w,_2, x,_ls x,_2, r,_, and r* (foreign interest rate - 1YEURIBOR). We assume that the parameters in the Eqs. (6) and (7) are time-invariant. Next, the correlation between the standardized residuals 1- >
- rt r, + v
V J 1 J
Our estimation framework begins with the following regression:
where ^t+i is yearly inflation ;' months ahead, where ;=12,....,24. Next, we control for the lagged inflation terms:
n h=\
where for simplicity we set n=4.17
(9)
1 \
km = 00+01 \rt-r, r,
vv J, ' J
(10)
Using Eqs. (9) and (10), we investigate the information content of monetary policy stance on the future level of inflation. We also re-specify the above equations to address the future change in the inflation rate as follows:
(( _ > 1 >
*m ~ n, = 00 + 01 \rt-r, r
K\ J i j
(f _ \
- 71, = 0 + 01 \rt-r, r
k\ j 1 j
+v,
(11)
(12)
The results from Eq. (9) are given in Table A.3 in the Appendix. Our definition of monetary policy stance seems to be informative for future inflation, explaining typically about 1/3 of its variance. These results are largely confirmed, when controlling for the lagged inflation terms, as suggested the estimation of Eq. (10) presented in Table A.4. The results suggest that when actual interest rate is 10% above the policy neutral rate, inflation is likely to fall by about 1 p.p. at the monetary policy horizon. Similarly, policy neutral rate seems to be relatively good predictor of the future change of inflation rate, as presented in Table A.5. This result is largely robust to inclusion of lagged inflation as well (see Table A.6). All in all, the results suggest usefulness of policy neutral rate in understanding future behavior of inflation.18
5 Conclusions
This paper analyzes the policy neutral rate in the Czech Republic. In order to do so, we estimate various specifications of simpleTaylor-type monetary policy rules at the monthly
/ 7 We also included higher lags, but with little impact on the results.
18 We also tested the robustness of our results by including other macroeconomic variables to Eqs. (10) and (12) such as real effective exchange rate, credit and monetary aggregates. The results remain largely unchanged and are available upon request.
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frequency from 2001:1 to 2006:9. To address the sensitivity of results, the specifications differ based on whether we include real-time or ex-post revised data, employ backward or forward-looking monetary policy rules or vary the measure of output gap.
To estimate time-varying policy neutral rate, we use time-varying parameter model with endogenous regressors (Kim, 2006).This approach is especially appealing, when estimating monetary policy rules, as it addresses the endogeneity of inflation (forecast) and output gap. Indeed, the results support the usefulness of applying time-varying parameter model with endogenous regressors. The bias correction terms, accounting for the endogeneity of regressors, are typically significant, the log likelihood improves after their inclusion and the estimated path of policy neutral rate is for certain periods considerably different.
The results indicate that policy neutral rate decreases gradually over the course of sample period from some 5% in 2001 to about 2.5% in 2006 showing a substantial interest rate convergence to the levels comparable to the euro area. Over the longer time horizon, the decrease may be supported a number of factors such as capital accumulation, the decrease in risk premium, real equilibrium exchange rate appreciation as well as successful disinflation of Czech economy and well-anchored inflation expectations.
One of our primary policy applications, except for measuring policy neutral rate by the novel technique, is also proposing a measure of monetary policy stance based on a deviation of actual interest rate from policy neutral rate. Our results indicate that this measure is quite useful in predicting future inflation developments. More specifically, monetary policy stance affects both the level as well as change of future inflation rate. In terms of future research, it would be interesting to see more evidence on other inflation targeting countries to uncover, whether our proposed monetary policy stance measure remains useful predictor of future inflation developments, as we find in the case of Czech Republic.
Abstract
This paper examines time-varying policy neutral interest rate in real time for the Czech Republic in 2001:1-2006:09 estimating various specifications of simple Taylor-type monetary policy rules. For this reason, we apply a structural time-varying parameter model with endogenous regressors.The results indicate that policy neutral rate gradually decreased over sample period to the levels comparable to those of in the euro area. Next, we propose a measure of monetary policy stance based on a difference between the actual interest rate and estimated policy neutral rate and find it a useful predictor of the level as well as change of future inflation rate.
