ARTICLE IN PRESS

Journal of Monetary Economics 53 (2006) 1225–1234

www.elsevier.com/locate/jme

Forward-looking information in VAR

models and the price puzzle$
Sophocles N. Brissimisa,b,, Nicholas S. Magginasc,d
a
Economic Research Department, Bank of Greece, Athens 10250, Greece
b
Department of Economics, University of Piraeus, 80 Karaoli & Dimitriou St, Piraeus 18534,Greece
c
Department of International and European Economic Studies, Athens University of Economics and Business,
76 Patission St, Athens 10434, Greece
d
Strategic Planning and Research Department, National Bank of Greece, 86 Eolou St, Athens 10232, Greece
Received 5 November 2004; accepted 13 May 2005
Available online 30 May 2006

Abstract

With a view to addressing the major disadvantage of the VAR model, namely the inadequate
description of the central bank reaction function, we propose a VAR specification that proves
successful in solving the price puzzle featuring in monetary VARs for the US. This specification
consists in augmenting a standard VAR with two forward-looking variables: the federal funds
futures rate (or alternatively a money market forward rate) reflecting monetary policy expectations
and a composite leading indicator of economic activity. These two variables appear to effectively
control for the information set that the Federal Reserve may use in monetary policy decision-making.
With this modification, theory-consistent responses to monetary policy shocks are obtained.
r 2006 Elsevier B.V. All rights reserved.

JEL classification: E44; E52; F41; G1

Keywords: Monetary transmission mechanism; VAR models; Fed funds futures; Price puzzle

$
We would like to thank the editor, Robert King, and an anonymous referee for constructive comments and
suggestions. This research also benefited from the helpful comments of Stelios Arvanitis, Antonis Demos, Heather
Gibson and George Tavlas. The views expressed in this paper are those of the authors and do not necessarily
reflect those of their respective institutions.
Corresponding author. Economic Research Department, Bank of Greece, Athens 10250, Greece.
Tel.: +30 210 320 2388; fax: +30 210 3202432.
E-mail address: sbrissimis@bankofgreece.gr (S.N. Brissimis).

0304-3932/$ - see front matter r 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmoneco.2005.05.014
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1226 S.N. Brissimis, N.S. Magginas / Journal of Monetary Economics 53 (2006) 1225–1234

1. Introduction

The empirical analysis of monetary policy transmission made on the basis of identified
VARs often leads to puzzling responses of some of the system’s variables to a monetary
policy innovation. The positive response of the price level to a monetary policy
tightening—the price puzzle—is the most frequently cited puzzle in the literature. This
counterintuitive response to the policy shock is viewed as evidence of a misspecification
problem in the underlying system, and in particular, in the model’s equation corresponding
to the monetary policy reaction function.
Several proposals to solve the price puzzle have been put forward. Most of them at best
only partially deal with the major disadvantage of the VAR approach, i.e. the inadequate
description of the central bank’s reaction function. This disadvantage reflects the inability
to incorporate in a VAR the large information set that a central bank typically uses in
monetary policy decision-making and the absence of any forward-looking element in the
reaction function specification.
This paper suggests a VAR specification with forward-looking variables that proves
successful in solving the price puzzle featuring in monetary VARs for the US. We augment
a standard VAR with the expected level of the monetary policy instrument—as reflected in
the federal funds futures rate or in a money market forward rate—and a composite leading
indicator of near-term developments in economic activity. These two variables appear to
effectively control for the information set of the central bank. With this modification,
theory-consistent responses to monetary policy shocks are obtained. The model is
estimated on US data covering the period 1989–2004, characterized by a relatively
homogeneous monetary policy regime (Judd and Rudebusch, 1998) and a pronounced
price puzzle in conventional VAR specifications. The increasing ability of financial markets
to better predict monetary policy movements makes financial asset prices, like the federal
funds futures rate, ideal for conditioning the VAR analysis of monetary policy on a richer
information set, retaining at the same time the statistical advantage of a low-dimension
system. An implied one-month forward rate is used alternatively to the federal funds
futures rate as a proxy of expectations about the future course of monetary policy with
satisfactory results for a longer sample spanning the period 1986–2004 that corresponds to
the federal funds rate targeting regime in US monetary policy.
The remainder of the paper proceeds as follows. Section 2 outlines the identification
problem generating the price puzzle and briefly reviews some of the alternative suggestions
in the literature for its solution. Section 3 presents our specification of the VAR model.
Section 4 presents the empirical results and compares them with the results obtained from
a standard specification, which is subject to a strong price puzzle. Section 4 summarizes the
empirical findings and concludes.

