Seminar Interest rates theory. Empirical estimation of the term structure hypotheses

Seminar 9. Interest rates theory.

Empirical estimation of the term structure hypotheses:

• 
  weak empirical support for the expectations hypothesis
  
• 
  ARCH, GARCH, Engle 1982, Bollerslev 1986, Engle, Ng, Rotshild, 1990: introduction to the model conditional dispersion of forecast errors presenting strong fluctuations of time-series forward rates.
  
• 
  Non-stationarity, unit-root testing of time series of yields with different terms to maturity
  
• 
  Cointegration of time-series: long-term relationship between the rates of different terms, while their short-term fluctuations could be considered as “random walk”
  
• 
  Efcectiveness of the hypothesis of term structure: analysis of the possibikity of interest rates with different terms of maturity to forecast future inflation changes, i.e. Fisher hypothesis testing about the term structure.
  
• 
  Estimation of variant in time forward premium
  

Problem set.

1. 
   What are the main hypotheses in interest rates theory? What are the main testing methods and approaches?
   
2. 
   Make a brief overview (8-10 articles) where different kinds of interest rates theory estimation procedures are covered.
   
3. 
   Choose one article and one estimation procedure, stress the problem of estimation and perform the similar research.
   
4. 
   Empirical Exercise from Favero Chapter 3: GMM and monetary policy rules – Estimating monetary policy reaction functions. The approach follows Clarida, Gali and Gertler (1998, 2000). The dataset contains monthly observations from 1979:1-1996:12. It includes German and US data.
   

Define the central bank target for nominal short term interest rate, which depends on both expected inflation and output:

where is the long-run equilibrium nominal rate, is the rate of inflation over a one year horizon (12 reflecting the fact that we are using monthly data), is real output (GDP), and and are the inflation target and potential output.

It is assumed that the actual rate, , partially adjusts to the target as follows:

where is the smoothing parameter and is an exogenous random shock to the interest rate. To estimate a baseline equation, define and and re-write the partial adjustment mechanism (combined with the target for the nominal short term interest rate) as:

Eliminate the unobservable variables and re-write the policy rule in terms of realised variables as follows:

To estimate the baseline model using GMM, we define the central bank’s instrument set, , at the time it chooses the interest rate. This includes lagged values of GDP, inflation, interest rates, and commodity prices. This information set is orthogonal to the error term in the baseline equation; . The baseline equation therefore implies the following orthogonality conditions.

Estimate the baseline policy rule for the Fed using GMM. Why do you think GMM estimation potentially produces better estimates of the parameters?

Literature

Required

Brooks C. Introductory Econometrics for Finance. Cambridge University Press. 2008.

Cuthbertson K., Nitzsche D. Quantitative Financial Economics. Wiley. 2004.

Tsay R.S. Analysis of Financial Time Series, Wiley, 2005.

Y. Ait-Sahalia, L. P. Hansen. Handbook of Financial Econometrics: Tools and Techniques. Vol. 1, 1st Edition. 2010.

Recommended

Clarida, Richard, Jordi Gali, and Mark Gertler. 1998. "Monetary Policy Rules in Practice: Some International Evidence." European Economic Review, 42:6, pp. 1033-67.

Clarida, Richard, Jordi Gali, and Mark Gertler. 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory." Quarterly Journal of Economics, 115:1, pp. 147-80.

Davidson, Russell and James G. MacKinnon. 2004. Econometric Theory and Methods. Oxford University Press

Favero, Carlo A. 2001. Applied Macroeconometrics. Oxford University Press

Hansen, Lars Peter and Kenneth J. Singleton. 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models." Econometrica, 50:5, pp. 1269-86.

Hansen, Lars Peter. 1982. "Large Sample Properties of Generalized Method of Moments Estimators." Econometrica, 50:4, pp.1029-54.

Hansen, Lars Peter and Kenneth J. Singleton. 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns." Journal of Political Economy, 91:2, pp. 249-65.

Hayashi, Fumio. 2000. Econometrics. Princeton University Press

Matyas, Laszlo ed. 1999. Generalized Method of Moments Estimation. Themes in Modern Econometrics. Cambridge