Overnight Monetary Policy in the United States: Active or Interest-Rate Smoothing? Amir Kia Department of Economics Carleton University Ottawa, Ontario K1S 5B6 Canada Phone: 613-520-2600 ext. 3753 Fax: 613-747-1352 Email: [email protected]July 2005 ________________________________________________________________________ Abstract This paper investigates the behavior of agents in the United States money and Fed funds markets for the period 1982-2004. It was found that, while agents are forward looking in the money market, their behavior is policy invariant in the Fed funds market. Consequently, the optimal overnight monetary policy would be an interest-rate- smoothing process. It was found, in fact, that such a policy has been followed in the United States. Furthermore, this paper suggests that the lack of a policy invariant relationship between overnight and short-term interest rates is another explanation for conducting an interest-rate-smoothing policy. Keywords: Interest-rate smoothing, discretionary overnight monetary policy, forward- looking agents, money market, and Fed funds market. JEL Codes: E43, E51, E52, E58
Transcript
Overnight Monetary Policy in the United States: Active orInterest-Rate Smoothing?
This paper investigates the behavior of agents in the United States money and Fed fundsmarkets for the period 1982-2004. It was found that, while agents are forward looking inthe money market, their behavior is policy invariant in the Fed funds market.Consequently, the optimal overnight monetary policy would be an interest-rate-smoothing process. It was found, in fact, that such a policy has been followed in theUnited States. Furthermore, this paper suggests that the lack of a policy invariantrelationship between overnight and short-term interest rates is another explanation forconducting an interest-rate-smoothing policy.
Overnight Monetary Policy in the United States: Active orInterest-Rate Smoothing?
I. IntroductionShould a central bank follow an active overnight monetary policy or should it
follow an interest-rate-smoothing process? The answer to this question generally depends
on the behavior of agents in the economy and particularly in the money market. By active
monetary policy we mean a “discretionary” policy, where the central bank is free at any
time to alter its instrument setting instead of complying with a rule. In an “interest-rate-
smoothing” regime the central bank follows a “rule-based” policy. However, the
discretionary conduct of policy also includes interest-rate smoothing, as the central bank
is free to react at any time to the movements of the market.
This paper, using high-frequency data, attempts to analyze the above question. An
active monetary policy reflects open market operations, when central banks influence, by
purchasing or selling securities, the supply of non-borrowed reserves. The initial effect of
these operations is reflected in interbank rates and subsequently in other short-term
interest rates. An active monetary policy may also be conducted through “open mouth
operations”. In this case, the central bank signals, directly or indirectly, the market its
desired level of interest rate. Market participants, knowing that the central bank can and
will achieve its desired level, drive the interbank rate to the level desired by monetary
authorities, see Thornton (2004) and the relevant literature therein. An effective active
monetary policy, either through open market or open mouth operations, leads to a
liquidity effect.
2
Note that Finn E. Kydland and Edward C. Prescott received the 2004 Nobel prize
in economics in part for showing that even well-meaning policymakers could be better
off with rules. Here in this paper, I will show this is true for the U.S. monetary policy
because of the forward-looking behavior of market participants in the U.S. money
market. There are at least seven explanations in the literature for why central banks may
wish to follow interest-rate-smoothing operations. The first five explanations were
mentioned by Gerlach-Kristen (2004) who also presents a framework, which allows for
both unobserved variables and monetary policy inertia and their importance in
interest-rate-smoothing operations. (i) Interest-rate-smoothing operations reduce the
possibility of excessive reactions in the financial markets, Goodfriend (1987). (ii) These
operations facilitate the communication between the central bank and market participants,
Goodfriend (1991). (iii) Interest-rate-smoothing operations reduce the negative impact of
the policy due to the central bank misperception of the state and the structure of the
economy, e.g., Rudebusch (2001). (iv) Interest-rate-smoothing operations help to avoid
frequent policy reversals, as reversals could be interpreted as reflecting a lack of skills on
the part of policy makers, Goodhart (1999). (v) Because of the existence of unobserved
variables and monetary policy inertia, monetary authorities found interest-rate-smoothing
operations desirable, Rudebusch (2002) and Gerlach-Kristen (2004). (vi) Interest-rate
smoothing leads to a reduction of liquidity risk facing banks as it lowers the risk of large
fluctuations in the cost of servicing short-run liabilities. Gerlach-Kristen (2004) finds
unobserved variables are more important than monetary policy inertia in the United
States.
3
According to Smith and van Egteren (2005), the financial stability of the interest-
rate smoothing is only due to what they call the “direct effect”. However, they assert
there are also indirect effects of the interest-rate smoothing, which are likely to move
financial stability in the opposite direction of the direct effect. This occurs, as they
attempt to show theoretically, because interest-rate smoothing alters banks’ risk-taking
incentives by entering less familiar lines of business activities, e.g., over-the-counter, off-
balance sheet, etc. In contrast to their finding this paper provides evidence that while
agents in the money market in the United States are forward looking, i.e., their behaviors
change as a result of policy or other exogenous shocks, banks are policy invariant in the
interbank (Fed funds) market.
(vii) It is argued that the monetary inertia may be an optimal behavioral response
on the part of central banks as policy inertia (or interest-rate-smoothing) behavior helps
the central bank to focus on the expectations of agents in the economy. This will lead to a
better outcome, e.g., Sack and Wieland (2000). In fact, Rudebusch (2002), using
quarterly monetary policy inertia, in the framework of the partial adjustment of the short-
term-policy interest rate, shows that the optimal policy inertia can be achieved when
private agents are forward looking. Namely, “[…] a large amount of predictable future
variation in the policy rate […] is the essence of optimal policy inertia: Because private
agents know that the policy rate is likely to be adjusted by a certain amount in the future,
they change their behavior today.” [Rudebusch (2002, p. 1174)].
The condition of forward-looking expectations is one of the major requirements
for many monetary policy recommendations. For example, it is argued [Woodford
(1999)] that a purely discretionary monetary policy when the central bank minimizes the
4
social cost function without any pre-commitment leads to an inefficient stabilization in
the face of cost shocks. The reason is that an optimal pre-commitment policy imparts
inertia when expectations are forward looking. In other words, the central bank’s current
actions directly affect private agents’ expectations of future interest or inflation rate.
Walsh (2003, p. 276) concludes that “A policy aimed at stabilizing inflation and the
change in the output gap (a speed limit policy) imparts inertia that can lead to improved
stabilization relative to pure discretion or inflation targeting. Simulations suggested that a
speed limit targeting policy dominates inflation targeting except when forward-looking
expectations are relatively unimportant. […] price level targeting leads to significantly
poorer outcomes than either inflation targeting, nominal income growth targeting, or
speed limit targeting if inflation is primarily backward looking.” In fact, the forward-
looking assumption and models, although in an explicit form of Fair (1978, 1979) and
Taylor (1993) type, are common in this literature, e.g., beside the above authors, see,
Kerr and King (1996), Woodford (1996), Bernanke and Woodford (1997), McCallum and
Nelson (1998), Clarida et al. (1999), as well as Bernanke and Boivin (2003).
Note that, by influencing the overnight rate of interest, a central bank can directly
affect only the short-term interest rates. And since long-term interest rates are a function
of short-term rates as well as expectations, a central bank can indirectly affect the
long-term rates by influencing not only short-term rates, but also the expectations.
Furthermore, as Goodfriend (1991) also mentioned, output and prices do not respond to
daily fluctuations in the overnight rate, but they respond only to the variation in the
longer-term interest rates. Consequently, in order for a discretionary monetary policy to
successfully affect inflation and/or output gap, a stable relationship between overnight
5
and other short-term interest rates is required. If such a stable relationship does not exist,
then the central bank’s actions can only create a higher volatility in the money market. By
stability we do not mean only temporal stability as Sarno and Thornton (2003) show for
the relationship between Fed funds rate and three-month Treasury bill rate, but the
relationship should also be policy invariant. As Lucas (1976) points out, temporal
stability and policy invariance are two distinctly different concepts. Estimated parameters
of a given relationship may remain constant over time, but the parameters could still vary
in response to a policy regime change or other exogenous shocks in the economy. If asset
holders are forward looking, then any regime change will alter the agents’ behavior,
which will then undermine policy effectiveness. In such a situation a policy of interest-
rate smoothing can be effective. Such a suggestion is consistent with the result found by,
e.g., Woodford (1999) and Walsh (2003). In fact, Thornton (2004) finds such a policy
may have been followed by the Fed.