2. Monetary policy analysis in VARs and the price puzzle

2.1. Identifying monetary policy shocks

To trace the response of macroeconomic variables to monetary policy shocks in a VAR,

specific restrictions are needed for the identification of the structural shocks and especially
the ones related to the interest rate equation, which corresponds to the monetary policy
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reaction function. Nevertheless, some of the assumptions made in order to identify the
structural VAR model from its reduced form may not accord well with reality:

1. Evidently, the information set of the monetary authorities is much richer than that
implied by the VAR specification. The central bank makes its decisions based on an
information set that contains many additional variables as well as its own information
(Romer and Romer, 2000). If a significant part of this information is omitted from the
VAR, which provides a simplified reduced-form expression of the central bank’s feedback
rule, the specification is inappropriate for identifying structural shocks (Brunner, 2000).
2. The existence of long lags in the effect of monetary policy can induce the central bank to
adopt a pre-emptive strategy responding to the forecast values of its goal variables rather
than their actual past values. However, VARs are not in general well equipped to directly
handle issues related to the forward-looking strategies followed by modern central banks.

The above sources of misspecification are often reflected in theoretically implausible

patterns of dynamic responses to the policy shock obtained from VAR systems used for
monetary policy analysis. An expression of these problems is the well-known price puzzle.

2.2. The price puzzle: definition and brief survey of the evidence

The price puzzle is one of the most frequently cited empirical puzzles1. It refers to the
positive response of the price level to a monetary tightening (Sims, 1992) as well as to
the implausibly long (compared with the average duration of price and wage contracts in
the economy) time lags for the decline in prices to become statistically significant. The
empirical literature has suggested ways to deal with the puzzle, although these proposals
do not appear to be very robust across different countries or time periods. The inclusion of
a commodity price index as a proxy for inflationary expectations in the VAR system,
proposed by Gordon and Leeper (1994), has been extensively used in the VAR literature.
Other studies have attempted to identify monetary policy shocks by taking account of the
workings of the market for reserves, in addition to the federal funds rate (Strongin, 1995;
Bernanke and Mihov, 1998).
Bernanke and Boivin (2003) augmented a standard VAR model with a small number of
factors derived from the application of Stock and Watson’s methodology to alternative
data sets considered as representative of the Federal Reserve’s information set. The
information contained in the factors in conjunction with the inclusion of the commodity
price index as an exogenous variable in the system, was claimed to substantially reduce and
often eliminate the price puzzle in the data.
Bagliano and Favero (1998, 1999) investigated the sensitivity of the monetary
transmission process to alternative policy shocks by augmenting a standard VAR model
to include three alternative non-VAR measures of policy shocks, including Rudebusch’s
(1998) measure based on federal funds futures2, as exogenous variables. The estimated
1
In addition to the price puzzle, which is addressed in this paper, the ‘liquidity’, ‘exchange rate’, and ‘forward
discount bias’ puzzles have also been discussed, see e.g. Strongin (1995) and Eichenbaum and Evans (1995).
2
Rudebusch noted that one can construct a market-based measure of the unanticipated component of the
federal funds rate change by using data from the federal funds futures market. He measured the exogenous shock
to monetary policy as the part of the unanticipated component of the federal funds rate, which was orthogonal to
a measure of news about employment. The observed degree of correlation between his measure of monetary policy
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impulse responses for the price variable were not substantially altered by the use of these
financial market data; the price response to a monetary policy contraction under the
alternative measures was negative, but not statistically significant, for the US and
Germany, while the inclusion of commodity prices seemed to be a necessary condition for
this observed pattern.