Keywords
policy neutral rate, Taylor rule, time-varying parameter model with endogenous regressors JEL classification / JEL klasifikace
E43, E52, E58
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Souhrn
Tento článek analyzuje politicky neutrální („rovnovážnou") úrokovou míru s tzv. daty v reálném čase v České republice od 2001:1 do 2006:09 na základě odhadů různých specifikací Taylorova pravidla. Aplikujeme strukturální model s časově proměnlivými parametry a s endogenními regresory, abychom vyhodnotili fluktuace politicky neutrální sazby v čase. Nalézáme, že politicky neutrální sazba v čase klesá na úroveň srovnatelnou se zeměmi eurozóny. Dále navrhujeme způsob měření nastavení měnové politiky založeném na rozdílu mezi skutečnou úrokovou mírou a námi odhadnutou politicky neutrální sazbou a nalézáme, že tímto způsobem jsme schopni dobře predikovat budoucí inflaci i budoucí změnu inflace.
Klíčová slova
politicky neutrální úroková míra, Taylorovo pravidlo, model s časově proměnlivými parametry a endogenními regresory
Kontaktní adresa / Contact address Roman Horváth, M .A,
Česká národní banka a Institut ekonomických studií, Karlova univerzita v Praze (e-mail: roman.horvath@gmail.com)
Roman Horváth, M.A.
Je absolventem Central European University. V současné dobé pracuje jako starší ekonom odboru ekonomického výzkumu a finanční stability v České národní bance.
Je editorem AUCO Czech Economic Review a členem redakční rady Finance a úvěr - Czech Journal of Economics and Finance. Je členem Ekonometrické společnosti a Evropské ekonomické asociace.
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APPENDIX
Table A.I - KPSSTest
Series Test statistic
PRIBOR3M 0.355*
CPI Inflation 0.165
I CPI Inflation forecast (t+12) 0.163
Net Inflation 0.147
Output gap - HP filtered 0.106
Output gap - Real-time 0.293
I Output gap - Ex-post 0.214
M2 growth 0.168
Real effective exchange rate 0.447*
The null hypothesis is that the series is level stationary. Critical values for the null hypothesis: 10% - 0.347, 5% - 0.463, 1%- 0.739. Sample period: 2001:1-2006:09. * ** *** denotes significance at the 10,5 and I percent level, respectively.
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Chart A.I
- Interest Rate, Output Gap and Inflation
Note: This chart presents current inflation, short-term interbank interest rate (3M PRIBOR) and CNB output gap as of October 2006 forecast round.
Chart A.2 - Comparison of Output Gap Estimates
2001 2002 2003 2004 2005 2006 —'- Gap - ex post —*— Gap - real-time —"- Gap - HP filter
Note: This chart presents three measures of output gap used in the paper: Output gap estimated by the CNB as of their October 2006 forecast round (Gap - ex post), Real-time based output gap estimated by the CNB (Gap - real-time) and the output gap calculated using HP filter (Gap - HP filter) as the estimate of potential output.
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Table A.2 - Monetary Policy Rules Estimation
rt={\ -p) r )+ßx, + pr,_x + £
rt = r,-\ + #„ 0t ~ i.i.d.N(o,al)
e, = Kv,e(Te,tvt+K9,e i, ~ Mo,(i-<£ )
Model
: Parameters l 2 3 4 5 6:7 s 9 10 11 12
P 0.40"' : 0.40*** 0.40*** 0.41*** 0.40*** : 0.40*"" : 0.42*** 0.40*** ■■ QA2„, 0.42*** 0.45*** 0.40"'
(0.02) : (0.09) (0.06) (0.06) (0.07) : (0.09) : (0.11) (0.10) ■■ (0.10) (0.09) (0.10) (0.15)
