Estimation of the NAIRU in the Czech Republic:
Traditional, DSGE and Hysteretic Approaches
Daniel Nemec
Faculty of Economics and Administrations
Masaryk University
Brno, Czech Republic
ESF MU (Brno) Estimating NAIRU November 27-28, 2008 1 / 41
Content
1 Introduction
2 Hysteretic Phillips curve
3 Dynamic macroeconomic model
4 Trajectories of the NAIRU
5 Summary and topics for further research
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Introduction
1 Introduction
2 Hysteretic Phillips curve
3 Dynamic macroeconomic model
4 Trajectories of the NAIRU
5 Summary and topics for further research
ESF MU (Brno) Estimating NAIRU November 27-28, 2008 3 / 41
Introduction
Motivation
Important indicators of monetary stability and potential economicgrowth - unemployment gap and output gap
Estimating NAIRU – various models and techniques
Unobserved variable → arising uncertainty
Phillips curve included + inflationary expectations
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Introduction
Our approach
Hysteretic model with adaptive expectations
Dynamic macroeconomic model with rational expectations
Rational expectations – solved within the model identification
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Hysteretic Phillips curve
1 Introduction
2 Hysteretic Phillips curve
3 Dynamic macroeconomic model
4 Trajectories of the NAIRU
5 Summary and topics for further research
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Hysteretic Phillips curve
The hysteresis model
Simple Phillips curve with adaptive expectations (Gordon (1989))
Hysteretic approach = ”law of motion” for the NAIRU
NAIRU follows the path of actual unemployment rate
Consequences for economic policy
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Hysteretic Phillips curve
Basic equations
Simple Phillips curve:
πt = απt−1 + β(Ut − U∗t )
Assumption of hysteresis hypothesis:
U∗t = ηUt−1 + Zt
Estimated model:
πt = απt−1 + β(1− η)Ut + βη(Ut − Ut−1)− βZt
πt = λ1 + λ2πt−1 + λ3(Ut − Ut−1) + ǫt
πt inflation rate (y-o-y), Ut unemployment rate, U∗t NAIRU, Zt
microeconomic determinants of the labor market
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Hysteretic Phillips curve
Estimation techniques
NLRM with independent normal-gamma prior
Gibbs sampler (Bayesian approach)
Savage-Dickey ratio → particular model probabilities (based on Bayesfactor)
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Hysteretic Phillips curve
Data
Quarterly seasonally adjusted macroeconomic data (using Kalmanfilter procedure)
Czech Republic – 1Q 1996 - 3Q 2007
Net inflation (y-o-y), unemployment rate; source: CNB, CZSO
New Zealand – 4Q 1990 - 3Q 2007
CPI inflation (y-o-y), unemployment rate; source: RBNZ
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Hysteretic Phillips curve
Estimation results - Czech Republic
Prior mean Posterior mean Geweke’s CD Bayes factor(std. deviation) (std. deviation) λi = 0
λ1 2.0000 2.3339 0.2637 0.0528(1.5000) (0.8058)
λ2 0.5000 0.7450 −0.5451 0.0000(0.2500) (0.0747)
λ3 0.5000 −0.2443 −0.0514 0.2726(1.0000) (0.0921)
λ4 0.5000 −0.7848 0.3689 0.5026(1.0000) (0.4259)
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Hysteretic Phillips curve
Estimation results - New Zealand
Prior mean Posterior mean Geweke’s CD Bayes factor(std. deviation) (std. deviation) λi = 0
λ1 2.0000 0.1398 −0.2410 0.5529(1.5000) (0.0464)
λ2 0.5000 0.8429 0.3404 0.0000(0.2500) (0.0747)
λ3 0.5000 −0.0111 0.1832 4.5302(1.0000) (0.0041)
λ4 0.5000 −0.1202 0.2162 0.3993(1.0000) (0.0433)
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Hysteretic Phillips curve
Structural parameters and model probabilities
Structural parameters
α β η Z
Czech Republic 0.7450 −1.0291 0.7627 2.268New Zealand 0.8429 −0.1314 0.9151 1.064
Posterior probabilities of the models
η = 0 η = 1 η ∈ (0; 1)Czech Republic 0.2831 0.1537 0.5632New Zealand 0.0673 0.7638 0.1689
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Hysteretic Phillips curve
Comments
The signs of structural parameters – in accordance with economictheory
Czech economy – hysteresis in unemployment (probability of fullhysteresis 14%)
New Zealand – probability of full hysteresis 76% – decceleratingunemploment in the 1990s was not accompanied by acceleratinginflation
Traditional hysteresis hypothesis in NZ? × structural changes on thelabor market + effective inflation targeting
Verification in the ”non-hysteretic” model
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Dynamic macroeconomic model
1 Introduction
