EC404-Lecture 7

The Labour Maket IS-PC-MR model and supply-side policies Unemployment persistence and hysteresis

Macroeconomic CSI: Supply-side shocks andpolicies

Rodolphe Desbordes

http://www.rodolphedesbordes.com/

http://www.rodolphedesbordes.com/


Table of Contents I

1 The Labour MaketWage settingPrice-settingEquilibrium outputEmpirical evidence

2 IS-PC-MR model and supply-side policiesA cut in the payroll tax rate: Initial equilibriumA cut in the payroll tax rate: Medium-run effectsA cut in the payroll tax rate: Initial effectA cut in the payroll tax rate: The central bank

3 Unemployment persistence and hysteresisPath-dependenceHysteresis and persistenceExplaining persistence: unemployment duration theory


The Wage-Setting curve: wages are related to theunemployment rate

The Wage (W ) received by workers depends on

1 The consumer price level (PC) as workers care about how many goodsthey can buy with their money.

2 Labour market conditions (Unemployment rate U) as they influenceworkers’ bargaining position.

3 Labour market institutions (I) such as unemployment insurance.

Hence we can write that

W = PC(I − αU)

WPC

= I − αU

where α is the sensitivity of wage-setting to labour market conditions. U isdefined as U = L−E

L = 1− EL , where L is the labour force and E is the level of

employment.


The Wage-Setting curve: wages are related toproduction

We can relate wages to production such as αU = −βY :

WPC

= IWS − αU

WPC

= IWS + βY

The wage-setting real wage depends on the level of employment/output.


Price-setting under perfect competition

Under perfect competition, firms are price-takers: P = P.

They hire workers until the value of their marginal product is equal to their cost:

MPL× P = W

P =W

MPL

WMPL is their marginal cost (MC), i.e. the cost of producing one additional unitof output.

If we assume that MPL is constant, marginal product and labour productivity(λ) are equal: MPL = Y

E = λ.


Price-setting under imperfect competition

Under imperfect competition, firms are no more price-takers. They charge aconstant mark-up over marginal cost. This mark-up depends on the degree ofproduct market competition.

P = (1 + µ̂)MC

P = (1 + µ̂)Wλ

WP

=λ

1 + µ̂

And, in line with C&S, we can define µ = µ̂1+µ̂

which gives

WP

= (1− µ)λ

Note that the price-setting real wage does not depend on the level of unem-ployment/output given the assumptions that we have made.


Price-setting and taxesFirms may have to pay payroll taxes. Workers may have to pay income taxesand indirect taxes such as VAT.

Define W as the post-tax money wage such as the full cost of labour to firmsis Wgross = W (1 + td), where td is the direct tax rate (including payroll taxesand income taxes). Wgross

P is called the real product wage.

Define PC as the consumer price index P(1 + tv ), where tv is the indirecttax rate. W

PCis called the real consumption wage. Our price-setting equation

becomes:

P = (1 + td)W

(1− µ)λ

PC = (1 + td)(1 + tv )W

(1− µ)λ

WPC

=(1− µ)λ

(1 + td )(1 + tv )

where the tax wedge (1+ td)(1+ tv ) is the ratio between the real product wageand the real consumption wage.


The ERU and the equilibrium rate of output

The Equilibrium Rate of Unemployment (ERU) (Ue) is achieved when the realwage chosen in wage-setting is equal to the real wage implied by price-setting:

IWS − αU = (1− µ)λ

(1 + td )(1 + tv )

Ue =IWS

α− (1− µ)λ

α[(1 + td)(1 + tv )]

We have seen that αU = −βY ⇐⇒ Y = −αβ

U. Hence the equilibrium levelof output (Ye) is

Y = −α

β[IWS

α− (1− µ)λ

α[(1 + td )(1 + tv )]]

Ye =(1− µ)λ

β[(1 + td)(1 + tv )]− IWS

β

The ERU determines the equilibrium level of output.


Determinants of the ERU

The ERU

Ue =IWS

α− (1− µ)λ

α[(1 + td )(1 + tv )]

depends negatively on:

1 Labour productivity λ.

depends positively on:

1 The mark-up µ.

2 Labour market institutions: IWS and the tax wedge (1 + td)(1 + tv ).


Structural unemployment rate and product marketregulation (1990-2001)

Australia

Austria

BelgiumCanada

Denmark

Finland

France

Germany

IrelandItaly

Japan

Netherlands

New Zealand

Norway Portugal

Spain

Sweden

Switzerland

United Kingdom

United States

05

1015

Stru

ctur

al u

nem

ploy

men

t rat

e (%

)

2 3 4 5Product market regulation (0−6)

Source: CEP-OECD database http://eprints.lse.ac.uk/19789/. This OECD indicator of regulatory reform

summarises regulatory provisions in seven non-manufacturing sectors. The range is 0,6 increasing in regulation.