This paper focuses on the issue of stability as an additional explanation for
following interest-rate-smoothing operations. Specifically, it is possible that monetary
authorities find an active monetary policy, including open market or open mouth
operations, destabilizes the money market. This is possible if agents in the money market
are not policy invariant in the sense of Lucas (1976). In this case, the rule-based policy of
interest-rate smoothing is more desirable and, therefore, the central bank should follow
such operations. This is because under the interest-rate-smoothing policy, even if banks
are forward looking in the interbank market, the central bank in changing the target rate
or influencing the effective funds rate would only react to the movements of short-term
interest rates (the economy). This reaction cannot be destabilizing. This important fact, to
6
the best of my knowledge, was ignored in this literature. It was found in this paper that
agents in the money markets are forward looking and so their expectations are formed
rationally. This implies that a discretionary monetary policy would be destabilizing in the
United States and the interest-rate-smoothing process would be an optimal monetary
policy. Furthermore, it was found the agents in the Fed funds market are not forward
looking and so a stable and policy invariant relationship between the Fed funds rate and
the three-month Treasury bill rate exists. It was found the Fed actually has been
following an interest-rate-smoothing policy. Finally, findings in this paper suggest that
the lack of a policy invariant relationship between the overnight and short-term interest
rates is another explanation for following an interest-rate-smoothing policy.
Section II provides the model and the description of the data. Section III is
devoted to the estimation of the long run relationships, the conditional and marginal
models as well as the superexogeneity test results. Section IV investigates the type of
monetary policy actions, which have been followed in the United States during our
sample period (October 1982-December 2004). The final section provides a summary and
conclusions.
II. The Model and Description of the Data1. The Model
Following Cook and Hahn (1988), Sarno and Thornton (2003) and
Thornton (2004), we assume that Treasury bill rates (TB) are linked to the Fed funds rate
(FF). Suppose a long-run relationship between TB and FF exists and can be described as:
F(TBt, FFt, ß) = 0, (1)
where ß is the long-run parameter, TB is a non-policy variable, say three-month Treasury
bill rate, and FF is a policy variable, say Fed funds rate, Fed funds target rate or Fed’s
7
operating target for the funds rate.1 Note that, “[…], although the funds rate was not
pegged to the target on a daily basis, the Fed appears to have enforced the targets over the
course of a few days.” [Woodford (1999, p. 253)]. We can envision TB as a variable that
summarizes the status of the economy facing the central bank during the course of a day.
From such a relationship we will have two error-correction models as:
∆TBt = B0 ∆FFt + ∑=
−∆k
1iiti TBC + ∑
=−∆
k
1iiti FFB +∑
=−
k
1iit1i ECψ + ∑
=−
k
1i
2it2i ECψ
∑=
−
k
1i
3it3iECψ + ut, (2)
∆FFt = A0 ∆TBt +∑=
−∆k
1iiti FFD + ∑
=−∆
k
1iiti TBA +∑
=−
k
1iit1iECλ + ∑
=−
k
1i
2it2i ECλ
∑=
−
k
1i
3it3i ECλ + vt, (3)
where ∆ before any variable means the first difference of that variable and u and v are
orthogonal disturbances. B’s, A’s, D’s, ψ’s as well λ’s are constant coefficients.
Variable EC is the error correction term, which is assumed to enter in the equation in a
non-linear form. Specifically, if agents ignore a small deviation from equilibrium, while
reacting substantially to large ones, the error-correction equation is non-linear.
Consequently, we follow Kia (2003) and allow all kinds of non-linearity in our error
correction models. In fact, a non-linear error-correction model, in a restricted form, was
originally developed by Escribano (1985). This model was used, among others, by
Hendry and Ericsson (1991), and recently Teräsvirta and Eliasson (2001) developed two
unrestricted versions of the model. Moreover, Sarno and Thornton (2003) developed a
1 Note that the effective Fed funds rate is the market rate and the target rate is the rate that the central bankenforces in the market. However, this rate is not the desired rate, “[…] that the central bank would set as itstarget if unconstrained by a desire to adjust the target rate slowly.” [Rudebusch (2002, p.1162)]. For theFed’s operating target rate, see Rudebusch (1995) and Woodford (1999).
8
restricted non-linear error correction model (ECM) between FF and TB. Equations (2)
and (3) are not identified.
The first possible identifying assumption is A0=0. The identified system will be:
∆TBt = B0 ∆FFt +∑=
−∆k
1iiti TBC + ∑
=−∆
k
1iiti FFB + ∑
=−
k
1iit1i ECψ + ∑
=−
k
1i
2it2iECψ
+ ∑=
−
k
1i
3it3iECψ + ut, (4)
∆FFt = ∑=
−∆k
1iiti FFD + ∑
=−∆
k
1iiti TBA + ∑
=−
k
1iit1iECλ + ∑
=−
k
1i
2it2i ECλ
+ ∑=
−
k
1i
3it3i ECλ + vt, (5)
In this case the Fed follows a discretionary policy. If we assume λ’s are equal to zero in
Equation (5), then Equation (5’) would be the marginal model for the behavioral
Equation (4) in the sense of Engle et al. (1983) and Engle and Hendry (1993).
∆FFt = ∑=
−∆k
1iiti FFD + ∑
=−∆
k
1iiti TBA + z’tγ + v’t, (5’)
where vector z includes all current and past values of other valid conditioning variables
as well as a constant term and vector γ is constant parameters. Note that the joint density
function of ∆ΤΒt and ∆FFt, conditional on information set It, is equal to the product of the
conditional model of ∆ΤΒt, given ∆FFt and information set It (i.e., ∆ΤΒt│∆FFt, It), and
the marginal model of ∆FFt, given information set It (i.e., ∆FFt│It). Information set I
includes lagged values of ∆ΤΒ, ∆FF and current and lagged values of other valid
conditioning variables. It should be mentioned that, as shown by Hamilton (1994,
pp. 310-311), disturbances ut and v’t are independent by construction.
Define, respectively, the conditional moments of ∆TBt and ∆FFt as
ηTBt=E(∆TBt│∆FFt, It), ηFF
t=E(FFt│It), σtTB=E[(∆TBt – ηTB
t)2│It] and σtFF=E[(∆FFt –
9
ηFFt)2│It], and let σt
TBFF=E[(∆TBt – ηTBt)(∆FFt – ηFF
t)│It]. Consider the joint distribution
of ∆TBt and ∆FFt conditional on information set It to be normally distributed with mean
ηt=[ηTBt, ηFF
t] and a non-constant error covariance matrix ∑ = ⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
σσ
σσ
FF
TBFF
FFTB
TB. Then,
following Engle et al. (1983), Engle and Hendry (1993) and Psaradakis and Sola (1996),
we can write the relationship between ∆TBt and ∆FFt, i.e., Equation (4) as:
where α0, ζ 0, ζ 1, ζ 2, ζ 3, ζ 4, ζ 5, ζ 6, δ0 and δ1 are regression coefficients of ∆TBt on ∆FFt
conditional on q’tα where q includes past values ∆TBt, ∆FFt and other valid conditioning
variables included in Equation (4). The error term ut is assumed, as before, to be
heteroscedastic (due to the overlapping observations), normally, identically and
independently distributed. Because the error is heteroscedastic, the term DevFF (= the
deviation of the variance of the error term from a five-period ARCH error of ∆FF) is
added, see Engle and Hendry (1993).
Note that ∆FFt is the control/target variable that is subject to policy interventions.
Although the parameter of ∆FFt is assumed to be constant over the sample period, it is
possible that this parameter changes [Lucas (1976)] under interventions affecting DGP
(data generating) process of ∆FFt, i.e., Equation (5’). In this case, agents have a forward-
looking behavior and the conditional model (4) is not policy invariant. Hence, the
parameters of interest in the analysis will be δ and ζ in the behavioral relationship (6).
Under the null of weak exogeneity, δ0- ζ 0=0. Under the null of invariance,
10
ζ1=ζ2=ζ3=ζ4=ζ5=ζ6=0 in order to have ζ0=ζ. Finally, if we assume that σtFF has distinct
values over different, but clearly defined regimes, then under the null of constancy of δ,
we need δ1=0. If these entire hypotheses are accepted, the equation will be reduced to
Equation (4), and the agents in the money market are not forward looking. In other
words, expectations are not formed rationally. It should also be mentioned that
“superexogeneity is sufficient but not a necessary condition for valid inference under
intervention” [Engle et al. (1983), p. 284]. This is due to the fact that estimable models
with invariant parameters, but with no weakly exogenous variables are easily formulated.
