Unemployment in an Estimated New Keynesian Model › images › media › pdf › NPWPE_GALIS... · 2015-05-28 · •An increasing number of central banks have developed and estimated

Unemployment in an Estimated New Keynesian Model

Jordi Galí Frank Smets Raf Wouters

Central Bank of Cyprus19 February 2010

The opinions expressed are our own and not necessarily those of the ECB, the Eurosystem or the N

• An increasing number of central banks have developed and estimated medium-scale New Keynesian DSGE models for forecasting and policy analysis.

• See, for example, Smets et al (2010) for a brief description of the two aggregate euro area models used at the ECB (NAWM and CMR).

• Typically, the labour market is modelled using the Erceg, Henderson and Levin (2000) model of monopolistic competition and Calvo wage setting.

– Plus: Fits the time series of hours worked and real wages quite well (e.g. Smets and Wouters, 2007)

– Minus: no reference to unemployment

Introduction and motivation

• Gali (2009): – proposes a reformulation of the EHL model, which

implies a simple dynamic relation between wage inflation and unemployment;

– Shows that this structural wage equation accounts reasonably well for the comovement of wage inflation and the unemployment rate in the US economy.

– Variations in unemployment are associated with changes in wage mark-ups, either exogenous or resulting from nominal wage rigidities.

• This (forthcoming) paper embeds this reformulation in the Smets-Wouters (2007) model by adding the unemployment rate as an observable variable.


• This allows us to overcome the identification problem of wage mark-up and labour supply shocks mentioned in SW (2003, 2007) and emphasized by Chari et al (2009) as an illustration of the immaturity of the New Keynesian framework:

– In SW (2007) wage mark-up shocks account for almost 50 percent of variations in real GDP beyond 10 years.

– With only wages and employment/hours as observables those shocks can not be distinguished from labour supply/preference shocks.

– The source of the shock is, however, important for welfare analysis.

– Using unemployment (or labour participation) helps overcoming the identification problem


• It also allows us to:

• Better identify the wage Phillips curve;

• Analyze the sources of unemployment variations;

• Better identify the output gap in the model.


• This paper is part of a growing body of work that improves the modelling of the labour market in DSGE models:

• Recent examples of more complicated estimated models are Christoffel et al (2007), Gertler, Salaand Trigari (2008) and Christiano, Trabandt and Walentin (2009)

• We only look at the extensive margin:

• See de Walque et al (2009) for a model that has both margins.


• Modifications to the Smets-Wouters (2007) model for the US economy

• Estimation results

• Conclusions

Outline

• Benchmark model without unemployment differs slightly from Smets-Wouters (2007):

• Somewhat different data and sample: Employment (rather than hours); Wage per worker

• Jaimovich-Rebelo preferences;

• Priors on standard deviation of shocks are uniform distributions instead of inverse-gamma;

• Dixit-Stiglitz rather than Kimball aggregator.

The modified Smets-Wouters model

• Large representative household with a continuum of members:

where

and

• Extends Jaimovich-Rebelo (JR, 2009) preferences to allow for external habit formation


• The marginal rate of substitution between consumption and employment is:

or in natural logs:


• As in EHL, workers supplying a labor service of a given type get to reset their nominal wage with probability each period.

• The nominal wage in period t+k for workers who last re-optimised their wage in period t:

• The first-order condition is:

• The aggregate wage index can be written as:


• Log-linearisation leads to the following equation for nominal wage inflation:

where

and


• An individual will find it optimal to participate in the labour market in period t if:

• The marginal supplier of type i labor is given by:

• Taking logs and integrating over i:

Introducing unemployment

• Following Gali (2009), the unemployment rate is defined as:

• Combining the definition of the average mark-up with the above and the labour supply equation:

• Putting this in the wage equation yields:


• Wage equation:

In contrast to SW, the error term only captures shocks to the wage mark-up, no preference shocks

• Labor supply equation:

• The Phillips curve will only include wage mark-up shocks, whereas the labour supply equation will only include preference shocks


• With the exception of the consumption Euler equation which reflects the change to JR preferences, all the other equations are as in SW (2007):

• New Keynesian Phillips curve;

• Capital accumulation equations;

• Investment equation based on q-theory;

Modified Smets-Wouters model

• US data (1965:1-2008:4);

• Use employment (extensive margin) rather than hours worked;

• Add unemployment.

