial production and a temporary increase in default risk as indicated by the rise in corporate bond yield spreads. These two responses are consistent with each other and are matched by a significant fall in the price level and nonsignificant fall in commodity prices. The real money demand shock also leads to a brief spike in the federal funds rate. What appears to be happening is that a typical positive real money demand shock leads to a temporary decline in spending that slows down the economy. That, in turn, raises the default risk and creates deflationary pressure. The increased real money demand also increases short-term interest rates but has no significant effect on long-term interest rates. The increase in the money multiplier and the monetary base in response to this shock suggests that the banking system and the Federal Reserve accommodate the real money demand shock. However, given the decline in economic activity and the price level, the accommodation by the Federal Reserve is not adequate to offset the typical real money demand shock. The VAR bears out, then, the standard story told in macroeconomics that a sudden increase in real money demand that is not fully accommodated by the Federal Reserve will result in a slowdown in economic activity, higher interest rates, and a lower price level. It also suggests that we have indeed measured a real money demand shock with our identification restrictions.

[FIGURE 2 OMITTED]

The second thing to note from Figure 2 is that the positive money-multiplier shock--which means an unexpected increase in inside money--also leads to responses consistent with standard macroeconomic theory. First, the sudden money-multiplier driven increase in the money supply leads to a temporary increase in industrial production and, as a result, a decline in the default risk as measured by the corporate bond yield spreads. Second, the unexpected money supply increase leads to a liquidity effect on both long-term and short-term interest rates with only the former being significant. Third, the money supply increase also leads to a significant increase in the price level and a significant increase in commodity prices. Given this money-multiplier driven increase in the money supply and the related stimulus it provides to the economy, the negative monetary base response suggests the Federal Reserve typically attempts to offset these changes by reducing the monetary base. These results also suggest that we have identified a money-multiplier shock.

The third thing to note from Figure 2 is that the positive monetary policy shock to the monetary base also creates responses in the other variables that are consistent with standard macroeconomic theory. First, the monetary policy shock leads to a hump-shaped increase in industrial production and a similar-shaped decrease in the default risk as seen in the corporate yield spreads. Second, there are strong and significant liquidity effects for both the short-term and long-term interest rates in response to this shock. Third, the positive monetary policy shock to the monetary base results not only in a permanent increase in the monetary base but also in the money supply and the price level. Commodity prices increase as well but are never significant. The innovation to the monetary base being identified here, therefore, creates responses that are consistent with what macroeconomic theory predicts will happen in response to an exogenous change in monetary policy. Given that we have identified and thus controlled for real money demand and money-multiplier shocks, it is reasonable to infer that the shocks to the monetary base identified here are indeed monetary policy shocks. The main point of Figure 2, then, is that our estimated VAR along with the identifying restrictions have allowed us to reasonably identify monetary policy shocks.

Now that we have established our model properly identifies monetary policy shocks, we can examine the effect of these shocks on the term structure of interest rates for the full period as well as the two subperiods of December 1964 to September 1979 and October 1979 to December 2007. Figure 3 reports the cumulative IRFs for each of the Treasury interest rates to a one unit or 1% shock to the monetary base in the VAR. A 1% shock is used here to facilitate comparison across the periods. Recall that the IRF of each Treasury interest rate is estimated separately with each one filling the slot of [lt.sub.t] in the vector of endogenous variables. (22)

For the entire sample period, there are strong liquidity effects for the entire term structure of interest rates with the short end having a slightly higher effect. The biggest decline across all maturities occurs at 2 months with the 10-year Treasury declining 0.64 percentage points and the 3-month Treasury declining 0.82 percentage points. Interestingly, although the liquidity effect is slightly stronger in terms of magnitude for the short end of the term structure it actually lasts longer on the long end: the 10-year Treasury decline remains significantly different from zero for 11 months while that of the 3-month Treasury is different than zero for only 4 months.