The second possible identifying assumption is B0=0 in Equation (2), which means
assuming that there is no feedback from policy actions to the economy within a day. In
this case, the policy actions affect the economy (money market) only with lags. The
identified system will be:
∆TBt = ∑=
−∆k
1iiti TBC + ∑
=−∆
k
1iiti FFB + ∑
=−∆
k
1iiti FFB + ut, (7)
∆FFt = A0 ∆TBt +∑=
−∆k
1iiti FFD + ∑
=−∆
k
1iiti TBA + ∑
=−
k
1iit1iECλ + ∑
=−
k
1i
2it2i ECλ
+ ∑=
−
k
1i
3it3i ECλ + vt, (8)
In this case Equation (7) would be the marginal model for the behavioral
Equation (8) while we also assume ψ’s are equal to zero. In the same fashion as in
Equation (4), if the contemporaneous variable ∆TBt in (8) is not superexogenous the
agents in the Fed funds market are forward looking. Then Equation (8) will not be policy
invariant. However, since the target rate changes and intra-day central bank actions are in
response to changes in the money market rate (∆TBt), they will affect ∆FFt first
spontaneously and then dynamically through lagged values of ∆FF. Consequently, in this
11
case the Fed’s (rule-based) interest- rate-smoothing policy does not destabilize the
market. In this paper, I will make some use of these assumptions and provide plausible
evidence. Note that the Fed, in conducting its monetary policy, influences the Fed funds
rate by changing the target rate and, according to, e.g., Rudebusch (1995), intervening in
the interbank market at least one or two times each day.
In the first case, i.e., when (4) is the behavioral equation and the Fed follows a
discretionary monetary policy, if agents are forward looking then any action of the central
bank creates instability in the money market as agents change their behavior for any
policy or any other exogenous shocks. However, in the second case, i.e., when
Equation (8) is the behavioral equation of the Fed, i.e., Fed follows an interest-rate-
smoothing policy, even if agents (banks) in the Fed funds market are forward looking
[i.e., ∆TBt is not superexogenous in Equation (8)], the rule-based policy of the central
bank does not create instability. In this case, the central bank is leaning against the wind
and reacting to the shocks rather than generating shocks. We will investigate in this
paper, first if agents are forward looking in the money and interbank markets and then
what policy the Fed has been following in our sample period.
2. Description of Data
The daily data on the effective Fed funds rate and the three-month Treasury bill
rate (secondary market) for the period 1982 (October 5)-2004 (December 31) are used.
The three-month Treasury bill rate, as an indicator for the equilibrium rate in the U.S.
money market rate, is chosen since this default-risk-free rate is often used by researchers,
see Sarno and Thornton (2003) for the references on all those studies. Three-month
Treasury bills are the most liquid assets in the money market. Consequently, the three-
12
month Treasury bill rate has been used by influential empirical studies for testing the
Expectation theory of term structure, see Sarno and Thornton (2003). The period covers
more than 21 years with 5558 effective daily observations. The source of these data is the
St. Louis Federal Reserve website. The effective Fed funds rate is a weighted average of
the rates on Fed funds transactions of a group of Fed funds brokers who report their
transactions daily to the Federal Reserve Bank of New York. Both Fed funds and three-
month Treasury bill rates are expressed as bond equivalent yields on a 365-day basis. The
sample mean of the Fed funds rate (FF) is 5.74% with a standard error of 2.60%, a
minimum of 0.87% and a maximum of 16.39%. The sample mean of the Treasury bill
rate (TB) is 5.27% with a standard error of 2.33%, a minimum of 0.81% and a maximum
of 10.81%.
The choice of the sample period is based on the availability of data on target Fed
funds rates. According to Sarno and Thornton (2003), the Fed was explicitly targeting the
funds rate from 1974 to October 1979. The Fed switched to a non-borrowed reserves
operation procedure in October 1979, and in October 1982 switched to a borrowed
reserves operating procedure. However, “Exactly when the Fed switched from a
borrowed reserve operating procedure to an explicit funds rate targeting procedure is
contentious [...] there seems to be general agreement that the Fed has explicitly targeted
the funds rate at least since the late 1980s.” [Sarno and Thornton (2003, p. 1099)].
To the best knowledge of the author, a non-interrupted set of data on Fed funds
target rates is only available from October 1982. For the period 1982-1989, I use a series
prepared by the Federal Open Market Committee (FOMC) Secretariat. This series is
based on the staff’s interpretations of FOMC transcripts and other documents publicly
13
available.2 Note that May 7, 1988 corresponds to a Saturday, when markets were closed.
Following Rudebusch (1995), I use May 9, 1988 as the day when the target was changed.
Furthermore, for the target change of “early January 1989”, I assume January 5 as the day
when the target was changed. For the period 1990 onwards, the series reported on the
Board of Governors of the Federal Reserve System’s website was used.
III. Long-Run Relationships, Conditional and Marginal Models and
Superexogeneity Test Results
1. Long-Run Relationships
The existing literature provides empirical evidence for the long-run relationship
between Fed funds and Treasury bill rates. For example, Sarno and Thornton (2003) have
shown that FF and TB rates are cointegrated. Furthermore, the adjustment toward the
long-run equilibrium largely occurs through the movements in the FF rate rather than the
TB rate. However, as Granger (1986) notes, if two or more economic variables are
cointegrated, they should not diverge from each other by too great an extent in the long
run. It is possible, however, for such variables to drift apart in the short run or according
to seasonal factors, but if they continue to be too far apart in the long run, then economic
forces, such as a market mechanism or government intervention, will begin to bring them
back together. Consequently, as Kia (2005) shows, the exclusion of a short-run set of
variables, which account for government interventions, results in biased coefficients if, in
fact, some policy regime changes included in this set cause variables in the model to
move together over the long run. The existing literature ignores this fact. Consequently,
2 Rudebusch (1995) also constructed a Federal funds target rate series. His series is available for the periods1974-1979 and 1984-1992. Although Rudebusch’s series has been widely used by researchers, I use theFOMC Secretariat’s series because it allows us to study the longest consecutive time period.
14
contrary to Sarno and Thornton (2003), I allow the short-run dynamics of the system to
include policy regime changes or other exogenous factors, which affect such system.
To allow the short-run dynamics to be affected by the appropriate policy regime
changes or other exogenous effects which could only influence the short-run dynamics of
the system, a vector of dummy variables (DUM) was constructed, where DUM = (Mt, Tt,
D020319t, EDAYt, TARATEt). Dummy variables Mt, Tt, WEDt and THt are for
Mondays, Tuesdays, Wednesdays and Thursdays, respectively. For example, M = 1 for
Mondays and is equal to zero, otherwise. Dummy variables D851231t and D861231t are
equal to one on December 30 and 31, 1985 and December 31, 1986, respectively, and are
equal to zero, otherwise. These dummy variables are included to capture the high
volatility of Fed funds rate on those days. Dummy variable GREENt =1 since August 11,
1987 when Alan Greenspan was appointed chair of the Fed and is equal to zero,
otherwise. OCT87t and ASIAt are dummy variables accounting for the October 87 and
Asian crises, respectively. In both events, central banks in industrial countries flooded the
money markets with liquidity to ease the downfall in the stock markets. The easing of the
markets took at least until the end of October of the year the crisis took place.
Consequently, I constructed OCT87t = 1 for October 19 to 30, 1987 and is equal
to zero, otherwise, and ASIAt = 1 for October 17 to 30, 1997 and is equal to zero,
otherwise. Dummy variable TAt = 1 since February 4, 1994 (when Fed started to
announce target changes) and is equal to zero, otherwise. Dummy variable TAFt = 1
since October 19, 1989 (when the Fed has followed the practice of changing the FF
15
targets by 25 or 50 basis points) and is equal to zero, otherwise. Dummy variable SWEDt
accounts for settlement days on Wednesdays, i.e., it is equal to one on Wednesdays when
it is a settlement day and is equal to zero, otherwise. Dummy variable REMAt = 1 since
February 2, 1984 when the reserve maintenance period was modified from one week (for
most large institutions) to two weeks (for all institutions) and is equal to zero, otherwise.
Dummy variable D970819t =1 since August 19, 1997, when the FOMC started
including a quantitative Fed funds target rate in its Directive to the New York Fed
Trading Desk, and is equal to zero, otherwise. Dummy variable D99518t =1 since May
18, 1999, when the Fed extended its explanations regarding policy decisions, and started
including in press statements an indication of the FOMC’s view regarding prospective
developments (or the policy bias), and is equal to zero, otherwise. Dummy variable
D000202t = 1 since February 2, 2000, when the FOMC started to include a balance-of-
risks sentence in its statements replacing the previous bias statement, and is equal to zero,
otherwise. Dummy variable D020319t = 1 since March 19, 2002, when the Fed included
in FOMC statements the vote on the directive and the name of dissenter members (if
any), and is equal to zero, otherwise.
