Technical Paper Series

Macroeconomic Analysis and Tax Analysis Divisions

Congressional Budget Office

Washington, D.C.

Draft Framework for Determining the 

Spreads of Commercial Paper Rates and 

LIBOR to the Rate on Three Month Treasury Bills

 and the Volatility of those Interest Rates

Robert Arnold, Angelo Mascaro, Matthew Salomon

with the research assistance of David Arnold

Macroeconomic Analysis Division

Congressional Budget Office

July 1999

1999-7

Technical papers in this series are preliminary and are circulated to stimulate

discussion and critical comment. The analysis and conclusions expressed in

these papers are those of the authors and do not necessarily represent the

position of the Congressional Budget Office. References in publications should

be cleared with the authors. Papers in this series can be obtained by sending an

email to techpapers@cbo.gov.
-iiTable of Contents

INTRODUCTION 1

BACKGROUND ON THE ALTERNATIVE RATES 2

Market Size and Major Characteristics

Treasury Bills 2

Commercial Paper 3

London Interbank Dollar Deposits (LIBOR) 3

Determinants of Yields and Spreads of the Alternative Rates 4

Treasury Bill Rates 6

Commercial Paper Rates 6

LIBOR 7

Why Spreads Have Narrowed 10

Determinants of Volatility of the Alternative Rates 11

PROJECTIONS OF THE SPREADS 13

How CBO Currently Projects Rates 13

A Model for Projecting Commercial Paper Rates and LIBOR 14

One-month Commercial Paper—Three-month Treasury Bill Spread 15

Three-month Commercial Paper—Three-month Treasury Bill Spread 16

One-month LIBOR - Three-month Treasury Bill Spread 17

Three-month LIBOR - Three-month Treasury Bill Spread 19

Spreads of Eurodollar Deposit Rates to Three-month Treasury Bill Rates 20

Forecast of Volatility of Alternative Instruments 22

Uncertainty Associated with Explanatory Variables 23

Uncertainty Associated with the Alternative Rates 24

Probabilities Associated with Alternative Rates 24

TECHNICAL APPENDIX: 

ESTIMATION METHODOLOGY AND ECONOMETRIC DETAIL 25
-iiiTABLES

1. Relative Size of Markets 2

2. British Bankers’ Association List of 16 Banks Used to Construct LIBOR 5

3. Spread to Three-Month Treasury Bill Rate of Alternative Short-Term Rates 5

4. Volatility and Level of Commercial Paper Rate and LIBOR to Treasury Bill Rate 11

5. Average Spreads of LIBOR to Eurodollar Deposit Rates 19

6. Illustrative Baseline for Commercial Paper Rate, LIBOR, and Eurodollar Rates 21

7. Average Levels of Determining Factors 22

8. Illustrative Probabilities for Alternative Interest Rates 25

APPENDIX TABLES

1 Ordinary Least Squares Estimates of Interest Rate Spreads 28

2. Autoregressive Conditional Heteroskedastic Model of Squared Residuals 29

3. Generalized Least Squares Estimates of Interest Rate Spreads 30

FIGURES

1. Percentage Distribution of Issuers of Commercial Paper 3

2. Distribution of Holder Of Commercial Paper 4

3. Spreads of 3-Month and 1-Month Commercial Paper Rates to 3-Month Treasury Bill 7

4. Spreads of 1-Month LIBOR and Commercial Paper to 3-Month Treasury Bill 8

5. Spreads of 3-Month LIBOR and Commercial Paper to 3-Month Treasury Bill 8
-ivFIGURES - con’t

6. Spreads of Fedfunds and 1-Month LIBOR and Commercial Paper to 3-Month TBill 9

7. One and 3-Month Spreads between LIBOR and Commercial Paper 10

8. Volatility of Spreads to TBill, 1972Q1 - 1998Q4 12

9. Inflation and the Volatility of the 1-Month LIBOR to 3-Month Treasury Bill Spread 13

10. Spread of 1-Month Commercial Paper versus 3-Month Treasury Bill 16

11. Spread of 3-Month Commercial Paper versus 3-Month Treasury Bill 17

12. Spread of 1-Month LIBOR versus 3-Month Treasury Bill 18

13. Spread of 3-Month LIBOR versus 3-Month Treasury Bill 18

14. Spread of 1-Month Eurodollar versus 3-Month Treasury Bill 19

15. Spread of 3-Month Eurodollar versus 3-Month Treasury Bill 20
1

INTRODUCTION

The Higher Education Amendments of 1998 direct CBO and other organizations to participate in a

study group which shall evaluate the spread between each of the 30-day and 90-day commercial

paper rates, and the 90-day London Interbank Offered Rate (LIBOR) to the 91-day Treasury bill rate.

The study group, chaired by the Comptroller General (GAO) and the Secretary of Education, has

asked CBO to present an illustration of its projections of these spreads as well as that between 30-

day LIBOR and the 91-day Treasury bill rate. The study group has also asked CBO to present

illustrations of probability ranges for the levels of commercial paper, London interbank, and

Treasury bill rates which would emerge from these projections. The levels and volatilities of these

interest rates would be used in CBO's probability scoring of proposed changes to the federal studentloan programs. Under current legislation due to expire in 2003 federal student loan programs use

the 91-day Treasury bill rate in the context of various formulas that establish payments by students,

receipts by lenders, and special allowance payments by the federal government. Though CBO makes

projections of the 91-day Treasury bill rate, it currently makes no projections of the alternative rates

considered here. The CBO did prepare one-time projections of rates on commercial paper and

LIBOR in 1997, however, when these rates were first proposed as alternatives to Treasury interest

rates for use in the Federal Student Loan program.

This paper provides illustrative projections for the spreads of one- and three-month commercial

paper rates and one- and three-month London interbank offer rates (LIBOR) to the interest rate on

three-month Treasury bills. Projections are also included for spreads of one- and three-month

Eurodollar rates to the rate on three-month Treasury bills. The projections are illustrative because

CBO does not currently make forecasts for commercial paper and LIBOR. The projections are

consistent with the economic assumptions discussed in the Congressional Budget Office's January

1999 outlook, The Economic and Budget Outlook: Fiscal Years 2000-2009.

The paper provides a brief background on the instruments, a discussion of the determinants of

the spreads and their volatility, a summary of the quantitative procedures developed for the

illustrative projections, and a summary table that consolidates information on the projections for

commercial paper and LIBOR, given the outlook for Treasury bill rates from CBO's January 1999

budget outlook. Following that is a description of CBO's methodology for developing probability

bands around the baseline outlook, and illustrative results for the interest rates examined in the

paper. A technical appendix provides additional discussion of the methodology and presents

econometric information on the projection equations.

The paper is being issued in draft form to solicit comment prior to issuing a final version. It is

being distributed to staff of the Committee on Education and the Workforce of the U.S. House of

Representatives and the Committee on Health and Education of the U.S. Senate, members of the

federal student loan working group, CBO’s panel of economic advisers, and other interested

individuals and organizations.
2

BACKGROUND ON THE ALTERNATIVE RATES

Market Size and Major Characteristics

Treasury bills, commercial paper, and London interbank deposits of U.S. dollars are all instruments

of the money market--that segment of the capital market encompassing short-term financial

instruments. The money market gives issuers a flexible debt-management tool for smoothing cash

flows and managing various balance-sheet exposures. It gives holders a financial asset with cashlike properties to better manage investment portfolios.

