Modeling and Forecasting the Yield Curve

Transcription

1 Modeling and Forecasting the Yield Curve III. (Unspanned) Macro Risks Michael Bauer Federal Reserve Bank of San Francisco April 29, 2014 CES Lectures CESifo Munich The views expressed here are those of the authors and do not necessarily represent the views of others in the Federal Reserve System.

2 Outline Interactions between the macroeconomy and financial markets Macro-to-yields Yields-to-macro Macro-finance models Reduced-form models Structural models Risk premia and the macroeconomy Spanned and unspanned macroeconomic risks

3 Outline Interactions between the macroeconomy and financial markets Macro-to-yields Yields-to-macro Macro-finance models Reduced-form models Structural models Risk premia and the macroeconomy Spanned and unspanned macroeconomic risks

4 Outline Interactions between the macroeconomy and financial markets Macro-to-yields Yields-to-macro Macro-finance models Reduced-form models Structural models Risk premia and the macroeconomy Spanned and unspanned macroeconomic risks

5 The Taylor (1993) rule A simple rule for the short rate i t = r + π + α(π t π ) + β(y t ȳ) + u t

6 The Taylor (1993) rule A simple rule for the short rate i t = r + π + α(π t π ) + β(y t ȳ) + u t Taylor (1993): α = 1.5, β = 0.5, π = 2%

7 The Taylor (1993) rule A simple rule for the short rate i t = r + π + α(π t π ) + β(y t ȳ) + u t Taylor (1993): α = 1.5, β = 0.5, π = 2% Simple rules often accurately describe actual monetary policy

8 The Taylor (1993) rule A simple rule for the short rate i t = r + π + α(π t π ) + β(y t ȳ) + u t Taylor (1993): α = 1.5, β = 0.5, π = 2% Simple rules often accurately describe actual monetary policy Taylor principle: real short rate rises with inflation, α > 1

9 The Taylor (1993) rule A simple rule for the short rate i t = r + π + α(π t π ) + β(y t ȳ) + u t Taylor (1993): α = 1.5, β = 0.5, π = 2% Simple rules often accurately describe actual monetary policy Taylor principle: real short rate rises with inflation, α > 1 Policy shock u t captures everything else

10 Policy rules variations on the theme Estimate coefficients Unemployment gap instead of output gap Time-varying inflation target Time-varying coefficients Interest-rate smoothing/policy inertia Include lagged short rate Persistent policy shocks

11 Simple policy rules a mainstay of modern macro

12 Simple policy rules a mainstay of modern macro Part of most (New-Keynesian) macro models Clarida, Gali, Gertler (1998, EER; 1999, JEL; 2000, QJE) In many cases closely approximates optimal monetary policy

13 Simple policy rules a mainstay of modern macro Part of most (New-Keynesian) macro models Clarida, Gali, Gertler (1998, EER; 1999, JEL; 2000, QJE) In many cases closely approximates optimal monetary policy Used in empirical analysis to describe policy Monetary VARs Evans and Marshall (1998, CRCS), Christiano, Eichenbaum, Evans (1996, REStat; 1999, Handbook;...)

14 The effects of macroeconomic news Macroeconomic data releases contain new information

15 The effects of macroeconomic news Macroeconomic data releases contain new information Revisions to expectations about economic activity and inflation

16 The effects of macroeconomic news Macroeconomic data releases contain new information Revisions to expectations about economic activity and inflation Revisions to expected policy path (anticipated policy response)

17 The effects of macroeconomic news Macroeconomic data releases contain new information Revisions to expectations about economic activity and inflation Revisions to expected policy path (anticipated policy response) Yield curve responds to macro news

18 The effects of macroeconomic news Macroeconomic data releases contain new information Revisions to expectations about economic activity and inflation Revisions to expected policy path (anticipated policy response) Yield curve responds to macro news Response is procyclical

