Online Appendix to Lower-Bound Beliefs and Long-Term Interest Rates

Transcription

1 Online Appendix to Lower-Bound Beliefs and Long-Term Interest Rates Christian Grisse, a Signe Krogstrup, b and Silvio Schumacher a a Swiss National Bank b International Monetary Fund Proof of Proposition 1 The proof closely follows Ruge-Murcia (26), with a slight modification to allow for a non-zero lower bound. Define δ t ε t /σ such that δ t N(, 1) and where from (2) r t+1 = E(r t+1)+σδ t+1, E(r t+1) =α + ψr t. Then, r t+1 = r t+1 if r t+1 > r or, equivalently, if δ t+1 > r E(r t+1) c t+1. σ Note that c t+1 is observed in t. Thus, we have E(r t+1 )=E(r t+1 δ t+1 >c t+1 )Pr(δ t+1 >c t+1 )+ rpr(δ t+1 c t+1 ), where and Pr(δ t+1 >c t+1 )=1 Φ(c t+1 ) E(r t+1 δ t+1 >c t+1 )=E(r t+1)+σe(δ t+1 δ t+1 >c t+1 ) =( r σc t+1 )+ σφ(c t+1) 1 Φ(c t+1 ), 1

2 2 International Journal of Central Banking September 217 where the second line uses a result in Maddala (1983, p. 366). Substituting back into the expression for E(r t+1 ) and simplifying, we get E(r t+1 )= r σc t+1 (1 Φ(c t+1 )) + σφ(c t+1 ), which is the expression in the text.

3 Vol. 13 No. 3 Lower-Bound Beliefs and Long-Term Interest Rates 3 Data Sources and Definitions Table 1. Data Sources and Description Datastream Variable Source Code Units Description Monetary Policy Surprises Bloomberg and National Central Banks N/A bps Announced policy rate change, less the median from the Bloomberg survey. The survey is conducted among financial analysts, typically on the Friday before the central bank decision. Interest Rate Swap Yields Datastream CCmmY3* % Yield on interest rate swap with a Central Bank Policy Rates variable leg of three months, based on prices as of 5: p.m. CET London. Reserve Bank of Australia Datastream RBACASH % Official cash rate Bank of Canada Datastream CN1439 % Key interest rate (target overnight rate) Czech National Bank Datastream PRREPOR % Two-week repo rate Danmarks Nationalbank Datastream DKCTDEP % Certificates of deposit Central Bank of Hungary Datastream HNBBASE % Base rate Bank of Japan Datastream JPCALLT % Uncollateralized call rate Reserve Bank of New Zealand Datastream NZRBCSH % Official cash rate Norges Bank Datastream NWFOLIN % Sight deposit rate National Bank of Poland Datastream POPRATE % Reference rate (seven-day bill rate) Sveriges Riksbank Datastream SDREPOR % Repo Swiss National Bank Datastream SWSNBTI % Three-month LIBOR target rate Bank of England Datastream LCBBASE % Base rate U.S. Federal Reserve Datastream USFDTRG % Federal funds target rate European Central Bank Datastream EURODEP % Overnight deposit rate Note: *CC = country code, mm = maturity.

4 4 International Journal of Central Banking September 217 Appendix Tables Table 2. Panel Regression Results: Robustness Excluding Lower-Policy-Rate Country Observations Specification (16) Specification (17) Maturities Δrt (.5) (.8) (.8) (.9) (.5) (.8) (.8) (.9) ri,t (.44) (.57) (.55) (.56) Δrt ri,t (.1) (.2) (.2) (.2) Ri,t (.53) (.63) (.59) (.57) Δrt Ri,t (.1) (.2) (.1) (.1) Constant (.81) (1.38) (1.58) (1.83) (.87) (1.49) (1.73) (2.2) No. Obs R Notes: Observations for countries where the policy rate is already lower than the policy rate reached in the announcing country are excluded. Cluster-robust standard errors are in parentheses. Statistical significance is indicated by *** if p<.1, ** if p<.5, and * if p<.1. ΔRi,t for the announcing country has been excluded.

5 Vol. 13 No. 3 Lower-Bound Beliefs and Long-Term Interest Rates 5 Table 3. Panel Regression Results: Robustness Excluding Australia and New Zealand Specification (16) Specification (17) Maturities Δrt (.5) (.7) (.8) (.9) (.5) (.7) (.7) (.8) ri,t (.44) (.56) (.55) (.59) Δrt ri,t (.2) (.3) (.3) (.3) Ri,t (.49) (.55) (.49) (.51) Δrt Ri,t (.2) (.2) (.2) (.2) Constant (.73) (1.2) (1.41) (1.66) (.76) (1.14) (1.35) (1.62) No. Obs R Notes: Cluster-robust standard errors are in parentheses. Statistical significance is indicated by *** if p<.1, ** if p<.5, and * if p<.1. ΔRi,t for the announcing country has been excluded.