Of the markets for the three instruments, the largest is that for commercial paper (see Table 1).

It became the largest of the three markets in the late 1980s, spurred on by the surge in financial

intermediation and innovation. Once the largest of the three as measured by the dollar volume

outstanding, the Treasury bill market has fallen to second place and could fall behind the London

interbank dollar market within the next decade if federal surpluses persist. The London interbank

dollar market is about one-half the size of the commercial-paper market and is growing more slowly.

Since 1980, the London interbank market has grown at about 5.2 percent per year compared with

growth in the commercial paper market of 10.9 percent per year. It is uncertain how future growth

of the London interbank dollar market will be influenced by the launching of the Euro and other

aspects of the monetary unification in Europe. 

 Table 1. Relative Size of Markets ($billions)

Treasury Bills

Commercial Paper

Outstanding

London Interbank

Dollar Deposits

1970: 76 33 48

1980: 200 164 195

1990: 482 610 397

1997: 715 958 487

1998: 691 1,161 494

Sources: Treasury Bills: Economic Report of the President; Commercial Paper: Flow of Funds

Accounts; London Interbank Dollar Deposits: Bank for International Settlements Forty-Fifth

Annual Report for 1970, and Bank of England, Monetary & Banking Statistics for other years.

Treasury Bills

Treasury bills are issued by the Federal government as a means of financing deficits, in maturities

of 13, 26, and 52 weeks, and in denominations of up to $1 million. Treasury bills are distinguished

from other money market instruments by their perception as an instrument free from default or credit

risk, and as having a high degree of moneyness or liquidity--their ready acceptability by a wide

variety of investors here and abroad and their easy resale ability in turbulent markets as well as
3

during normal economic and financial conditions. Though a breakdown of overall Treasury-debt

ownership is available, no regularly available breakdown of holders of Treasury bills exists.

Commercial Paper

Commercial paper is issued in maturities up to 270 days (longer maturities would trigger registration

requirements of the Securities and Exchange Commission), in amounts ranging upwards of several

million dollars. Issuers mostly include funding corporations of nonfinancial firms, finance

companies, issuers of asset-backed securities, funding subsidiaries of banks, and analogous foreign

entities (see Figure 1). Holders include money market mutual funds (which tend to dominate),

retirement-type entities (trusts, public and private pensions, and insurance), banks, corporations, and

various foreign entities including foreign governments and central banks (see Figure 2).

Figure 1. Percentage Distribution of Issuers of Commercial Paper as a Percentage of all Commercial Paper

NOTE: “Other” includes Commercial Banking and REITs; ABS = Asset Backed Securitizers.

London Interbank Dollar Deposits

London interbank deposits of U.S. dollars are funds placed in large amounts at fixed maturities in

international banks in London and loaned and borrowed among those banks in what is called the

interbank market. The deposits themselves--known as Eurodollar deposits--come originally from

other financial institutions, large corporations, individuals, and governments. The lending and

borrowing of these deposits among banks, which is the defining characteristic of this market, mostly

reflects cash- and risk-management activities by individual banks in relation to their domestic and

international operations.
4

Figure 2. Percentage Distribution of the Holders of Commercial Paper

NOTE: “Other” includes Nonfinancial Corporate Business, Monetary Authority, Commercial Banking, Savings

Institutions, Credit Unions, Bank Personal Trusts and Estates, Private Pension Funds, State and Local

Government Retirement Funds, Government Sponsored Enterprises, and Brokers and Dealers.

SOURCE FOR FIGURES 1 & 2: CBO calculations based on data from the Federal Reserve Board of Governors.

Rates on London interbank dollar deposits are quoted on an offer and bid basis. The rate asked

by the lender is the offering rate--LIBOR for London interbank offered rate, and the rate on funds

wanted by the borrower is the bid rate--LIBID for London interbank bid rate.

The British Bankers' Association compiles a measure of LIBOR from a sample list of participants

that changes as conditions warrant. The 1999 panel of contributing banks is shown in the following

table, along with each bank's home country (see Table 2).

Determinants of Yields and Spreads of the Alternative Instruments

Overall levels of interest rates on Treasury bills, commercial paper, and London interbank deposits

of dollars are determined by inflation and expectations of inflation and by overall conditions of

demand and supply in credit markets which, in turn, are importantly influenced by the stance of

monetary policy. In general, however, rates on Treasury bills tend to average lower (see Table 3).
5

Table 2. British Bankers' Association List of 16 Banks Used to Construct LIBOR

Bank Home Country

Bank of America

Chase Manhattan Bank

Citibank

United States

Abbey National

Barclays Bank

HSBC

Lloyds Bank

The Royal Bank of Scotland

National Westminster Bank

United Kingdom

Bank of Tokyo Mitsubishi

The Fuji Bank

The Norinchukin Bank

Japan

Credit Suisse First Boston

UBS

Switzerland

Deutsche Bank

Westdeutsche Bank

Germany

Source: British Bankers' Association

TABLE 3. Spread to Three-Month Treasury Bill Rate of Alternative Short-Term Rates

1960-1998 1971-1998 1980-1998 1985-1998

Commercial Paper:

1-month 0.48 0.53 0.55 0.46

3-month N.A. 0.39 0.36 0.41

LIBOR:

1-month 1.13 1.13 1.01 0.68

3-month N.A. 1.31 1.13 0.77

N.A. = not available

Source: CBO calculations based on data from Federal Reserve, London Financial Times.

Differences among interest rates on Treasury bills, commercial paper, and London interbank

deposits depend on factors influencing the comparative risk and return structures of the instruments.

These factors are determined by the characteristics of the participants who issue, market, and hold

the instruments and by the institutional and legal arrangements governing participants and markets.

Generally, the differences widen when inflation and inflation expectations increase, or when
6

monetary policy becomes tighter or more volatile. During these occasions, differences in riskiness

among the three instruments intensify with the result that spreads themselves widen. 

Treasury Bill Rates

Interest rates on Treasury bills are mostly influenced by inflation expectations and by overall

conditions of demand and supply in credit and goods markets, including perceptions about risk and

uncertainty. Interest rates on Treasury bills contain an inflation premium to compensate holders for

any expected loss of purchasing power. At the same time, however, Treasury bills probably have

little or no liquidity premium--compensation for holding bills instead of cash--because holders have

a ready market in which to sell Treasury bills should they need cash before the Treasury bills mature.

For large transactions, the bills themselves could be used for payment. Treasury bills also do not

contain a credit-risk premium--compensation to offset the chance the issuer might default-- owing

to the credit standing of the federal government. In fact, during turbulent times, the desire for safe

assets tends to produce unusually low interest rates on Treasury bills compared to money-market

instruments issued by private-sector entities.

Commercial Paper Rates

Interest rates on commercial paper are typically higher than rates on Treasury bills, mostly because

of liquidity and credit-risk premiums. While these premiums are not directly observable, their

presence is subsumed in the spread between commercial paper rates and Treasury bill rates (see

Figure 3).

The spread between commercial paper and Treasury bill rates widens when overall interest rates

rise, when inflation rises, and when monetary policy is tightened. The spread narrows when those

conditions are reversed. That is probably because high interest rates, high inflation, and tight

monetary policy tend to amplify the liquidity premium and credit-risk premium of commercial paper

compared to Treasury bills.