19 Payroll news Response of forward curve to employment surprises Source: Bauer (2014) Payroll news major driver of interest rates Response is procyclical Response largest at 1 3 years, no response at the long end

20 Effects of macro variables on risk premia

21 Effects of macro variables on risk premia Announcement effects: macro news affect long rates because expectations of future policy change

22 Effects of macro variables on risk premia Announcement effects: macro news affect long rates because expectations of future policy change But: macro aggregates also affect long rates through risk premia Cochrane and Piazzesi (2005): expected excess returns are high at troughs and low at peaks Ludvigson and Ng (2009, RFS): macroeconomic variables help predict excess returns, term premia are countercyclical

23 Effects of macro variables on risk premia Announcement effects: macro news affect long rates because expectations of future policy change But: macro aggregates also affect long rates through risk premia Cochrane and Piazzesi (2005): expected excess returns are high at troughs and low at peaks Ludvigson and Ng (2009, RFS): macroeconomic variables help predict excess returns, term premia are countercyclical Risk premia vary at lower frequencies (business cycle)

24 Effects of macro variables on risk premia Announcement effects: macro news affect long rates because expectations of future policy change But: macro aggregates also affect long rates through risk premia Cochrane and Piazzesi (2005): expected excess returns are high at troughs and low at peaks Ludvigson and Ng (2009, RFS): macroeconomic variables help predict excess returns, term premia are countercyclical Risk premia vary at lower frequencies (business cycle) Risk premia are counter-cyclical

25 Macro-to-yields linkages Linkages from macroeconomic aggregates to interest rates are both theoretically and empirically important Simple policy rules: relationship between macro variables and short rate Policy expectations: macro news affect policy expectations and long rates procyclical Changes in risk premia: macro variables related to term premium at business-cycle frequencies countercyclical

26 Outline Interactions between the macroeconomy and financial markets Macro-to-yields Yields-to-macro Macro-finance models Reduced-form models Structural models Risk premia and the macroeconomy Spanned and unspanned macroeconomic risks

27 Monetary transmission Interest rates affect aggregate demand (see lecture 1)

28 Monetary transmission Interest rates affect aggregate demand (see lecture 1) Conventional New-Keynesian model IS curve / Euler equation x t = ρ(i t E t π t+1 ) + E t x t+1 + g t Real short rate affects consumption decision Only short rate matters, but not other yields

29 Monetary transmission Interest rates affect aggregate demand (see lecture 1) Conventional New-Keynesian model IS curve / Euler equation x t = ρ(i t E t π t+1 ) + E t x t+1 + g t Real short rate affects consumption decision Only short rate matters, but not other yields More generally Interest rates of all maturities matter for aggregate demand

30 The effects of monetary policy Response of investment to expansionary policy shock Source: Christiano, Eichenbaum, Evans (2005, JPE) Significant response of real activity to MP shock Price level responds very slowly Policy shocks account for only a small share of output variability

31 Predictive power of the yield curve Yield spread (slope of the yield curve) is an indicator of monetary policy Positive spread Expansionary monetary policy Often followed by further expansion of economic activity Negative spread High policy rate contractionary policy Typically followed by recessions Key papers: Estrella and Hardouvelis (1991), Estrella and Mishkin (1998)

32 Yield spread and recessions 10y 3m Treasury yield spread Source: Slope of the yield curve is a reliable predictor of recessions

33 Yield-to-macro linkages The effects of the yield curve on the macroeconomy are at the center of the transmission of monetary policy. Policy rate affects aggregate demand in theoretical models and monetary VARs. Monetary transmission works through rates of different maturities. The yield spread predicts economic activity (correlation, not causation).

