Labor Market Participation, Unemployment and Monetary Policy

Labor Market Participation, Unemployment and

Monetary Policy

Alessia Campolmi1 Stefano Gnocchi2

1Central European University and Magyar Nemzeti Bank

2Universitat Autònoma de Barcelona and MOVE

Trobada BGSE 2011

October 21st, 2011

Campolmi and Gnocchi () Labor Market Participation 1 / 37

Motivation

New-Keynesian Perspectives on Business Cycles and

Labor Markets

Large literature exploring the implications of two main frictions formacroeconomic uctuations

I Nominal price rigidities: ination, monetary policy and thebusiness cycle. Calvo (1983), Yun (1996), King and Wolman(1996), Walsh (2003), Woodford (2003), Galí (2008)

I Labor market matching frictions: unemployment uctuations andthe business cycle. Diamond (1982), Mortensen (1982), Pissarides(1984)


Motivation

New-Keynesian Perspectives on Business Cycles and

Labor Markets

Interaction between nominal rigidities and labor market frictions calledinto question to explain

I Phillips and Beveridge Curves: Chéron and Lanogot (2000)

I Persistence of monetary policy shocks: Walsh (2005), Trigari(2009)

I Ination dynamics: Christoel and Linzert (2005)

I The role of real wage rigidities: Gertler and Trigari (2009), Krauseand Lubik (2007), Sveen and Weinke (2008).


Motivation

The Missing Margin

NK-DMP imports from the DMP strand the assumption of inelasticlabor force. This implies:

I Households cannot substitute unemployment with voluntarynon-employment


Motivation

The Missing Margin

Yet, PARTICIPATION MOVES

Table: Percentage standard deviations of output and selected unconditionalmoments (relative to output) - U.S. data: 1964-2007, HP-ltered

Unconditional Moments Data

Output volatility 1.53Unemployment rate volatility 7.40

Employment volatility 0.63Participation rate volatility 0.20

Correlation of Participation with Output 0.42

I Barnichon and Figura, 2010: labor supply components account for1/4 of unemployment's variance at business cycle frequency. Theyexplain most of the low frequency movements.


Our Paper: Overview

Our Contribution

I We consider the baseline NK-DMP model;

I We introduce the participation choice by making costly the entryto the labor market, modelling home production activity andsearch activity as both requiring time;

I We calibrate the model to US data;

I We draw policy implications and we show that neglecting theparticipation margin leads to incorrect evaluation of the eects ofmonetary policy


Our Paper: Overview

Results Preview

Moving from Flexible to Strict Ination Targeting:

I Exogenous Participation ⇒ increases volatility of unemploymentand employment rates;

I Endogenous Participation ⇒ reduces the volatility ofunemployment and employment rates while increasing thevolatility of participation.

Intuition: exogenous participation models abstract from substitutionbetween unemployment and non-participation


The Model

Model Setup

I HOUSEHOLDS

I Innitely many members consuming a composite consumption goodand home production; perfect insurance

I Each member can be employed, unemployed ornon-participant

I Unemployed and Non-participants home produce

I FIRMS

I Final goods producers: monopolistic competition and pricerigidity

I Intermediate goods producers: perfect competition andmatching frictions

Final goods sector

Intermediate goods sector

I MONETARY POLICY: Central bank sets the nominal rateresponding to ination

Monetary Policy


The Model Households

Household's decision problem

HH F.O.C.

I Households choose Ct, Dt and Nt so as to maximize:

E0

∞∑t=0

βt

[Zt log(Ct) + φ

ht1+ν

1 + ν

](1)

I subject to:

PtCt + R−1t Dt ≤ Dt−1 + WtEt + PtbUt + Tt (2)

ht = [ξt(1− Et − ΓUt)]1−αh (3)

Et = (1− ρ)Et−1 + ft(Nt − (1− ρ)Et−1) (4)

Nt = Et + Ut (5)