Interest rates on commercial paper are generally higher than rates on Treasury bills partly because

commercial paper is less liquid than Treasury bills-- commercial-paper holders might not readily find

a buyer should they wish to sell prior to maturity of their commercial-paper holdings. At the same

time, however, purchasers normally expect to hold commercial paper to maturity and the influence

of this lesser liquidity on the spread of commercial paper over Treasury bills is judged normally to

be small. As already noted, the liquidity premium varies with the monetary policy cycle, rising for

example when monetary policy tightens and reduces liquidity, and conversely.

Interest rates on commercial paper are also generally higher than rates on Treasury bills because

commercial paper rates contain a credit-risk premium--compensation holders demand because

issuers of commercial paper can encounter unexpected financial difficulties that might jeopardize

their solvency or at least their ability to honor their commercial paper obligations on time. The
7

economy's cyclical position influences the credit-risk premium, causing the spread to shrink during

periods of economic expansion when concerns for credit risk might lapse, and causing the spread

to rise abruptly during economic downturns when financial difficulties surface. 

Figure 3 Three-Month and One Month Commercial Paper Rates: Spreads vs. Rate on 3-Month T-Bill

SOURCE: CBO calculations based on data from the Federal Reserve Board of Governors.

NOTE: Shaded areas indicate US recessions.

Finally, the credit and liquidity premiums both tend to widen substantially when financial

markets move from normal to turbulent periods. In such times, potential holders become more risk

averse and seek safe haven in instruments such as Treasury bills.

LIBOR

Spreads between LIBOR and Treasury bills tend to be higher than those between commercial paper

and Treasury bills, though the gaps have narrowed over the past few years (see Figures 4 and 5).

Rates on London interbank dollar deposits do contain liquidity and credit-risk premiums like those

on commercial paper. As a result, they also should vary with overall interest rates, inflation, and

monetary policy. However, because the instruments in both markets are denominated in dollars, the

difference in the spreads probably stems from differences in participation and possibly location that

produce stronger liquidity and credit-risk premiums in rates on London interbank deposits than in

rates on commercial paper.
8

Figure 4. Spreads of 1-month LIBOR and 1-month Commercial Paper to 3-month TBill.

Figure 5. Spreads of 3-month LIBOR and 3-month Commercial Paper to 3-month T-bill.

Sources for Figures 4 and 5: Federal Reserve, British Bankers Association.

Three factors apparently have accounted for the higher spreads for LIBOR versus commercial

paper, though no systematic analysis has quantified the degree of their influence. First, the London

interbank market for dollar deposits is linked closely to the interbank market for Fedfunds--the

reserves banks have on deposit at the Federal Reserve and buy and sell among each other (see Figure
1. For additional discussion of regulatory effects see, Richard C. Marston, International Financial Integration: A Study

of Interest Differentials Between the Major Industrial Countries, (Cambridge, England: Cambridge University Press,

1995).

9

6). For example, a U.S. bank needing reserves to meet its regulatory requirement to hold reserves

in proportion to demand deposits can meet that requirement by borrowing Fedfunds from another

bank in the U.S. or by borrowing Eurodollars from a bank in London. London interbank dollars,

Fedfunds, and commercial paper all trade on an unsecured basis and this induces credit-risk

premiums in their interest rates relative to the rate on Treasury bill. However, banks typically

operate with much higher leverage than do nonbank financial institutions such as finance companies.

That higher leverage might produce higher credit-risk premiums for banks and thus for interbank

rates to the extent that banks are perceived to be riskier than participants in commercial paper. At

the same time, however, a participant in the London interbank market does have access to its home

country's central bank and that might be a mitigating factor in the bank premium. 

Figure 6. Spreads of Fedfunds, 1-month LIBOR and Commercial Paper to 3-month Treasury Bill Rate

Second, country risk may play an important role as well. A bank's home country might itself be

a source of risk because of its economic and financial circumstances, its regulatory policies, or its

political situation, any or all of which cause the bank to be willing to pay a premium for the funds

it borrows through the interbank market. As a result, this premium could influence the measure of

LIBOR compiled by averaging rates from banks with different home countries. The size of this

premium can be expected to vary through time.

Finally, banks have been subject to reserve requirements and deposit insurance premiums that

should also drive a wedge between LIBOR rates and commercial paper rates. However, research

attempting to determine the size of that effect has not shown it to be very significant.1
10

Why Spreads Have Narrowed

The LIBOR-TBill spreads have moved close to the commercial paper-Treasury bill spreads since the

early 1990s, resulting in a very narrow spread between LIBOR and commercial paper (see Figure

7). Since the early 1990s, the spread between LIBOR and commercial paper has averaged about 23

basis points for the 3-month spread and about 15 basis points for the 1-month spread.

Figure 7. One and Three Month Spreads Between LIBOR and Commercial Paper.

An important reason for the narrowing of the spread between LIBOR and commercial paper

probably stems from the favorable circumstances facing money markets. Throughout the 1990s,

monetary policy has become progressively more stable--the rate on Fedfunds has become less

volatile compared to past decades and the Federal Reserve has tended to provide more information

with which market participants can anticipate changes in monetary policy. With low volatility, the

overall liquidity and credit-risk premiums might have been reduced, narrowing differences in

liquidity and credit-risk premiums between London interbank and commercial paper rates. Another

reason might just be the low level of interest rates themselves that also has greatly benefitted money

markets and reduced spreads among short-term interest rates. 

Spreads between LIBOR and commercial paper have probably also narrowed as a result of the

closer integration of domestic and international financial markets. That integration was facilitated

by the technological advances in computers and telecommunications that have enabled issuers and

holders to shift among the Eurodollar market, the commercial paper market, and other money and

capital markets in such a way as to globalize money markets and reduce the spreads relative to the

past. Advances in finance have also played a role. For example, the rise in the interest-rate swaps

market has increased the connection between the commercial paper and London interbank markets.
11

Yet another factor in the narrowing of the LIBOR-commercial paper spread could be the lapse

of regulatory influences cited earlier. Reserve requirements imposed by the Federal Reserve on

funds borrowed abroad have been eliminated since 1990; and insurance premiums on bank deposits

have been reduced since the mid-1990s in response to the replenishment of insurance funds

administered by the Federal Deposit Insurance Corporation and the stronger capital position of

banks. No doubt other reasons can be found as well.

Determinants of Volatility of the Alternative Rates

A striking feature of the decline in spreads of commercial paper rates and LIBOR relative to the rate

on Treasury bills has been an associated decline the volatility of those spreads. Most of the decline

in volatility has occurred since the middle 1980s (see Table 4 and Figure 8).

Table 4. Volatility and Level of Commercial-Paper Rate and LIBOR Spreads to TBill Rate 1972-

1984 versus 1985-1998

Commercial Paper to 3-Month TBill

Rate

LIBOR to 3-Month TBill Rate

Volatility of

Spread*

One-Month Three Month One-Month Three-Month

1972-1984 0.32 0.24 0.51 0.55

1985-1998 0.12 0.13 0.15 0.15

Level of Spread

1972-1984 0.62 0.35 1.55 1.82

1985-1998 0.46 0.41 0.68 0.77

* Average of four-quarter, sample standard deviation of quarterly spread. 
2. For additional discussion see Testimony of Chairman Alan Greenspan, "the Federal Reserve's semiannual

monetary policy report," Committee on Banking, Housing, and Urban Affairs, U.S. Senate, July 18, 1996.

