The Bond Yield “Conundrum” from a Macro-Finance Perspective

1. The Bond Yield “Conundrum” from a Macro-Finance Perspective Tao Wu Federal Reserve Bank of Dallas Glenn D. Rudebusch Federal Reserve Bank of SF Eric T. Swanson Federal Reserve Bank of SF Seminar, Bank of England November 13, 2006 Note: The views expressed in this presentation are the authors’ and do not necessarily reflect the views of the management of the Federal Reserve Bank of San Francisco, the Federal Reserve Bank of Dallas, or any other individuals within the Federal Reserve System.

2. The Bond Yield “Conundrum” [L]ong-term interest rates have trended lower in recent months even as the Federal Reserve has raised the level of the target federal funds rate by 150 basis points. This development contrasts with most experience, which suggests that, other things being equal, increasing short-term interest rates are normally accompanied by a rise in longer-term yields… For the moment, the broadly unanticipated behavior of world bond markets remains a conundrum. —Testimony of Fed Chairman Alan Greenspan to the U.S. Senate, February 16, 2005

3. 10-year Treasury Yield, 1984–2005 Is There A Bond Yield “Conundrum”? or, Are current long-term interest rates simply an extension of 20 years of bond market trends?

4. Macro-Finance Models of the Term Structure • Estimate historical, dynamic relationships between macroeconomic variables and interest rates • Provide a rigorous econometric framework with which to analyze bond yields • Like finance models, recognize that Treasury yields consist of two components: • “risk-neutral” component: i.e., expected future short rates • “term premium” component (time-varying) • But macro-finance models recognize that macroeconomic variables and bond yields are determined jointly: • Interest rates affect output, employment, inflation, etc. • Butoutput, employment, inflation also affect current and future short-term interest rates (through central bank) • Much theory (and empirical evidence) that macro variables also affect term premia

5. Macro-Finance Models of the Term Structure • Price of an n-period zero-coupon bond at time t, from finance: • Simplifying functional form assumption on m (e.g., Duffie-Kan, 1996, Dai-Singleton, 2000, Ang-Piazzesi, 2003): • Where λt is an affine function of the state of the economy Xt:

6. Bernanke-Reinhart-Sack Model • State variables Xt are observable macro variables, follow a VAR: • Five variables in Xt: • employment (HP-filtered) • core PCE deflator inflation (trailing 12-month) • federal funds rate • one-year inflation expectations from Blue Chip (inflation outlook) • four-quarter-ahead Eurodollar futures rate (policy outlook)

7. Rudebusch-Wu Model • State variables Xt are divided into two groups: • three observed macro variables • two unobserved (latent) variables, Lt and St • Bond risk premia are assumed to depend only on Lt and St • Model dynamics are governed by a structural hybrid New Keynesian model, with macroeconomic interpretations placed on Lt and St • Ltdenotes medium- to long-run inflation level • St denotes a cyclical indicator, the term structure slope

8. Rudebusch-Wu Model • Dynamics of Lt and St: • Three macroeconomic variables: • capacity utilization • core PCE deflator inflation (trailing 12-month) • federal funds rate

9. Differences Between BRS and RW Models RW BRS more structural NK model Model dynamics reduced-form VAR Yes – 2 Latent factors? No Parameterization: model dynamics risk pricing 100 25 13 4 Estimation technique two-step one-step Estimation sample Jan 1984 – Dec 2005 Jan 1988 – Dec 2000 month-average end-of-month Bond yield data

10. Model Estimation • Estimate BRS model over 1984–2005 period (1988–2000 for RW) • begin estimation after Volcker disinflation • monetary policy may have changed since Volcker • inflation expectations may have become more stable • update original BRS sample through end of 2005 • try to fit the “conundrum” in-sample as opposed to out-of-sample (gives model the best possible chance to fit the conundrum) • Models are fairly simple: linear, only a few state variables • Nonetheless, estimation of the models is nonlinear in the parameters, can be tricky • dozens of local minima

11. BRS Model Decomposition of 10-year Yield

12. 50-75 bp conundrum BRS Model Residuals

13. RW Model Decomposition of 10-year Yield

14. 20-50 bp conundrum RW Model Residuals

15. Summary of Macro-Finance Model Analysis • Simple Macro-Finance models explain behavior of Treasury yields from 1984-2005 remarkably well • Neither model fits the 10-year yield perfectly: there are model residuals • The recent episode of low long-term rates is one that the models fail to fit • i.e., there is a bond yield conundrum • Magnitude of the conundrum is in the range of 25-75 bp

16. What Factors Could Explain the Conundrum? No – accounted for by the model already • Low term premium? No – accounted for by the model already • Low inflation/low inflation risk? Unsatisfying • Irrational pricing or an interest rate “bubble”? • Model specification error? Maybe (but why now, and why so large?) Most promising explanation • Omitted variable? • Story: term premium may be lower than models predict because one (or more) omitted factors is lower than in the past • Some candidate variables that are not in the BRS and RW models: • time-varying interest rate uncertainty • time-varying inflation uncertainty • time-varying output uncertainty • foreign central bank purchases of U.S. Treasuries

17. What Factors Could Explain the Conundrum?

18. What Factors Could Explain the Conundrum? • We consider: • Three measures of financial market uncertainty: • Implied volatility on long-term Treasuries (Merrill-Lynch MOVE index) • Implied volatility on eurodollar rate (from options) • Implied volatility on S&P 500 (VIX index) • Two measures of macroeconomic uncertainty: • 8-quarter trailing standard deviation of GDP growth • 24-month trailing standard deviation of core PCE deflator inflation • One measure of foreign official purchases of U.S. Treasuries: • 12-month change in custodial holdings at the Federal Reserve Bank of New York

19. What Factors Could Explain the Conundrum?

20. What Factors Could Explain the Conundrum?

21. BRS Model Residuals

22. What Factors Could Explain the Conundrum?

23. What Factors Could Explain the Conundrum?

24. What Factors Could Explain the Conundrum?

25. Foreign Official Purchases

26. Conclusions • A rigorous, macro-finance econometric analysis documents that there is a bond yield conundrum in the 2004–2005 period • The magnitude of the conundrum is in the range 25–75 bp • Low volatility of long-term Treasuries appears to have played a role • Foreign official purchases of long-term Treasuries appear to have played little or no role

27. Foreign Official Holdings/Purchases

28. Foreign Official Holdings/Purchases

29. U.S. Treasury Issuance (Gross and Net)

30. BRS Model Residuals

31. RW Model Residuals