Imperfect Information, Macroeconomic Dynamics and the Term Structure of Interest Rates: An Encompassing Macro-Finance Model

Transcription

1 Imperfect Information, Macroeconomic Dynamics and the Term Structure of Interest Rates: An Encompassing Macro-Finance Model Hans Dewachter KULeuven and RSM, EUR October 28 NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 1 / 34

2 Overview Main goals of the paper Motivation Macro-Finance framework Econometric issues Empirical ndings Conclusions NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 2 / 34

3 Main goals of the paper Main goals of the paper Main goals of the paper NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 3 / 34

4 Main goals of the paper Main goals of the paper The central question of this paper: Can we improve the existing empirical Macro-Finance models of the yield curve? Methodological approach: Assess/estimate the empirical relevance of three types of extensions of the standard Macro-Finance framework: Deviations from full information rational expectations by introducing learning dynamics (imperfect information). Time variation in the equilibrium real interest rate. Deviations from Gaussian no-arbitrage pricing: time invariant liquidity premiums. The empirical analysis is performed using Bayesian techniques combining: Priors consistent with a simple New-Keynesian semi-structural framework. Data on macroeconomic variables, the yield curve and survey data on ination expectations. NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 4 / 34

5 Motivation Motivation Motivation NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 5 / 34

6 Motivation Motivation A need for more elaborated Macro-Finance models? Motivation: Despite the long-standing postulate and empirical ndings of a close link between the yield curve and the macroeconomic factors, no fully satisfactory macroeconomic model of the yield curve exists: Standard New-Keynesian models cannot replicate the variation at the long end of the yield curve: Long-term yields display excessive variation relative to standard NK model, e.g. Kozicki and Tinsley (21). Excess sensitivity of long-term yields to macroeconomic shocks, e.g. Gürkaynak et al. (25). Standard Macro-Finance models introduce a time-varying ination target (long-run ination expectations) and t the yield curve but face an interpretation problem: Excess volatility in the implied long-run ination expectations relative to surveys or market indicators of ination expectations (US data). Implied path for the ination target does not align with the historical record. NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 6 / 34

7 Motivation Motivation A need for more elaborated Macro-Finance models? Performance of the standard NK and Mac-Fin model (US data ). Yields In. Exp. (SPF) Maturity 1/2 yr 1 yr 3yr 5 yr 1 yr 1yr 1yr Total variation yield (st. dev.) Standard New-Keynesian model Residual variation (st. dev.) Resid var./total var Standard Macro-Finance model Residual variation (st. dev) Resid var/total var Pure nance model (3 factor Vasicek) Residual variation (st. dev.) n.a. n.a. NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 7 / 34

8 Motivation Motivation A need for more elaborated Macro-Finance models? Fit of the US yield curve: standard Mac-Fin model (196-27)..3 Yield curve fit maturity 1/4 years.3 Yield curve fit maturity 1/2 years Yield curve fit maturity 1 years.3 Yield curve fit maturity 3 years Yield curve fit maturity 5 years.3 Yield curve fit maturity 1 years.2.2 Actual data Fitted Fitting error NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 8 / 34

9 Motivation Motivation A need for more elaborated Macro-Finance models? But (excessively?) volatile implied ination expectations and target? Inflation expectations (1 yr.): SPF data Inflation.2expectations (1 yr.): model Inflation expectations (1 yr.): break even Fitting 5 error Long term inflation expectations Inflation Volcker disinflation period Inflation.2 target: model implied 5.5 Implied inflation target NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 9 / 34

10 Macro-Finance Framework Macro-Finance Framework Macro-Finance Framework NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 1 / 34

11 Macro-Finance Framework Macro-Finance Framework Overview The standard Macro-Finance model The encompassing model Afne yield curve representation Perceived Law of Motion Learning NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