3. Enhancing the informational content of monetary VARs

This paper proposes a VAR specification that succeeds in solving the price puzzle by
taking advantage of the forward-looking informational content that some financial market
variables and other indicators can provide.

3.1. Measures of monetary policy expectations

Financial market instruments, especially those related more closely to short-term

interest rates, such as federal funds futures or forward contracts, reflect market
expectations about monetary policy changes and thus, implicitly, expectations about
short-term developments in a number of variables to which monetary policy responds. By
including the price of these instruments in a VAR, we are able to obtain a more realistic
account of the information available to the Fed at the time its policy decisions are made.
The ability of markets to anticipate policy actions has increased3,4 significantly during the
past 15 years as a result of the greater openness, accountability and transparency of
monetary policy.
We use two measures of monetary policy expectations. First, the federal funds futures
rate5 which holds a prominent position among other forward-looking variables in the
recent literature because it provides market-based expectations about the stance
of monetary policy that seem to be relatively unclouded by time-varying term premia
or non-federal-funds-market idiosyncratic movements (Rudebusch, 1998)6. At the
same time, rates implied by federal funds futures contracts, representing market’s

(footnote continued)
shocks and shocks derived from a VAR model was not sufficiently high to advocate the use of the latter as a
measure of monetary policy shocks.
3
Lange et al. (2001), among others, argue that market yields are characterized by an increasing ability to predict
monetary policy moves in advance, while their response to contemporaneous policy changes has diminished.
Poole and Rasche (2000) and Kuttner (2001) used data from the federal funds futures market to estimate whether
this market had anticipated the Fed’s actions. Their study looked at the reaction of the federal funds futures rate
on days when the Fed changed the federal funds rate target. In this way, they estimated the extent to which the
market was surprised by the Fed’s actions, and argued that markets tend to successfully forecast future monetary
policy.
4
Several institutional changes have contributed to the increased ability of markets to better anticipate US
monetary policy, including the shift away from the borrowed reserves operating regime toward strict federal funds
rate targeting as well as the provision of more information by the Federal Reserve in recent years regarding its
policy decisions and their rationale.
5
The market for the federal funds futures was established in 1988 at the Chicago Board of Trade and current-
month and one- to five-month-ahead contracts are traded in this market.
6
Gürkaynak et al. (2002) show that the federal funds futures rate dominates all market interest rates in
forecasting near-term changes in the federal funds rate. They also show that the risk premia embedded in other
instruments, that could be used alternatively to the federal funds futures, are more sizable as these instruments
additionally incorporate the credit risk associated with loans having maturities longer than overnight.
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expectations about future policy actions, provide potentially useful information to

the Fed’s policy makers. Second, an alternative measure of monetary policy expectations
is used which can be obtained from the short end of the money market yield curve
under the assumption that the expectations theory of the term structure is approximately
true.

3.2. Measures of future economic activity

The inclusion of a measure of the expected path of economic activity as summarized by a

composite leading indicator can be an additional response to the argument that the
information set available to policy makers may include several forward-looking variables.
Being a weighted average of a number of forward-looking and coincident indicators—that
include inter alia manufacturing employment, confidence indicators, measures of new
orders in the manufacturing sector, a monetary aggregate and the term spread—related to
future economic activity and thus indirectly to inflation expectations, it allows the
incorporation in a VAR of a large amount of contemporaneously available information
without unduly increasing its dimension.