Dummy variables D940418t, D981015t, D010103t, D010418t and D010917t are
equal to one for April 18, 1994; October 15, 1998; January 3, 2001; April 18, 2001 and
September 17, 2001 (when the Fed changed the FF target rate outside its regular
meetings), respectively, and is equal to zero otherwise. Dummy variable EDAYt is equal
to one for the days (“event”) when the Fed funds target rate was changed whether at a
regularly scheduled FOMC meeting, or otherwise, and also for the days on which the
FOMC met, but did not change the target rate. It is equal to zero, otherwise. Dummy
16
variable TARATE is equal to one for the days when the Federal funds target rate actually
was changed and is equal to zero, otherwise. These days can be among the regularly
scheduled FOMC meeting dates or other days. Note that TARATE is a subset of EDAY,
as it excludes the days when FOMC met, but did not change the target. It should be
emphasized again that DUM enters only in the short-run dynamics of the system in the
long-run relationship between FF and TB.
I will test if two non-stationary series TB and FF are cointegrated3. I will use λmax
and Trace tests developed by Johansen and Juselius (1991) while allowing the short-run
dynamics of the system to be affected by dummy variables included in vector DUM.
Table 1, the top panel, reports the result of λmax and Trace tests for lag length of twenty
days. A twenty-lag length was needed in order to ensure that the error term is not
autocorrelated. Both λmax and Trace tests reject r (degree of cointegration) = 0 at 5% level
while they cannot reject r ≤ 1, implying that r = 1. This result confirms the finding of
Sarno and Thornton (2003). The estimated long-run relationship between TB and FF
rates normalized on TB coefficient is:
3 For variable TB, the absolute value of the augmented Dickey Fuller t statistic (for a lag length of 5) is0.5167 and the absolute value of the Phillips-Perron non-parametric t statistic (for a lag length of 4) is0.9870. Both t statistics are less than 2.86 (5% critical value), indicating that TB has one unit root. Forvariable ∆TB, the absolute value of the augmented Dickey Fuller t statistic (for a lag length of 4) is 28.23and the absolute value of the Phillips-Perron non-parametric t statistic (for a lag length of 4) is 24.27. Botht statistics are more than 2.86 (5% critical value), indicating that ∆TB is stationary. For variable FF, theabsolute value of the augmented Dickey Fuller t statistic (for a lag length of 20) is 1.0647 and the absolutevalue of the Phillips-Perron non-parametric t statistic (for a lag length of 4) is 3.323. While the augmentedDickey Fuller t statistic is less than 2.86 (5% critical value) indicating that FF also has a unit root, thePhillips-Perron non-parametric t statistic is more than 5% critical value indicating that FF is stationary.However, a graphical demonstration of this variable (not reported, but available upon request) clearlyindicates FF is not stationary. Consequently, we accept the augmented Dickey Fuller t statistic result. Forvariable ∆FF, the absolute value of the augmented Dickey Fuller t statistic (for a lag length of 20) is 24.27and the absolute value of the Phillips-Perron non-parametric t statistic (for a lag length of 4) is 96.33. Botht statistics are more than 2.86 (5% critical value), indicating that ∆FF is stationary. Note that the lag lengthin all of these tests was chosen according to the minimum of Akaike’s (1970, 1974) information criterion(AIC) and Schwarz’s (1978) information criterion (SC).
As we can see while the constant is not statistically significant the slope is highly
significant; however, a Likelihood Ratio test [χ2(1) = 19.93, p-value = 0.00] rejects the
null hypothesis that the slope coefficient is one implying that there is no one-to-one
relationship between these rates over the long run. We now need to investigate the
long-run stability of the relationship. Figure 1 shows Hansen and Johansen’s (1993) LR
test for the stability of the cointegration space for the relationship. BETA_Z (broken line)
pictures the actual disequilibrium as a function of all short-run dynamics. At the same
time, BETA_R (solid line) is corrected for the short-run effects, including the policy
effects, and shows the ‘clean’ disequilibrium. In fact, it is the BETA_R series that is
tested for stationarity and thus determines the number of cointegration relationships in the
maximum likelihood procedure [Hansen and Juselius (1995)].
Figure 1 about here
As we can see from Figure 1, according to the recursive LR test, the relationship
is stable over the long run when series are corrected for the short-run effects.
Furthermore, when the first seven years are reserved for the initial estimate, even without
correcting for the short-run effects, the relationship is stable over the long run.
2. Conditional and Marginal Models: Superexogeneity Test Results
A. Are agents in the money market forward looking?
To answer this question we need to construct the error-correction model. Using
our estimated long-run relationship (9), we will be able to estimate the identified
conditional Model (4) where EC (the error term) already incorporated day-of-the-week
18
dummies and dummy variables accounting for the internal and external shocks in the
sample period, which could affect the relationship between FF and TB, see Sub-section 1.
Table 2 reports the error-correction or conditional model (ECM) for TB. The estimation
method is Least Squared and to correct for overlapping observations and
heteroscedasticity, Newey and West’s (1987) robusterror for 5-order moving average was
used. In order to ensure that the tests are not biased or do not lack power because of an
inappropriate choice of lag length or too many lagged values, I report the parsimonious
relationship of Equation (4), for the initial lag length of k=30, in Table 2. In this table and
thereafter, R 2, σ and DW, respectively, denote the adjusted squared multiple correlation
coefficient, the residual standard deviation and the Durbin-Watson statistic. Furthermore,
White is White’s (1980) general test for heteroskedasticity, ARCH is the five-order
Engle’s (1982) test, and Godfrey is the five-order Godfrey’s (1978) test.
Table 2 about here
According to diagnostic tests reported in the last row of the table, the error term is
both autocorrelated and heteroscedastic and, according to the results reported in column 3
of Table 2, Hansen’s (1992) stability Li test for the null hypothesis that the estimated
coefficient is stable denotes all of the coefficients are stable. However, as we would
expect, due to overlapping observations and heteroscedasticity, the variance is not stable.
Consequently, the joint Hansen’s (1992) stability Lc test result, which is equal to
14.52 (p-value=0.00), rejects the null of joint stability of the coefficients together with the
estimated associated variance.
As the results of the ECM indicate, the short-run relationship between TB and FF
is non linear implying that a small deviation from the equilibrium may be ignored, but
19
market participants react substantially to a large deviation. As for the linear impact,
(second column of the table), a deviation from the long-run equilibrium takes a day to
return to equilibrium while there are some tendencies toward further deviation from
equilibrium after twelve days. However, the sum of these coefficients is negative. The
sum of the coefficients of non-linear error correction terms is also negative indicating an
error-correcting behavior. It should be mentioned that, as we will see later in this section,
the contemporaneous variable ∆FFt is weakly exogenous and so it is a valid conditioning
variable in Equation (4) [see, e.g., Hendry and Richard (1983)] and all estimated
coefficients are both efficient and consistent, see Banerjee et al. (1996). The estimated
coefficient of ∆FFt is positive and according to this coefficient an increase of 1% in FF
results in an increase of 0.03% in TB. However, we will show that ∆FFt is not
superexogenous in the sense of Engle et al. (1983) and Engle and Hendry (1993).
Therefore, the relationship is not policy invariant and not stable contrary to what is
claimed by Sarno and Thornton (2003). Specifically, a discretionary monetary policy by
changing FF in order to influence TB has an uncertain consequence.
For the superexogeneity test, we need to specify the stochastic mechanism, which
generates our contemporaneous variable ∆FFt, i.e., the marginal model. To estimate the
marginal model, using dummy variables included in DUM, I allowed both intercept and
slopes of the marginal equation to be influenced by these dummy variables. Column 4 of
Table 2 reports the parsimonious estimation of the marginal model (5’). The estimation
method, similar to the conditional model, is Least Squared, where standard errors are
corrected for autocorrelation and heteroscedasticity. Diagnostic tests reported in the last
20
row of column 4 of Table 2 suggest that, as one would expect, due to overlapping
observations, the error term is both autocorrelated and ARCH heteroscedastic.
According to Hansen’s (1992) stability Li test reported in column 5 of Table 2, all
coefficients are stable. However, again as we would expect, due to overlapping
observations and heteroscedasticity, the variance is not stable. Consequently, the joint
Hansen’s (1992) stability Lc test result, which is equal to 5.20 (p-value=0.00), rejects the
null of joint stability of the coefficients together with the estimated associated variance.
The estimated model seems a reasonable marginal model for the analogue of ηFF.
Based on the significance of the dummy coefficients, there is strong evidence for
a structural break due to the “event” days, the days FOMC met, the policy regime
changes of October 19, 1989, when the Fed adopted the practice of changing the FF
targets by 25 or 50 basis points, the policy regime changes of February 2, 1984, when the
modification in the reserve maintenance period from one week (for most large
institutions) to two weeks (for all institutions) took place, the policy regime changes of
February 4, 1994, when the Fed started to announce target changes and the policy regime
changes of August 19, 1997 when FOMC started to include a quantitative Fed funds
target rate in its Directive to the New York Fed Trading Desk. The instability of the
marginal model implies that the parameters of the associated conditional models will not
be policy invariant when economic agents are forward-looking.