12 Macro-Finance Framework Macro-Finance Framework The standard Macro-Finance model Standard Macro-Finance models (Hordahl et al. (26), Bekaert et al. (26), Doh (26), Dewachter and Lyrio (26), De Graeve et al. (27), Rudebusch and Wu (24)...) Extended expectations hypothesis relates the long-term yield, y t (m); to expectations of short-term interest rates, E t (i t+j ); and maturity-specic risk premiums, {(m): y t (m) = 1 P m 1 m j= E t [i t+j ] + {(m) Benchmark NK macro model relates interest rate expectations to macroeconomic variables, i.e. ination, output gap, the policy rate and the ination target: E t [i t+j ] = f (y t ; ( t t ); i t ; t ; j) lim j!1 E t [i t+j ] = + t The yield curve implied by the standard Macro-Finance model is: y t (m) = 1 P m 1 m j= f (y t; ( t t ); i t ; t ; j) + {(m) NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

13 Macro-Finance Framework Macro-Finance Framework The standard Macro-Finance model Encompassing/extended Macro-Finance model: Extended expectations hypothesis under the Perceived Law of Motion (E P PLM): y t (m) = 1 m P m 1 j= EP t [i t+j ] + rp t Extended NK macro model including perceived (time-varying) equilibrium real rate, P t : Et P [i t+j ] = f (y t ; ( t P t ); i t ; P t ; P t ; j) lim j!1 E P t [i t+j ] = P t + P t The yield curve implied by the extended model (allowing for liquidity effects and time-varying premiums): y t (m) = 1 m P m 1 j= f (y t; ( t P t ); i t ; P t ; P t ; j) + { t (m) + (m) NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

14 Macro-Finance Framework The Macro-Finance framework Afne yield curve representation We obtain an afne yield curve representation in the (perceived) state, Xt P assuming log-normal pricing (Ang and Piazzesi (23)): by y t (m) = a(m)=m (b(m)=m) Xt P {z } No-Arbitrage + (m) {z } + t (m) {z } Liq. effect meas. err. NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

15 Macro-Finance Framework The Macro-Finance framework Afne yield curve representation We obtain an afne yield curve representation in the (perceived) state, Xt P assuming log-normal pricing (Ang and Piazzesi (23)): by No-Arbitrage: y t (m) = a(m)=m (b(m)=m) Xt P {z } No-Arbitrage + (m) {z } + t (m) {z } Liq. effect meas. err. PLM dynamics: Xt P = C P + P Xt P 1 + P S P " P t No-arbitrage conditions: P t(m) = Et P [M t;t+1 P t+1 (m 1)] M t;t+1 = exp( i t c m t "P t ) t = + 1 X P t NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

16 Macro-Finance Framework The Macro-Finance framework Afne yield curve representation We obtain an afne yield curve representation in the (perceived) state, Xt P assuming log-normal pricing (Ang and Piazzesi (23)): by No-Arbitrage: PLM dynamics: y t (m) = a(m)=m (b(m)=m) Xt P {z } No-Arbitrage + (m) {z } + t (m) {z } Liq. effect meas. err. Afne yield curve representation (No-Arbitr.): Xt P = C P + P Xt P 1 + P S P " P t No-arbitrage conditions: P t(m) = Et P [M t;t+1 P t+1 (m 1)] M t;t+1 = exp( i t c m t "P t ) t = + 1 Xt P y t(m) = a(m)=m (b(m)=m) X P t No-arbitrage restrictions: a(m) = a(m 1) + b(m 1)(C P P S P S P ) + JIT b(m) = b(m 1)( P P S P S P 1 ) 1 : NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

17 Macro-Finance Framework The Macro-Finance framework Perceived Law of Motion: Macroeconomic dynamics The Perceived Law of Motion is a VAR(I) in the perceived state, X P t : X P t = C P + P X P t 1 + P S P " P t ; X P t = [ t ; y t ; i t ; P t ; P t ] NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

18 Macro-Finance Framework The Macro-Finance framework Perceived Law of Motion: Macroeconomic dynamics The Perceived Law of Motion is a VAR(I) in the perceived state, X P t : X P t = C P + P X P t 1 + P S P " P t ; X P t = [ t ; y t ; i t ; P t ; P t ] New-Keynesian model with stoch. trends P t and P t : t = E P t t+1 + (1 ) t 1 + y t + " ;t y t = y E P t y t+1 + (1 y )y t 1 (i t E P t t+1 P t ) + y"y;t i t = (1 i )i T t + i i t 1 + i" i;t i T t = P t + Et P t+1 + ( t P t ) + y y t P t = lim s!1 E P t [ t+s] P t = lim s!1 E P t [i t+s t+s] NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

