Endogenous Regime Switching Near the Zero Lower Bound 1 Kevin J. - PowerPoint PPT Presentation

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Endogenous Regime Switching Near the Zero Lower Bound 1 Kevin J. Lansing Federal Reserve Bank of San Francisco January 26, 2018 Conference on Nonlinear Models in Macroeconomics and Finance in a Nonlinear World 1 Any opinions expressed here do not necessarily reflect the views of the Federal Reserve Bank of San Francisco or the Board of Governors of the Federal Reserve System.

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Numerous ZLB (or ELB) episodes in global data

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion ZLB not (yet) binding in Norway

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Standard NK model has multiple RE equilibria Taylor rule + Fisher Eqn. + ZLB ⇒ Two steady states. (Benhabib, Schmitt-Grohé & Uribe AER, JET 2001a,b). (1) Targeted: i = r ∗ + π ∗ > 0 . (2) Deflation: i = 0 and π = − r ∗ . r ∗ = “natural rate of interest.” Evidence: r ∗ shifts over time and can drop below zero (Laubach & Williams 2016, Eggertsson, Mehrotra & Robbins 2017) .

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion U.S. data: ZLB binding 2008.Q4 to 2015.Q4 Bullard 2010: “Promising to remain at zero for a long time is a double-edged sword.”

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion U.S. data: ZLB binding 2008.Q4 to 2015.Q4 Bullard 2010: “Promising to remain at zero for a long time is a double-edged sword.”

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Summary of paper NK model with two local equilibria. Agent employs weighted-average of the two sets of local linear forecast rules. Weight optimized to minimize RMSFE over past T w quarters. Unlike Arouba et al. (2018), regime switching here is endogenous. Results: Adverse shock ⇒ more weight on deflation forecast rules ⇒ deflation can become self-fulfilling. Episode accompanied by severe recession (highly negative output gap) with nominal rate at ZLB. Similar to 2007-09 Great Recession. But even in normal times, agent may place nontrivial weight on deflation forecast rules, causing central bank to consistently undershoot π ∗ (like now: π U.S. < 0 . 02 since mid-2012). t

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Related literature (partial list) Transition between regimes driven by exogenous sunpots Aruoba, Cuba-Borda, & Schorfheide (2018, REStud forthcoming ) Aruoba & Schorfheide (2016, FRBKC Jackson Hole Symposium Infrequent but long-lived ZLB episodes in global data Dordal-i-Carreras, Coibion, Gorodnichenko & Wieland (2016 ) ) Adaptive learning to select among multiple equilibria Evans & Honkapohja (2005, RED ), Eusepi (2007, JME ) Benhabib, Evans & Honkapohja (2014, JEDC) Arifovic, Schmitt-Grohé & Uribe (2018, JEDC ) Optimal monetary policy with shifting natural rate Eggertsson and Woodford (2003, BPEA ) Evans, Fisher, Gourio & Krane (2015, BPEA ) Hamilton, Harris, Hatzius, & West (2016. IMF Econ. Rev. ) Gust, Johannsen, López-Salido (2017, IMF Econ. Rev. ) Basu & Bundick (2015, NBER WP 21838)

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion New Keynesian model with zero lower bound (ZLB) Fisher relationship � �� � y t = E t y t + 1 − α [ i t − E t π t + 1 − r t ] + v t , v t = ρ v v t − 1 + ǫ v , t π t = β E t π t + 1 + κ y t + u t , u t = ρ u u t − 1 + ǫ u , t t + π ∗ + g π ( π t − π ∗ ) + g y ( y t − y ∗ )] i ∗ ρ i ∗ t − 1 + ( 1 − ρ ) [ E t r ∗ = t π t = ω π t + ( 1 − ω ) π t − 1 , π t � π 4 , t ≡ 4-qtr. inflation rate . max { 0 , i ∗ i t = t } . ≡ − log [ β exp ( ζ t )] + ( 1 / α ) E t ∆ ¯ r t y t + 1 � �� � � �� � Discount factor Expected potential output growth � � ρ r r t − 1 + ( 1 − ρ r ) r ∗ 0 , σ 2 r t = t + ε t , ε t ∼ N ε � � r ∗ r ∗ 0 , σ 2 = t − 1 + η t , η t ∼ N t η r ∗ ≡ Natural rate of interest (long-run endpoint of r t ) t

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Two long-run endpoints (steady states) Targeted Endpoint Deflation Endpoint π t = π ∗ π t = − r ∗ t y t = y ∗ ≡ π ∗ ( 1 − β ) / κ y t = − r ∗ t ( 1 − β ) / κ � � 1 − g π − g y ( 1 − β ) i ∗ t = r ∗ t + π ∗ i ∗ t = ( r ∗ t + π ∗ ) κ i t = i ∗ i t = 0 t