12

Figure 8. Volatility of Spreads to TBill 1972Q1- 1998Q4 (volatility is defined in Table 3)

What explains the decline in the volatility of the spreads? It is unlikely to be due to financial

market developments alone. In fact, such financial-market events as the Asian financial turmoil,

the Russian debt default, and others have had opposite effects. Instead, a likely source of reduced

interest-rate volatility is the substantial decline in inflation which has helped to improve the overall

climate in financial markets. Its timing coincided with the decline in volatility, just as the surges in

inflation in the 1970s and early 1980s coincided with jumps in interest-rate volatility (see Figure 9).

Inflation affects interest-rate volatility through diverse channels. A sustained period of low

inflation helps financial markets to work more efficiently and leads businesses to focus on improving

productivity and operating efficiency. Eventually, profitability is improved, balance sheets are

strengthened, and perceived risks associated with investing for the long term are reduced, all of

which ultimately contribute to reduced volatility in asset returns and interest rates.2

 Thus, when

unanticipated shocks erupt, such as those in Asia and elsewhere, such companies that issue

commercial paper and such banks that borrow in the London dollar market are not perceived to be

in jeopardy. The associated interest rates do not react as adversely as otherwise, and volatility is

smaller.
13

Figure 9. Inflation and the Volatility of the 1-month LIBOR - 3-month TBill Spread

[Inflation = left scale; volatility = right scale.]

PROJECTIONS OF THE SPREADS

How CBO Currently Projects Interest Rates

CBO's budget outlook, prepared annually with an update at midyear, does not contain an outlook for

commercial paper rates or LIBOR but does contain an outlook for Treasury interest rates. The

budget outlook spans a horizon of 10 years. It consists of a short-term projection for a two-year span

adjoined with a medium-term projection for the remaining 8-year span. The 2-year projection

embodies an attempt to describe the likely evolution of the business cycle. It is usually quite close

to the Blue Chip consensus forecast. For the long-term projections, CBO does not try to project

cyclical movements but instead attempts to approximate typical relationships--taking account of the

possibility of booms and recessions. CBO uses historical data to identify trends in factors such as

the growth of the labor force, the rate of national saving, and the growth of productivity. For

Treasury interest rates, the projections are based on underlying trends of real interest rates and

inflation, and reflect CBO's baseline projections of government borrowing needs.

CBO prepared special projections of rates on commercial paper and LIBOR in 1997 when these

rates were first proposed as alternatives to Treasury rates for use in the Federal Student Loan

programs. For rates on commercial paper and LIBOR, the 2-year segment assumed an adjustment

from their current cyclical position to a level in the medium-term projection period that, in turn, was

determined by the historical average spread to the rate on 3-month TBill. The adjustment to the

historical average spread was assumed to have been completed within two years. The period over
14

which the historical average was calculated was from the early 1970s to late 1997, a period

encompassing shocks such as from the commercial paper default of Penn Central Railroad near the

start of the 1970s, the shift to floating exchange rates in the early 1970s, the oil shocks of the mid

and late 1970s, the default of the German bank Herstatt in mid-1974 that affected LIBOR, the

monetary policy shock of the late 1970s and the sovereign debt crisis of the early 1980s. Those

shocks affected both commercial paper and especially LIBOR spreads to Treasuries. 

The Asian-related turmoil of 1998 provided an important test for interest rates, however, one that

suggests the need to augment the approach taken in 1997 for determining spread of commercial

paper rates and LIBOR relative to the rate on the 3-month Treasury bill. During the turmoil, spreads

rose sharply but not to the extent observed during the 1970s to mid-1980s. That attenuated rise

partly reflects structural features cited earlier that have led to the closer integration of these two

segments of the money markets. Part of the attenuated rise also could reflect the confluence of

favorable cyclical circumstances--corporations and financial institutions had come a long way

towards rebuilding their finances just before the Asian turmoil hit and governments of the United

States, the United Kingdom, and Western Europe had worked hard to restore their finances as well.

That meant that borrowers in commercial paper and London interbank markets warranted roughly

similar credit-risk and liquidity premiums in the eyes of lenders. Historically though, industrial

economies have not always faced similar credit-risk premiums and some allowance must be made

for the possibility that cyclical circumstances--like those emerging during the Gulf War and

recession period of 1990-91--might occur which would have uneven effects on commercial paper

and London interbank markets and influence spreads.

A Model for Projecting Commercial Paper Rates and LIBOR

The structural approach taken here explains the decline in the spreads of commercial paper rates and

LIBOR to TBill rates, and the reduced volatility of those spreads, by taking into account the

fundamental factors affecting them. The approach works directly with the spreads, rather than the

levels of rates, because CBO's outlook already includes projections for the interest rate on 3-month

Tbills.

The most significant structural aspect affecting spreads favorably is the economy's overall

improvement. Compared to the 1970s and 1980s, inflation has subsided, interest rates have declined,

large federal deficits have lapsed, and monetary policy has been relatively stable. Those

improvements are carried into the projections made by CBO--inflation and interest rates remain

lower than in the past, the budget shows surpluses, and monetary policy continues to reflect this

improved outlook. Incorporating this improved macroeconomic environment will lower projected

spreads of both commercial paper rates and LIBOR relative to Treasury rates, and the spreads

between commercial paper and LIBOR instruments as well, so long as the economy's overall

improvement is expected to hold.

A second, related aspect of the economy's overall improvement--the decline in interest rate
15

volatility after the middle 1980s--affects the methodology of the approach. That decline remains

even after taking into account the role played by the determinants of the spread. To economic

statisticians, the observed change in volatility is referred to as "heteroskedasticity." Adjusting for

its presence with specific procedures of analysis will enable the use of a sufficiently long historical

sequence with which to detect quantitatively the role played by the determinants of the spread. In

addition, and as will explained later on, taking into account the decline in volatility through such

procedures will also improve estimates of the probability distribution of the range of variation in the

spreads.

The balance of this section provides qualitative discussion and graphical results of the approach

as applied to each spread, followed by a summary of results. The details of the statistical equations

for each spread appear in the technical appendix.

One-month Commercial Paper-3-month Treasury Bill Spread

The first spread for which an outlook is prepared is that for the one-month commercial paper to

three-month Treasury bill. An essential step in building a framework to project future values of the

spread is to relate its historical behavior to the factors already described as most likely to influence

it. One factor is the level of the TBill itself. Higher levels of the TBill rate would raise the spread,

to the extent that the credit risk of commercial paper is proportional to the level of the rate on Tbills.

Another factor is the stance of monetary policy which can be represented by the yield-curve spread

between long-term and short-term Treasury rates. Typically, the wider the yield-curve spread the

easier is monetary policy and the narrower is the spread between commercial paper and Tbill rates--

possibly also because an easy monetary policy eases perceptions of risk. A third factor is the rate

of inflation: the spread has tended to be high when inflation is high, probably because high rates of

inflation have, in the past, been associated with high levels of volatility in markets and presumably

heightened perceptions of credit risk. A fourth factor is volatility in the rate on federal funds as a

proxy for uncertainty about monetary policy. Historically, it has had smaller effects on commercial

paper rates than on London interbank dollar rates, probably because of the close connection between

interbank dollar markets here and in London. Incorporating monetary-policy uncertainty here as well

as in the LIBOR-Treasury bill rate spread is a way to take into account the possible effect of a more

stable monetary policy on the narrowed gap between London interbank and commercial paper rates.