4. Empirical analysis

We extend a standard VAR model by including the expected value of the federal
funds rate implied by the one-month futures contract (written on this rate) along with
a leading indicator of aggregate economic activity. We show that a shock to the
federal funds rate conditional on its expected value obtained from the futures market
and on the information included in the other variables of the VAR provides a
sharper measure of the monetary policy shock, on the assumption that the Fed has at
its disposal at least as much information as markets do7. To confirm our empirical results
for the whole period of strict federal funds rate targeting we use, alternatively to the federal
funds futures rate, a one-month forward rate derived from the short end of the term
structure.
We start by estimating a four-variable system including industrial production (INDP) as
a proxy for economic activity, consumer prices (CPI), a commodity price index (COMP)
for primary goods and the federal funds rate (FFR) as the monetary policy instrument. We
use monthly data for the period 1989:1–2004:6, which corresponds to a homogeneous
monetary policy regime under the Greenspan chairmanship. As indicated by the impulse
responses presented in Fig. 1 the system is characterized by a strong counter-theoretical
response of CPI to the monetary policy shock8.
We next proceed to estimate an alternative system, which includes variables that
enhance its forward-looking informational content. Specifically, along with INDP and
CPI, we also include, as an endogenous variable, the composite index of leading indicators
7
The Fed is obviously better at processing and interpreting information as it commits far more resources to
forecasting than even the largest commercial forecasters (Romer and Romer, 2000) and also has inside
information about future monetary policy.
8
We also estimated a seven-variable VAR similar to the one suggested by Christiano et al. (1999) and Kim
(2001) including industrial production, consumer prices, a commodity price index, the federal funds rate, total and
non-borrowed reserves and a broad monetary aggregate (M2) with no significant gains in terms of dealing with
the price puzzle.
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Response of COMP to FFR Response of INDP to FFR

0.008 0.004

0.002
0.006
0.000

0.004
-0.002

0.002 -0.004

-0.006
0.000
-0.008

-0.002 -0.010
5 10 15 20 25 30 35 40 45 5 10 15 20 25 30 35 40 45

Response of CPI to FFR Response of FFR to FFR

0.005 0.5

0.4
0.004
0.3
0.003
0.2

0.002 0.1

0.0
0.001
-0.1
0.000
-0.2

-0.001 -0.3
5 10 15 20 25 30 35 40 45 5 10 15 20 25 30 35 40 45

Fig. 1. Impulse responses to a FFR shock—Baseline system (1989:1–2004:6).

(LCOM)9 published by the Conference Board (a component of which is the index of

commodity prices) and, as an exogenous variable, the expected federal funds rate for the
current month (FFF) as implied by the price of the one-month-ahead futures contract
written on this rate at the last business day of the previous month.
The system is estimated again with monthly data for the same period 1989:1–2004:6, as
under the baseline system. In selecting this period, we are constrained by the availability of
data for the federal funds futures. As suggested by the relevant lag selection criteria
(Akaike Information Criterion, Schwartz Bayesian Criterion) we use six lags. The Wold
ordering used for the identification of shocks (i.e. {LCOM, INDP, CPI, FFR}) allows for a
contemporaneous response of the policy rate to innovations in output, CPI and the
composite leading indicator. The choice of this ordering is motivated by the fact, that the
Fed collects and publishes the data for INDP, thus having contemporaneous information
about the level of this variable (Croushore and Evans, 2003). The contemporaneous
response of monetary policy to incoming information about developments in the price

9
Given that information about some of the variables comprising this index is available only with a lag that
exceeds, in many cases, 15 days since the end of the month under consideration, this variable is used with a one-
month lag.
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level is also plausible in view of the importance of this variable as a policy target and the
large amount of resources channeled in forecasting it. The expected federal funds rate in
the previous month as implied by the federal funds futures is included as an exogenous
variable in order to bring its informational content into the analysis without conditioning
this expected value on the information set of the VAR.
The orthogonalized residuals of the FFR equation are identified as the monetary policy
shock. Fig. 2 reports, over a period of 48 months, the impulse responses of the system’s
variables to a one standard deviation shock in the FFR equation. The main results of this
contractionary shock on the other variables in the system can be summarized as follows.
The maximum response of the FFR to a shock in itself occurs contemporaneously and is
smaller in magnitude than the one obtained from other VAR systems used for monetary
policy analysis, like the Christiano et al. (1999) specification. More importantly, the shock
dies out very quickly, 4–5 months after the initial impulse so that there is no policy
innovation paradox.
The price puzzle is solved—a small, but not statistically significant positive response
appears for the first 2–3 months—as the price level declines gradually to reach a trough 30
months after the initial shock. The decline becomes significant after 14 months. Finally,
INDP declines steadily after the second month to reach its lowest level 5–6 months later,
and returns to its pre-shock level 2 years after the policy impulse. The dynamic path of the

