An experimental investigation of the
term structure of interest rates
James Watson
School of Economics, University of East Anglia
An experimental investigation of the term
structure of interest rates
Introduction
The term structure of interest rates
Macroeconomic experiments
Experimental design
Experimental results
Conclusions






2
Introduction

Policymakers set short term nominal interest rates

Main instrument of modern monetary policy

Long term interest rates are anchored to the return on
long term government bonds

Private sector investment, personal mortgages and
refinancing government debt depend on longer term
interest rates
3
Introduction

The price of government bonds is determined by the
market

Policymakers control the short rate but want to control
the long rate

Understanding the link between the two is crucial for
policy

This is the term structure of interest rates
4
The term structure of interest rates

The yield on a government bond is the annualised return
to maturity

A 2-year UK treasury bond matures for £100

If you were to buy one for £90.70 you are guaranteed a
5% return (or yield) on your investment (unless UK plc
goes bust of course!
£ 100
1 . 05 
5
2
 £ 90 . 70
The term structure of interest rates

If you thought a certain 5% return on your money over
the next two years was good (!) you would buy these
bonds – as would everybody else…

Clearly demand is driven by the certain return you might
expect to get elsewhere

The term structure of interest rates (or yield curve) is the
line connecting yields of differing maturities. Long interest
rates are anchored to the term structure
6
The term structure of interest rates

5
4
3
2
This is the expectations
hypothesis of the term
structure
1

UK term structure 10th June 2010
0
The upward slope suggests
an expectation that interest
rates will increase
yield (%)

0
3
6
9
12
15
maturity (years)
18
21
24
An upward slope is also thought to represent a risk averse
attitude to the future – a premium for holding a risky
asset
7
The term structure of interest rates
The expectations hypothesis says:

E [ return
for holding
a bond
for period t] 
[the short rate for period t]  risk premium

The short interest rate should predict the long interest
rate up to some risk premium

For an excellent review of theory, testing and some
empirical results see Cuthbertson & Nitzche (2004)
8
The term structure of interest rates

Could a clear policy objective flatten the term structure?

Does it help if the policymaker is trustworthy?
15
UK 10 year nominal treasury bond yields
UK inflation target 1992-

Formal BoE independence 1997-
year
9
20
10
20
05
20
00
19
95
19
90
19
85
19
80
19
75
19
70
0
5
yield (%)
10

The term structure of interest rates

Mixed results: the term structure must be governed by
arbitrage plus risk. This has proved difficult to observe
empirically…

Time-varying risk, monetary policy regime, global economic
shocks, cross-country variation, causality, non-stationarity of
data

For a review see Campbell (1995) and Kozicki and Tinsley
(2001)
10
Macroeconomic experiments

The laboratory can control for these confounds

Test a theory in the laboratory

Does the laboratory approximate the real world?

Testing policy: it’s difficult to experiment on the real
economy

For surveys see Duffy (2008), Ricciuti (2005)
11
Experimental design

Does a trustworthy policymaker have more control over
the term structure?

Does it matter if signals about the future are more (or
less) accurate?
12
Experimental design

5 subjects participate in a simple 2-period economy

Buy and/or sell bonds to alter the ratio of cash to bonds held
via an interactive computerised auction programmed in z-Tree

Value of cash is certain, value of bonds depends on the future
state of the world – this implies a 2-period term structure

Subjects participate in 15 independent rounds and are paid
according to their performance in one randomly selected
round
13
Experimental design

Two policymakers:

Inflation targeter: trustworthy, expect high inflation get
high interest rates

Second policymaker cares about inflation and output:
policy response is more uncertain
14
Experimental design

Subjects receive signals about future output & future
inflation

Subjects face one policymaker with either low noise or
high noise signals

4 treatments

2-by-2 design
15
Low risk
High risk
Inflation
targeter
A2
A4
Policy
uncertainty
B2
B4
Experimental design

Subjects receive information about their policymaker type

Statement of intent:


To deliver stable inflation
To deliver a steady increase in production and deliver stable
inflation

Examples of previous policy decisions
16
Experimental design

Predictions:

Increasing policy uncertainty increases the risk premium

Increasing risk increases the risk premium
17
Experimental results

Is testing the term structure in the laboratory viable?