The projection relation between the spread and the determining factors just described draws on

the historical data from 1971 to 1998. Data for that span are available for each of the four interest

rates to be analyzed. The span also encompasses diverse regimes for interest rates, inflation, the

stance and volatility of monetary policy, and the state of credit risk in banks and corporations who

participate in commercial paper and interbank markets. The diversity provides a reasonable test of

the usefulness of the framework for determining the spreads.

The projections also depend on projected values of the determining factors. Any departures of

those factors in CBO's projections from their historical averages would then show up as a departure
16

of the spread from its historical average. For example, over the period from 1970 to 1998, inflation

as measured by the consumer price index for all urban workers (CPIU), averaged about 5 percent.

In CBO's January 1999 outlook, inflation over the next decade is projected to average just over 2.5

percent or about one-half the level of past decades. That can be expected to influence the projections

of spreads to Treasury bill rates of rates on London interbank dollars and commercial paper

compared to what those spreads have been in the past.

An illustration of the approach, using as the determining factors the level of the Tbill, the yieldcurve (as measured by the difference between rates on 10-year Treasury notes and 3-month Tbill),

inflation, and monetary policy volatility (as defined in the annex of the Summary Table), is shown

in the following figure (see Figure 10). It depicts the level of the spread between the 1-month

commercial paper rate and the 3-month Treasury bill rate, the estimate of the level based on the

determining factors over 1971 - 1998, and the projection for the years 1999 to 2009. In the exercise,

the CBO's baseline of December 1998 is used for projections of the level of the Treasury bill rate,

the yield curve, and CPIU inflation. For monetary-policy uncertainty, the average level of Fedfundsrate volatility in the 1990-1998 period is used. It is much lower than in the past and the assumption

is that this relatively stable behavior of monetary policy will prevail.

Figure 10. Spread of 1-month Commercial Paper versus 3-month TBill

3-month commercial paper-3-month Treasury bill spread

The outlook for the spread between rates on 3-month commercial paper and 3-month Treasury bills

uses the same approach as before since both 1-month and 3-month commercial paper rates are

influenced by approximately similar factors. The equation for this spread (3-month commercial

paper - 3-month Treasury bill) uses the same variables as that for the previous spread (1-month

commercial paper - 3-month Treasury bill). In contrast to the past, when this spread averaged

smaller than the 1-month commercial paper, it predicts a fairly similar spread (see Figure 11). The

main reason is the absence in the forecast period of shocks like those of the mid-1970s and early

1980s that drove the 1-month commercial paper rate to much higher levels than the rate on 3-month
17

commercial paper.

Figure 11. Spread of 3-month Commercial Paper versus 3-month Treasury Bill Rates

One-month LIBOR - 3-month Treasury Bill Spread

The projection for the LIBOR-Treasury bill spread begins with the spread of the one-month LIBOR

to the three-month Treasury bill rate. A successful procedure must be able to explain the historical

behavior of the spread including the narrowing of the spread that was described earlier.

LIBOR-Tbill spreads should be influenced by the liquidity and credit-risk factors described

earlier. As also described earlier, the likely determining factors are the level of the Treasury bill rate,

the yield curve, inflation, and monetary-policy volatility. For example, fluctuations in the Tbill rate

should have a more pronounced influence on the LIBOR-Tbill spread than on the commercial paperTbill spread to the extent interbank credit and liquidity risk are more influenced by the overall

movement in interest rates. A steep yield curve also might affect the LIBOR-Tbill spread more to

the extent easier monetary policy has stronger effects on the interbank market. High levels of

inflation and higher monetary-policy volatility would also have stronger effects on credit-risk

premiums in interbank markets for reasons given earlier. Application of these determining factors

gives the following outlook for the LIBOR-Treasury bill rate spread (see Figure 12).
18

Figure 12. Spread of 1-month LIBOR versus 3-month Treasury Bill Rate

As can be seen above, the framework shows an ability to explain the LIBOR-Treasury bill spread

over all three decades, 1970s, 1980s, and 1990s. As a result, the determining factors go a long way

towards explaining why the LIBOR-commercial paper rate spread was wide before the 1990s, and

why the spread has narrowed in this decade.

Three-month LIBOR -3-month Treasury Bill Rate Spread

The corresponding outlook for the spread between rates on 3-month LIBOR and 1-month LIBOR

proceeds analogously to that of the 3-month and 1-month commercial paper spread and it is shown

here (see Figure 13): 

Figure 13. Spread of 3-month LIBOR versus 3-month Treasury Bill Rate
19

Eurodollar Deposit Spreads versus 3-month Tbill Rates 

Closely associated to LIBOR are Eurodollar deposits rates--the rates paid by banks in London and

elsewhere other than in the United States to corporations and other investors outside the interbank

community for deposits of dollar-denominated funds. Unlike LIBOR which is not available on a

regular and frequent basis in any U.S. government publication, an estimate of Eurodollar deposit

rates is made available, for reference purposes only, by the Federal Reserve on a daily basis in

maturities of one, three, and six months. The estimates published by the Federal Reserve are bid

rates for deposits quoted in London. Compared to LIBOR, rates on Eurodollar deposits have tended

to be slightly lower (see Table 5).

Table 5. Average Spreads of LIBOR to Eurodollar Deposit Rates (in percentage points)

LIBOR less Eurodollar: 1971-1998 1980-1998 1985-1998

One-Month Rates 0.09 0.13 0.12

Three-Month Rates 0.09 0.13 0.12

Since there may be interest in using rates provided by the Federal Reserve, spread equations for

one-month and three-month Eurodollar deposit rates to three-month Treasury bill rates have also

been estimated. In both cases, the framework is the same as that used for the LIBOR-Treasury bill

spreads. The results are shown in Figures 14 and 15 and included in the Summary table to follow.

Figure 14. One Month Eurodollar - T-Bill Spread
20

Figure 15. Three Month Eurodollar - T-Bill Spread
21

TABLE 6. Illustrative Baseline for Commercial Paper Rate, LIBOR, and

Eurodollar Rates using CBO Outlook of January 1999.

Spreads to 3-month Tbill of 1- and 3-month Rates for Commercial Paper, LIBOR, and Eurodollars

3-month

Treasury

Bill

1-month

Commercial

Paper Spread

3-month

Commercial

Paper Spread

1-month

LIBOR

Spread

3-month

LIBOR

Spread

1-month

 Eurodollar 

Spread

3-month

Eurodollar

Spread

1971-98 average 6.73 0.53 0.39 1.13 1.31 1.04 1.22

1998(actual) 4.79 0.63 0.58 0.78 0.77 0.66 0.66

1999 4.45 0.46 0.48 0.73 0.60 0.53 0.55

2000 4.50 0.44 0.45 0.74 0.65 0.56 0.59

2001 4.50 0.42 0.42 0.74 0.68 0.56 0.62

2002 4.50 0.42 0.42 0.74 0.68 0.56 0.62

2003 4.50 0.42 0.42 0.74 0.68 0.56 0.62

2004 4.50 0.42 0.42 0.74 0.68 0.56 0.62

2005 4.50 0.42 0.42 0.74 0.68 0.56 0.62

2009 4.50 0.42 0.42 0.74 0.68 0.56 0.62

Levels: 3-month Tbill, 1- and 3-month Rates for Commercial Paper, LIBOR, and Eurodollars