For the pre-1979 period, when inflationary expectations were not anchored there is still a liquidity effect but it is only significant for the short end of the term structure and there is wider variation around the point estimate. Additionally, on the short end--and to a lesser extent on the long end--the liquidity effect appears to be soon dominated by an expected inflation effect that pushes the interest rate up above zero. For example, at the short end, the liquidity effect pushes the 3-month Treasury to a maximum decline of 1.04 percentage points at 2 months but then this effect gradually gets swamped by an expected inflation effect that pushes the interest 0.90 percentage points above zero by month 12. There is hardly any liquidity effect at all on the 10-year Treasury as it barely budges with an insignificant decline of 0.24 percentage points at 2 months. Its point estimate also gets pushed above zero, indicating that the expected inflation effect may also be at work here. In short, long-term interest rates in the pre-1979 are barely responsive at all to the positive monetary policy shock and arguably this is the result of the expected inflation effect. The only significant decline from the liquidity effect comes at the short end of the term structure.

[FIGURE 3 OMITTED]

By way of contrast, the response of Treasury interest rates during the post-1979 period to the monetary policy shocks is actually slightly greater the longer the maturity. Moreover, the liquidity effect is longer lasting on the long end of the term structure. Here, the 10-month Treasury declines 0.58 percentage points at 2 months and continues to be significantly different than zero through 6 months. The 3-month Treasury, on the other hand, is significantly different than zero for only the first month with a decline of 0.48 percentage points. Overall, then, the magnitudes of declines are not that different among the term structure while the persistence of the liquidity effect is more pronounced at the long end. The post-1979 period, then, shows that monetary policy shocks can not only meaningfully affect the long end of the Treasury term structure of interest rates, but also that the impact can actually be greater on the long end.

The effect of the positive 1% shock to the monetary base on the term structure of interest rates can also be seen by examining movement in the actual treasury yield curve following such a shock. This is done in Figure 4 by plotting the average treasury yield curve over each subperiod and then adding to it all the treasury interest rate IRFs at the 1-month, 3-month, 6-month, and 9-month horizons. Thus, the average treasury yield curve is being changed by the average interest rate responses (i.e., the IRFs) across all horizons. This approach provides a nice way to summarize the information in the IRFs into one figure. It allows one to easily see how much influence the Federal Reserve had over the term structure of interest rates for each subperiod.

The top graph in Figure 4 shows that for the pre-1979 period at the 1-month horizon the positive 1% monetary policy shock drops the short end of the yield curve from 5.76% to 5.01% which by the 3-month horizon falls to 4.91%. On the long end of the Treasury yield curve the monetary policy shock lowers the interest rate from 6.70% to 6.55% at 1-month and 6.45% at 3 months. By 6 months, the liquidity effect begins to disappear as the short end goes to 5.38%, while the long end goes to 5.65%. At 9 months, the expected inflation effect is swamping the short end of the Treasury yield curve and to some extent the long end as well. This top graph, again, suggests that there was a strong expected inflation effect in the pre-1979 period and that only the short-term interest rates meaningfully responded to the positive monetary policy shocks. The bottom graph of Figure 4 shows that for the post-1979 period at the 1-month horizon the monetary policy shock lowers the short end of the yield curve from 5.84% to 5.38% while it reduces the long end from 7.47% to 6.95%. By 6 months, the short end is at 5.71% indicating the liquidity effect is diminishing while at the long end the liquidity effect remains more persistent with a value of 7.18%. Here, the yield curve has largely returned to its average value by 9 months without overshooting as was the case in the top graph. This response suggests a much milder expected inflation effect for the post-1979 period. Monetary policy shocks, therefore, in the post-1979 period had a considerably larger effect on the long end of the yield curve than in the pre-1979 period.

[FIGURE 4 OMITTED]

The findings indicate that monetary policy can strongly affect long-term interest rates, but that this influence can vary over time. These findings specifically show that after controlling for the 1979 regime shift in U.S. monetary policy, monetary policy shocks did not have a large effect on long-term interest rates prior to 1979 but did so afterwards. The most likely reason for this difference is that the Federal Reserve had inflation-fighting credibility in the post-1979 period, but not in the pre-1979 period. To check this hypothesis, we use the VAR to create an expected inflation series for each treasury security's time horizon and examine whether its response to a monetary policy shock changes over the two periods. If our hypothesis is true, we would expect to see a larger response in expected inflation to a monetary policy shock in the pre-1979 period.