2 Hysteretic Phillips curve
3 Dynamic macroeconomic model
4 Trajectories of the NAIRU
5 Summary and topics for further research
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Dynamic macroeconomic model
The model
Dynamic macroeconomic model with rational expectations(Laxton(2000))
NAIRU follows random walk process - unobserved state
NAIRU + potential output - estimated jointly
System of reduced causal equations
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Dynamic macroeconomic model
Basic equations
Output gap definition
ygapt = 100 · (gdpt − gdpt)
Output gap dynamics
ygapt = α1ygapt−1 − α2rgapt−1 − α3zgapt−1 + ǫygapt
Stochastic process of potential output
gdpt = γt + gdpt−1 + ǫgdpt
γt = βγss + (1− β)γt−1 + ǫγt
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Dynamic macroeconomic model
Basic equations
Unemployment gap definition
ugapt = ut − ut
Stochastic process of the NAIRU
ut = ut−1 + ǫut
Unemployment gap dynamics
ugapt = −φ1ygapt + φ2ugapt−1 + ǫugapt
Inflation equation (Phillips curve)
πt = δ1πmt + δ2Etπt+4 + (1− δ1− δ2)πt−1− δ4ugapt − δ5∆ugapt + ǫπt
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Dynamic macroeconomic model
Estimation techniques
Dynare toolbox (version 3) – Bayesian approach (R-WMetropolis-Hastings algorithm), Kalman filter
Rational expectations solved
Toolbox for solving and simulating DSGE model
For the Czech Republic – estimates using extended Kalman filter (inaddition)
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Dynamic macroeconomic model
Estimation results
Quarterly seasonally adjusted macroeconomic data (using Kalmanfilter procedure)
Czech Republic – 1Q 1996 - 3Q 2007
Net inflation (y-o-y), unemployment rate, GDP, real exchange rate, 3Minterest rate; source: CNB, CZSO
New Zealand – 4Q 1990 - 3Q 2007
CPI inflation (y-o-y), unemployment rate, GDP, real exchange rate, 3Minterest rate; source: RBNZ
Exchange rate gaps and interest rate gaps – Hodrick-Prescott filter
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Dynamic macroeconomic model
Comments I
Czech economy - posterior results are not sensitive to prior setting ofhyperparameters (shocks)
NZ economy - three estimations with different values of prior shocks
→ three patterns of the economy: hysteresis, natural rate hypothesis,time-varying NAIRU
Model comparison based on log-likelihood
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Dynamic macroeconomic model
Parameters estimation - Czech Republic
Prior m. Post. m. HPDI Prior Prior s.d.
α1 0.400 0.6499 0.5277 0.8032 Beta 0.100α2 0.200 0.1763 0.0578 0.3084 Beta 0.100α3 0.150 0.1507 0.0437 0.2796 Normal 0.300β 0.800 0.8178 0.6792 0.9526 Beta 0.100φ1 0.200 0.1615 0.0666 0.2448 Beta 0.100φ2 0.850 0.9795 0.9613 0.9993 Beta 0.100δ1 0.100 0.0847 0.0553 0.1223 Beta 0.100δ2 0.300 0.1229 0.0632 0.1844 Beta 0.100δ4 0.500 0.0351 0.0001 0.0694 Normal 0.200δ5 0.500 0.4051 0.1221 0.7165 Normal 0.200
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Dynamic macroeconomic model
Std. dev. of the shocks - Czech Republic
Prior m. Post. m. HPDI Prior Prior s.d.
ǫygap 1.000 0.7181 0.3143 1.1675 Inv.Gamma 30.00
ǫgdp 0.500 0.0841 0.0664 0.1015 Inv.Gamma 30.00ǫγ 0.500 0.0842 0.0666 0.1027 Inv.Gamma 30.00ǫNAIRU 0.500 0.1234 0.0867 0.1553 Inv.Gamma 30.00ǫugap 0.500 0.1213 0.0862 0.1557 Inv.Gamma 30.00ǫπ 0.500 0.6705 0.4768 0.7955 Inv.Gamma 30.00
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Dynamic macroeconomic model
Comments II - Czech Republic
Empirical validity of Okun’s law not confirmed (φ1, φ2)
Similar dependence of the lagged inflation as hysteretic PC (δ1, δ2)
Small influence of the imported inflation (× long term realappreciation of the Czech currency)
High variability of the shocks in output gap eq. and PC eq. (unstableeconomy in trasition)
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Dynamic macroeconomic model
Parameters estimation - New Zealand (”case NAIRU”)
Prior m. Post. m. HPDI Prior Prior s.d.
α1 0.700 0.7954 0.6676 0.8977 Beta 0.100α2 0.200 0.1887 0.0913 0.3020 Beta 0.100α3 0.200 0.0132 0.0028 0.0224 Beta 0.100β 0.200 0.2901 0.1261 0.4631 Beta 0.100φ1 0.200 0.2800 0.1464 0.4104 Beta 0.100φ2 0.800 0.9119 0.8860 0.9749 Beta 0.100δ1 0.200 0.0123 0.0048 0.0202 Beta 0.050δ2 0.200 0.0750 0.0277 0.1228 Beta 0.100δ4 0.500 0.0624 0.0116 0.1137 Normal 0.300δ5 0.500 0.9623 0.4050 1.4704 Normal 0.300
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Dynamic macroeconomic model
Std. dev. of the shocks - New Zealand
Prior m. Post. m. HPDI Prior Prior s.d.