6 6 International Journal of Central Banking September 217 Table 4. Panel Regression Results: Robustness Excluding Australia, New Zealand, Poland, and Hungary Specification (16) Specification (17) Maturities Δrt (.4) (.6) (.7) (.8) (.2) (.3) (.2) (.3) ri,t (.99) (.97) (.94) (1.1) Δrt ri,t (.6) (.6) (.6) (.6) Ri,t (1.22) (1.25) (1.23) (1.21) Δrt Ri,t (.8) (.8) (.8) (.8) Constant (.67) (1.16) (1.38) (1.63) (.57) (.85) (.97) (1.1) No. Obs R Notes: Cluster-robust standard errors are in parentheses. Statistical significance is indicated by *** if p<.1, ** if p<.5, and * if p<.1. ΔRi,t for the announcing country has been excluded.

7 Vol. 13 No. 3 Lower-Bound Beliefs and Long-Term Interest Rates 7 Table 5. Panel Regression Results: Robustness to Omitted-Variable Lower Bound Specification (16) Specification (17) Maturities Δrt (.4) (.7) (.8) (.9) (.4) (.7) (.8) (.8) ri,t (.38) (.45) (.42) (.42) Δrt ri,t (.1) (.1) (.1) (.1) Ri,t (.44) (.52) (.48) (.46) Δrt Ri,t (.1) (.1) (.1) (.1) Constant (.82) (1.28) (1.47) (1.71) (.91) (1.42) (1.62) (1.85) No. Obs R Notes: Cluster-robust standard errors are in parentheses. Statistical significance is indicated by *** if p<.1, ** if p<.5, and * if p<.1. ΔRi,t for the announcing country has been excluded. ri,t 1 denotes the difference between ri,t 1 and the minimum of policy rates observed across the countries in the sample and up to t. A similar definition holds for Ri,t 1.

8 8 International Journal of Central Banking September 217 Appendix Figures Figure 1. Response of Two-Year Yields on Interest Rate Swaps around the Riksbank s Policy Announcement of February 12, EZ DK NW.1 SE : 9:3 1: 1:3 11: 11:3.8 9: 9:3 1: 1:3 11: 11:3 Figure 2. Response of Two-Year Yields on Interest Rate Swaps around the Riksbank s Policy Announcement of March 18, 215 EZ DK NW SE : 13:3 14: 14:3 15: 15: : 13:3 14: 14:3 15: 15:3

9 Vol. 13 No. 3 Lower-Bound Beliefs and Long-Term Interest Rates 9 Figure 3. Response of Two-Year Yields on Interest Rate Swaps around the Riksbank s Policy Announcement of July 2, EZ DK NW.9 9: 9:3 1: 1:3 11: 11: SE.9 9: 9:3 1: 1:3 11: 11:3 Figure 4. Response of Two-Year Yields on Interest Rate Swaps around the Riksbank s Policy Announcement of February 11, EZ DK NW.1 SE : 9:3 1: 1:3 11: 11:3.5 9: 9:3 1: 1:3 11: 11:3 Notes: The cut was partly unexpected and the unexpected component is included in our sample. Vertical lines mark the time of the announcement. Yields are normalized by adding a constant so that the average of the last two observations before the announcement is zero. Yields are based on transaction prices from Bloomberg.

10 1 International Journal of Central Banking September 217 Figure 5. Response of Two-Year Yields on Interest Rate Swaps around the Danmarks Nationalbank s Policy Announcement of January 19, EZ SE NW.1 DK :15:316:16:317:17:318:18:3.4 15:15:316:16:317:17:318:18:3 Figure 6. Response of Two-Year Yields on Interest Rate Swaps around the Danmarks Nationalbank s Policy Announcement of January 22, EZ SE NW.2 DK :15:316:16:317:17:318:18:3.2 15:15:316:16:317:17:318:18:3

11 Vol. 13 No. 3 Lower-Bound Beliefs and Long-Term Interest Rates 11 Figure 7. Response of Two-Year Yields on Interest Rate Swaps around the Danmarks Nationalbank s Policy Announcement of January 29, EZ SE NW.1 DK :15:316:16:317:17:318:18:3.5 15:15:316:16:317:17:318:18:3 Figure 8. Response of Two-Year Yields on Interest Rate Swaps around the Danmarks Nationalbank s Policy Announcement of February 5, EZ SE NW.1 DK :15:316:16:317:17:318:18:3.7 15:15:316:16:317:17:318:18:3

12 12 International Journal of Central Banking September 217 References Maddala, G. S Limited-Dependent and Qualitative Variables in Econometrics. Econometric Society Monograph No. 3. Cambridge: Cambridge University Press.