To do this, we take the fact that the price level IRF is a dynamic forecast of the price level and use it to construct an expected inflation IRF to a monetary policy shock. Specifically, for a given forecast horizon the price level IRF is calculated, then converted into a series of monthly annualized inflation rates, and then averaged over the forecast horizon. This average creates a monthly point estimate for the expected inflation IRF. This process is repeated for subsequent periods so that there are enough point estimates to produce a 3-year expected inflation IRF. Figure 5 shows this expected inflation rate response over different forecast horizons for both periods given a 1% monetary policy shock.

This figure reveals that for all forecast horizons expected inflation is markedly higher in the pre-1979 period. On the long end, expected inflation for the 10-year forecast reaches as much as 0.16 percentage points for the pre-1979 period compared with 0.07 percentage points for the post-1979 period. Expected inflation for the pre-1979 period remains higher for 14 months. The gap between the expected inflation series widens and lasts longer the shorter the forecast horizons. At the 3-month forecast, expected inflation tops out at 3.07% for the pre-1979 period compared with 0.25% for the latter period. This gap persists for 25 months.

A convenient way to summarize these responses is to construct a term structure of expected inflation similar to term structure of interest rates produced in Figure 4. Here, we plot the expected inflation forecast using the IRF point estimates of 3-month, 6-month, 9-month, and 12-month horizons. This is done in Figure 6 using separate graphs for each period. The scales on the two graphs are the same for sake of comparison.

Here again, the results are striking. The pre-1979 period has a much larger increase in expected inflation across all horizons. This figure makes a strong case that relative to the post-1979 period monetary policy during the pre-1979 had little inflation-fighting creditability. It seems, then, that a positive monetary policy shock in the first period was viewed as highly inflationary while in the latter period it was viewed in a more benign manner.

VI. ROBUSTNESS

The findings in the previous section relied upon long-run identifying restrictions that imposed zero constraints upon certain elements in D(1), the infinite-horizon sum of D(L), in a manner consistent with long-run monetary neutrality. While these restrictions are supported by standard macroeconomic theory and commonly used, their use may create problems when making inferences about the infinite horizon. In particular, Faust and Leeper (1997) show that dynamic models estimated from a finite sample generally do not contain information about infinite horizons. Therefore, conclusions drawn from such an exercise may be fragile. In our study, this potential problem may be especially pronounced for the subperiods which have smaller sample periods. For example, the pre-Volker period has about 15 years. Is that really long enough for monetary neutrality to be seen in the data? Or, are we asking too much of data by imposing infinite-horizon monetary neutrality? The key implication here is that a reliable inference may require finite-horizon restrictions rather infinite-horizon restrictions.

To examine whether our findings are subject to this critique, we follow Lastrapes (1998) who recommends comparing IRFs from the infinite-horizon restrictions to those estimated when monetary neutrality is imposed at long but finite horizons. Lastrapes notes that if the IRFs from the finite-horizon restrictions are similar to those from the infinite horizon, then inferences are robust to the Faust and Leeper (1997) critique. To do this, we impose long-run finite restrictions on the structural moving average representation in Equation (2) such that the sum of k dynamic multiplier matrices,

(5) [y.sub.t] = ([D.sub.0] + [D.sub.1]L + [D.sub.2][L.sup.2] + ... + [D.sub.k][L.sup.k] + [D.sub.k+1][L.sup.k+1] + ...)[u.sub.t],

is zero for the same elements that are zero in D(1). That is, we impose the same long-run monetary neutrality restrictions as before only now on a finite k-number of horizons. Here, we impose the finite long-run restrictions at k = 36, k = 60, and k = 120. Thus, we impose finite long-run neutrality at 3, 5, and 10 years.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Although the subperiods are the ones most likely to be problematic, we reestimate the VAR with the various finite restrictions for all sample periods. The results from this robustness check are reported in Figure 7. This figure shows the infinite-horizon IRFs originally reported in Figure 3 along with the three finite-horizon IRF estimates for each interest rate. In each case, the finite IRFs are very similar to the infinite-horizon IRFs, even for pre-Volker period. These results indicate, then, that our infinite-horizon restrictions are not subject to the Faust and Leeper (1997) critique.