a 0.27™ 0.07 0.28*** 0.06 0.28*** 0.07 ' -0.15 -0.15 -0.18 -0.16 -0.17 -0.14
(0.07) (0.07) (0.08) (0.06) (0.07) ' (0.06) ' (0.12) (0.11) i (0.11) (0.11) (0.10) (0.09)
ß 0.21 0.11 -0.06 0.57" -0.06 -0.06 ' 0.12 0.14 ' 0.66" 0.66" 0.18 -0.02
(0.24) (0.24) (0.28) (0.29) (0.22) ' (0.23) ' (0.27) (0.25) ' (0.28) (0.31) (0.23) (0.19)
K'v., -0.06"* ' -0.07*** -0.06" \ \ 0.01 0.02 0.02
(0.01) ; (0.02) (0.02) ! (0.01) : (0.01) (0.01)
-0.02* -0.02* -0.02* ! 0.01 -0.01 -0.02***
(0.01) ; (0.01) (0.01) i (0.01) (0.02) (0.01)
AIC -1.10 -1.00 -1.07 -1.00 -0.95 -0.94 . -0.91 -0.94 -0.94 -0.96 -0.91 -0.88
Note: Robust standard errors in brackets. ***, ** and *indicates the significance at 1,5 and 10%, respectively. Models differ according to whether bias correction terms are included and the specification of ^",+, and xt. ftt+i is eitherCNB inflation forecast one year ahead (abbreviated as IF below) or current inflation rate (IC). xt is a measure of output gap: 1. as estimated by HP filtering (HP), 2. CNB ex-post output gap measure based on multivariate Kalman filter procedure (EX), 3. CNB real-time output gap measure based on multivariate Kalman filter procedure (REAL). Model 1and2 = IC, HP; Model 3 and 4 = IC, EX; Model 5 and 6 = IC, REAL; Model 7 and 8 = IF, HP; Model 9 and 10 = IF, EX and Model 11 and 12 = IF, REAL;
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Chart A.3 - Importance of Bias Correction Terms in Estimating Policy Rules
Backward-looking policy rule
2001 2002 2003 2004 2005 2006
\
\ lift
w vis
V
2001 2002 2003 2004 2005 2006
2001 2002 2003 2004 2005 2006
Current inflation, output gap - HP filter
Current inflation, output gap - ex-post
Forward-looking policy rule
Current inflation, output gap - real-time
> <
1/5
A ^
\ •
V A - —^ wv—' —
i if/ **y r v WV >--=— /"\
w—^~~v— ■•v 1 Jl Ml -'WV---
■U If
i
2001 2002 2003 2004 2005 2006
2001 2002 2003 2004 2005 2006
2001 2002 2003 2004 2005 2006
nflation forecast - real-time, output gap - HP filter ! Inflation forecast - real-time, output gap - ex-post ! Inflation forecast - real-time, output gap - real-time
Note chart A3: The difference between the policy neutral rates estimated from the time-varying parameter model with endogenous regressors, rt,e with its confidence intervals, and from the conventional time-varying parameter model, r t,c. The measure of output gap and inflation is used for estimation of policy neutral rate is reported below each chart. Consequently, if the confidence intervals are different from zero, it means that r,,c does not lie within the confidence intervals of rt.B .
Table A.3 - Monetary Stance and Future Level of Inflation
(I \ /_ \
rt - r, A'
j / )
\ i Adj. R2
12 \ 1.43*** \ -6.89 \ 0.07
13 \ 1.31*** i -9.91* \ 0.15
14 \ 1.26*** \ -11.30** \ 0.19
15 i i 26*** | -11.58** | 0.20
16 \ 1.22*** \ -13.23** \ 0.27
17 \ 1.20*** \ -14.31*** \ 0.32
18 \ 1.23*** \ -13.93*** \ 0.31
19 i 1.14*** \ -16.02*** \ 0.39
20 \ 1.18*** \ -15.81*** \ 0.39
21 \ 1.25*** \ -14.81*** \ 0.36
22 \ 1.31*** \ -13.82** \ 0.32
23 ; i _42*** \ -12.54** \ 0.30
24 \ 1.57*** i -10.16* 0.21
Note: Robust standard errors. ***, ** and ^indicates the significance at 1,5 and 10%, respectively.
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Table A.4 - Monetary Stance and Future Level of Inflation, Controlling for Lagged Inflation
ff = i rt vv h=\ -h +V,H
: / 0O 0 0, 0, 0: 0s ! Adj. R2 !
