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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 27 28 29