3-month

Treasury

Bill

1-month

Commercial

Paper

3-month

Commercial

Paper

1-month

 LIBOR 

3-month

LIBOR

1-month

Eurodollar

3-month

Eurodollar

1998(actual) 4.79 5.42 5.37 5.57 5.56 5.45 5.45

1999 4.45 4.91 4.91 5.18 5.05 4.98 5.00

2000 4.50 4.95 4.94 5.24 5.15 5.06 5.09

2001 4.50 4.92 4.93 5.24 5.18 5.06 5.12

2002 4.50 4.92 4.93 5.24 5.18 5.06 5.12

2003 4.50 4.92 4.93 5.24 5.18 5.06 5.12

2004 4.50 4.92 4.93 5.24 5.18 5.06 5.12

2005 4.50 4.92 4.93 5.24 5.18 5.06 5.12

2009 4.50 4.92 4.93 5.24 5.18 5.06 5.12

SOURCE:

Why do the long-run values in all cases fall below the historical averages? The main reason

stems from CBO's outlook. Compared to history, the Treasury bill rate is lower, the yield curve is

flatter, inflation is lower, and the volatility of the rate on Fedfunds is assumed to be lower (see Table

7).
22

Table 7. Average Levels of Determining Factors: 1971-1998 versus 1999-2009

3-month Tbill Treasury yield

curve

Inflation Fedfunds Volatility

1971-1998: 6.73 1.64 5.03 1.14

1999-2009: 4.50 0.87 2.61 0.72

Forecast of Volatility of Alternate Instruments

In order to estimate the cost associated with the federal student loan programs, CBO analysts require

knowledge of more than just the baseline path of interest rates. Since special allowance payments

to lenders are triggered if interest rates exceed certain predetermined thresholds during the projection

period, the cost of the program depends on both the baseline path of a particular interest rate and

on the volatility associated with that path. Therefore, any cost estimate for the student loan program

requires an estimate of both a mean and a variance for each interest rate. 

CBO used Monte Carlo simulations to estimate the uncertainty surrounding the baseline forecasts

of the alternate interest rates. Monte Carlo simulations are a technique of statistical inference used

to assess the uncertainty in estimates and projections of economic variables. A common application

would be to use this technique to approximate the sampling distribution of a test statistic, for

example, a parameter in a regression equation. In the current analysis, the method was used to

estimate the probability distribution associated with the baseline forecasts of LIBOR and commercial

paper rates.

The basic concept underlying the Monte Carlo simulations is relatively simple. It involves

constructing a large number of simulated (or hypothetical) projections of an economic variable, such

as an interest rate, and computing the distribution of the resulting projections. The baseline

forecasting equations--which determine each spread as a function of the 91-day Treasury bill rate,

the yield curve, CPI inflation, and a measure of interest rate volatility–are used to compute the

simulated forecasts. To model the uncertainty inherent in the future evolution of the alternate rates,

random variation is added to each equation via two channels. 

First, rather than being held to baseline levels, the explanatory variables in each equation were

simulated randomly. Doing so allows uncertainty about the future vagaries of the overall economy

to affect the spreads. Second, for each period of the simulation, each of the spread equations was

shocked using a random variable that is based on the historical properties of the residuals from that

equation. Each of the simulated forecasts starts at the same level and evolves according to the

baseline forecasting equation, but each incorporates a different path for the explanatory variables and

a different set of random shocks.
23

Uncertainty Associated With Explanatory Variables

CBO’s baseline projection for each alternate interest rate is determined by the baseline projection

wfor each of the explanatory variables in the equation. However, the future behavior of those

variables is not known with complete certainty. Indeed, the baseline projection is only one of an

infinite number of paths that the explanatory variables could follow in the coming years. To model

the uncertainty that stems from the explanatory variables, CBO calculated simulated paths for the

explanatory variables and then used those paths to calculate the simulated forecasts for the alternate

instruments.

When constructing a set of simulated projections, it is important that the projection for each

variable is consistent with the historical behavior of that variable and with the projections for all of

the other explanatory variables. To ensure both types of consistency, one must use a model, or

system of interrelated equations, to compute the hypothetical projections of the explanatory

variables.

CBO uses an econometric model to compute its baseline set of economic assumptions. However,

that model is too large to use for stochastic simulations, so CBO adopted a simpler approach used

by time-series analysts, that of Vector Autoregression, or VAR. Vector Autoregression is a method

by which the statistical relationships among a set of economic variables can be estimated without

placing many a priori restrictions on those relationships. In effect, it allows the data to determine

which links among the variables are strong and which are weak. In contrast, traditional methods use

economic theory to place as many restrictions as possible on the structure of statistical models to

make estimation easier. Advocates of VARs contend that such restrictions are inappropriate

because, in a complex economy, most variables in macroeconomic models are endogenous (that is,

they are affected by the other variables in the system).

Under the VAR approach, a system in which all of the variables are endogenous can be expressed

as a series of equations, in which each variable is expressed as a function of its own lagged values

and the lagged values of all of the other variables of the system. Each equation in the system can be

estimated using Ordinary Least Squares (OLS) because the right-hand side of each equation contains

only predetermined variables. Estimating a VAR involves little more than determining the variables

to be included in the system and how long the lags should be.

CBO’s VAR includes the following variables: the 10-year Treasury note rate, the spread between

the 10-year note rate and the three-month Treasury bill rate, the rate of CPI inflation, the rate of

unemployment, a measure of volatility, and the spread between the 10-year note rate and the 30- year

Treasury bond rate. Each equation includes three lags of each variable in the model and is estimated

using quarterly data from 1961 through the third quarter of 1998. The results are not sensitive to the

length of the lag used.
3. CBO used an estimation technique known as generalized autoregressive conditional heteroskedasticity

(GARCH) to correct for the heteroskedasticity displayed by the residuals. The technique adds a regression

equation which explains the variance of the residuals (see technical appendix).

24

Uncertainty Associated with Alternate Rates

The second source of random variation in the simulations for the alternate rates stems from the

residuals of the baseline forecasting equations. When estimated over history, regression equations

do not explain all of the variation in the dependent variable. The errors in regression equations are

known as the residuals and are assumed to result from completely random shocks to the dependent

variable. To capture the uncertainty imparted by these random shocks in the simulations, a shock

term is added to the value of the spread that is predicted by the baseline forecasting equation. These

shocks, however, are not random draws from a statistical distribution.

Statistical tests indicated that the residuals of the spread equations were heteroskedastic, which

means that they did not have constant variance throughout the sample. CBO’s estimation corrected

for heteroskedasticity by exploiting the fact that the variance of the residuals was positively

correlated with the rate of inflation.3 The method used to correct for heteroskedasticity, which

improved the statistical efficiency of the baseline spread equations, also supplied the shocks that

were applied to the baseline equations. The practical impact of the correction was to reduce the

estimated volatility of the interest rates during the projection period because the variance of the

residuals of the interest rates is positively related to the rate of inflation. Since CBO’s projection for

inflation is lower than the historical average, the variance imposed in the simulated projections is

lower than that observed during the historical sample.

Probabilities Associated With Alternate Rates

A set of illustrative probabilities associated with each of the alternate rates is presented in Table 8,

below, along with probabilities for the 91-day Treasury bill rate. The probabilities are computed

from a series of 1,000 simulations of the model, where each simulation is a forecast from the model

that includes the two sources of random variation described above. Once the simulated forecasts

have been computed, it is straightforward to count the number of occurrences (out of 1,000) in which

the interest rate exceeded a specific threshold and approximate the distribution of forecasts.