34 Outline Interactions between the macroeconomy and financial markets Macro-to-yields Yields-to-macro Macro-finance models Reduced-form models Structural models Risk premia and the macroeconomy Spanned and unspanned macroeconomic risks

35 Reduced-form macro-finance models 1. Factors 2. Dynamic system 3. Relationship between yields and risk factors

36 Reduced-form macro-finance models 1. Factors Macro aggregates (e.g., output, inflation) Yield-curve variables (e.g., short-rate, level, slope) 2. Dynamic system 3. Relationship between yields and risk factors

37 Reduced-form macro-finance models 1. Factors Macro aggregates (e.g., output, inflation) Yield-curve variables (e.g., short-rate, level, slope) 2. Dynamic system Reduced-form time series model, e.g., VAR 3. Relationship between yields and risk factors

38 Reduced-form macro-finance models 1. Factors Macro aggregates (e.g., output, inflation) Yield-curve variables (e.g., short-rate, level, slope) 2. Dynamic system Reduced-form time series model, e.g., VAR 3. Relationship between yields and risk factors Simple factor loadings, or

39 Reduced-form macro-finance models 1. Factors Macro aggregates (e.g., output, inflation) Yield-curve variables (e.g., short-rate, level, slope) 2. Dynamic system Reduced-form time series model, e.g., VAR 3. Relationship between yields and risk factors Simple factor loadings, or No-arbitrage restrictions (pricing Kernel)

40 Macro-finance factor model using Nelson-Siegel Diebold, Rudebusch, Aruoba (2006, JoE)

41 Macro-finance factor model using Nelson-Siegel Diebold, Rudebusch, Aruoba (2006, JoE) Model structure 1. Factors Yield factors: level, slope, curvature (latent) Macro factors: capacity utilization, funds rate, inflation 2. Gaussian VAR 3. Nelson-Siegel loadings

42 Macro-finance factor model using Nelson-Siegel Diebold, Rudebusch, Aruoba (2006, JoE) Model structure 1. Factors Yield factors: level, slope, curvature (latent) Macro factors: capacity utilization, funds rate, inflation 2. Gaussian VAR 3. Nelson-Siegel loadings Evidence for effects form macro to yields and vice versa

43 The first macro-finance DTSM Ang and Piazzesi (2003, JME)

44 The first macro-finance DTSM Ang and Piazzesi (2003, JME) Major innovation First to incorporate macro variables in no-arbitrage model Policy rule: short rate is affected by output and inflation

45 The first macro-finance DTSM Ang and Piazzesi (2003, JME) Major innovation First to incorporate macro variables in no-arbitrage model Policy rule: short rate is affected by output and inflation Additional methodological contribution Dynamic term structure model in discrete time Solve for yield loadings

46 Ang-Piazzesi: Model structure

47 Ang-Piazzesi: Model structure 1. Factors Observed macro factors: inflation and output growth Three unobserved (latent) factors

48 Ang-Piazzesi: Model structure 1. Factors Observed macro factors: inflation and output growth Three unobserved (latent) factors 2. VAR(12) for monthly observations

49 Ang-Piazzesi: Model structure 1. Factors Observed macro factors: inflation and output growth Three unobserved (latent) factors 2. VAR(12) for monthly observations 3. No-arbitrage restrictions Short rate is function of observable and latent factors (Taylor rule) Pricing Kernel is exponentially affine Difference equations for yield loadings

50 Ang-Piazzesi: Take-aways

51 Ang-Piazzesi: Take-aways Macro variables explain significant amount of variation in yields Mostly short and medium maturities Latent variables explain long maturities

52 Ang-Piazzesi: Take-aways Macro variables explain significant amount of variation in yields Mostly short and medium maturities Latent variables explain long maturities Forecasting Imposing no-arbitrage restrictions improves forecasts from a VAR Forecasts can be further improved by incorporating macro variables

53 Ang-Piazzesi: Take-aways Macro variables explain significant amount of variation in yields Mostly short and medium maturities Latent variables explain long maturities Forecasting Imposing no-arbitrage restrictions improves forecasts from a VAR Forecasts can be further improved by incorporating macro variables Criticisms Assumption that short rate and yields do not affect macro variables Some of the findings have been questioned recently (Duffee, 2011; Joslin-Priebsch-Singleton) Enforced macro-spanning