The mark-up is likely to depend positively on product market regulation as thelatter reduces the degree of market competition.

http://eprints.lse.ac.uk/19789/


Structural unemployment rate and unemploymentbenefits (1990-2001)

Australia

Austria

BelgiumCanada

Denmark

Finland

France

Germany

IrelandItaly

Japan

Netherlands

New Zealand

NorwayPortugal

Spain

Sweden

Switzerland

United Kingdom

United States

05

1015

Stru

ctur

al u

nem

ploy

men

t rat

e (%

)

0 20 40 60Gross benefit replacement rates (%)

Source: CEP-OECD database http://eprints.lse.ac.uk/19789/. Unemployment benefits in the first year

are expressed as a percentage of average earnings before tax.

High unemployment benefits allow unemployment workers to hold out for higherwages. Hence, higher unemployment benefits increase the wage at any givenunemployment rate.



Structural unemployment rate and union coverage(1990-2001)

Australia

Austria

BelgiumCanada

Denmark

Finland

France

Germany

Italy

Japan

Netherlands

New Zealand

NorwayPortugal

Spain

Sweden

Switzerland

United Kingdom

United States

05

1015

Stru

ctur

al u

nem

ploy

men

t rat

e (%

)

20 40 60 80 100Union coverage (%)

Source: CEP-OECD database http://eprints.lse.ac.uk/19789/. Union coverage refers to the number of

workers covered by collective agreements normalised on employment.

High union coverage implies that a large fraction of employed workers benefitsfrom the wage negotiated by unions above the competitive wage.



Structural unemployment rate and the tax wedge(1990-2001)

Austria

BelgiumCanada

Denmark

Finland

France

Germany

Italy

Japan

Netherlands

NorwayPortugal

Spain

Sweden

Switzerland

United Kingdom

United States

05

1015

Stru

ctur

al u

nem

ploy

men

t rat

e (%

)

30 40 50 60 70 80Tax wedge (%)

Source: CEP-OECD database http://eprints.lse.ac.uk/19789/. The tax wedge is equal here to the sum

of the employment tax rate, the direct tax rate and the indirect tax rate.

A higher tax wedge leads to a fall in the price-setting real wage.



Equilibrium

PC

MR

WS

PS

E L

In�ation

Output

T

Y_e

A

A

The ERU determines the equilibrium level of output [A]. Note that U = L−EL .


Medium-run effect I

PC

MR

WS

PS

E L

In�ation

Output

T

Y_e

E’

Y_e’

PS’

A

A

Z

The cut in the payroll tax leads to an upward shift of the PS curve, leading to lower ERU[Z ] (U′ = L−E′

L ).


Medium-run effect 2

PC

MR

WS

PS

E L

In�ation

Output

T

Y_e

E’

Y_e’

PS’

A

A

MR’

Z

Z

The new ERU leads to a higher equilibrium level of output. Hence, for a given inflationtarget, the MR curve shifts to the right.


Initial effect

PC

MR

WS

PS

E L

In�ation

Output

T

Y_e

E’

Y_e’

PS’

PC’

A

A

B

B

MR’

C

Negative gap

In�ation falls

Z

Z

The payroll tax cut allows firms to increase the nominal wage of workers. There is nowa negative gap between the PS-real wage and the WS-real wage, as workers receivesa real wage which exceeds their previously bargained real wage. They accept a lowernominal wage increase than in the previous year and inflation falls [A→ B].


Intervention of the central bank I

PC

MR

WS

PS

E L

In�ation

Output

T

Y_e

E’

Y_e’

PS’

PC’

A

A

B

B

MR’

C

E’’

Z

Z

The central bank realises that a) current inflation is below target inflation and that b)the equilibrium level of output has increased. It chooses its preferred position on thenew PC curve given its preferences, which take into account the new equilibrium levelof output. The economy moves in the next period to point C.


Intervention of the central bank II

PC

MR

WS

PS

E L

In�ation

Output

T

Y_e

E’

Y_e’

PS’

PC’

A

A

B

B

MR’

C

E’’

In�ation rises

Positive gap

Z

Z

CC

C

At point C, inflation is still below target inflation but is rising as indicated by the positivegap between the PS-real wage and the WS-real wage. The central bank will guide theeconomy along the MR′ curve, slowly rising the interest rate and depressing the positiveoutput gap until the new medium-run equilibrium.


New medium-run equilibrium

PC

MR

WS

PS

E L

In�ation

Output

T

Y_e

E’

Y_e’

PS’

PC’

A

A

B

B

MR’

C

PC’’

Z

Z

The new medium-run equilibrium is Z .


The ERU and actual rate of unemployment

The actual unemployment rate can be decomposed into a

1 Cyclical component, which is the difference between the actual rate and theequilibrium rate. It is associated with short-run fluctuations (AD shocks).

2 Equilibrium component, which reflects the institutional characteristics of thelabour market.

So far, we have assumed that AD shocks can influence the total unemployment rate, byinfluencing cyclical unemployment, but cannot influence the ERU. This is why we makea distinction between AD policies and SS (Supply-Side) policies.