Each of the alternate rates is highly correlated with the three-month Treasury bill rate, so it is not

surprising that the probabilities associated with the alternate rates are broadly similar to that of the

bill rate. For the 91-day CP rate, in particular, the distribution of estimated probabilities is almost

indistinguishable from that of the bill rate. Probabilities for the one-month CP rate are only slightly

higher. LIBOR rates appear to be more volatile, with estimated probabilities exceeding those of the

bill rate by slightly larger amounts.
25

TABLE 8: Illustrative Probabilities for Short-Term Interest Rates

Probability That Interest Rate Will Exceed Baseline Rate

By At Least __ Percentage Points During Forecast Period 

0 pp 1 pp 2 pp 3 pp 4 pp

3-Month Treas. Bill 49 33 20 10 5

1-Month C. P. 49 34 22 12 6

3-Month C.P. 49 34 20 11 5

1-Month LIBOR 49 36 24 14 8

3-Month LIBOR 49 36 24 15 9

Notes: CBO’s model calculates the probability that an interest rate will exceed its baseline level (by 0

percentage points, 1 percentage point, and so forth) for each year from 1999 through 2030. 

Entries in the table are averages of those probabilities for the period 1999 - 2030.

pp = percentage points

C.P. = commercial paper

LIBOR = London Interbank Offered Rate

TECHNICAL APPENDIX:

ESTIMATION METHODOLOGY AND ECONOMETRIC DETAIL

The projections have been prepared using a statistical model whose determining factors were

discussed in the text. To recapitulate, a model for the behavior of each spread is approximated as

a function of: the level of the 3-month Tbill rate to capture covariations between credit-risk and the

overall level of interest rates; the spread between a long-term and short-term interest rate to capture

the influence of the stance of monetary policy on liquidity and credit risk; the level of inflation to

capture the effect of overall market uncertainties affecting credit risk; and the volatility of the interest

rate on Fedfunds to capture the effect of monetary-policy uncertainty on money-market interest rates

such as commercial paper and London dollar rates. The models differ among the spreads according

to the different size of the impact of the determining factors on each spread--that is, each equation

has the same set of explanatory variables, but a different set of coefficients.

The methodology for estimating the model draws from standard econometric theory in selecting

the appropriate form of the spread and the techniques to be applied. A summary of the methodology

is incorporated in the following set of equations, and the discussion which follows.
4. For example, it reduces peak values of the spread between 1-month LIBOR and 3-month Tbills by about 40

to 50 basis points compared to that constructed as the simple difference between the two rates.

26

ln{

( )

( ) } ln{ } ln{

( )

( ) } ln{ }

ln{ }

,

, ,, , ,

,

, ,

, ,, , ,

1

1 1

1

1 1

1 74 3 80 4

01 1 2

1

1

3 1

4 15 6

+

+

=+ + +

+

+

+ +

++ + + +

−

−

− −

−

R

R aa R a

R

R a Inflation

a aDQ a Dq u

j t

Tbill t

j j Tbill t j

Tnote t

Tbill t

j t

j Fedfunds t j j j t σ

Equation 1. Spread over Tbill:

where, for Rj,t , the upper case, R, signifies an interest rate and the subscript j stands respectively for

1- month commercial paper, 3-month commercial paper, 1-month LIBOR, 3-month LIBOR, 1-month

Eurodollar, and 3-month Eurodollar; "ln" signifies the natural logarithm of the expression within

braces; the two variables preceded with an upper case D signify ( for reasons described later) that

the variable takes on the value one in the year and quarter (1974Q3, and 1980Q4) and zero

otherwise; and the variable uj,t represents unobservable random factors.

In equation 1, the spread appears in ratio form as shown to the left of the equality sign. It is

expressed as the logarithm of ratio of one plus the interest rate under examination to one plus the

rate on 3-month Treasury bills. This form of the spread is approximately equal to the numerical

difference between interest rates when the level of rates is small. It was chosen to help reduce the

effect of extreme values of the spread on the statistical estimates of parameters (a0, ....., a6).4 Even

so, two extreme values of the spread occurred in the third quarter of 1974 and the fourth quarter of

1980 that were still sufficiently large and unaccounted for by the determining factors despite the

logarithmic transformation. As a result, the two variables, D74Q3 and D80Q4, were introduced to

help remove the effects of those two extreme values on the parameter estimates.
27

Equation 2. Residual Volatility (ARCH Model):

ln{ } ln{ } ln{ } , ,, , , u b b u b Inflation jt j j jt j t

2

01 1

2

2 =+ + +1 −

Equation 2 is that part of the structural model which helps to account for nonuniform variations

in the volatility of the spread such as that in the period before the middle 1980s when inflation was

climbing and high versus that in the period since then when inflation has declined and become low.

Nonuniform volatility introduces heteroskedasticity. Its systematic variation, characterized in part

by a clustering of large values followed by a period of relative calm, has given rise to the term

"autoregressive-conditional-heteroskedasticity," or ARCH, to signify this type of time variation. 

Accounting for ARCH as in equation 2 improves the empirical estimates of the parameters of

equation 1 over longer data intervals such as the nearly 30 year period encompassing the 1970s

through 1990s. Otherwise, the potential range of variation around the estimated values of the

parameters in equation 1 might be too large to yield much confidence in the estimates themselves.

An unattractive alternative would be to shorten the period of analysis--unattractive because using

a shorter the period, such as the 1990s alone or the late 1980s to late 1990s for example, limits the

ability to gauge the role played by the determining factors in the behavior of the spread. 

But the inclusion of ARCH also helps importantly in developing sensible probability ranges in

the projection span. In particular, as specified in equation 2, the low inflation of the 1990s turns out

to have played an important role in reducing volatility. As such, a baseline projection of low

inflation in the years ahead contributes to projections with a lower volatility of the spread than

otherwise. That, in turn, produces probability ranges that are lower than otherwise.

The estimation of equations 1 and 2 involves a sequence of three steps that comprise the method

of generalized least squares. In the first step, equation 1 is estimated by ordinary least squares to

derive an estimate of the unobservable series of residuals, uj,t. Appendix Table 1 shows the estimates

of equation 1 for each of six spreads. The difference between the actual value of the spread and the

value predicted by the equation yields the residuals used in the second step.

In the second step, the residuals obtained from the first step are squared to obtain the volatility

of the spread. This measure of volatility is used along with the inflation rate to estimate equation

2 for each of the six spreads. Appendix Table 2 shows the estimates for equation 2. From this

equation, the predicted values of volatility are retrieved for the final step of generalized least squares.

In the third and final step of generalized least squares the square root of the predicted values of

volatility are divided into all the observable variables of equation 1 and the resulting equation is

estimated by ordinary least squares. Appendix Table 3 shows the generalized least squares estimates

of equation 1 for each of the six spreads.
28

APPENDIX TABLE 1:

ORDINARY LEAST SQUARES ESTIMATES OF INTEREST-RATE SPREADS

Dependant Variable: ln{(1+Rate)/(1+Tbill)}, where Rate = {Commercial Paper, LIBOR, Eurodollar}.