54 Subsequent reduced-form macro-finance DTSMs Ang, Dong, Piazzesi (2007), Ang, Boivin, Dong, Loo-Kung (2011, REStud) Bikbov and Chernov (2010, JoE) Joslin, Le, Singleton (2013, JFEC; 2013, JFE) Joslin, Priebsch, Singleton (forthcoming JF)

55 Structural macro-finance DTSMs 1. Factors 2. Dynamic system 3. Relationship between yields and risk factors

56 Structural macro-finance DTSMs 1. Factors Macro and yield-curve variables 2. Dynamic system 3. Relationship between yields and risk factors

57 Structural macro-finance DTSMs 1. Factors Macro and yield-curve variables 2. Dynamic system IS curve 3. Relationship between yields and risk factors

58 Structural macro-finance DTSMs 1. Factors Macro and yield-curve variables 2. Dynamic system IS curve New-Keynesian Philips Curve 3. Relationship between yields and risk factors

59 Structural macro-finance DTSMs 1. Factors Macro and yield-curve variables 2. Dynamic system IS curve New-Keynesian Philips Curve Taylor rule 3. Relationship between yields and risk factors

60 Structural macro-finance DTSMs 1. Factors Macro and yield-curve variables 2. Dynamic system IS curve New-Keynesian Philips Curve Taylor rule Solution mechanism if forward looking 3. Relationship between yields and risk factors

61 Structural macro-finance DTSMs 1. Factors Macro and yield-curve variables 2. Dynamic system IS curve New-Keynesian Philips Curve Taylor rule Solution mechanism if forward looking 3. Relationship between yields and risk factors No-arbitrage pricing

62 Structural macro-finance DTSMs 1. Factors Macro and yield-curve variables 2. Dynamic system IS curve New-Keynesian Philips Curve Taylor rule Solution mechanism if forward looking 3. Relationship between yields and risk factors No-arbitrage pricing Pricing Kernel either micro-founded (restrictive) or ad hoc (more flexible)

63 A new-keynesian macro-finance model Rudebusch and Wu (2008, EJ)

64 A new-keynesian macro-finance model Rudebusch and Wu (2008, EJ) Model structure: 1. Factors Two latent factors: level and slope Inflation and output growth 2. Small-scale New-Keynesian macro model 3. Reduced-form pricing Kernel

65 Rudebusch-Wu: level factor and inflation expectations Source: Rudebusch and Wu (2008)

66 Rudebusch-Wu: Results

67 Rudebusch-Wu: Results Economic interpretation of latent factors Level factor: Time-varying inflation target correlated with inflation expectations Slope factor: Monetary policy instrument correlated with output gap

68 Rudebusch-Wu: Results Economic interpretation of latent factors Level factor: Time-varying inflation target correlated with inflation expectations Slope factor: Monetary policy instrument correlated with output gap No evidence for deliberate interest-rate smoothing

69 Rudebusch-Wu: Results Economic interpretation of latent factors Level factor: Time-varying inflation target correlated with inflation expectations Slope factor: Monetary policy instrument correlated with output gap No evidence for deliberate interest-rate smoothing Forward- and backward-looking macro dynamics

70 Other structural macro-finance DTSMs Hördahl, Tristani, Vestin (2006, JoE) Policy shocks affect short-term rates Inflation and output shocks affect medium-term maturities Changes in perceived inflation target affect long maturities Macro information helps forecast yields Sensible risk premia (reproduces and fixes Campbell-Shiller) Dewachter et al. (2006, 2011, 2014) Bekaert, Cho, Moreno (2010, JMCB)

71 Outline Interactions between the macroeconomy and financial markets Macro-to-yields Yields-to-macro Macro-finance models Reduced-form models Structural models Risk premia and the macroeconomy Spanned and unspanned macroeconomic risks