VII. CONCLUSION

Owing to the Federal Reserve's mandate to maintain full employment it is important to study the ability of monetary policy to influence long-term interest rates. To that end, we examine the relationship between monetary policy and the term structure of interest rates over the period December 1964 through December 2007 using a VAR with long-run monetary neutrality restrictions. As in previous studies, we also examine the pre- and post-1979 subperiods to account for regime shifts in monetary policy. Our findings indicate that short-term interest rates are responsive to monetary shocks for the overall sample period and for both the pre- and post-1979 subperiods. Long-term interest rates are similarly responsive to monetary shocks for the overall sample period. But the results are strikingly different in the two subperiods. Long-term interest rates are very responsive to monetary shocks in the post-1979 period, and in contrast, barely responsive at all in the pre-1979 period.

What would explain this dramatically different response for long-term interest rates during the post-1979 period? We believe the answer is directly related to difference in the Federal Reserve's inflation-fighting credibility between the two subperiods. A number of studies have shown that prior to 1979, U.S. monetary policy did not respond systematically to inflationary pressures. As a result, inflationary expectations became unanchored and the Federal Reserve lost credibility as an inflation fighter. After 1979, however, inflationary expectations were reigned in as Paul Volker, the new Federal Reserve chairman, aggressively pursued low and stable inflation. Under his tenure, the Federal Reserve gained inflation-fighting credibility that was maintained under his successor, Alan Greenspan (Clarida et al. 2000; Hugh and Lansing 1998; Lindsey et al. 2005; Stock and Watson 2007; Taylor 1999). This credibility is important when considering whether monetary policy can influence long-term interest rates. It is widely accepted that if the Federal Reserve generates a positive monetary shock to stimulate economic activity, short-term interest rates will respond in the desired direction in the short run due to the liquidity effect. However, the degree to which this liquidity effect gets transmitted into long-term interest rates depends on how such a monetary policy shock influences long-term inflation expectations. If monetary authorities lack inflation-fighting credibility then a positive monetary policy shock is likely to be perceived as inflationary and would further heighten inflationary expectations. In this case, via the expectations hypothesis, any downward pressure on the expected future short-term interest rate from the liquidity effect would be offset by higher long-term inflationary expectations. On the other hand, if monetary authorities had such credibility, then long-term inflationary expectations would be anchored and the liquidity effect would be transmitted more thoroughly in expected future short-term interest rates. (23) The policy implication of this study is clear: only if the Federal Reserve maintains credibility in its mission to keep long-term inflation low and stable will the long end of the yield curve "cooperate" with the short-end response to a monetary policy shock. Monetary policy's ability, then, to influence long-term interest rates depends on its inflation-fighting credibility.

[FIGURE 7 OMITTED]

doi: 10.1111/j.1465-7295.2011.00412.x

ABBREVIATIONS

GDP: Gross Domestic Product

IRF: Impulse Response Function

MZM: Money Zero Maturity

VAR: Vector Autoregression

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DAVID BECKWORTH, KENNETH P. MOON and J. HOLLAND TOLES *

* We would like to acknowledge the editor, two referees, and Josh Hendrickson for helpful comments. All remaining errors are our own.

Beckworth: Assistant Professor, Department of Finance and Economics, Texas State University-San Marcos, San Marcos, TX 78666. Phone 512-245-6067, Fax 512-245-3089, E-mail db52@txstate.edu

Moon: Associate Professor, Department of Finance and Economics, Texas State University-San Marcos, San Marcos, TX 78666. Phone 512-245-6659, Fax 512-245-3089, E-mail kmoon@txstate.edu

Toles: Senior Lecturer, Department of Finance and Economics, Texas State University-San Marcos, San Marcos, TX 78666. Phone 512-245-3242, Fax 512-245-3089, E-mail ht04@txstate.edu

(1.) This goal is outlined in the Humphrey-Hopkins Full Employment Act of 1978.

(2.) Other studies have exploited policy shocks to the monetary base before via innovations to non-borrowed reserves (Christiano et al. 1996, 1999). These studies, however, focus on the relationship between monetary policy shocks and broader economic activity such as the response of real gross domestic product (GDP) and inflation. Our study is different from these studies in that it focuses on the relationship between monetary policy shocks and long-term interest rates.

(3.) The distinction between these shocks can be seen using the equation of the exchange, MV = PK where M is the money supply, V is velocity, and PY is nominal spending. As the money supply is equal to the monetary base, B, times the money multiplier, m, the equation of exchange can be restated as follows: BmV = PY. The Federal Reserve directly controls B and can use it to offset destabilizing changes in m and V. Our goal is to avoid using such endogenous changes in the B when measuring monetary policy shocks. One way we do this is by estimating and, thus, controlling for exogenous shocks to m and V.