From the estimated marginal model, estimates of ηFF and σtFF were calculated. As
for σtFF, since the error is heteroscedastic, according to ARCH test, a five-period ARCH
error, therefore, was estimated. I also constructed DevFF as differences between the
variance of the error term of the marginal model and the variance constructed by ARCH
21
estimation. All of these constructed variables were used to estimate Equation (6). The
estimation result on these constructed variables is given in column 2 of Table 3. The
estimated method is Least Squared where standard errors, as before, are corrected for
autocorrelation and heteroscedasticity, using Newey and West’s (1987) robusterror for
5-order moving average.
Table 3 about here
The individual χ2 test is on the null hypothesis that the coefficient of each variable
is zero. The χ2 or F-test on the null hypothesis that the coefficients of all constructed
variables are jointly zero, is given in the last row of the table. As the estimation result in
Table 3 shows, the joint F-test (or χ2-test) on the null hypothesis that coefficients of these
constructed variables are jointly zero is rejected, indicating that these variables together
should be included. This result immediately implies that the contemporaneous variable
(∆FFt) in the conditional model, reported in Table 2, second column, failed to be
superexogenous, i.e., agents are forward looking and expectations are formed rationally.
Since the coefficient of (∆FFt –ηFF) is statistically insignificant, ∆FFt, as it would
be expected, is weakly exogenous.4 Furthermore, the coefficients of other constructed
variables, except DevFF, are also statistically insignificant, implying that the null of
constancy cannot be rejected. However, since the coefficient of DevFF is statistically
significant at the conventional level, the null of invariance with respect to policy changes
is violated. Consequently, we reject the null of invariance, while accepting weak
exogeneity and constancy conditions for our contemporaneous variable. Note that
constancy and invariance are two different concepts. Parameters could vary over time,
4 Note that FF is a monetary authorities control variable.
22
but be invariant with respect to policy changes. It should also be noted that since ∆FF is
weakly exogenous and its coefficient is constant, the inference on the parameters in the
agents’ model (ECM) is efficient and consistent.
However, as it was mentioned by Engle and Hendry (1993), we need all three
conditions to be satisfied in order to ensure superexogeneity. The failure of the invariance
condition, therefore, justifies the result of the joint F-test (or χ2-test) on the null
hypothesis that all coefficients of the constructed variables are jointly zero. Namely, in
general, we reject the null hypothesis that ∆FF is superexogenous. That is, although the
coefficient of ∆FF in our ECM is weakly exogenous and constant over the sample period,
any change in the regime affecting money markets in the U.S. influences economic
agents’ investment behavior.
In fact, since most policy rules relate to past information about the economy, the
possibility of a policy variable, like the Fed funds rate, being superexogenous seems
unlikely. Consequently, a change in the monetary policy, which alters the process that the
control variable ∆FF is formed, will affect investment decisions made by economic
agents in the money market in the United States. Namely, the agents in this market are
forward looking. Furthermore, since the contemporaneous variable in the ECM reported
in Table 2 is weakly exogenous, it can be treated as though it is fixed in repeated
samples.
To ensure the robustness of the results, I pursue additional tests. Specifically,
I follow Psaradakis and Sola (1996) and adjust the conditional TB model by sequentially
deleting constructed variables with insignificant coefficients. Results from the modified
model persist in suggesting that the contemporaneous variable ∆FF in ECM for TB is not
23
superexogenous. The final specification for TB included DevFF with a coefficient of
-0.026 and a t-ratio (adjusted for heteroscedasticity and autocorrelation) of -2.40, so the
superexogeneity of ∆FFt variable in the conditional model of TB is further rejected.
As a second check, it should be noted that the structural invariance implies that
the determinants of parameter non-constancy in the marginal process should not affect
the conditional model [Psaradakis and Sola (1996)]. Hence, I examine the significance of
the dummy variables, affecting the intercept (which is none) or slopes, in the marginal
model for FF when added to the conditional model for TB. The only variable with a
statistically significant coefficient is ∆TBTAFt-18 with a coefficient of 0.0445 and a t-ratio
(adjusted for heteroscedasticity and autocorrelation) of -2.72. Furthermore, the
conditional model for TB, reported in Table 2, fails to parsimoniously encompass the
conditional model which includes ∆TBTAFt-18 on a χ2-test, adjusted for
heteroscedasticity and autocorrelation, of 43 with a p-value of 0.00, thereby rejecting
superexogeneity. Since agents are forward looking and the coefficients reported in
Table 2 are not policy invariant the correct specification of ECM for TB for our sample
period would include all structural breaks over the sample period. I, therefore,
reestimated the ECM allowing all policy regime changes as well as other exogenous
shocks to affect both the intercept and slopes. The parsimonious results are reported in
Table 4.
Table 4 about here
Recall that ∆FF is weakly exogenous and, therefore, there is no simultaneity bias
in the results given in Table 4 and all estimated coefficients are both efficient and
consistent. As we can see, a 1% change in FF during the sample period would result in a
24
change of 0.02% in TB the same day and of 0.05% within three days if no policy shock
or other exogenous shocks had occurred during the sample. However, since policy shocks
or other exogenous shocks like the Asian crisis can change the behavior of agents, a
discretionary policy to influence the economy (money market) may lead to a very
uncertain result. For example, as the estimated coefficient of ∆FFD970819t, ∆FFD99518t,
∆FFD000202t and ∆FFSWEDM indicates, a 1% rise in FF, provided the day is a
settlement Wednesday, would result in a rise of 0.11% in TB the same day since the
FOMC started including a quantitative Fed funds target rate in its Directive to the New
York Fed Trading Desk on August 19, 1997. However, no such reaction can be certain
since the agents are not policy invariant.
Note that, as it was previously shown, ∆FF is weakly exogenous, but since it is
not strongly exogenous for ∆TB, the ECM cannot be used for forecasting.5 As before, the
short-run relationship between TB and FF is non linear implying that a small deviation
from the equilibrium may be ignored, but market participants react substantially to a large
deviation. But, market reaction to deviation from equilibrium varies as regime changes or
other exogenous shocks like the Asian crisis occur. Consequently, a discretionary
monetary policy to influence money market is not successful in the United States. It
should be mentioned that considering other rates instead of TB ― three-month corporate
paper rate, one-month Treasury bill rate or one-year Treasury Bill rate ― did not
materially change any of the above results (the results are available upon request), as
would be expected.
5 To test if ∆FF is strongly exogenous, I regressed ∆FF on its 20 lagged values and on the 20 lagged valuesof ∆TB. A χ2-test (adjusted for heteroscedasticity and autocorrelation) of 92.12 with a p-value of 0.00rejects the null hypothesis that the 20 lagged values of ∆FF should be excluded and a χ2-test (adjusted for
25
It may also be argued that, instead of the effective Fed funds rate, Federal
Reserves may have a daily operating (desired) funds target rate which is a valid policy
variable. Rudebusch (1995) characterizes the Fed’s interest rate targeting behavior during
the 1974-1979 and 1984-1992 periods and finds that the Fed allows the spot rate to
deviate from the target rate on a daily basis, but deviations are transitory and are largely
eliminated by the following day. Assuming this behavior continues for the rest of our
sample period and based on Woodford’s (1999) suggestion, I construct the operating
target (OFFT) rate according to the following law of motion:
FFt = a FFt-1 + (1 - a) FFTt, (10)
where the parameter a is the degree of inertia and FFT is the target rate. Equation (10)
can be written as:
FFTt - FFt = a (FFTt - FFt-1). (11)
Using Equation (11), I estimated â = 0.9533 and generated the operating target
rate (OFFT) as OFFTt = 0.9533 FFt-1 + (1 - 0.9533) FFTt.6 I repeated all the above
exercises by replacing FF by OFFT. None of the result was materially different than what
it reported. Consequently, for the sake of brevity, the results are not reported, but are
available upon request.
B. Are agents in the Fed funds market forward looking?
Having established in the previous sub-section that agents are forward looking in
the U.S. money market and so that a Fed’s discretionary monetary policy to influence the
money market would result in uncertain consequences, we will investigate whether
heteroscedasticity and autocorrelation) of 307.87 with a p-value of 0.00 also rejects the exclusion of thelagged values of ∆TB.6 Note that according to both the augmented Dickey Fuller and the Phillips-Perron non-parametric testresults (not reported, but available upon request) OFFT has a unit root, but its first differences arestationary.
