A Regime-Switching SVAR Analysis of ZIRP

Transcription

1 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 1 / 32 A Regime-Switching SVAR Analysis of ZIRP Fumio Hayashi and Junko Koeda Prepared for CIGS Conference on Macroeconomic Theory and Policy 2013 June 25, 2013

2 To get started... Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 2 / 32

3 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 3 / 32 What This Paper Does VAR/SVAR analysis of the effect of ZIRP/QE on macro variables (inflation and output) Japan has, by our count, 130 months of ZIRP (as of Dec. 2012), maybe enough for time-series analysis Unique in two respects: The regime is observable and endogenous (unlike in the hidden-stage Markov switching model) can study IR to regime changes.

4 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 4 / 32 Relation to the Lit Previous SVAR-IR papers using Japanese data Iwata-Wu (JME 2004): VAR with nonnegativity constraint on the interest rate. Honda et. al. (2007): straight SVAR-IR (prices, output, money) on the 2nd QE period ( ). Fujiwara (JJIE 2006), Inoue-Okimoto (JJIE 2008): Markov-switching SVAR-IR (prices, output, policy rate, money).

5 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 5 / 32 Plan of Talk Identifying the Zero Regime The Model Estimation Results IRs Conclusions about BOJ s ZIRP

6 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 6 / 32 Identify Zero Regime: the L, r r against m, % 8% 7% r - r bar (net policy rate) 6% 5% 4% 3% 2% 1% 0% 0% 50% 100% 150% 200% excess reserve rate m (log of actual to required reserves)

7 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 7 / 32 Identify Zero Regime: the L, r r against m, magnified 1.0% r - r bar (policy rate minus interest rate on reserves) 0.8% 0.6% 0.4% 0.2% 0.0% 0% 10% 20% 30% 40% 50% excess reserve ratio m (log of actual to required reserves)

8 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 8 / 32 Identifying Zero Regime: Three Spells of Z Periods of Zero Regime (i) March July 2000 (ii) March June 2006 (iii) December 2008 to date

9 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 9 / 32 Policy Rate (r) in Japan, August 1985-December % 8% 7% 6% 5% 4% 3% 2% 1% 0%

10 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 10 / 32 The Model, 1 of 4: textbook SVAR Point of departure: textbook 3-variable SVAR (p, x, r), p = monthly inflation rate, x = output gap, r = policy rate, in that order. The first two equations are reduced forms in (p, x). The third equation is the Taylor rule. The error in the Taylor rule is independent of (p, x) reduced-form shocks. Taylor rule: with π t 1 12 (p t + + p t 11 ), r t = ρ r rt + (1 ρ r )r t 1 }{{} +σ r v rt, r rt e, Taylor rate t αr + β r (1 2) [ π t x t ] }{{} desired Taylor rate, v rt N (0, 1). See, e.g., Stock-Watson s review article in J. of Economic Perspectives, 2001.

11 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 11 / 32 The Model, 2 of 4: Add Zero Lower Bound Impose the lower bound (censored Taylor rule) r t = max [ r e t + σ r v rt, r t ], vrt N (0, 1). Equivalently, r t e + σ r v rt, v rt N (0, 1) if s t = P, r t = r t if s t = Z, P if rt e + σ r v rt r t, where s t = Z otherwise. Note: the regime s t is endogenous.

12 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 12 / 32 The Model, 3 of 4: Add m Add m to (p, x, r). 0 if s t = P, m t = max [ mt e + σ m v mt, 0 ], v mt N (0, 1) if s t = Z, where m e t ρ m ( α m + β m [ π t x t ]) + (1 ρ m )m t 1, (reminder) p monthly inflation rate, πt 1 12 (p t + + p t 11 ), x output gap, r policy rate, ( m log actual reserves required reserves ).

