Understanding and Influencing the Yield Curve at the Zero Lower Bound

Understanding and Influencing the Yield Curve at the Zero Lower Bound Glenn D. Rudebusch Federal Reserve Bank of San Francisco September 9, 2014 European Central Bank and Bank of England workshop European Central Bank My comments do not necessarily represent the views of others in the Federal Reserve. 1 / 36

Understanding and influencing the yield curve at the ZLB Understanding the yield curve 1. What do financial economists do at the ZLB? 2 / 36

Understanding and influencing the yield curve at the ZLB Understanding the yield curve 1. What do financial economists do at the ZLB? Develop new term structure models 2 / 36

Understanding and influencing the yield curve at the ZLB Understanding the yield curve 1. What do financial economists do at the ZLB? Develop new term structure models Influencing the yield curve 2. What do central bankers do at the ZLB? 2 / 36

Short-term rates at ZLB in many countries Percent 15 US UK Germany/ECB Japan 12 9 6 3 90 92 94 96 98 00 02 04 06 08 10 12 Source: OECD, Federal Reserve Board 0 3 / 36

So far: Almost 6 years at ZLB in U.S.! Percent 0 2 4 6 8 10 12 10y T yield 2y T yield 3m T bill rate 1985 1990 1995 2000 2005 2010 Year 4 / 36

1. What do financial economists do at the ZLB? Problem: Standard Gaussian term structure models do not restrict interest rates to be nonnegative. Term structure models that do respect ZLB: Shadow-rate term structure models Stochastic-volatility models with square-root processes Gaussian quadratic models AR gamma zero process of Monfort, Pegoraro, Renne, Roussellet (2014) Literature has focused on shadow-rate models: Issues include tractability, whether ZLB is reflecting or absorbing barrier, and familiarity away from ZLB. 5 / 36

Some related literature Japan Gorovoi and Linetsky (2004). Ueono et al. (2006), Ichiue and Ueno (2007) Kim and Singleton (2012). Christensen and Rudebusch (2014), Monfront et al (2014) United States Bomfim (2003), Hamilton and Wu (2011) Krippner (2013), Xia and Wu (2013), Christensen and Rudebusch (2013), Andreasen and Meldrum (2013, Kim and Priebsch (2013), Christensen, Lopez, and Rudebusch (2014) Euro Area Renne(2014) 6 / 36

Christensen and Rudebusch (JFinEc 2014): Estimate 1-, 2-, 3-factor shadow-rate models Rate in percent 0 1 2 3 4 5 10 year yield 4 year yield 1 year yield 6 month yield 1996 2000 2004 2008 2012 Japanese Government Bond Yields weekly frequency 7 / 36

Fit of Standard and Shadow-Rate Models (RMSE) RMSE, all yields (in b.p.) One-factor models affine: V(1) 34.4 shadow: B-V(1) 32.7 Two-factor models affine: AFNS(2) 12.2 shadow: B-AFNS(2) 10.3 Three-factor models affine: AFNS(3) 9.7 shadow: B-AFNS(3) 7.0 Shadow-rate models have somewhat closer fit. 8 / 36

Why Use a Shadow-Rate Model? Zero Probability of Negative Future Short Rates Probability 0.0 0.2 0.4 0.6 0.8 1.0 AFNS(3) model 1995 2000 2005 2010 Affine model produces significant probability that short rate will be negative three months ahead. 9 / 36

Why use a shadow-rate model? Volatility compression for intermediate yields Rate in basis points 0 20 40 60 80 100 AFNS(3) model B AFNS(3) model Three month realized volatility of two year yield Correlation = 72.4% 1995 2000 2005 2010 Near ZLB, volatility of two-year yield is also near zero. Shadow-rate model can replicate this correlation. 10 / 36

Bauer and Rudebusch (2014): Shadow-rate model with U.S. data Advantages of shadow-rate models at ZLB: Better cross-sectional fit Shadow-rate models fit the yield curve better Avoid violations of ZLB by affine models Forward curves and short-rate expectations dip below zero Probability of negative future rates while mean positive Greater forecast accuracy Shadow-rate models forecast better out of sample Macroeconomic information improves performance 11 / 36

Shadow-rate model gives more accurate forecasts Out-of sample RMSEs (in basis points). For forecasts of three-month T-bill rate, December 2008 to June 2011, 12-month forecast horizon Model RMSE Yields-only affine (2,0) 32.3 shadow (2,0) 17.8 affine (3,0) 22.3 shadow (3,0) 14.3 Macro-finance affine (1,2) 103.5 shadow (1,2) 10.9 affine (2,2) 49.6 shadow (2,2) 10.4 12 / 36