Response of LCOM to FFR Response of INDP to FFR

0.002
0.004
0.001

0.000 0.002

-0.001
0.000
-0.002
-0.002
-0.003

-0.004 -0.004
5 10 15 20 25 30 35 40 45 5 10 15 20 25 30 35 40 45

Response of CPI to FFR Response of FFR to FFR

0.16

0.000 0.12

0.08
-0.001

0.04
-0.002
0.00

-0.003 -0.04
5 10 15 20 25 30 35 40 45 5 10 15 20 25 30 35 40 45

Fig. 2. Impulse responses to a FFR shock—System with FFF (1989:1–2004:6).

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Baseline system System with implied forward rate

0.004 0.002
0.001
0.003 0.000
-0.001
0.002 -0.002
-0.003
0.001
-0.004
-0.005
0.000
-0.006
-0.001 -0.007
5 10 15 20 25 30 35 40 45 5 10 15 20 25 30 35 40 45

Fig. 3. Impulse responses of CPI to a FFR shock (1986:1–2004:6).

INDP index follows, with a 1–2 month lag, the dynamic pattern of response of the
composite index of leading indicators to the policy shock.
Alternatively, we replace the expected FFR obtained from the federal funds futures with
the respective forward rate derived on the basis of a two-month interbank rate (Libor) and
the current-month average effective FFR. The inclusion of the implied forward rate
enables us to assess the robustness of our results to an alternative measure of monetary
policy expectations and also to extend our estimation to the period before the operation of
the federal funds futures market. We derive the implied one-month forward rate as the
difference between the two-month Libor on deposits denominated in US dollars and the
monthly average of daily observations on the effective FFR during the first of the two
months10:

ff rt;tþ1 ¼ 2
it1  ff rt , (1)

where ff rt;tþ1 is the expected in period t average effective FFR for the period t+1, it1 is the
two-month Libor rate on the last business day of period t1, and ff rt is the average
effective FFR during period t.
The use of the implied one-month forward rate in the VAR system in place of the federal
funds futures rate also helps deal with the price puzzle. After a short-lived initial positive
response of the price level to a contractionary monetary policy shock, which is not
statistically significant, the price level decreases gradually remaining below its baseline path
until the end of the time horizon. However, the price level response becomes statistically
significant several months after it turns into negative values. Similar results, shown in
Fig. 3, are derived from the estimation of the VAR including the implied forward rate for
the period 1986:1–2004:611.

10
Longstaff (2000) argues that term rates at the extreme short end of the term structure are almost unbiased
estimates of the average overnight rate. Thus, the monthly average of daily observations on the federal funds rate
may be considered as a good approximation to the one-month Libor rate despite the somewhat larger risk premia
associated with Libor rates which are due to the lower credit quality of the participants in the eurodollar market
(Gürkaynak et al., 2002).
11
January 1986 is the earliest date for which data on two-month Libor rates is available from Datastream.
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5. Conclusions

This paper proposes a VAR specification that helps solve the price puzzle featuring in
VAR models of monetary policy transmission in the US. This specification addresses the
main shortcomings of the standard VAR monetary policy reaction function: the restricted
information set and the absence of any forward-looking element in it. In this respect, we
showed that by augmenting a standard VAR with a measure of monetary policy
expectations (obtained either from federal funds futures or from the short end of the term
structure) and a composite leading indicator of economic activity, we are able to obtain
plausible impulse responses to monetary policy innovations.
The greater openness and transparency that characterize monetary policy-making
during the last 15 years have increased the ability of the markets to anticipate policy
actions. In particular, financial market instruments, such as the federal funds futures,
emerge as effective means for incorporating in a parsimonious way a large amount of
information in VARs, thus avoiding constraints related to the dimension of the system and
to difficulties in modeling directly forward-looking behavior.
The VAR including the two alternative measures of monetary policy expectations along
with a composite leading indicator of economic activity was estimated on US data for the
period of federal funds rate targeting. The empirical results showed that the VAR
incorporating expectational variables is free of the price puzzle plaguing standard VAR
specifications.