72 Expected excess returns over the business cycle Expected/realized excess returns and yields Source: Cochrane and Piazzesi (2005)

73 Expected excess returns over the business cycle Risk premia are counter-cyclical return forecast has a clear business cycle pattern, high in troughs and low at peaks (CP, p. 154) Expectations hypothesis does not hold High slope is not usually followed by rising yields, bond returns are good

74 Macro factors in bond risk premia Ludvigson and Ng (2009, RFS)

75 Macro factors in bond risk premia Ludvigson and Ng (2009, RFS) Extract macro factors from large dataset

76 Macro factors in bond risk premia Ludvigson and Ng (2009, RFS) Extract macro factors from large dataset Macro factors predict excess bond returns Real factor and inflation factor Add information that is not in the yield curve

77 Macro factors in bond risk premia Ludvigson and Ng (2009, RFS) Extract macro factors from large dataset Macro factors predict excess bond returns Real factor and inflation factor Add information that is not in the yield curve Predicted returns are more strongly countercyclical than in the absence of macro predictors

78 Ludvigson-Ng: countercyclical term premium Source: Ludvigson and Ng (2009)

79 Outline Interactions between the macroeconomy and financial markets Macro-to-yields Yields-to-macro Macro-finance models Reduced-form models Structural models Risk premia and the macroeconomy Spanned and unspanned macroeconomic risks

80 Three important observations Joslin, Priebsch, Singleton (2012) make three observations about the yield curve

81 Three important observations Joslin, Priebsch, Singleton (2012) make three observations about the yield curve 1. Macroeconomic risks are unspanned by bond yields Regress macro variables on yield curve (level, slope, curve) R 2 is often substantially below one

82 Three important observations Joslin, Priebsch, Singleton (2012) make three observations about the yield curve 1. Macroeconomic risks are unspanned by bond yields Regress macro variables on yield curve (level, slope, curve) R 2 is often substantially below one 2. Macro risk factors forecast excess returns Ludvigson-Ng: macro factors add predictive power Robust to the use of more yield-curve information

83 Three important observations Joslin, Priebsch, Singleton (2012) make three observations about the yield curve 1. Macroeconomic risks are unspanned by bond yields Regress macro variables on yield curve (level, slope, curve) R 2 is often substantially below one 2. Macro risk factors forecast excess returns Ludvigson-Ng: macro factors add predictive power Robust to the use of more yield-curve information 3. Bond yields have low-dimensional factor structure

84 Three important observations Joslin, Priebsch, Singleton (2012) make three observations about the yield curve 1. Macroeconomic risks are unspanned by bond yields Regress macro variables on yield curve (level, slope, curve) R 2 is often substantially below one 2. Macro risk factors forecast excess returns Ludvigson-Ng: macro factors add predictive power Robust to the use of more yield-curve information 3. Bond yields have low-dimensional factor structure In contrast, most macro-finance DTSMs imply macro-spanning Macro variation is spanned by yields Conditional on yield curve, macro variables do not matter for expectations

85 A DTSM with unspanned macro risks

86 A DTSM with unspanned macro risks Risk factors: Z t = (P t, M t ) Yield-curve factors and macro factors

87 A DTSM with unspanned macro risks Risk factors: Z t = (P t, M t ) Yield-curve factors and macro factors Current interest rates load only on P t

88 A DTSM with unspanned macro risks Risk factors: Z t = (P t, M t ) Yield-curve factors and macro factors Current interest rates load only on P t But expectations of future rates/returns also depend on M t

89 A DTSM with unspanned macro risks Risk factors: Z t = (P t, M t ) Yield-curve factors and macro factors Current interest rates load only on P t But expectations of future rates/returns also depend on M t Key finding Unspanned macro risks important for variation in term premia