Estimation interval: 1971Q2 - 1998Q3

 Commercial Paper LIBOR Eurodollar 

Determinants 1-month 3-month 1-month 3-month 1-month 3-month

constant

(t-Stat)

.0028

(2.325)

.0048

(4.174)

.0014

(0.671)

-.0001

(-0.049)

.0009

(0.406)

-.0008

(-0.319)

ln(1+Tbill-1)

(t-Stat)

.0628

(4.613)

-.0093

(-0.721)

.0986

(4.126)

.0939

(3.830)

.0794

(3.225)

.0763

(3.143)

ln(1+Tnote-1)/(1+Tbill-1)

(t-Stat)

-.1017

(-3.571)

-.0132

(-0.489)

-.1821

(-3.642)

-.1221

(-2.379)

-.2003

(-3.887)

-.1380

(-2.717)

ln(1+inflation-1)

(t-Stat)

.0147

(1.179)

.0115

(0.973)

.0464

(2.115)

.0837

(3.716)

.0598

(2.646)

.0909

(4.077)

ln(1+Fedfunds Volatility-1)

(t-Stat)

-.0126

(-2.397)

-.0093

(-1.861)

.0251

(2.715)

.0326

(3.435)

.0302

(3.166)

.0397

(4.224)

D1974Q3

(t-Stat)

.0123

(4.503)

.0063

(2.423)

.0208

(4.325)

.0228

(4.614

.0204

(4.108)

.0236

(4.823)

D1980Q4

(t-Stat)

.0060

(2.208)

-.0079

(-3.073)

.0141

(2.929)

.0070

(1.434)

.0137

(2.801)

.0077

(1.600)

Measures of Fit: 

R-bar Squared .574 .130 .640 .652 .669 .670

Standard Error, basis points

F(6,103)

26

25.46

27

3.72

47

33.33

48

35.02

48

33.16

47

37.91

Measures of Residual 

 Randomness: 

D.W. 

1.11 1.13 0.77 0.83 0.64 0.79

Q(4) 48.4 19.0 62.9 26.5 52.8 35.6

 first order autocorrelation 

coefficient: .442 .432 .569 .541 .568 .561

 
29

APPENDIX TABLE 2:

AUTOREGRESSIVE-CONDITIONAL HETEROSKEDASTIC (ARCH) MODEL OF SQUARED

RESIDUALS 

ln ln ln( ) u u Inflation tt t

2

1

2 = + ++ constant α β − 1

Estimation Interval: 1971Q3 - 1998Q3

Commercial Paper LIBOR Eurodollar 

Determinants 1-month 3-month 1-month 3-month 1-month 3-month

constant

(t-Stat)

-12.722

(-8.665)

-11.964

(-8.964)

-8.013

(-6.387)

-11.259

(-8.013)

-8.627

(-6.782)

-8.645

(-7.718)

ln(12

-1 )

(t-Stat)

.133

(1.386)

.181

(1.974)

.400

(4.498)

.191

(2.020)

.367

(4.123)

.370

(4.285)

ln(1+Inflation)

(t-Stat)

24.451

(2.872)

20.545

(3.009)

13.891

(1.944)

26.920

(2.745)

16.990

(2.112)

20.526

(3.061)

Measures of Fit: 

R-bar Squared .098 .107 .226 .120 .196 .264

Standard Error

F(2,106)

2.38

 6.87

1.98

7.49

1.974

16.78

2.73

 8.35

2.269

14.14

1.855

20.42
30

APPENDIX TABLE 3: GENERALIZED LEAST SQUARES ESTIMATES OF INTERESTRATE SPREADS

Dependant Variable: [ln{(1+Rate)/(1+Tbill)}]/1, where 1 is the square root of the fitted values from the ARCH model.

Estimation Interval: 1971Q3 - 1998Q3.

Commercial Paper LIBOR Eurodollar 

Determinants:# 1-month 3-month 1-month 3-month 1-month 3-month

constant

(t-Stat)

.0022

(2.581)

.0049

(6.021)

.0007

(0.596)

-.0020

(-1.453)

-.0010

(-1.009)

-.0020

(-1.630)

ln(1+Tbill-1)

(t-Stat)

.0776

(6.556)

-.0005

(-0.053)

.1041

(5.401)

.1125

(6.416)

.1167

(6.761)

.0921

(4.926)

ln(1+Tnote-1)/(1+Tbill-1)

(t-Stat)

-.0854

(-3.890)

-.0450

(-2.214)

-.1727

(-5.082)

-.1046

(-2.626)

-.1617

(-5.647)

-.1229

(-3.525)

ln(1+inflation-1)

(t-Stat)

.0079

(0.689)

.0038

(0.384)

.0657

(4.297)

.0607

(3.214)

.0329

(2.651)

.0744

(4.470)

ln(1+Fedfunds Volatility-1)

(t-Stat)

-.0153

(-3.285)

-.0067

(-1.640)

.0224

(2.694)

.0407

(4.745)

.0261

(3.402)

.0440

(5.433)

D1974Q3

(t-Stat)

.0130

(2.182)

.0059

(1.319)

.0195

(1.847)

.0246

(2.160)

.0230

(2.208)

.0249

(2.187)

D1980Q4

(t-Stat)

.0061

(1.316)

-.0078

(-1.943)

.0127

(1.591)

.0080

(0.981)

.0148

(1.903)

.0083

(1.073)

Measures of Fit: 

R-bar Squared .485 .276 .782 .515 .793 .650

Standard Error, basis points 26 25 43 45 45 44

Measures of Residual 

 Randomness: 

D.W.

1.05 1.03 1.22 0.85 0.98 1.05

Q(4) 49.0 23.6 35.6 44.3 32.7 32.9

first order autocorrelation

coefficient: .464 .480 .358 .521 .463 .450

# Determinants all divided by, 1t

, the square root of the fitted values from the ARCH model.
31

Notes to Models:

Variables:

Commercial Paper Rates:

Quarterly average of daily data published in Federal Reserve release H.15. Data before 1997

fourth quarter based on historical statistics gathered by Federal Reserve Bank of New York.

Data for 1997 fourth quarter and later gathered by Depository Trust Company and reported

to Federal Reserve Bank of New York.

London Interbank Offer Rates:

Quarterly average of daily data published by the British Bankers' Association.

Eurodollar Deposit Rates:

Quarterly average of daily data published in Federal Reserve release H.15.

Tbill Rate:

Quarterly average of daily data on 3-month Treasury Bill Rate, secondary market, discount basis.

10-Year Tnote Rate:

Quarterly average of daily data on 10-year Treasury note, constant maturity.

Inflation:

Annualized quarterly percentage change of consumer price index (all urban), where price index

is quarterly average of monthly levels.

Fedfunds Volatility:

Square root of 8-quarter moving average squared deviation of Fedfunds rate. Deviation is

measured as difference between log first difference-change of Fedfunds rate and trend of log

first-difference change in Fedfunds rate. Trend is measured as 8 quarter moving average.

Quarterly data based on average of daily data as published in Federal Reserve release H.15.

Statistics:

t-statistic --tests the significance of individual parameter estimates;

F-statistic --tests the significance of the combined set of parameter estimates;

Standard error of estimate--measures the range of variation around the model's projection.

Measure of fit-- the proportion of total variation explained by model;

Measure of residual randomness-- D.W. reveals whether omitted factors are correlated from

quarter-to-quarter (the nearer a value is to 2, the more it suggests the absence of such correlation;

Q = Box-Pierce Q-statistic is a general test of randomness [G.E.P. Box and D.A. Pierce,

"Distribution of residual autocorrelations in autoregressive-integrated moving average time series

models," Journal of American Statistical Association, vol. 65, 1970, pp.355-365.]