26
agents in the U.S. interbank market are forward looking. To answer this question we need
to estimate Equation (8) and its associate marginal model [Equation (7)]. Table 5 reports
the parsimonious estimation results of both conditional model (ECM) for ∆FF
[Equation (8)] and the marginal model for ∆TB. The estimation method is Least Squared
and to correct for overlapping observations and heteroscedasticity, Newey and
West’s (1987) robusterror for 5-order moving average was used.
Table 5 about here
According to diagnostic tests reported in the last row of the table, the error term is
heteroscedastic and according to the results reported in columns 3 and 5 of Table 5,
Hansen’s (1992) stability Li test for the null hypothesis that the estimated coefficient is
stable denotes all of the coefficients are stable. However, as we would expect due to
overlapping observations and heteroscedasticity, the variance in both conditional and
marginal models is not stable. Consequently, the joint Hansen’s (1992) stability Lc test
result, which is equal to 7.73 (p-value=0.00) for the conditional model and
14.76 (p-value=0.00) for the marginal model, rejects the null of joint stability of the
coefficients together with the estimated associated variance.
The estimated marginal model seems a reasonable marginal model for the
analogue of ηTB. Based on the significance of the dummy coefficients, there is strong
evidence for a structural break due to the Fed’s extension of its explanation regarding the
policy decision since May 18, 1999 and when FOMC started to include a balance-of-risk
sentence in its statements replacing the previous bias statement since February 2, 2000 as
well as when the Fed started to include in FOMC statements the vote on the directive
since March 19, 2002. Furthermore, there are also breaks on “event” days, the days
27
FOMC met, and the days the target rate actually is changed. As it was noted earlier in this
paper, the instability of the marginal model implies that the parameters of the associated
conditional models will not be policy invariant when economic agents are forward
looking.
From the estimated marginal model for TB, column 4 of Table 5, estimates of ηTB
and σtTB were calculated. As for σt
TB, since the error is heteroscedastic, according to
ARCH test, a five-period ARCH error, therefore, was estimated. I also constructed DevTB
as differences between the variance of the error term of the marginal model and the
variance constructed by ARCH estimation. All of these constructed variables were added
to the conditional model and the extended model was estimated. The estimation result on
these constructed variables is given in column 2 of Table 6. The estimated method is
Least Squared where standard errors, as before, are corrected for autocorrelation and
heteroscedasticity, using Newey and West’s (1987) robusterror for 5-order moving
average.
Table 6 about here
Similar to the result in Table 3, the individual χ2 test is on the null hypothesis that
the coefficient of each variable is zero. The χ2 or F-test on the null hypothesis that the
coefficients of all constructed variables are jointly zero is given in the last row of the
table. As the estimation result in Table 6 shows, both the individual test result on the null
hypothesis that the coefficient of the variable is zero, and the joint F-test (or χ2-test) on
the null hypothesis that coefficients of these constructed variables are jointly zero, cannot
be rejected, indicating that these variables together should be excluded. This result
immediately implies that the contemporaneous variable ∆TBt in the conditional model,
28
reported in Table 5, second column, is superexogenous, i.e., agents are not forward
looking. Since the coefficient of (∆TBt –ηTB) is statistically insignificant, ∆TBt is weakly
exogenous implying that the inference on the parameters in the agents’ model (ECM
reported in column 2 of Table 5) is efficient and consistent.
Again as before, to ensure the robustness of the results, I pursue additional tests.
Adjusting the extended conditional FF model by sequentially deleting constructed
variables with insignificant coefficients, I found none of the constructed variables to be
statistically significant. As a second check, I examine recursive estimates of the
coefficient of ∆TBt in the conditional model for FF, reported in Table 5. Figure 2 depicts
these estimated coefficients together with a confidence region based upon plus-or-minus
1.96 of the estimated coefficient standard error, adjusted for heteroscedasticity and
autocorrelation, at each sample size. According to this graph, it is visually apparent that,
when regime shifts are not accounted for there is no significant change in the estimated
coefficient of the contemporaneous variable ∆TBt, providing further support for the
superexogeneity of this variable.
Figure 2 about here
Moreover, as before, I examine the significance of the dummy variables, affecting
the intercept or slopes, in the marginal model for TB when added to the conditional
model for FF. Only four variables ― ∆FFD010418t-18, ∆TBD000202t-5, ∆TBD020319t-4
and ∆TBD020319t-5 ― were found to be statistically significant. The estimated
coefficients of these variables, respectively, with t-ratio adjusted for heteroscedasticity
and autocorrelation in brackets are 1.00 (4.19), 0.37 (2.31), -0.43 (-2.54) and -0.57
(-3.16). Only two of these dummy variables, i.e., D000202t-5 and D020319t are associated
29
with policy regime changes. Specifically, the impact of the change in TB after four and
five days became different since February 2, 2000 (when FOMC started to include a
balance-of-risks sentence in its statements, replacing the previous bias statement) and
since March 19, 2002 (when the Fed started to include in FOMC statements the vote on
the directive).
Furthermore, the conditional model for ∆FF, reported in Table 5, fails to
parsimoniously encompass the conditional model which includes these variables on a χ2
(adjusted for heteroscedasticity and autocorrelation) test [χ2 (3)= 20.37 with
p-value=0.00], thereby weakening the earlier test results in favor of superexogeneity of
∆TBt in the conditional model. For a further check, I, therefore, reestimated the ECM for
FF allowing all policy regime changes as well as other exogenous shocks to affect both
the intercept and slopes. The parsimonious results are reported in Table 7.
Table 7 about here
Apparently from the estimation result in Table 7 there is a shift in the estimated
coefficient of the contemporaneous variable ∆TBt since February 2, 2000 (when FOMC
started to include a balance-of-risks sentence in its statements, replacing the previous bias
statement), since May 18, 1999, when the Fed extended its explanations regarding policy
decisions, and started including in press statements an indication of the FOMC’s view
regarding prospective developments (or the policy bias) and since the appointment of
Alan Greenspan as the chair since August 11, 1987. However, a three-order RESET
[Ramsey (1969)] test for omitted variables and incorrect functional form (adjusted for
heteroscedasticity and autocorrelation) [χ2=10.99, p-value=0.02] indicates that the
conditional model reported in Table 5 specification-dominates the conditional model
30
reported in Table 7. Furthermore, a three-order RESET test (adjusted for
heteroscedasticity and autocorrelation) [χ2=2703.70, p-value=0.00] strongly rejects the
null hypothesis that the conditional model reported in Table 7, which includes all policy
regime shifts, has the correct specification.
Consequently, we have strong evidence that the conditional model (ECM for FF)
reported in Table 5 does not suffer from omitted variables and incorrect specification.
This implies that, we cannot strongly reject that ∆TBt in the conditional model for FF is
superexogenous. In other words, agents in the U.S. interbank market are not forward
looking. Specifically, the error-correction model for the effective Fed funds rate as
described in the second column of Table 5 is stable and policy invariant. Consequently,
an interest-rate-smoothing policy, i.e., changes in Fed funds rate in response to daily
shocks as described by this estimate is an optimal policy for the Federal Reserves. It
should be mentioned that even if agents in the Fed funds market were forward looking
the interest-rate-smoothing policy would also be an optimal policy. This is due to the fact
that the Fed reacts to changes in the money market as they occur rather than to influence
that market. As the estimated coefficients of ∆FFt-1, ∆FFt-2, …, ∆FFt-9 in Table 5, column 2,
indicate, the policy actions then dynamically affect the Fed funds rate up to nine days.
I again repeated all the above exercises by replacing FF by OFFT. None of the result was
materially different than what is reported. Consequently, for the sake of brevity, the
results are not reported, but are available upon request. The final question, which we will
investigate in the next section, is whether the Fed has been following an interest-rate-
smoothing policy during our sample period.
31
IV. Federal Reserve Interest Rate Smoothing
The interest-rate-smoothing policy implies that the Fed does not change rates per
se, but rather leans against the wind, by changing its target for the nominal interest rate in
response to economic shocks. In this section we investigate whether the Fed has been
following an interest-rate-smoothing policy in our sample period. It was evidenced in the
previous section that the change in the Fed funds rate is not superexogenous in a
relationship between Treasury bill and Fed funds rates indicating that an outright open
market operation to influence money market (the economy) may not result in a precise
consequence as the Fed expects since agents are forward looking. Alternatively, if the
Fed follows an interest-rate-smoothing policy, it can effectively conduct its monetary
policy for two reasons: (i) agents are not be forward looking in the Fed funds market and
so a stable and policy invariant relationship between FF and TB can be estimated and (ii)
even if agents were forward looking in the Fed funds market since the Fed reacts to
changes in the economy, then the result would be certain and optimal.