Why are macro variables helpful at the ZLB? Unemployment rate can help pin down shadow rate: Percent 10-5.8 8 6 3m T-bill rate -5.3-4.9 4 2-2.7 Unemployment gap -2.2-4.5 0-2 -4 1985 1990 1995 2000 2005 2010-6 13 / 36

Caution: Shadow short rate is sensitive to model specification Percent 4 2 0 2 4 3m T Bill YZ(2) YZ(3) MZ(1) MZ(2) 2006 2008 2010 2012 2014 Years 14 / 36

Caution: Shadow short rate is sensitive to lower bound Short rate lower bound: r t = max(r min, s t ) Percent 4 2 0 2 4 3m T Bill YZ(3) YZ(3) 5 YZ(3) 10 YZ(3) 15 YZ(3) 20 YZ(3) 25 2006 2008 2010 2012 2014 Years 15 / 36

2. What do central bankers do at the ZLB? Unconventional tools and strategies: Mitigate effects of ZLB Try to ease financial conditions e.g., lower long-term yields Conduct quantitative easing (QE) Provide forward guidance about future policy Conduct credit easing Avoid future episodes at ZLB Reconsider the level of the inflation target Put greater emphasis on avoiding financial crises 16 / 36

ZLB was sizable constraint on U.S. monetary policy Federal Funds Rate Quarterly average Percent 12 10 Fed's Target Rate 8 6 4 Simple estimated policy rule recommendation 2 0 Monetary policy shortfall Target Rule = 2.1 + 1.5 x Inflation - 2.0 x Unemployment gap (Unemployment Gap = Unemployment rate - CBO NAIRU) 88 90 92 94 96 98 00 02 04 06 08 10 12 14-2 -4-6 -8 17 / 36

2. What do central bankers do at the ZLB? Unconventional tools and strategies: Mitigate effects of ZLB Try to ease financial conditions e.g., lower long-term yields Conduct quantitative easing (QE) (A) Provide forward guidance about future policy (B) Conduct credit easing Avoid future episodes at ZLB Reconsider the level of the inflation target Put greater emphasis on avoiding financial crises (C) 18 / 36

A. Central banks purchase assets (QE) Treasury Bond Yields Treasury bond yields fall after March 18th FOMC announcement of $300 billion future purchases of Treasury securities. Percent 3.5 3 Before Announcement (March 17, 2009) 2.5 2 After Announcement (March 18,2009) 1.5 1 0.5 0 0 12 24 36 48 60 72 84 96 108 120 Bond Maturity (in months) 19 / 36

How did QE Work? Chairman Bernanke (2010) saw portfolio balance channel: Purchases work primarily through the so-called portfolio balance channel [...] Different financial assets are not perfect substitutes in investors portfolios, so that changes in the net supply of an asset available to investors affect its yield and those of broadly similar assets. But LSAPs also may have provided news about a longer period of near-zero policy rate and slower liftoff lower risks around a little-changed policy path higher medium-term inflation and lower real rates improved prospects for real activity (esp. lower tail) 20 / 36

Bauer-Rudebusch (IJCB, 2014) Signaling vs. portfolio balance channels for QE How did QE affect long-term Treasury yields? Yield decomposition: y n t = n E t r t+i + TPt n 1 n 1 i=0 Signaling Channel: Announcements of asset purchases signal lower future policy rates to market participants, so QE reduces expectations component of Treasury yields. Portfolio Balance Channel: Changes in supply have price effects because of imperfect substitutability. Reduction in supply lowers term premium component of Treasury yields. 21 / 36

Changes in expected policy path during QE1 Unrestr. risk prices (URP) Restr. risk prices (RRP) basis points 150 100 50 0 forward rates expectations conf. int. 150 100 50 0 0 20 40 60 80 120 months forward 0 20 40 60 80 120 months forward 22 / 36

Christensen-Rudebusch (EJ, 2012) Support signaling channel in U.S. Net change in basis points 100 80 60 40 20 0 Instantaneous forward rate Forecasted future spot rate Instantaneous forward term premium 0 2 4 6 8 10 Time to maturity in years Policy expectations declined the most at the two- to three-year horizon as one would expect from a signaling effect. 23 / 36