13 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 13 / 32 The Model, 4 of 4: Introduce Exit Condition/Forward Guidance If s t 1 = Z, P if rt e + σ r v rt r t and π t π + σ π v πt, }{{} s t = period t target inflation rate Z otherwise. If s t 1 = P, as before, i.e., s t = P if r e t + σ r v rt r t, Z otherwise. (reminder) Taylor rule: with π t 1 12 (p t + + p t 11 ), r t = ρ r rt + (1 ρ r )r t 1 }{{} +σ r v rt, r rt e, Taylor rate t αr + β r (1 2) [ π t x t ] }{{} desired Taylor rate.

14 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 14 / 32 Model Recap: Sequence of Events from t to r + 1 (1) (p t, x t ) (inflation and output) determined by the reduced form equations. (2) CB draws (v rt, v πt ) and determines s t. st is a Markov chain. Transition probabilities depend on (p t, x t ). (3) CB draws v mt. If st = P, then r t = rt e + σ r v rt, m t = 0. If st = Z, then r t = r t, m t = max[mt e + σ m v mt, 0]. (1) (p t+1, x t+1 ) determined given s t. (reminder) ( [ ]) mt e ρ m α m + β m π t + (1 ρ m)m t 1, x t

15 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 15 / 32 Implications for Estimation Reduced-form equations: will take Lucas critique seriously. Given estimation done conditional on regime, no need for selectivity correction. Taylor rule: if no exit condition/forward guidance, Tobit with exit condition/forward guidance, only slightly more complicated ML. Reserve supply function: No selectivity bias.

16 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 16 / 32 Plan of Talk Identifying the Zero Regime The Model Estimation Results IRs Conclusions about BOJ s ZIRP

17 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 17 / 32 Estimation: Data p (monthly inflation rate): p t 1200 [log(cpi t ) log(cpi t 1 )]. π (12-month inflation rate): π t = 1 12 (p t + + p t 11 ). m (excess reserve rate): m t 100 log ( actual reservest required reserves t ). r (policy rate): collateralized overnight interbank rate. rt =average of daily values over the reserve maitenance period (16th day of month t to 15th day of month t + 1). x (output gap): See next picture.

18 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 18 / 32 Japanese log IP, log industrial production HP-filtered log industrial production

19 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 19 / 32 Estimation Results: Executive Summary [ ] (reminder) r t = ρ r rt + (1 ρ r )r t 1 +σ r v rt, r t α r }{{} + β r π t. (1 2) x t rt e, Taylor rate }{{} desired Taylor rate [ ]) (reminder) m t = max[mt e + σ mv mt, 0], mt e ρ m (α m + β m π t + (1 ρ m )m t 1. x t Reserve supply on sample Z: has right sign, but not sharply estimated. Taylor rule (more in next picture): Need to allow α r to decline after the bubble period of Parameters sharply estimated. Satisfies Taylor principle. Reduced forms: Lucas should apply with full force. not sharply estimated.

20 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 20 / 32 Policy Rate and Desired Taylor Rates (r t ), % 5% percent per year 0% -5% -10% -15% -20% policy rate original desired Taylor rate estimated desired Taylor rate

21 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 21 / 32 Policy Rate and Desired Taylor Rates (r t ), Explain why α r has to be lower post-bubble Show the exit condition/forward guidance in action. [ ] (reminder) r t = ρ r rt + (1 ρ r )r t 1 +σ r v rt, r t α r + β r π t. }{{} (1 2) x t rt e, Taylor rate }{{} desired Taylor rate

22 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 22 / 32 Estimation: (p, x) Reduced Form sample period is January December 2012 subsample P (s t = P in the prev. month, sample size = 123) dep. var. const. p t x t r t m t R 2 p t [ 1.1] [1.1] [0.6] [3.6] x t [ 0.01] [0.6] [24] [ 0.8] subsample Z (s t = Z in the prev. month, sample size = 129) dep. var. const. p t x t r t m t R 2 p t [ 2.5] x t [ 0.5] 0.05 [0.6] 0.18 [1.1] 0.03 [1.2] 0.90 [25] [0.9] [0.8]

23 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 23 / 32 Things to Note about Reduced Forms Structural change in Inflation persistence (much higher before 1992). lagged m coeffficient under P and lagged r coefficient under Z set to 0. lagged m coefficient in p t+1 equation under P positive and significant. Intercepts lower under Z.