Appendix A. Data sources

All data series are monthly, beginning in 1986:1 and ending in 2004:6. Data on industrial
production (INDP), consumer prices (CPI), commodity prices (COMP) and the federal
funds rate (FFR), are all from the Federal Reserve System’s Database (FRED). Data on
the one-month federal funds futures rate (FFF) (that begin in 1989:1), the two-month
Libor rate on US dollar deposits and the Conference Board’s US leading index (LCOM)
were taken from Datastream.

References

Bagliano, F.C., Favero, C.A., 1998. Measuring monetary policy with VAR models: an evaluation. European
Economic Review 42, 1069–1112.
Bagliano, F.C., Favero, C.A., 1999. Information from financial markets and VAR measures of monetary policy.
European Economic Review 43, 825–837.
Bernanke, B.S., Boivin, J., 2003. Monetary policy in a data-rich environment. Journal of Monetary Economics 50,
525–546.
Bernanke, B.S., Mihov, I., 1998. Measuring monetary policy. Quarterly Journal of Economics 113, 869–902.
Brunner, A.D., 2000. On the derivation of monetary policy shocks: should we throw the VAR out with the bath
water? Journal of Money, Credit, and Banking 32, 254–279.
Christiano, L.J., Eichenbaum, M., Evans, C.L., 1999. Monetary policy shocks: what have we learned and to what
end? In: Taylor, J.B., Woodford, M. (Eds.), Handbook of Macroeconomics, vol. 1A. Elsevier, Amsterdam, pp.
65–148.
Croushore, D., Evans, C.L., 2003. Data revisions and the identification of monetary policy shocks. Federal
Reserve Bank of Philadelphia Working Paper No. 03-1.
Eichenbaum, M., Evans, C.L., 1995. Some empirical evidence on the effects of shocks to monetary policy on
exchange rates. Quarterly Journal of Economics 110, 975–1009.
 ARTICLE IN PRESS
1234 S.N. Brissimis, N.S. Magginas / Journal of Monetary Economics 53 (2006) 1225–1234

Gordon, D.B., Leeper, E.M., 1994. The dynamic impacts of monetary policy: an exercise in tentative
identification. Journal of Political Economy 102, 1228–1247.
Gürkaynak, R.S., Sack, B., Swanson, E., 2002. Market-based measures of monetary policy expectations. Finance
and Economics Discussion Series 2002-40. Federal Reserve Board, Washington, DC.
Judd, J.P., Rudebusch, G.D., 1998. Taylor’s rule and the Fed: 1970–1997. Federal Reserve Bank of San Francisco
Economic Review 98-03, 3–16.
Kim, S., 2001. International transmission of U.S. monetary policy shocks: evidence from VAR’s. Journal of
Monetary Economics 48, 339–372.
Kuttner, K.N., 2001. Monetary policy surprises and interest rates: evidence from the Fed funds futures market.
Journal of Monetary Economics 47, 523–544.
Lange, J., Sack, B., Whitesell, W., 2001. Anticipations of monetary policy in financial markets. Mimeo. Board of
Governors of the Federal Reserve System.
Longstaff, F.A., 2000. The term structure of very short-term rates: new evidence for the expectations hypothesis.
Journal of Financial Economics 58, 397–415.
Poole, W., Rasche, R.H., 2000. Perfecting the market’s knowledge of monetary policy. Journal of Financial
Services Research 18, 255–298.
Romer, C.O., Romer, D.H., 2000. Federal Reserve information and the behavior of interest rates. American
Economic Review 90, 429–457.
Rudebusch, G.D., 1998. Do measures of monetary policy in a VAR make sense? International Economic Review
39, 907–931.
Sims, C.A., 1992. Interpreting the macroeconomic time series facts: the effects of monetary policy. European
Economic Review 36, 975–1000.
Strongin, S., 1995. The identification of monetary policy disturbances: explaining the liquidity puzzle. Journal of
Monetary Economics 35, 463–497.