Christensen-Rudebusch (EJ, 2012) Support portfolio balance channel in U.K. Net change in basis points 80 60 40 20 0 20 40 Instantaneous forward rate Forecasted future spot rate Instantaneous forward term premium 0 2 4 6 8 10 Time to maturity in years Term premiums declined at all horizons, but the most in the three- to ten-year maturity range. 24 / 36

Will QE be part of the new normal? Event studies suggest QE did effect yield curve But did effects persist? Did changes in yields pass through to private rates? Did changes in asset prices alter aggregate demand? Potential costs: Loss of monetary/fiscal credibility (and pi*) Capital losses to central bank Financial instability Impaired securities market functioning Increased difficulty of managing monetary policy Analysis needed to integrate QE into DTSM 25 / 36

B. Central bank guidance on future policy Modern central banking stresses importance of guiding expectations about future monetary policy actions. Monetary policy is process of shaping or managing yield curve. How can central banks best guide private expectations of future monetary policy actions? Old answer: Actions speak louder than words New answer: Talk, talk, talk, plus forecasts Rudebusch, Glenn, and John C. Williams, 2008, Revealing the Secrets of the Temple: The Value of Publishing Central Bank Interest Rate Projections. in Asset Prices and Monetary Policy. 26 / 36

Narrative forward guidance by Federal Reserve Aug. 2003 - June 2006 accommodation can be maintained for a considerable period, or removed at a pace that is likely to be measured, March 2009 economic conditions are likely to warrant exceptionally low levels of the federal funds rate for an extended period. August 2011 economic conditions...are likely to warrant exceptionally low levels for the federal funds rate at least through mid-2013. December 2012 the low range for the federal funds rate will be appropriate at least as long as the unemployment rate remains above 6.5%... 27 / 36

Quantitative forward guidance by Fed 28 / 36

Liftoff estimate based on modal path Bauer and Rudebusch (2013): Forward rates (E Q t r t+h ), shadow forward rates (E Q t s t+h ), and modal path, December 31, 2012 Percent 2 1 0 1 2 3 forward rates shadow forward rates modal path 0 10 20 30 40 50 60 Horizon 29 / 36

Estimated horizon (in months) until policy liftoff Months 0 10 20 30 40 50 60 based on forward curve based on modal path 2008 2009 2010 2011 2012 2013 2014 Year 30 / 36

Assessing effectiveness of forward guidance Merits of clear forward policy guidance Greater policy effectiveness through greater transparency Potential pitfalls of forward policy guidance Misinterpretation of conditionality of policy guidance... tendency for the public to infer more of a commitment to following the implied path than would be appropriate for good policy. Kohn (2008) Incorrect inference about the meaning of the policy guidance (Rudebusch and Williams, 2008) Reduction in incentives for the collection of private-sector information. (Morris and Shin) 31 / 36

C. Policy actions to avoid financial crises Should monetary policy take a more active role and try to offset financial imbalances (e.g. deflate an asset price bubble)? To do so, three questions must be addressed: Can an asset price bubble be identified? Will the bubble cause significant macro problems? Is monetary policy a good tool to deflate bubble? (Alternative would be macroprudential policy) see Rudebusch, Glenn D., 2005, Monetary Policy and Asset Price Bubbles, FRBSF Economic Letter. 32 / 36

Equity prices in 1999-2000 US Stock Market Indices January 3, 2005 = 100 Index 800 700 NASDAQ 600 500 400 S&P 500 300 200 100 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 0 33 / 36

House price bubble? Ratio of House Prices to Rent U.S. National Case-Shiller Index divided by Owner's Equivalent Rent 1.75 1.5 Average 1970-2000 2014Q1 1.25 1 0.75 1970 1975 1980 1985 1990 1995 2000 2005 2010 0.5 34 / 36

Was there a 2004-06 bond yield conundrum? RW Model Residuals for 10-Year Yield 60 40 20 basis points 0 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006-20 -40-60 40-50 bp conundrum Rudebusch, Glenn D., Eric Swanson, and Tao Wu, 2006, The Bond Yield Conundrum from a Macro-Finance Perspective, Monetary and Economic Studies 24, 83-128. 35 / 36

Lessons for everyone at the ZLB Probability of hitting ZLB seems higher This has implications for modeling the yield curve Possible implications for inflation target Central Bank affects whole yield curve Recommends macro-finance term structure approach Should unconventional policies become conventional? Financial stability may be emphasized as goal for policy Credit risk for sovereign debt. Government fiscal issues effect yield curve flight to quality adjustments as well 36 / 36