24 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 24 / 32 Plan of Talk Identifying the Zero Regime The Model Estimation Results IRs Conclusions about BOJ s ZIRP

25 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 25 / 32 GRT s IR of i to j Gallant-Rossi-Tauchen (Econometrica, 1993): For a possibly nonlinear stationary process in general, y t (n 1) E ( y i,t+k y jt + δ, y j 1,t,..., y 1t, y t 1, y t 2,... }{{} alternative history E ( y i,t+k y jt, y j 1,t,..., y 1t, y t 1, y t 2,... }{{} baseline history Generally history-dependent and not proportional to δ in general. Baseline history doesn t have to be the actual history. Calculation by Monte Carlo integration. Natural extension to nonlinear case. Reduces to the familiar orthogonalized IR in the linear case (see Hamilton s time series text). ) ).

26 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 26 / 32 Application to our Model: m-ir and r-ir m-ir (IR to a change in m): E ( y t+k s t = Z, (m t + δ m, r t, p t, x t ), y t 1,... ) }{{} y t in the alternative history E ( y t+k s t = Z, (m t, r t, p t, x t ), y t 1,... ), y = p, x, r, m. }{{} y t in the baseline history r-ir (IR to a change in r): ( E t yt+k s t = P, (0, r t δ r, p t, x t ), y t 1,... ) }{{} y t in the alternative history ( E t yt+k s t = P, (0, r t, p t, x t ), y t 1,... ), y = p, x, r, m. }{{} y t in the baseline history

27 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 27 / 32 Estimated m-ir and r-ir Reserve increases are expansionary: m p, x. Consistent with previous studies (Inoue-Okimoto, Honda et. al.). Price puzzle observed: r p, x.

28 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 28 / 32 ZP-IR: IR to Regime Change from P to Z ZP-IR: E ( y t+k s t = P, (0, r t, p t, x t ), y t 1,... ) }{{} y t in the alternative history E ( y t+k s t = Z, (m t, r t, p t, x t ), y t 1,... ), y = p, x, r, m. }{{} y t in the baseline history Can be rewritten as [E ( y t+k s t = P, (0, r t, p t, x t ),... ) E ( y t+k s t = Z, (0, r t, p t, x t ),... )] }{{} pure regime change effect [E ( y t+k s t = Z, (m t, r t, p t, x t ),... ) E ( y t+k s t = Z, (0, r t, p t, x t ),... )] } {{ } m-ir

29 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 29 / 32 Estimated ZP-IR The pure ZP-IR tend to be expansionary: Z P p, x. Does the effect of m-ir more than offset it? Depends on t. See IR plots for: t = February 2004 (peak of QE), t = June 2006 (one month before the BOJ terminated Z).

30 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 30 / 32 ZP-IR, February Monthly Inflation (p) 2 Output Gap (x) % per year 0 % months months 1 Policy Rate (r) 50 Excess Reserve Rate (m) % per year % months months

31 Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 31 / 32 ZP-IR, June Monthly Inflation (p) 2 Output Gap (x) % per year 0 % months months 1 Policy Rate (r) 50 Excess Reserve Rate (m) % per year % months months

32 Conclusions about BOJ s ZIRP Fumio Hayashi and Junko Koeda A Regime-Switching SVAR Analysis of ZIRP June 25, 2013, 32 / 32 Increases in reserves under ZIRP (the Zero regime) raise both inflation and output. Terminating ZIRP is not necessarily deflationary. In particular, the termination in July 2006 may have been inflationary. However, note the wide error bands.