12 \ 2.33*** \ -0.94 0.03 0.04 \ 0.07 \ -0.48 i 0.33
13 \ 1.95** i -2.49 -0.11 0.19 i -0.06 i -0.33 i 0.41
14 \ 1.67* i -3.59 -0.14 0.04 i 0.19 i -0.36 i 0.46
15 | 1.49 | -4.26 -0.25 0.24 | -0.07 | -0.15 | 0.48
16 \ 0.66 \ -6.86** -0.09 -0.07 \ -0.22 \ 0.30 \ 0.52
17 \ 0.02 I -8.89*** -0.25 -0.16 \ 0.14 \ 0.31 \ 0.57
18 \ -0.33 I -9.98*** -0.55*** 0.19 \ 0.14 \ 0.33 ; o.60
19 ; -1.05 \ -12.12*** -0.57*** 0.20 \ 0.27 \ 0.36 \ 0.63
20 \ -1.12 \ -12.27*** -0.62** 0.36 \ 0.17 \ 0.38 ; o.60
21 j -0.78 \ -11.09** -0.46 0.18 \ 0.21 \ 0.34 | 0.51
22 j -0.57 \ -10.31** -0.42** 0.25 \ -0.09 \ 0.52 \ 0.45
23 i -0.48 i -9.86** -0.26 -0.06 i 0.01 i 0.61* i 0.41
24 i -0.53 i -9.89** -0.40 0.12 i -0.12 \ 0.73* . 0.39
Note: Robust standard errors. ***, ** and indicates the significance at 1,5 and 10%, respectively.
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Table A.5 - Monetary Stance and Future Change of Inflation
Km -Kt=A+x
rt - r,
r,
+ Vt.
i 0o 0, Adj. R2
12 i -3.04*** \ -15.39*** \ 0.53
13 \ -3.29*** \ -16.55*** \ 0.57
14 i -3.48*** \ -17.47*** \ 0.59
15 j -3.54*** J -17.77*** J 0.59
16 \ -3.58*** \ -18.01*** \ 0.60
17 \ -3.60*** \ -18.09*** \ 0.60
18 \ -3.56*** \ -17.93*** \ 0.59
19 \ -3.60*** \ -18.05*** \ 0.60
20 \ -3.54*** \ -17.81*** \ 0.60
21 \ -3.42*** \ -17.24*** \ 0.60
22 \ -3.28*** \ -16.62*** \ 0.58
23 i -3.10*** \ -15.88*** i 0.56
24 \ -2.89*** \ -15.11*** 0.53
Note: Robust standard errors.
(and ^indicates the significance at 1,5 and 10%, respectively.
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Table A.6 - Monetary Stance and Future Change of Inflation, Controlling for Lagged Inflation -n,=0o+0i {jj< ~ r< r< j + 2 0*+!*«-*
: Z 0o 02 I 03 04 I 0s Adj. R2
12 \ 2.12*** \ -1.26 -1.11*** i -0.08 \ 0.53* i -0.59 \ 0.82
13 j 1.62* \ -3.18 -1.26*** i 0.05 i 0.43 i -0.42 i 0.84
14 i 1.41 i -4.06 -1.28*** i -0.11 i 0.67* i -0.46 \ 0.85
15 i 1.44 \ -4.10 -1.41 *** i 0.08 i 0.46 i -0.33 \ 0.86
16 i 0.56 \ -6.82* -1.24*** i -0.23 i 0.33 i 0.13 \ 0.86
17 i -0.08 i -8.89** -1.41 *** i -0.31 i 0.69** i 0.14 \ 0.89
18 i -0.33 ! -9.70*** -1.72*** i 0.05 i 0.68* i 0.14 \ 0.89
19 i -1.13 \ -12.05*** -1.74*** i 0.07 i 0.80** i 0.19 \ 0.88
20 i -1.19 \ -12.20*** -1.79*** i 0.23 i 0.70* i 0.20 \ 0.87
21 i -0.86 \ -11.03*** -1.63*** i 0.02 \ 0.77* i 0.16 \ 0.86
22 i -0.67 \ -10.31*** -1.61*** i 0.12 i 0.45 i 0.36 \ 0.85
23 i -0.49 ! -9.55*** -1.45*** i -0.13 i 0.42 i 0.48* \ 0.85
24 J -0.51 ' _9 49*** -1.57*** J 0.02 J 0.32 J 0.59** J 0.86
Note: Robust standard errors. ***, ** and indicates the significance at 1,5 and 7 0%, respectively.
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