The Model Calibration and Steady State

Some Conventional Parameters

Table 2: Parameter Values

Parameter Mnemonic Value

Discoun Factor β 0.99

Inter. elast. of subst. participation ν -5

Elast. Substitution ε 6

Workers Bargaining Power 1− η 0.6

Calvo Parameter ξ 2/3

Separation Rate ρ 0.12

Matching Elasticity γ 0.6

Returns to Employment 1− α 2/3

Returns to Home production 1− αh 2/3

Ination Reaction Coecient φπ 1.5


The Model Calibration and Steady State

Targets

Table 3: Steady State Moments

Targets Value U.S. Data

Employment Rate 0.94

Participation Rate 0.64

Job Filling Rate (q) 2/3

Replacement Rate (b/w) 0.4

Vacancy Cost as fraction of wages (κ/(w ∗ q)) 0.045

Table 4: Implied Parameters

Parameter Mnemonic Value

Matching Eciency ω 0.66

Vacancy Cost κ 0.0196

Search Cost Γ 0.44

Preference Shifter Φ 0.04

Unemployment Benet b 0.2617


The Model Second Moments

IRMTFP IRPref IRHTFP

Table: Matching unconditional moments. Both models have been calibratedso as to give the best possible t for the rst 4 moments.

Unconditional Moments Data Endogenous Exogenous

Output volatility 1.53 1.43 1.56Unemployment rate volatility 7.40 7.36 7.55

Employment volatility 0.63 0.67 0.47Corr. Unempl. rate with Output -0.85 -0.75 -1

Participation rate volatility 0.20 0.24 -Corr. of Part. with Output 0.42 0.56 -

Calibrated Parameters

st.dev. market TFP 0.0070 0.0074st.dev. home TFP 0.0037 0.0070

st.dev. preference shock 0.0147 0corrA,AH 0.9474 1


Results: Participation, Frictions and Monetary Policy Incentives

The Participation Choice

I Matching frictions generate undesirable movements in homeproduction ⇒ home production gap: ht(nt, ft)− h∗t

I Participation uctuates to close the gap and replicate exible labormarket home production

Figure 1


Results: Participation, Frictions and Monetary Policy Policy Experiment

Participation and Monetary Policy

I How do second moments change if monetary policy switches fromexible (φ = 1.5) to strict (φ = 100) ination targeting?

I How does the presence of the participation margin aect theanswer?

I What is the relevance of the search cost?



Table: Percentage standard deviations of output and of selected moments(relative to output) in the endogenous and exogenous participation models,conditionally on market technology shocks. The table reports the value ofmoments under strict ination targeting. In parenthesis it is reported thevalue for an ination coecient equal to 1.5 in the Taylor rule.

Moments Cond. on MTFP Shocks Endogenous Exogenous

Output volatility 1.24 (1.12) 1.17 (1.08)Unempl. rate volatility 8.33 (5.40) 2.07 (0.12)

Empl. volatility 0.20 (0.07) 0.13 (0.008)Empl. rate volatility 0.52 (0.34) 0.13 (0.008)Part. rate volatility 0.32 (0.27) 0 (0)

Corr. of Part. with Output -0.99 (-0.99) 0 (0)Corr. of Unempl. rate with Output -1 (-1) -1 (-1)



Endogenous Vs Exogenous: TFP Shocks

I Strict ination targeting makes vacancy posting more volatileunder both models

I If participation free to vary, households substitute unemployedwith non-participation

I Volatility of the labor force increases, counterbalancing the surgein volatility of vacancy posting

I The volatility of employment and unemployment rates increase byless than under exogenous participation

Pref. Shock Home Tech. Shock



Monetary Policy: Unconditional Moments

I Exogenous Participation ⇒ strict ination targeting increasesvolatility of unemployment rate, employment and employment rate;

I Endogenous Participation ⇒ strict ination targeting reduces thevolatility of unemployment rate, employment and employment ratewhile increasing the volatility of participation.

Unconditional Moments


Conclusions

Conclusions

I Participation responds to frictions and changes in monetary policyaect the relevance of frictions

I Models overlooking participation may deliver wrong policyimplications

I The strength of the channel depends on the search costs

Search Cost


Households

Household's rst order conditions

We dene the utility loss needed to marginally increase employment as

Ωt ≡(1− ft)

ft

[φΓhν

t Ct

Ztξt(1− αh)h

− αh1−αh

t − b

](6)

I Participation condition

Ωt =Wt

Pt− φhν

t Ct

Ztξt(1− αh)h

− αh1−αh

t + Et

βCt(1− ρ)

Ct+1

Zt+1

ZtΩt+1

I Euler equation

βRtEt

Ct

Ct+1

Zt+1

Zt

Pt

Pt+1

= 1 (7)

Back


Households

The Participation Condition

I Frictions introduce a wedge between home production andemployment decision

I Increase in ft increases participation, given Ct ⇒ substitute homeproduction with consumption

I Increase in Ct reduces participation, given ft ⇒ wealth eect

Forces driving participation choice

I Finding rates

I Marginal rate of substitution between consumption and homeproduction

Back


Firms-Intermediate Goods

Matching frictions

I Production function of producer j when matched with a worker

Xt(j) = At (8)

I To nd a worker j needs to open a vacancy and search paying κnal goods

I Labor market tightness: θt ≡ VtSt

I Job lling rate: qt ≡ ωθ−γt ,

I Job nding rate: ft ≡ θtqt.