Cook and Hahn (1988), using the Expectations theory, relate FF to TB and
assume that movements in the Fed funds target rate cause movements in other market
rates. Based on a simple regression without considering policy regime and/or other
exogenous changes, they concluded that over the 1973-1985 period the Fed conducted a
discretionary policy. They also concluded that the Fed, using signal effects, changed FF,
which in turn caused TB and other longer term money market rates to change.
Furthermore, in a later work, Cook and Hahn (1989), using the same sample period,
found that by changing the target rate the Fed will influence TB and other money and
capital market rates. Thornton (2004) provides some evidence that the Fed’s actions
actually were not discretionary during the sample period of Cook and Hahn (1988 and
32
1989), but rather were rule-based interest-rate-smoothing processes. Furthermore, he
provides evidence consistent with interest-rate-smoothing hypothesis during the
1984-1997 period.
In this section, I provide stronger evidence that the Fed actually has been
following an interest-rate-smoothing policy over our sample period (1982-2004). It is
possible in the long-run relationship (1), where two variables are cointegrated, for one of
the variables to be weakly exogenous for the long-run parameter ß. In such a case, the
loading parameter α associated with the variable will be zero. This implies that the first
differences of the variable do not contain information about the long-run parameters ß. If,
for example, α associated with TBt is zero, then ∆ΤΒt is weakly exogenous in the sense
that the conditional distribution of ΤΒ and FF, given ∆TBt as well as the lagged values of
∆TBt and ∆FFt, contains the parameters α and ß, whereas the distribution of ∆ΤΒt, given
the lagged values of ∆TBt and ∆FFt, does not contain the parameters α and ß.7 This
means ∆TBt is not affected by ∆FFt, but because TB and FF are cointegrated, ∆FFt is
affected by ∆TBt. In other words, the Fed has followed an interest-rate-smoothing policy.
If, on the other hand, α associated with FFt is zero, then FF will be weakly exogenous,
and we will conclude that the Fed has been following a discretionary policy, excluding a
consistent interest-rate smoothing during the sample period.
Consider long-run relationship (9). According to [χ2(1) = 1.04, p-value = 0.31],
we cannot reject the null hypothesis that TB is weakly exogenous for the long-run
7 This also implies that the parameters in the conditional and marginal distributions are variation-free[Johansen and Juselius (1991)]. Namely, these parameters are constant over time when there is nointervention. However, here again, weak exogeneity for long-run parameters does not guarantee that theagents would not change their behavior in relation to interventions. That is in a given regime the parametersare constant, but their variation between regimes is interrelated.
33
coefficients, while according to [χ2(1) = 88.94, p-value = 0.00], we can strongly reject the
null hypothesis that FF is weakly exogenous for the long-run coefficients. This implies
that the first differences of TB do not contain information about the long-run parameter,
whereas the reverse is true for the first differences of FF. The economic interpretation of
this result is that the Fed has been following an interest-rate-smoothing policy during our
sample period. This result confirms the finding of Thornton (2004, p. 475) “that the Fed
does not move rates per se but, rather, smoothes the transition of rates to the new
equilibrium required by economic shocks”, but here we evidence this finding for a longer
sample period and with a different approach.
As a robust check for this finding, using the Fed’s operating target rate estimated
according to Equation (11) and generated by OFFTt = 0.9533 FFt-1 + (1 - 0.9533) FFTt, I
will investigate the temporal ordering between OFFT and TB. According to
Granger (1988), such a test requires the existence of an error-correction model. The last
panel of Table 1 reports the result of λmax and Trace tests for a lag length of twenty days
for the relationship between TB and OFFT. Clearly, there is one cointegrating
relationship between these two variables. This relationship is given by the following
The equation, as one would expect, is very similar to Equation (9) where the
constant is not statistically significant either. Using the error-correction term generated
from Equation (12), the Granger causality between these two variables was conducted.
First, I estimated ∆TB on its twenty lagged values and twenty lagged values of ∆OFFT
including the lagged value of the error-correction term. According to χ2(20) = 116,
34
p-value = 0.00, we reject the null hypothesis that the coefficients of lagged values of ∆TB
are jointly zero, while according to χ2(20) = 31, p-value = 0.05, we cannot reject (at the
conventional level) the null hypothesis that the coefficients of lagged values of ∆OFFT
are jointly zero, indicating that OFFT does not Granger-cause TB. Second, I estimated
∆OFFT on its twenty lagged values and twenty lagged values of ∆TB including the
lagged value of the error-correction term. According to χ2(20) = 215, p-value = 0.00, we
reject the null hypothesis that the coefficients of lagged values of ∆OFFT are jointly zero,
and according to χ2(20) = 68, p-value = 0.00, we also reject the null hypothesis that the
coefficients of lagged values of ∆TB are jointly zero, indicating that TB Granger-causes
OFFT. This result immediately confirms the earlier finding in this paper that the Fed has
been following an interest-rate-smoothing policy. Note that in both of the above cases the
coefficient of the error-correction term was negative and statistically significant.
Finally, I carry out the above exercise, but between ∆TB and ∆FF. When ∆TB
was estimated on its twenty lagged values and twenty lagged values of ∆FF including the
lagged value of the error-correction term [from Equation (9)], a χ2(20) = 112, p-value =
0.00, rejects the null hypothesis that the coefficients of lagged values of ∆TB are jointly
zero. Moreover, χ2(20) = 39, p-value = 0.01 cannot reject (at the 1% level) the null
hypothesis that the coefficients of lagged values of ∆FF are jointly zero. This means FF
does not Granger-cause TB, or the Fed has not followed a discretionary policy during our
sample period. The result, as one would expect, is clearly not as strong as the one
obtained by studying the operational Fed funds target rate.8 Alternatively, when ∆FF was
8 This is because the effective Fed funds rate is a weighted average of the rates on Fed funds transactions ofa group of Fed funds brokers who report their transactions daily to the Federal Reserve Bank of New York.
35
estimated on its twenty lagged values and twenty lagged values of ∆TB, including the
lagged value of the error-correction term, χ2(20) = 207, p-value = 0.00 rejects the null
hypothesis that the coefficients of lagged values of ∆FF are jointly zero. Furthermore,
χ2(20) = 47, p-value = 0.00 also rejects the null hypothesis that the coefficients of lagged
values of ∆TB are jointly zero. This result implies that TB Granger-causes FF, or the Fed
has followed an interest-rate-smoothing policy during our sample period. In sum, from
the evidence presented in this section, we conclude that the Fed has been following an
interest-rate-smoothing process during our sample period. In addition, U.S. Federal
Reserve Chair Alan Greenspan clearly confirmed this finding during an appearance at a
U.S. congressional committee on June 9, 2005. He stated: "The U.S. economy seems to
be on a reasonably firm footing, and underlying inflation remains contained." […] The
most recent data support the view that the soft readings on the economy observed in the
early spring were not presaging a more-serious slowdown in the pace of activity […]
Consumer spending firmed again, and indicators of business investment became
somewhat more upbeat." He then repeated that the Fed would continue to raise interest
rates at a modest pace.
V. Summary and ConclusionsMany studies using the Federal Reserve reaction function, the type initiated by
Fair (1978, 1979) and then revived by Taylor (1993), show the interest-rate-smoothing
policy is optimal when agents are forward looking. However, for the overnight monetary
policy, the central bank does not observe the daily changes in the actual inflation and
The Fed, by intervening one or two times during the day tries to achieve its desired rate. By the closing of
36
output gap ratio. These macrovariables are available only with few month lags and their
true values are known sometimes after many revisions. What the central bank observes
during the course of a day is actually the movements in nominal interest rates. Depending
on its objective, and based on past available data on inflation rate, output gap ratio, etc.,
the central bank conducts daily its monetary policy by affecting, or reacting to, the
movements of short-term interest rates. This action is done by influencing the overnight
rate (Fed funds rate in the United States).
However, the effectiveness of the overnight monetary policy depends on a stable
and policy invariant relationship between the overnight and short-term interest rates.
When agents in the money market are forward looking, a discretionary monetary policy
through changes in the overnight rate leads to an uncertain result. However, an interest-
rate smoothing process where the overnight rate (Fed funds rate) is changed according to
the movements in the short-term rates would be an optimal overnight monetary policy.
Consequently, it is important to investigate the behavior of agents in the money and
interbank markets.
This paper investigates the behavior of agents in the United States money and Fed
funds markets for the period 1982-2004. It was found that, while agents are forward
looking in the money market, their behavior is policy invariant in the Fed funds market.
Consequently, the optimal overnight monetary policy would be an interest-rate-
smoothing process. It was found in this paper, in fact, such an optimal monetary policy
has been followed by the Federal Reserves. As an extension to this study, it would be
interesting to investigate, using the appropriate conditional model for Treasury bill as
the day, depending on the intra-day events and expectations the effective rate can be very close to or farfrom the desired rate.