19 Macro-Finance Framework The Macro-Finance framework Perceived Law of Motion: Macroeconomic dynamics The Perceived Law of Motion is a VAR(I) in the perceived state, X P t : X P t = C P + P X P t 1 + P S P " P t ; X P t = [ t ; y t ; i t ; P t ; P t ] New-Keynesian model with stoch. trends P t and P t : t = E P t t+1 + (1 ) t 1 + y t + " ;t y t = y E P t y t+1 + (1 y )y t 1 (i t E P t t+1 P t ) + y"y;t i t = (1 i )i T t + i i t 1 + i" i;t i T t = P t + Et P t+1 + ( t P t ) + y y t Updating the perceived stochastic trends: P t = P t 1 + f (Xt; :::; Xt n) P t = P t 1 + f (Xt; :::; Xt n) X t = [ t; y t; i t; P t ; P t ; t ; t ] P t = lim s!1 E P t [ t+s] P t = lim s!1 E P t [i t+s t+s] NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

20 Macro-Finance Framework The Macro-Finance framework Learning dynamics Learning dynamics are modeled along the lines of Kozicki and Tinsley (25): P t = P t 1 + w " ;t + (1 w ) b ;t + g ( t Et P 1 t) P t = P t 1 + w " ;t + (1 w ) b ;t + g (i t t Et P 1 (i t t )) The learning rule updates perceived trends in function of three types of information: Actual shocks to the 'true' ination target and/or equilibrium real rate (e.g. ination target announcements, release of productivity data, risk perceptions...). Subjective and exogenous belief shocks b ;t ; b ;t ( e.g. changes in credibility,...). Subjective and endogenous forecast errors of ination and real interest rates, ( t Et P 1 t) and (it t EP t 1 (it t)). Although ad hoc, the learning rule embeds as limiting cases: The full info. RE models (w = w = 1): e.g. stand; Mac-Fin ; = : Constant gain learning rule (w = w = ; b = b = ; g > g > ): NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

21 Econometric issues Econometric issues Econometric issues NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

22 Econometric issues Data Econometric issues Overview Data Summary of Bayesian estimation procedure Sets of estimated parameters Prior distributions Likelihood Alternative model versions NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

23 Econometric issues Data Econometric issues Data Model is estimated on US data: 196Q2 till 26Q4. Ination: quarter-by-quarter GDP deator (p.a. terms) is used. Source: Federal Reserve Economic Data archive (FRED). Output gap: CBO output gap measure is used (no- real time data). Source: Congressional Budget Ofce. Policy rate: Fed fund effective rate is used. Source: FRED. Yield curve: 1/4, 1/2, 1, 3, 5, 1 yr. maturities. Sources: Gürkaynak et al. (26) and FRED. Ination expectations: average ination expectations over 1 and 1 year horizons. Source: Survey of Professional Forecasters, FED Philadelphia. NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

24 Econometric issues Summary Bayesian Econometric issues Summary: Bayesian estimation framework MCMC (Metropolis-Hastings) identication of the posterior density p( i j Z T ) : p( i j Z T ) = L(Z T j i )p( i )=p(z T ) Parameters i : structural parameters related to the NK model, learning, prices of risk, mispricing and measurement errors. Priors of the parameters, p( i ) : Priors related to structural parameters are in line with macro literature. The priors of the learning model are biased towards rational expectations (E(w) = :85; (w) = :1). Likelihood function, L(Z T j i ); generated by the prediction error decomposition (Kalman lter): Transition equation is based on the Actual Law of Motion. Measurement equation combines macroeconomic information ( t; y t; i t); yield curve variables and ination expectations surveys. NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 2 / 34