• Use two wage concepts:

• Compensation per employee, from the BLS Productivity and Costs Statistics

• Average Weekly Earnings from the Current Employment Statistics

• Compare model without unemployment with the model with unemployment as observable.

Data

• Quite large discrepancies between the two wage data series:

Data

LN(hourly wage data)

2.5

3

3.5

4

4.5

5

5.5

1964

1965

1967

1968

1969

1970

1972

1973

1974

1975

1977

1978

1979

1980

1982

1983

1984

1985

1987

1988

1989

1990

1992

1993

1994

1995

1997

1998

1999

2000

2002

2003

2004

2005

2007

2008

2009

hourly compensation Av hourly earnings

• Quite large discrepancies between the two wage data series:

Data

d(ln Hourly wage)

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

1964

.319

65.5

1966

.819

6819

69.3

1970

.519

71.8

1973

1974

.319

75.5

1976

.819

7819

79.3

1980

.519

81.8

1983

1984

.319

85.5

1986

.819

8819

89.3

1990

.519

91.8

1993

1994

.319

95.5

1996

.819

9819

99.3

2000

.520

01.8

2003

2004

.320

05.5

2006

.820

08

dwHC dwAHE

• In the baseline model, we use both series and add measurement error to account for the differences;

• Results also available for each series used separately:

• The higher volatility of the compensation series does affect estimates of the labour supply elasticity and some of the other parameters.

Data

Most parameter estimates are very similar.

Focus on wage Phillips curve and labour supply equation:

Without UR:

With UR:

Estimation results

{ } ntwt

pt

wtt

pt

wt u ,11 016.0048.017.099.017.0 μππππ +−−Ε+= +−

{ } ntwt

pt

wtt

pt

wt u ,11 018.0065.015.099.015.0 μππππ +−−Ε+= +−

tttt lzpw 02.3+=−

( )164.081.019.0 −−+= tttt CCzz

ttttt lzpw ξ++=− 63.3

( )163.001.091.0 −−+= tttt CCzz

– The standard deviation of the wage mark-up shock drops from 17% to 8.2%:

– This implies that the standard deviation of the natural unemployment rate is of the order of 2.25%.

– The standard deviation of the change in the labour supply shock is 0.96.

Estimation results

Variance decompositiony w n u l R

10 Quarter horizonProd 41/56 4/5 25/35 4/7 -/4 -/6 9/12

Cpref 7/6 3/2 2/2 12/14 -/19 -/0 17/16

Govt 6/2 1/1 0/0 13/5 -/7 -/0 4/6

Fin 18/15 9/9 9/13 22/21 -/20 -/3 37/38

Monp 7/5 9/8 4/5 11/12 -/14 -/1 16/12

Pmup 6/2 33/34 47/32 6/4 -/0 -/7 4/2

Wmup 14/4 41/41 13/13 33/12 -/32 -/3 13/11

Lpref -/9 -/0 -/1 -/24 -/4 -/80 -/3

40 Quarter horizonProd 42/64 4/5 53/70 2/7 -/2 -/8 8/11

Cpref 2/2 2/1 1/1 4/6 -/10 -/0 14/14

Govt 3/1 ½ 1/1 7/2 -/3 -/0 4/7

Fin 8/8 8/8 8/9 9/10 -/10 -/2 33/36

Monp 3/2 8/7 3/2 4/5 -/7 -/0 13/10

Pmup 3/1 27/28 28/12 3/2 -/0 -/2 4/2

Wmup 40/9 50/48 7/5 72/25 -/65 -/2 24/19

Lpref -/15 -/0 -/0 -/44 -/2 -/86 -/2

π

• The introduction of unemployment reduces substantially the role of wage mark-up shocks