However, in the eighties, unemployment rose dramatically in many OECD countries,without a strong fall in the level of inflation:

This macroeconomic outcome is at odd with our IS-PC-MR model since anunemployment rate above the equilibrium level should lead to lower inflation.

The only way for the IS-PC-MR model to predict this outcome is to assume thatthe equilibrium rate moves towards the actual unemployment rate.


Hysteresis and persistenceWhen a period of sustained unemployment due to weak aggregate demand feeds backto the supply side of the economy and results in a permanent rise in the ERU, a phe-nomenon known as “hysteresis” is said to occur. There is path dependency as the ERUdepends on the history of actual unemployment.

The current unemployment rate can be expressed as a function of the past value of theunemployment rate:

Ut = (1− β)α+ βUt−1 + εt

where ε is a random shock and α is a constant related to labour market institutions. Ifa one-time positive shock occurs (εt > 0), Ut increases by the full amount. What aboutUt+1:

1 β = 1: hysteresis. The unemployment rate in the next period increases bythe same amount as the current unemployment rate.

2 There is no tendency for the unemployment rate to converge towards theERU.

1 0 < β < 1: persistence. The The unemployment rate in the next periodincreases by a lower amount than the current unemployment rate.

2 The unemployment rate converges towards the ERU which is whenUt = Ut−1: ERU = (1−β)α

1−β= α.


Persistence (1970-2008): Ut = (1 − β)α + βUt−1 + εt

(1) (2) (3) (4) (5)France Japan Sweden UK USA

L1.France 0.927***(0.0345)

L1.Japan 0.958***(0.0360)

L1.Sweden 0.928***(0.0570)

L1.United Kingdom 0.922***(0.0586)

L1.United States 0.760***(0.106)

Constant 0.688** 0.197* 0.445 0.598 1.492**(0.278) (0.113) (0.300) (0.446) (0.663)

Standard errors in parentheses. Data come from http://www.bls.gov/fls/.*** p<0.01, ** p<0.05, * p<0.1

The unemployment rate in OECD countries displays high persistence but nohysteresis.

High persistence implies that the convergence towards the ERU is very slow.

http://www.bls.gov/fls/


Bargaining power and long-term unemployed

Two theories have been proposed to explain hysteresis/persistence:

1 The insider/outsider theory.2 The unemployment duration theory.

I will focus on the second one:

The share of long-term unemployed [LTU] (one year and over) in thetotal number of workers unemployed tends to increase when theunemployment rate increases.

Firms are unwilling to hire LTU workers: loss of skills and workconfidence or suspicions that they are the rejects from other firms.

Firms do not consider LTU as part of the labour force.

In that case, the unemployment rate that determines the bargainingpower of workers is no more E−L

L but E+LTU−LL .

The WS curve shifts upward and the ERU rises.


Long-term unemployment and the unemployment rate(1991-2009)

020

4060

80Lo

ng−

term

Une

mpl

oyed

(%

Tot

al U

nem

ploy

ed)

0 5 10 15 20Total unemployment rate (%)

Source: OECD http://stats.oecd.org/Index.aspx?DataSetCode=DUR_I/.

http://stats.oecd.org/Index.aspx?DataSetCode=DUR_I/


Impact of LTU on WS curve

WS

PS

E LE1+LTU_hE1

A

B

C

WS_LTU_h

1 The initial equilibrium is A.2 There is a negative AD shock, A to B.3 The share of LTU increases and stabilises at employment level E1.4 The bargaining power of workers/short-term unemployed increases.5 The WS curve shifts upward, as for a given level of real employment (e.g. E1),

workers make wage demands corresponding to a higher level of employment(E1 + LTUh).


Impact of LTU on ERUh

WS

PS

E LE1

A

B

C

D

E2

WS_LTU_h

The new medium-run equilibrium is D with a high share of LTU.


Impact of ERUm on LTU

WS

PS

E L

WS_LTU_h

AD

E2

E

F

WS_LTU_m

E2-LTU_m

1 At the equilibrium D, LTU begins to fall as employment has increased from E1 toE2. It reaches a new stable level.

2 The bargaining power of workers/short-term unemployed decreases.3 The WS curve shifts downward, as for a given level of real employment (e.g.

E2), workers make wage demands corresponding to a lower level of employment(E2− LTUm).

4 The new medium-run equilibrium becomes F and this process carries on until A.


Hysteresis: The crisis, long-term unemployment andstructural unemployment

Source: OECD http://www.oecd.org/dataoecd/19/22/45276571.pdf.

http://www.oecd.org/dataoecd/19/22/45276571.pdf


Hysteresis and the crisis: labour market policyresponse

Source: OECD http://www.oecd.org/dataoecd/19/22/45276571.pdf.

Note that some policies implemented, i.e. high unemployment benefits, have boostedAD and limited the rise of cyclical unemployment but may increase the ERU in the near

future. This is why the OECD recommends scaling them back.

http://www.oecd.org/dataoecd/19/22/45276571.pdf

EC404-Lecture 7

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