25 Econometric issues Model versions Econometric issues Versions of the model Table: PROPERTIES OF ALTERNATIVE VERSIONS OF THE MODEL Model Macro (# stoch. trends) Prices of Risk Expectations Mispricing NK NK model () Consistent IS Full-info RE Yes Stand. NK mod MF1 NK model (1) Consistent IS Full-info RE Yes Stand. MF mod MFS NK model (2) Consistent: IS Full-info RE No Struct. MF mod MFM NK model (2) Consistent: IS Full-info RE Yes Liq. MF mod MFF NK model (2) Free: ; 1 Full-info RE No Flex. MF mod MFE NK model (2) Free: ; 1 Learning Yes Encompass.mod NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

26 Empirical ndings Empirical ndings Empirical ndings NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

27 Empirical ndings Empirical ndings Improving standard Macro-Finance models? Comparing model versions Estimation results of the MFE model Parameter estimates Implied macroeconomic factors Macro factors and the yield curve implied by the MFE model Fit of the yield curve Liquidity effects NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

28 Empirical ndings Improving standard Macro-Finance models? Improving standard Macro-Finance models? Comparing model versions Conclusion 1: The encompassing model, incorporating time-varying equilibrium real rates, imperfect information and liquidity effects, is strongly favored by the data. Table: MODEL PERFORMANCE: MARGINAL LIKELIHOOD AND BIC Log Marginal likelihood and BIC Model NK MF1 MFS MFM MFF MFE Marg. Lik BIC Decomposition of BIC Model NK MF1 MFS MFM MFF MFE Macro (-2lnlik) Yields (-2lnlik) In. exp.(-2lnlik) Penalty NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

29 Empirical ndings Estimation results Estimation results Parameter estimates of the encompassing model Conclusion 2: The structural parameters of the encompassing model are plausible and aligned to the empirical macro literature. The behavioral parameters of the (semi-) structural NK model are in line with empirical macro literature: Relative to benchmark Mac-Fin models, we nd stronger forward looking components ( = :66; y = :69): e.g. Galí et al (25) Phillips curve: low but signicant ination indexation ( = :53) and output sensitivity ( = :12): IS-curve: signicant habit persistence ( h = :75 ) and risk aversion in line with macro lit. ( = 2:5): Taylor rule parameters in line with the literature. Relatively low interest rate smoothing : ( = :4; y = :63 and i = :69): e.g. Rudebusch (22). Actual stochastic trends: Ination target displays only small time variation ( = :4%) but imprecisely estimated. Signicant volatility in the equilibrium real rate ( = :7%) but imprecisely estimated. (e.g. Trehan and Wu (27), Bjornland et al (26, 27), Bekaert et al. (25), Laubach and Williams (23)...) NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

30 Empirical ndings Estimation results Estimation results Parameter estimates of the encompassing model Param. Mean Std. Dev. Mode Crit.val. 5% Crit. val. 95% Phillips curve Ination indexation! Output sensitivity! IS curve Habit persistence! h Risk aversion! Monetary policy rule Ination gap! Output gap! y Interest smoothing! i Shocks Supply shock Demand shock y Policy rate shock i Ination target shock! Eq. real rate shock! NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

31 Empirical ndings Estimation results Estimation results Parameter estimates of the encompassing model Conclusion 3: Imperfect information and learning effects dominate long-run ination expectations. The parameter estimates imply only weak anchoring of subjective ination expectations. Ination belief shocks and adaptive learning effects dominate subjective ination expectations (at the mode w = :65): Ination target shocks:.3% (w = :65 :4% = :3%). Ination belief shocks:.2% ((1 w ) b = :35 :58% = :2%). Ination forecast errors (gain=.8) : 2%. No strong learning effects observed for the equilibrium real interest rate ( at the mode w = :97): Real rate (target) shocks:.71% (w = :97 :73% = :71%). Real rate belief shocks:.4% ((1 w ) b = :3 1:2% = :4%). Real rate forecast errors (gain.1):.1%. NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

