The dynamic relationship between the federal funds rate and the Treasury bill rate: an empirical investigation

DISCUSSION PAPER SERIES

ZZZFHSURUJ

Available online at:

www.cepr.org/pubs/dps/DP3225.asp

www.ssrn.com/xxx/xxx/xxx

No. 3225

THE DYNAMIC RELATIONSHIP

BETWEEN THE FEDERAL FUNDS

RATE AND THE TREASURY

BILL RATE: AN EMPIRICAL

INVESTIGATION

Lucio Sarno and Daniel L Thornton

ISSN 0265-8003

THE DYNAMIC RELATIONSHIP

BETWEEN THE FEDERAL FUNDS

RATE AND THE TREASURY

BILL RATE: AN EMPIRICAL

INVESTIGATION

Lucio Sarno, Warwick Business School and CEPR

Daniel L Thornton, Federal Reserve Bank of St Louis

Discussion Paper No. 3225

February 2002

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CEPR Discussion Paper No. 3225

February 2002

ABSTRACT

The Dynamic Relationship Between the Federal Funds

Rate and the Treasury Bill Rate: An Empirical Investigation*

This article examines the dynamic relationship between two key US money

market interest rates – the federal funds rate and the 3-month Treasury bill

rate. Using daily data over the period from 1974-99, we find a long-run

relationship between these two rates that is remarkably stable across

monetary policy regimes of interest rate and monetary aggregate targeting.

Employing a non-linear asymmetric vector equilibrium correction model, which

is novel in this context, we find that most of the adjustment toward the long run

equilibrium occurs through the federal funds rate. In turn, there is strong

evidence for the existence of significant asymmetries and non-linearities in

interest rate dynamics that have implications for the conventional view of

interest rate behaviour.

JEL Classification: E43

Keywords: equilibrium correction, interest rates, non-linear dynamics and term

structure

Lucio Sarno

Finance Group

Warwick Business School

University of Warwick

Coventry

CV4 7AL

Tel: (44 24) 7652 8219

Fax: (44 24) 7657 2871

Email: lucio.sarno@warwick.ac.uk

For further Discussion Papers by this author see:

www.cepr.org/pubs/new-dps/dplist.asp?authorid=138519

Daniel L Thornton

Vice-President

Research Division

Federal Reserve Bank of St Louis

PO Box 442

St Louis MO 63166-0442

USA

Tel: (1 314) 444 8582

Fax: (1 314) 444 8731

Email: daniel.l.thornton@stls.frb.org

For further Discussion Papers by this author see:

* This Paper was begun while Lucio Sarno was a Visiting Scholar at the

Federal Reserve Bank of St. Louis. We are grateful to Tony Courakis, Mike

Dueker, Oscar Jorda, Adrian Pagan, Douglas Pearce, Bob Rasche, John

Seater, Giorgio Szego, Mark Taylor, Timo Terasvirta, and participants of

seminars at the University of Oxford, the University of Warwick and the Bank

of England for helpful comments. Stephen Majesky and Rachel Mandal

provided excellent research assistance. Any remaining errors are solely the

authors’. The views expressed do not necessarily reflect the views of the

Federal Reserve Bank of St. Louis or the Board of Governors of the Federal

Reserve System.

NON-TECHNICAL SUMMARY

Interest rates tend to move together. The nature of the forces that bind interest

rates together is not fully understood, however. This Paper investigates the

relationship between two important short-term interest rates in US financial

markets – the overnight federal funds rate and the 3-month Treasury bill (or

T-bill) rate. The importance of these two interest rates is widely recognized. The

Federal Reserve (Fed) implements monetary policy by targeting the effective

federal funds rate; the 3-month T-bill rate is the preeminent default-risk-free

rate in the US money market, and is often used by researchers to proxy the

risk-free asset whose existence is assumed by much conventional finance

theory. Given their importance and visibility, it is not surprising that these

interest rates have been studied extensively in economics and finance (see,

inter alia, Hall, Anderson and Granger, 1992; Taylor, 1993; Rudebusch, 1995,

1998; Anderson, 1997; Enders and Granger, 1998; Stock and Watson, 1999).

A number of authors have argued that the federal funds rate and the T-bill rate

move together because they are linked by the expectations hypothesis (EH)

(eg, inter alia, Cook and Hahn, 1989; Goodfriend, 1991; Poole, 1991;

Rudebusch, 1995, 2001; Woodford, 1999). That is, the T-bill rate is equal to

the market’s expectation for the federal funds rate over the term of the T-bill

rate plus a risk premium. Empirical support for the EH is generally weak (eg,

Campbell, Lo and MacKinlay, 1997). This is particularly true when the

short-term rate is the effective federal funds rate (see, inter alia, Simon, 1990, 1994;

Roberds, Runkle and Whiteman, 1996; Thornton, 2000). Nevertheless,

regardless of whether the EH holds, the empirical literature provides evidence

that these rates co-move in the long run.

The objective of the present study is to gain some insights into the dynamic

relationship between the federal funds rate and the T-bill rate. Rather than

hypothesizing and testing the implications of a particular hypothesis or theory

of interest rate behaviour, the approach taken in this Paper is agnostic. We

investigate the dynamic relationship using a model that relies solely on the

fact that the interest rates examined co-move in the long run.

empirical model that allows for both asymmetries and non-linearities in a fairly

comprehensive fashion.

Using daily data on the effective federal funds rate and the 3-month T-bill rate

for the sample period from 1974 to 1999, we find a long-run relationship

between the federal funds rate and the T-bill rate that is stable over the

sample period and across monetary policy regimes, although this relationship

is not consistent with all of the implications of the EH. We also find a general

non-linear, asymmetric dynamic model that is temporally stable and

significantly outperforms a number of alternative models.

Our most unexpected result is that the adjustment toward the long-run

equilibrium largely occurs through movements in the federal funds rate rather

than the T-bill rate. We note that, prima facie, this finding appears to be

inconsistent with the conventional EH/monetary policy view that the federal

funds rate ‘anchors’ the short end of the US money market. We discuss

circumstances that could reconcile the conventional EH/monetary policy

interpretation with our results.

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