37
well as Fed funds rates developed in this paper, the dynamic response of the Fed funds
rate to an unexpected shock to the economy (money market), i.e., impulse-response
functions.
38
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Figure 1: Long-Run Stability TestLong-Run Relationship Between Fed Funds and Three-Month Treasury Bill Rates
Figure 2: Recursive Estimates of the Coefficient of Contemporaneous Variable ∆TBIn the Conditional Model for ∆FF, With ± 1.96 Estimated Standard Errors
1 is the 5% significance level500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2BETA_Z
BETA_R
45
Table 1*: Tests of the Cointegration Rank H0=r λmax
(1) λmax 95(2) Trace(3) Trace 95(2)
Relationship between Fed funds and Treasury bill rates
0 98.23 18.96 103.47 25.32
1 5.35 12.25 5.35 12.25
LM(1) p-value = 0.45LM(4) p-value = 0.90
Relationship between Fed funds operating target and Treasury bill rates0 99.09 18.96 104.96 25.32
1 5.87 12.25 5.87 12.25
LM(1) p-value = 0.68LM(4) p-value = 0.93
* The model includes a constant as well as policy and day-of-the-week dummies. Lag length is 20. LM(1)and LM(4) are one and four-order Lagrangian Multiplier test for autocorrelation, respectively [Godfrey(1978)].(1) λmax has been adjusted to correct a possible small sample bias error. Namely, λmax has been multipliedby the small sample correction factor (N – kp)/N, where N is the number of observations, k is the numberof lags and p is the number of endogenous variables, see Cheung and Lai (1993). Consequently,λmax=(N-kp) ln(1- Dr).(2) The source is Osterwald-Lenum (1992), Table 1, p. 469.(3) Trace has been multiplied by the small sample correction factor (N – kp)/N, see Cheung and Lai (1993).
Consequently, Trace test = - (N-kp) ∑+=
P
1ri
.)i -ln(1 D Both Trace and λmax tests were developed in Johansen
and Juselius (1991).
46
Table 2: Conditional and Marginal Models: Treasury Bill and Fed Funds Rates Explanatory Variables* Dependent
R 2=0.23, σ=0.29DW=2.00, Godfrey (5)=29.23 (p-value=0.00),White=62.75 (p-value=1.00), ARCH(5)=2043 (p-value=0.00)
Joint (coeffs + var.)=5.20 (p-value=0.00)
* ∆TBt is the first difference of three-month Treasury bill rate, ∆FFt is the first difference of Fed funds rate, EC is the error-correctionterm. Dummy EDAY is equal to one for the days (“event”) when the Fed funds target rate was changed whether at a regularlyscheduled FOMC meeting, or otherwise, and also for the days on which the FOMC met, but did not change the target rate. It is equalto zero, otherwise. Dummy TARDAY is equal to one for the days when the Fed funds target rate actually was changed and is equal tozero, otherwise. Dummy TAF is equal to one since October 19, 1989 (when the Fed adopted the practice of changing the FF targets by25 or 50 basis points) and is equal to zero, otherwise. Dummy REMA, which is equal to one since February 2, 1984 [when the reservemaintenance period was modified from one week, for most large institutions, to two weeks] and is equal to zero, otherwise. DummyTA is equal to one since February 4, 1994 (when the Federal Reserve announced target changes) and is equal to zero, otherwise.Dummy variable D970819 is equal to one since August 19, 1997 (when the FOMC started including a quantitative Fed funds targetrate in its Directive to the New York Fed Trading Desk) and is equal to zero, otherwise.** Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelation and heteroscedasticity.
47
Table 3: Superexogeneity Tests for Variable ∆FFt*
χ2 (1)(p-values**)
∆FFt – ηFF 0.01(0.90)
σFF (∆FFt – ηFF) 0.03(0.87)
(ηFF)2 0.02(0.90)
(ηFF)3 0.006(0.94)
σFF ηFF 0.06(0.81)
σFF (ηFF)2 3.02(0.08)
(σFF)2 ηFF 0.76(0.38)
DevFF 5.21(0.02)
F-Statistics (or χ2) on the nullhypothesis that coefficients of allconstructed variables in this columnare jointly zero.
t)2 + ψ6 DevFFt + z’tγ + ut. ∆TB is the first difference of the three-
month Treasury bill rate, ∆FF is the first difference of the Fed funds rate, ηFF is the conditional mean of∆FF, σFF is the conditional variance of ∆FF, and DevFF is the deviation of variance of the error term from afive-period ARCH error of ∆FF.
** Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelationand heteroscedasticity. Specification tests for the Fed funds rate: R 2=0.05, σ=0.06, DW=1.97, Godfrey(5)=3.18 (significance level=0.00), White=294 (significance level=0.00) and ARCH (5)=198 (significancelevel=0.00).
48
Table 4: Final Error-Correction Model for Treasury Bill RateExplanatory Variables* Dependent
R 2=0.05, σ=0.06DW=1.99, Godfrey (5) = 3.29(p-value=0.00), White=1232(p-value=0.00), ARCH(5)=493 (p-value=0.00)
Joint (coeffs +var.)= 16.78(p-value=0.00)
* Dummy variable D99518 is equal to one since May 18, 1999 (when the Fed extended its explanations regarding policy decision) andit is equal to zero, otherwise. SWED is equal to one for Wednesdays when it is a settlement day and is equal to zero, otherwise.Dummy variable D000202 is equal to one since February 2, 2000 (when the FOMC started to include a balance-of-risks sentence in itsstatements replacing the previous bias statement) and is equal to zero, otherwise. Dummy variable D020319 is equal to one sinceMarch 19, 2002 (when the Federal Reserve included in FOMC statements the vote on the directive) and is equal to zero, otherwise.ASIA is equal to one for October 17 to 30, 1997 and is equal to zero, otherwise. Dummy variable D99518 is equal to one since May18, 1999 (when the Fed extended its explanations regarding policy decision) and is equal to zero, otherwise. Dummy variableD010418 is equal to one for April 18, 2001 when the Fed changed the target out of its regular meeting, and is equal to zero, otherwise.Dummy variables D940418 and D010917 are equal to one for April 18, 1994 and September 17, 2001, respectively, when the Fedchanged the target rate outside its regular meetings and are equal to zero, otherwise. See footnote to Table 2 for the remainingmnemonics.** Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelation and heteroscedasticity.
49
Table 5: Conditional and Marginal Models: Fed Funds and Treasury Bill RatesExplanatory Variables* Dependent
R 2=0.03, σ=0.06DW=2.00, Godfrey (5)=0.77(p-value=0.59), White=266(p-value=0.00), ARCH(5)=399 (p-value=0.00)
Joint (coeffs +var.)= 14.76(p-value=0.00)
* See Footnote to tables 2 and 4 for the description of mnemonics.** Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelation and heteroscedasticity.
50
Table 6: Superexogeneity Tests for Variable ∆TBt*
χ2 (1)(p-values**)
∆TBt – ηTB 3.02(0.99)
σTB (∆TBt – ηTB) 0.04(0.85)
(ηTB)2 0.49(0.48)
(ηTB)3 0.21(0.65)
σTB ηTB 0.15(0.70)
σTB (ηTB)2 0.63(0.43)
(σTB)2 ηTB 0.08(0.78)
DevTB 0.03(0.87)
F-Statistics (or χ2) on the null hypothesis thatcoefficients of all constructed variables in thiscolumn are jointly zero.
t)2 + ψ6 DevTBt + z’tγ + ut. ∆FF is the first difference of the Fed
funds rate, ∆TB is the first difference of the three-month Treasury bill rate, ηTB is the conditional mean of∆TB, σTB is the conditional variance of ∆TB, and DevTB is the deviation of variance of the error term froma five-order ARCH error of ∆TB.
** Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelationand heteroscedasticity. Specification tests for the Fed funds rate: R 2=0.32, σ=0.28, DW=1.98, Godfrey(5)=0.32 (significance level=0.93), White=692 (significance level=0.00) and ARCH (5)=13.16 (significancelevel=0.02).
51
Table 7: Final Error-Correction Models for Fed Funds RateExplanatory Variables* Dependent
* GREEN is equal to one since August 11, 1987, when Alan Greenspan was appointed as chair of the Fed, and is equal to zero,otherwise. D010103 is equal one for January 3, 2001 when the Fed changed the funds rate outside the regular FOMC meetings and isequal to zero, otherwise. OCT87 is equal to one for October 17 to 30, 1997 and is equal to zero, otherwise. See the footnote to tables2, 4 and 5 for the remaining mnemonics.** Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelation and heteroscedasticity.