32 Estimation results Empirical ndings Parameter estimates of the encompassing model Estimation results Table: POSTERIOR DENSITY ESTIMATES IB: LEARNING PARAMETERS Param. Mean Std. Dev. Mode Crit.val. 5% Crit. val. 95% Learning parameters: Long-run ination expectations: P t Weight RE! w Gain! g Belief shock! b Target shock! Learning parameters: perceived eq. real rate: P t Weight RE! w Gain! g Belief shock! b Eq. real shock! P t i = P t 1 + w " ;t + (1 w ) h b ;t + g ( t Et P 1 t) P t = P t 1 + w";t + (1 w) h b ;t + g (i t t E P t 1 (it t)) i NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

33 Empirical ndings Estimation results Estimation results Implied factors Inflation and long run inflation expectations Inflation and the inflation target 4 Conf. int. 95% 4 Conf. int. 95% 2 Inflation L R inflat. expect.(model) 2 Inflation Inflat. target L R inflat. expect.(spf) L R inflat. expect.(spf) Perceived equil. real interest rates 5 Actual equil. real interest rate Conf. int. 95% Conf. int. 95% Ex post real interest rate Ex post real interest rate Perceived equil. real rate Equil. real rate NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

34 Empirical ndings Macro factors and the yield curve Macro factors and the yield curve Yield curve t Conclusion 4: The encompassing Macro-Finance model captures a substantial part of the time variation of the yield curve and aligns ination expectations to survey data SPF (unlike standard Mac-Fin models). Yields In. Exp. (SPF) Maturity 1/2 yr 1 yr 3yr 5 yr 1 yr 1yr 1yr Total variation yield (st. dev.) Encompassing Macro-Finance model Residual variation (st. dev.) R-square Standard Macro-Finance model Residual variation (st. dev) Pure nance model (3 factor Vasicek) Residual variation (st. dev.) n.a. n.a. NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October 28 3 / 34

35 Empirical ndings Macro factors and the yield curve Macro factors and the yield curve Yield curve t Figure: OBSERVED AND FITTED YIELD CURVE OF THE MFE MODEL.2 Yield curve fit maturity 1/4 years.2 Yield curve fit maturity 1/2 years Yield curve fit maturity 1 years.2 Yield curve fit maturity 3 years Yield curve fit maturity 5 years.2 Yield curve fit maturity 1 years 5 5 Actual data Fitted Fitting error NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

36 Empirical ndings Macro factors and the yield curve Macro factors and the yield curve Yield curve t Long term maturity yields, real rate and inflation expectations Yield data (1 year maturity) Real rate(1yr av.): model implied Yield fit (1 year maturity) Fitting error Real rate(1yr av.): MF Long term inflation expectations actual and model implied Inflation expectations (1 yr.): SPF data Inflation expectations (1 yr.): model implied Fitting error Inflation expectations (1 yr.): MF NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

37 Empirical ndings Macro factors and the yield curve Macro factors and the yield curve Mispricing or liquidity effects Conclusion 5: There is evidence of signicant mispricing (liquidity preference effects), especially at the short end of the yield curve. x 1 3 Average mispricing: mode and 95% confidence interval mat= 1/2 yr. mat= 1 yr. mat= 3 yr. mat= 5 yr. mat= 1 yr. NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34

38 Conclusions Conclusions In this paper the standard (empirical) Macro-Finance models are extended by introducing (i) time variation in the equilibrium real interest rate (ii) liquidity effects and (iii) learning. The encompassing model outperforms all existing Macro-Finance models. The model 'explains' more than 95% of yield curve dynamics. The encompassing model, unlike standard Macro-Finance models, reconciles yield curve dynamics, ination expectations and the ination target. The results suggest that: Learning dynamics generate signicant differences between long-run ination expectations and the ination target. Important drivers of subjective ination expectations are ination forecasts errors and belief shocks. Perceived eq. real rate dynamics explain a substantial share of the variation in long-term yields. Signicant liquidity and risk premium effects at the short end of the yield curve. Open issues: Sources of dynamics in perceived and/or actual equilibrium real interest rate? NBB Colloquium (KULeuven and RSM, EUR) An Encompassing Macro-Finance Model October / 34