ǫygap 0.100 0.2090 0.0358 0.3154 Inv.Gamma 30.00
ǫgdp 0.100 0.0150 0.0122 0.0175 Inv.Gamma 30.00ǫγ 0.100 0.0153 0.0126 0.0179 Inv.Gamma 30.00ǫNAIRU 0.300 0.1278 0.0652 0.1792 Inv.Gamma 30.00ǫugap 0.200 0.0598 0.0392 0.0812 Inv.Gamma 30.00ǫπ 0.200 0.1887 0.0759 0.2669 Inv.Gamma 30.00
Log data density −225.351
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Dynamic macroeconomic model
Comments III - New Zealand
”NAIRU model” – ”the best one”
Influence of output gap on uemployment more significant (φ1)
Higher persistence in the trend growth rate of the potential output((1− β) = stability of the economy in the last 18 years)
Larger influence of past inflation → inflation targeting moresuccessful?
Lower variability of the shocks (output gap eq., inflation eq.)
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Trajectories of the NAIRU
1 Introduction
2 Hysteretic Phillips curve
3 Dynamic macroeconomic model
4 Trajectories of the NAIRU
5 Summary and topics for further research
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Trajectories of the NAIRU
Comments I
Estimates using Hodrick-Prescott filter added – for comparison (greenlines)
Estimated paths - differ in levels × dynamics of unobserved statesvery similar
Output gap CR - periods of economic recessions (1997, 2002)
Output gap NZ - very mild cyclical behaviour (effective monetarypolicy?)
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Trajectories of the NAIRU
Output gap - Czech Republic
1996 1998 2000 2002 2004 2006 2008−4
−3
−2
−1
0
1
2
3
[%]
Output gap
Laxton − DynareLaxton − KalmanHP filter
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Trajectories of the NAIRU
Output gap - New Zealand
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008−4
−3
−2
−1
0
1
2
3
[%]
Output gap
Laxton − hysteresisLaxton − NAIRULaxton − NRHHP filter
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Trajectories of the NAIRU
NAIRU - Czech Republic
1996 1998 2000 2002 2004 2006 20081
2
3
4
5
6
7
8
9
10
[%]
NAIRU
UnemploymentLaxton − DynareLaxton − KalmanGordon − HysteresisHP filter
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Trajectories of the NAIRU
Unemployment gap - Czech Republic
1996 1998 2000 2002 2004 2006 2008−2
−1.5
−1
−0.5
0
0.5
1
1.5
[%]
Unemployment gap
Laxton − DynareLaxton − KalmanGordon − HysteresisHP filter
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Trajectories of the NAIRU
Comments II - Czech NAIRU
Equilibrium unemployment - singnificant increase since 1996(transformation process and structural changes)
Unemployment pattern in accordance with hysteresis hypothesis(monetary shock in 1997 → unemployment growth; since 2000stabilised inflation + high unemployment prevailed)
Break in the trend of unemployment in 2005 (demand-orientedgovernment policy) → decreasing unemployment and stable inflation⇔ hysteresis effect
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Trajectories of the NAIRU
NAIRU - New Zealand
1990 1992 1994 1996 1998 2000 2002 2004 2006 20083
4
5
6
7
8
9
10
11
[%]
NAIRU
UnemploymentLaxton − HysteresisLaxton − NAIRULaxton − NRHGordon − HysteresisHP filter
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Trajectories of the NAIRU
Unemployment gap - New Zealand
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008−2
−1
0
1
2
3
4
5
6
7
8
[%]
Unemployment gap
Laxton − HysteresisLaxton − NAIRULaxton − NRHGordon − HysteresisHP filter
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Trajectories of the NAIRU
Comments III - New Zealand NAIRU
Hysteresis hypothesis rejected
Structural factors for lowering NZ unemploymentInflation targeting - inflation is stable regardless of the movements inunemployment gap (”false hysteresis”)
Significantly decreasing unemployment gap over time
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Summary and topics for further research
1 Introduction
2 Hysteretic Phillips curve
3 Dynamic macroeconomic model
4 Trajectories of the NAIRU
5 Summary and topics for further research
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Summary and topics for further research
Summary
Estimates of unobserved states → both economies close to theirpotential levels
Jointly estimation of the NAIRU and potential output
Hysteretic patterns of the Czech economy
Bayesian approach - allows to decide among competing models whichof them is the most probable → lowering uncrtainty related to NAIRUestimation
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Summary and topics for further research
Model extension and topics for further research
Model extension - Berg, Karam, Laxton (2006): short-term interestrate equation (monetary rule), uncovered interest rate parity (realexchange rate equation)
Preliminary estimation results (concerning NAIRU and output gap) -similar to Laxton (2000)
Model identification using Dynare 4
Preliminary results - parameter estimates very similar × problem withthe Bayesian smoothing of unobserved states
Global Sensitivity Analysis – Ratto (2008)
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Summary and topics for further research
Thank you for your attention!
Comments? Suggestions?
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