(4.) As we note later, there is one exception to this: the real money demand shock can permanently affect real money balances.

(5.) According to the Bank for International Settlement (2007), the U.S. dollar accounted for 86.3% of the turnover in foreign exchange markets in 2007. The Euro, by contrast, accounted for 37.0% in 2007.

(6.) Table L.204 in the flow of funds data contains the data for currency held by the rest of the world. Since the crisis began the share of the U.S. monetary base held abroad has declined given the large increase in the monetary base.

(7.) The Livingston Survey began in 1946 and is now conducted by the Federal Reserve Bank of Philadelphia. Documentation and data for the survey can be found at http://www.phil.frb.org/research-and-data/ realtime-center/livingston-survey/.

(8.) Boschen and Weise (2003) attribute the inflation of the 1960s and 1970s to a number of factors including expansionary economic policies, the political business cycle, and the abandonment of the Bretton Wood system.

(9.) For example, see Gali (1992), Lastrapes (1998, 2006), Fackler and McMillin (1998), and Rapach (2001).

(10.) Another commonly used approach to identify monetary policy shocks is to estimate a macroeconomic VAR with contemporaneous restrictions on the federal funds rate. This identification strategy allows federal funds rate innovations to be interpreted as unexpected deviations from a monetary policy rule or a monetary policy shock. However, as noted by Kim and Lastrapes (2007), this approach is sensitive to changes in the monetary policy rule while the long-run restriction strategy used above is not.

(11.) When the VAR was estimated without commodity prices the "price puzzle" emerged: the price level initially decreased in response to a positive monetary base innovation. Including commodity prices removed the "price puzzle" from our results.

(12.) Stated differently, a one-time change in the monetary base leads to a proportionate change in the monetary aggregate in the long run.

(13.) Keating (1996) shows that the ordering of the other variables is inconsequential to identifying the structural shocks in this manner.

(14.) We do not use the 20-year and 30-year Treasury securities as there are periods in the sample when they were not issued.

(15.) This approach follows that of Edelberg and Marshall (1996) who estimate separate VARs for each long-term interest rate. However, they use innovations to the federal funds rate to measure monetary policy shocks.

(16.) This database is updated regularly and can be found at http://www.federalreserve.gov/econresdata/ researchdata.htm.

(17.) MZM stands for Money Zero Maturity and is comprised of money assets with no maturity. It is equal to M2 minus small time deposits plus institutional money market funds.

(18.) This measure of the monetary base adjusts for changes in statutory reserve requirements.

(19.) Alternatively, we could have constructed a domestic monetary base by subtracting the foreign-held monetary base from the total U.S. monetary base. However, given that our monetary policy shock is measured using innovations to the monetary base, we believe adjusting it with an interpolated series would raise questions as to exactly what the innovation to the monetary base would be measuring. Consequently, we think the more innocuous approach is to simply include the foreign-held monetary base exogenously in the VAR.

(20.) The augmented Dicker-Fuller and the Phillips-Perron unit root test were used. First differencing the data was sufficient to remove the unit root. We follow Lastrapes (2006) and Lastrapes and McMillin (2004) in assuming the unit root data are not cointegrated and as result, the VAR can be estimated in first differences. Lastrapes and McMillin (2004) show that allowing for cointegration in the VAR system has no consequential bearing on identifying the monetary policy shocks using long-run monetary neutrality.

(21.) The standard error bands are calculated using standard Monte Carlo techniques.

(22.) In other words, each of these IRFs come from VARs estimated with the different Treasury interest rates. The IRFs of the other variables in the VAR are similar to those seen in Figure 1. For the sake of brevity, only the interest rates are reported here.

(23.) This transmission mechanism can be complicated by the changes in term premium. Rosenberg and Maurer (2008), however, show that most of the change in long-term interest rates comes from the changes in expected future short-term interest rates and not from the changes in the term premium.
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Author:Beckworth, David; Moon, Kenneth P.; Toles, J. Holland
Publication:Economic Inquiry
Date:Oct 1, 2012
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