Estimation of the NAIRU in the Czech Republic: Traditional ...ces.utia.cas.cz/Prednasky_Ekonometricky_Den_2008/ekonometricky_den_2008_Nemec.pdfEstimation of the NAIRU in the Czech

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


Introduction

1 Introduction






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


Introduction

Our approach

Hysteretic model with adaptive expectations

Dynamic macroeconomic model with rational expectations

Rational expectations – solved within the model identification


Hysteretic Phillips curve

1 Introduction







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



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



Estimation techniques

NLRM with independent normal-gamma prior

Gibbs sampler (Bayesian approach)

Savage-Dickey ratio → particular model probabilities (based on Bayesfactor)



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



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)



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)



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



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


Dynamic macroeconomic model

1 Introduction







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



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



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



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)



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



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



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



Std. dev. of the shocks - Czech Republic


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



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)



Parameters estimation - New Zealand (”case NAIRU”)


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



Std. dev. of the shocks - New Zealand


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



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.)


Trajectories of the NAIRU

1 Introduction







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?)



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



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



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



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



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



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



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



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


Summary and topics for further research

1 Introduction







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



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)



Thank you for your attention!

Comments? Suggestions?


Documents

Estimation of the NAIRU in the Czech Republic: Traditional ...ces.utia.cas.cz/Prednasky_Ekonometricky_Den_2008/ekonometricky_den_2008_Nemec.pdfEstimation of the NAIRU in the Czech