I Free entry condition in the market of intermediate producersdetermine vacancy posting

κ

qt=

P xt

PtAt −

Wt

Pt+ (1− ρ)Et

Qt,t+1

κ

qt+1

(9)

Back


Firms-Intermediate Goods

Wage Bargaining

I Value of employment

V wt =

Wt

Pt− b− φhν

t (1− Γ)Ct

Ztξt(1− αh)h

− αh1−αh

t + (10)

Et

Qt,t+1(1− ρ)(1− ft+1)V w

t+1

I Nash Bargaining (η: rm's bargaining power)

ηV wt = (1− η)V J

t (11)

I Wage equation

Wt

Pt= (1− η)

P xt

PtAt + η

[b +

φhνt (1− Γ)Ct

Ztξt(1− αh)h

− αh1−αh

t

]+ (1− η)(1− ρ)Et Qt,t+1κθt+1 (12)

BackCampolmi and Gnocchi () Labor Market Participation 22 / 37

Firms-Final Goods

Sticky prices

I Production function

Yt(i) = Xt(i)1−α (13)

I Demand

Yt(i) =[Pt(i)Pt

]−ε

[Ct + κVt] (14)

I Phillips Curve

πt = βEt πt+1+ λ

[P x

t

Pt+ αxt

](15)

λ = (1−ξ)(1−βξ)ξ

1−α1−α+αε

Back


Monetary Policy

Monetary Policy

I Simple Taylor rule

log(Rt) = − log(β) + φππt (16)

Back


Monetary Policy

Figure: Impulse Responses to a market production TFP shock ComparisonAcross Models

0 2 4 6 8 100.06

0.04

0.02

0

0.02

0.04Home Production FLEXIBLE PRICES

Time

% d

evia

tion

from

sts

t.

CGExog.Part.No Frictions

0 2 4 6 8 100.25

0.2

0.15

0.1

0.05

0Participation FLEXIBLE PRICES

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.01

0

0.01

0.02

0.03

0.04

0.05

0.06Home Production STICKY PRICES

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.2

0.15

0.1

0.05

0Participation STICKY PRICES

Time

% d

evia

tion

from

sts

t.

Back


Monetary Policy

Figure: Two calibrations of the search cost: high (η = 0.05) and low (η = 0.4)- Flexible Prices

0 2 4 6 8 100.06

0.04

0.02

0

0.02

0.04Home Production BIGGAMMA=0.44

Time

% d

evia

tion

from

sts

t.


0 2 4 6 8 100.25

0.2

0.15

0.1

0.05

0Participation BIGGAMMA=0.44

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 101

0

1

2

3

4

5x 10 3Home Production BIGGAMMA=0.99

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 104

3

2

1

0x 10 3Participation BIGGAMMA=0.99

Time

% d

evia

tion

from

sts

t.

Back


Monetary Policy

Figure: Two calibrations of the search cost: high (η = 0.05) and low (η = 0.4)- Sticky Prices

0 2 4 6 8 100.01

0

0.01

0.02

0.03

0.04

0.05


Time

% d

evia

tion

from

sts

t.


0 2 4 6 8 100.2

0.15

0.1

0.05


Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.01

0

0.01

0.02

0.03

0.04

0.05


Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.05

0.04

0.03

0.02

0.01


Time

% d

evia

tion

from

sts

t.

Back


Monetary Policy

Figure: Impulse Responses to a market production TFP shock

0 2 4 6 8 100.2

0.15

0.1

0.05

0Participation

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100

0.02

0.04

0.06Employment

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 104

3

2

1Unemployment Rate

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.2

0.4

0.6

0.8

1GDP

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.02

0.03

0.04

0.05

0.06Home Production

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.2

0.4

0.6

0.8

1TFP Shock

Time

% d

evia

tion

from

sts

t.