• At business cycle frequencies, unemployment is largely driven by demand shocks and the wage mark-up shock

• Labour preference shocks have a significant role for employment and labour supply, but not for unemployment

Variance decomposition

• “Demand” shocks

Impulse responses

0 5 10 15 20-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6Output

Risk Premium Investment Monetary Policy

0 5 10 15 20-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05Unemployment Rate

0 5 10 15 20-0.1

0

0.1

0.2

0.3

0.4Employment

0 5 10 15 20-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06Labor Force

0 5 10 15 20-0.02

0

0.02

0.04

0.06Inflation

0 5 10 15 20-0.1

0

0.1

0.2

0.3Real Wage

• Labour supply and mark-up shocks

Impulse responses

0 5 10 15 20-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1Output

Wage Markup Labor Supply0 5 10 15 20

-0.2

-0.1

0

0.1

0.2


0 5 10 15 20-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05Employment

0 5 10 15 20-0.3

-0.2

-0.1

0

0.1Labor Force

0 5 10 15 20-0.05

0

0.05

0.1

0.15

0.2Inflation

0 5 10 15 20-0.05

0

0.05

0.1

0.15

0.2Real Wage

• Productivity and price mark-up shocks

Impulse responses

0 5 10 15 200

0.2

0.4

0.6

0.8

1Output

Productivity Price Markup

0 5 10 15 20-0.05

0

0.05

0.1

0.15


0 5 10 15 20-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15Employment

0 5 10 15 200

0.02

0.04

0.06

0.08

0.1Labor Force

0 5 10 15 20-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1Inflation

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5Real Wage

Output gap and unemployment

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010-12

-10

-8

-6

-4

-2

0

2

4

6

Outputgap

Unemployment Rate

Output gap and unemployment

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010-20

-15

-10

-5

0

5

10

Outputgap without UROutputgap with UR

Output gap

Historical decomposition

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010-8

-6

-4

-2

0

2

4

6Output Gap decomposition

historical y-gapsupply shocksdemand shocksmon.pol. shocks

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010-8

-6

-4

-2

0

2

4

6

historical y-gaplabor supplywage mark-up

Unemployment rate


1965 1970 1975 1980 1985 1990 1995 2000 2005 20103

4

5

6

7

8

9

10

11Unemployment Rate decomposition

historical URsupply shocksdemand shocksmon.pol. shocks

1965 1970 1975 1980 1985 1990 1995 2000 2005 20103

4

5

6

7

8

9

10

11

historical URlabor supplywage mark-up

Unemployment gap


1965 1970 1975 1980 1985 1990 1995 2000 2005 2010-6

-4

-2

0

2

4Unemployment Gap decomposition

historical U-gapsupply shocksdemand shocksmon.pol. shocks

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010-6

-4

-2

0

2

4

historical U-gaplabor supplywage mark-up

• Adding unemployment (labour supply) in the standard CEE/SW model helps identifying labour supply from labour mark-up shocks; mark-up shocks do not explain a lot of output and the variance of the mark-up shocks is reasonable.

• Unemployment helps estimating the wage Phillips curve and generally improves the marginal likelihood of the original system by about 20; unemployment has relevant information.

Conclusions

• Labour supply comoves positively with employment; low wealth effects on labour supply

• Unemployment most driven by demand and labour mark-up shocks.

Conclusions

• Estimate a model for the euro area

• May improve the forecast for wages.

Extensions

Appendix: Data series used

50 100 150-5

0

5dy

50 100 150-5

0

5dc

50 100 150-10

0

10dinve

50 100 150-10

0

10N

50 100 1500

2

4pinfobs

50 100 150-5

0

5dwEC

50 100 1500

5robs

50 100 1500

10

20UR

50 100 150-2

0

2dwAWE

Appendix: Estimation results

Appendix: Estimation results

Appendix

Appendix

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Unemployment in an Estimated New Keynesian Model › images › media › pdf › NPWPE_GALIS... · 2015-05-28 · •An increasing number of central banks have developed and estimated