90 JPS term premium Two-to-three year forward term premium Source: Joslin, Priebsch, Singleton (2012) Substantial differences between term premium from unspanned model M us and model that imposes spanning M span

91 Unspanned macro risks: open questions

92 Unspanned macro risks: open questions How much macro variation is really unspanned? 80-90% of inflation is spanned Only 15% of CFNAI is spanned (JPS), but this variable was not actually available to investors at the time 80% of unemployment gap is spanned

93 Unspanned macro risks: open questions How much macro variation is really unspanned? 80-90% of inflation is spanned Only 15% of CFNAI is spanned (JPS), but this variable was not actually available to investors at the time 80% of unemployment gap is spanned What is unspanned macro risk? How is it related to monetary policy? Just noise? Or systematically relevant?

94 Unspanned macro risks: open questions How much macro variation is really unspanned? 80-90% of inflation is spanned Only 15% of CFNAI is spanned (JPS), but this variable was not actually available to investors at the time 80% of unemployment gap is spanned What is unspanned macro risk? How is it related to monetary policy? Just noise? Or systematically relevant? Could the evidence on predictability be partly spurious?

95 Some take-aways for you

96 Some take-aways for you 1. The yield curve is of central importance not only for monetary policy but for many areas of macroeconomics.

97 Some take-aways for you 1. The yield curve is of central importance not only for monetary policy but for many areas of macroeconomics. 2. The expectations hypothesis is strongly at odds with observed interest rate behavior high slope should be followed by rising yields but in fact is followed by high bond returns.

98 Some take-aways for you 1. The yield curve is of central importance not only for monetary policy but for many areas of macroeconomics. 2. The expectations hypothesis is strongly at odds with observed interest rate behavior high slope should be followed by rising yields but in fact is followed by high bond returns. 3. In modern yield-curve models, we combine elements from finance, macroeconomics, and statistics, in order to learn about the term structure of interest rates and its interactions with macroeconomic aggregates.

99 Some take-aways for you 1. The yield curve is of central importance not only for monetary policy but for many areas of macroeconomics. 2. The expectations hypothesis is strongly at odds with observed interest rate behavior high slope should be followed by rising yields but in fact is followed by high bond returns. 3. In modern yield-curve models, we combine elements from finance, macroeconomics, and statistics, in order to learn about the term structure of interest rates and its interactions with macroeconomic aggregates. 4. Estimates of the term premium suffer from large statistical uncertainty. However, we think that it is positive on average, and likely counter-cyclical and slow-moving.

100 Some take-aways for you 1. The yield curve is of central importance not only for monetary policy but for many areas of macroeconomics. 2. The expectations hypothesis is strongly at odds with observed interest rate behavior high slope should be followed by rising yields but in fact is followed by high bond returns. 3. In modern yield-curve models, we combine elements from finance, macroeconomics, and statistics, in order to learn about the term structure of interest rates and its interactions with macroeconomic aggregates. 4. Estimates of the term premium suffer from large statistical uncertainty. However, we think that it is positive on average, and likely counter-cyclical and slow-moving. 5. Interest rates are difficult to forecast a random walk can seldom be beat out-of-sample but a large share of excess bond returns is predictable in sample.

101 Some take-aways for you 1. The yield curve is of central importance not only for monetary policy but for many areas of macroeconomics. 2. The expectations hypothesis is strongly at odds with observed interest rate behavior high slope should be followed by rising yields but in fact is followed by high bond returns. 3. In modern yield-curve models, we combine elements from finance, macroeconomics, and statistics, in order to learn about the term structure of interest rates and its interactions with macroeconomic aggregates. 4. Estimates of the term premium suffer from large statistical uncertainty. However, we think that it is positive on average, and likely counter-cyclical and slow-moving. 5. Interest rates are difficult to forecast a random walk can seldom be beat out-of-sample but a large share of excess bond returns is predictable in sample. 6. There are many open questions for us to work on.