Back


Monetary Policy

Figure: Impulse Responses to a preference shock

0 2 4 6 8 100

0.05

0.1

0.15

0.2Participation

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.1

0.2

0.3

0.4Employment

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 103

2.5

2

1.5

1Unemployment Rate

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.05

0.1

0.15

0.2

0.25GDP

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.25

0.2

0.15

0.1

0.05Home Production

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.2

0.4

0.6

0.8

1Preference Shock

Time

% d

evia

tion

from

sts

t.

Back


Monetary Policy

Figure: Impulse Responses to a home productivity shock

0 2 4 6 8 100.1

0.2

0.3

0.4

0.5Participation

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.1

0.2

0.3

0.4

0.5Employment

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100

1

2

3Unemployment Rate

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.05

0.1

0.15

0.2

0.25GDP

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.05

0.1

0.15

0.2

0.25Home Production

Time

% d

evia

tion

from

sts

t.

0 2 4 6 8 100.2

0.4

0.6

0.8

1Home Productivity Shock

Time

% d

evia

tion

from

sts

t.

Back


The Other Shocks

Table: Percentage standard deviations of output and of selected moments(relative to output) in the endogenous and exogenous participation models,conditionally on preference shocks. The table reports the value of momentsunder strict ination targeting. In parenthesis it is reported the value for anination coecient equal to 1.5 in the Taylor rule.

Moments Cond. on Preference Shocks Endogenous Exogenous

Output volatility 0.29 (0.60) 0 (0)Unempl. rate volatility 7.56 (15.91) 23.97 (23.97)


Corr. of Part. with Output 0.99 (0.98) 0 (0)Corr. of Unempl. rate with Output 0.85 (-0.99) -1 (-1)

Back


The Other Shocks

Endogenous Vs Exogenous: Preference shocks

I Participation correlates positively with output and negatively withunemployment

I Strict ination targeting magnies participation volatility

I Constant volatility of employment, greater ows of searchingworkers dampen volatility of employment rates

I NO ACTION IN EXOGENOUS PARTICIPATION MODEL

Back


The Other Shocks

Table: Percentage standard deviations of output and of selected moments(relative to output) in the endogenous and exogenous participation models,conditionally on home technology shocks. The table reports the value ofmoments under strict ination targeting. In parenthesis it is reported thevalue for an ination coecient equal to 1.5 in the Taylor rule.

Moments Cond. on HTFP Shocks Endogenous Exogenous



Corr. of Part. with Output 0.99 (1) 0 (0)Corr. of Unempl. rate with Output 0.84 (0.98) -1 (-1)

Back


The Other Shocks

Endogenous Vs Exogenous: Home TFP shocks

I Participation correlates positively with output and withunemployment

I Strict ination targeting dampens participation volatility

I Constant volatility of employment, smaller ows of searchingworkers dampen volatility of employment rates

I NO ACTION IN EXOGENOUS PARTICIPATION MODEL

Back


The Other Shocks

Table: Percentage standard deviations of output and of selected unconditionalmoments (relative to output) in the endogenous and exogenous participationmodels. The table reports the value of moments under strict inationtargeting. In parenthesis it is reported the value for an ination coecientequal to 1.5 in the Taylor rule.

Unconditional Moments Endogenous Exogenous



Corr. of Part. with Output 0.13 (0.56) 0 (0)Corr. of Unempl. rate with Output -0.90 (-0.76) -1 (-1)

Back


The Search Cost

Monetary Policy: MTFP Shock - High Search Cost

Conclusions

Table: Percentage standard deviations of output and of selected moments(relative to output) in the endogenous and exogenous participation models,conditionally on MTFP shocks. Here we depart from the baseline calibrationand we assume a high households' search cost, equal to 0.99. The tablereports the value of moments under strict ination targeting. In parenthesis itis reported the value for an ination coecient equal to 1.5 in the Taylor rule.

Volatility Endogenous Exogenous

Values ∆ % Values ∆ %Empl. rate 0.1100 (0.0699) 52.47% 0.1107 (0.0726) 64.42%Unempl. rate 1.7682 (1.1606) 52.35% 1.7580 (1.0689) 64.46%Part. rate 0.0048 (0.0583) 0 (0)


The Search Cost

Endogenous Vs Exogenous: Search Cost

I If search cost is high, the participation margin matters less, beprices sticky or not

I Then, policy mistakes are less important

Conclusions


Economy & Finance

Labor Market Participation, Unemployment and Monetary Policy