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Two long-run endpoints (steady states) Targeted Endpoint Deflation Endpoint π t = π ∗ π t = − r ∗ t y t = y ∗ ≡ π ∗ ( 1 − β ) / κ y t = − r ∗ t ( 1 − β ) / κ � � 1 − g π − g y ( 1 − β ) i ∗ t = r ∗ t + π ∗ i ∗ t = ( r ∗ t + π ∗ ) κ i t = i ∗ i t = 0 t Shifting Endpoint Time Series Model (Kozicki-Tinsley, JMCB 2012) � r t − ρ r r t − 1 � E t r ∗ + ( 1 − λ ) E t − 1 r ∗ = λ t t − 1 1 − ρ r − ( 1 − ρ r ) 2 φ +( 1 − ρ r ) √ σ 2 ( 1 − ρ r ) 2 φ 2 + 4 φ Kalman η λ = φ ≡ , 2 σ 2 gain ε t + h ) = ( ρ r ) h ( r t − E t r ∗ E t ( r t + h − r ∗ ρ r = 0 . 86 t ) ,

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Two local rational expectations equilibria Targeted (Unique). Forecast rules assume i ∗ t = i t > 0 for all t   r t − E t r ∗   t y t − π ∗ ( 1 − β ) / κ   π t − 1 − π ∗     = A ×   π t − π ∗ i ∗ t − 1 − ( E t r ∗ t + π ∗ )     i ∗ t − ( E t r ∗ t + π ∗ ) v t u t Deflation (MSV). Forecast rules assume i ∗ t ≤ 0 , i t = 0 for all t   y t − ( − E t r ∗ t ) ( 1 − β ) / κ   = π t − ( − E t r ∗ t ) i ∗ t − ( E t r ∗ t + π ∗ ) [ 1 − g π − g y ( 1 − β ) / κ ]   r t − E t r ∗ t   π t − 1 − ( − E t r ∗ t )     i ∗ t − 1 − ( E t r ∗ t + π ∗ ) [ 1 − g π − g y ( 1 − β ) / κ ] B ×     v t u t

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Two local rational expectations equilibria Targeted (Unique). Forecasts assume i ∗ t = i t > 0 for all t   0 . 594 − 0 . 153 − 0 . 386 3 . 221 − 0 . 174   A = − 0 . 017 − 0 . 033 0 . 069 0 . 275 1 . 396 0 . 128 0 . 129 0 . 718 0 . 682 0 . 158 Deflation (MSV). Forecasts assume i ∗ t ≤ 0 , i t = 0 for all t   1 . 247 0 0 5 . 397 0 . 092   B = 0 . 213 0 0 0 . 661 1 . 429 0 . 279 0 . 162 0 . 8 1 . 171 0 . 215 Local solution coefficients for state variable r t − E t r ∗ t : B 11 B 21 B 31 = 2 . 1 = 3 . 1 = 2 . 2 A 11 A 21 A 31 ⇒ Deflation equilibrium exhibits much more volatility.

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Model parameter values 0 . 15 α Interest rate coefficient in Euler equation. β 0 . 995 Discount factor in Phillips curve. κ 0 . 025 Output gap coefficient in Phillips curve. σ v 0 . 010 Std. dev. of demand shock. σ u 0 . 005 Std. dev. of cost push shock. ρ v 0 . 8 Persistence of demand shock. ρ u 0 . 3 Persistence of cost push shock. π ∗ 0 . 02 Central bank inflation target. ω 0 . 459 π t � 4-quarter inflation rate. g π 1 . 5 Policy rule response to inflation. g y 1 . 0 Policy rule response to output gap. ρ 0 . 80 Interest rate smoothing parameter. ρ r 0 . 858 Persistence parameter for r t . σ ε 0 . 010 Std. dev. temporary shock to r t . σ η 0 . 002 Std. dev. permanent shock to r t . Optimal Kalman gain for E t r ∗ λ 0 . 025 t .

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Natural rate process approximates Laubach-Williams r-star Bounds for simulations: − 0 . 004 ≤ r ∗ t ≤ 0 . 037

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Real federal funds rate versus efficient real rate Efficient real rate: Cúrdia, Ferrero, Ng & Tambalotti ( JME , 2015)

Overview Related Literature Model Calibration Replicating U.S. Data Simulations Learning Conclusion Endogenous forecast rule switching based on past RMSFE Variables that the agent must forecast: y t + 1 and π t + 1 E t y t + 1 = µ t E targ � y t + 1 + ( 1 − µ t ) E defl y t + 1 t t E t π t + 1 = µ t E targ � π t + 1 + ( 1 − µ t ) E defl π t + 1 t t Choose µ t to minimize RMSFE t − 1 for moving window of recent data �� � 2 T w y t − j − µ t E targ 1 t − j − 1 y t − j − ( 1 − µ t ) E defl min ∑ t − j − 1 y t − j T w µ t j = 1 � 2 � 0 . 5 � π t − j − µ t E targ t − j − 1 π t − j − ( 1 − µ t ) E defl + t − j − 1 π t − j For simulations, impose 0 ≤ µ t ≤ 1 , with T w = 8 qtrs.