Subjects seemed to understand the environment. In all
treatments except B4 the term structure contains statistically
significant information about the path of the short interest
rate

The expectations hypothesis
does significantly better with
an inflation targeter than with
policy uncertainty
18
Low risk
High risk
Inflation
targeter
A2
A4
Policy
uncertainty
B2
B4
Experimental results

Between treatment differences are not as predicted

No statistically significant difference between risk premia

The difference is in the informational content of the term
structure
Low risk
High risk

The ‘A’ policymaker has
more control over the
term structure
19
Inflation
targeter
A2
A4
Policy
uncertainty
B2
B4
Experimental results

Subjects make significant use of the previous rounds trade
prices in all 4 treatments

As policy uncertainty increase subjects rely more on the
past

In treatment ‘B4’ subjects
make no significant use of
signals about the future
20
Low risk
High risk
Inflation
targeter
A2
A4
Policy
uncertainty
B2
B4
Experimental results

Statistically significant differences between policymakers

More risk leads to a significant change in behaviour

The effects are direction theoretically predicted, but
empirically are unexpected
21
Conclusions

Overall positive from the perspective of testing the term
structure in the laboratory

Policy uncertainty leads to less control of the term structure
or conversely, the term structure is less useful as a predictor
of the short rate

Evidence that increased policy uncertainty significantly changes
behaviour, but not in the way theory predicts

A possible insight into why the empirical results are mixed
22
Appendix: Expectations hypothesis

More trade in uncertain ‘B’ treatments. Wilcoxon tests: pvalues < 0.01

Expectation Hypotheses:
1
2
Change
in short rate       Slope of term structure

Treatment
Slope (ß)
p-value
Sig greater then
(Chow test)
A2
0.395
0.000
>A4*,B2**,B4***
A4
0.260
0.000
>B4*
B2
0.166
0.068
>B4*
B4
0.007
0.619
Results from multi-level restricted maximum likelihood regression
*,**,*** indicate significance at 10%, 5% and 1% levels respectively
23
Appendix: Adaptive expectations

What does the long rate depend on?
R r     1  R r 1    2  sig    3  y sig    4 trades
Treatment
β1
β2
β3
β4
A2
0.233***
0.476***
-0.010
0.079***
A4
0.572***
0.351***
-0.131
0.119***
B2
0.393***
0.264***
-0.033
0.119***
B4
0.551***
0.180
0.087
0.018
Results from multi-level restricted maximum likelihood regression
*,**,*** indicate significance at 10%, 5% and 1% levels respectively
24

Appendix: Experimental term structures
20
15
0
5
10
Yield (%)
0
5
10
Yield (%)
15
20
25
Treatment A4
25
Treatment A2
1
2
1
2
time
Treatment B2
Treatment B4
10
0
5
5
0
1
2
time
25
15
Yield (%)
10
Yield (%)
15
20
20
25
25
time
1
2
time
Appendix: Policy rule and noise

Policy via Taylor Rule

it  i  1 . 5     t  
*




*
  1 .5 1    y
Treatment ‘A’:
Treatment ‘B’:
ρ=1
ρ = 0.5
Treatment ‘2’:
Treatment ‘4’:
Noise ~ N[0,4]
Noise ~ N[0,16]
26
t
 y
*

References
Campbell, John Y. 1995. “Some lessons from the yield curve.”, Journal of Economic Perspectives, 9:
129-152
Cuthbertson, Keith, and Dirk Nitzche. 2004. Quantitative Financial Economics. Wiley
Duffy, John. 2008. “Macroeconomics: A Survey of Laboratory Research.” Working Paper 334,
University
of
Pittsburgh,
Dept.
of
Economics,
downloadable
at
http://www.econ.pitt.edu/papers/John_hee11.pdf
Fischbacher, Urs. 2007. “z-Tree: Zurich toolbox for ready made economic experiments.”
Experimental Economics, 10: 171-178
Kozicki, Sharon, and Peter Tinley. 2001. “Shifting endpoints in the term structure of interest
rates.” Journal of Monetary Economics, 47: 613-652
Ricciuti, Roberto. 2008. “Bringing macroeconomics into the lab.” Journal of Macroeconomics,
Elselvier, 30(1): 216-237
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