Leszek Wincenciak, Ph.D.coin.wne.uw.edu.pl/.../lecture_1.pdf · Lecture outline: Introduction Basic facts about the labour market performance Basic model of the neoclassical theory

Lecture 1

Macroeconomics of the Labour Market

Leszek Wincenciak, Ph.D.

University of Warsaw

Lecture 1 — Macroeconomics of the Labour Market

2/54

Lecture outline:

Introduction

Basic facts about the labour market performance

Basic model of the neoclassical theory of labour supplyChoice between consumption and leisureThe properties of labour supplyAggregate labour supply and Labour Force participation rate

Labour demand in the neoclassical model

Unemployment in neoclassical modelPossible explanations for unemploymentDifference in unemployment of skill groups in a neoclassical model


Introduction 3/54

What is it going to be about. . .

Labour market macroeconomics:

1. Introduction and basic facts on labour market performanceand basic model of neoclassical labour supply

2. The NAIRU model

3. Basic model of efficiency wages

4. Shapiro and Stiglitz model of efficiency wages

5. Wage bargaining and trade unions

6. Search and matching theory


Introduction 4/54

What is it going to be about. . .

◮ Read suggested literature (see the syllabus) + make notes◮ Bagliano F., Bertola G. (2004) Models for DynamicMacroeconomics, Oxford University Press, chapter 5.

◮ Cahuc P., Zylberberg A. (2004) Labor Economics, MIT Press.◮ Pissarides C. (2000) Equilibrium Unemployment Theory, MITPress.

◮ Boeri T., van Ours J. (2008) The Economics of ImperfectLabor Markets, Princeton University Press.

◮ Problem set - sample problems

◮ Office hours: Monday, 9.45-11.15, room B306

◮ E-mail: [email protected]


Basic facts about the labour market performance 5/54





◮ Definition: unemployment is an economic condition marked bythe fact that individuals actively seeking for jobs remainunhired.

◮ Unemployment is a fact – much of the labour market theory isdevoted to explain the existence and various aspects ofunemployment (its reasons, duration, persistence, etc.)



Basic measures of the labour market performance

Each individual member of the working age population might bepotentially in one three states:

◮ Not economically active (out of the labour market) – N

◮ Economically active, and:◮ Unemployed – U , or◮ Employed – E (either employee or employer)

Three basic measures:

◮ The participation rate: a = E+UN+E+U

◮ The employment rate: e = EN+E+U

◮ The unemployment rate: u = UE+U



Unemployment fluctuates over time but in the very long run seems to have notrend

4

6

8

10

Uni

ted

Sta

tes

1960 1970 1980 1990 2000 2006Time

Figure 1. Unemployment rate, USA 1960-2006.



Unemployment exhibits a lot of persistence

If we ran simple regression of the unemployment rate on its pastvalue for a very long period of time, we would get the followingresult:

Ut = 0.7139 + 0.8561(20.2)

Ut−1, R2 = 0.733 (UK, 1856-2005)

Ut = 0.9919 + 0.8567(17.7)

Ut−1, R2 = 0.735 (US, 1891-2005)




Take the time series representation of the unemployment rate:

Ut = α0 + α1Ut−1

then the long run equilibrium value U = α0

1−α1equals 4.96% for UK

and 6.92% for US. Let’s find the convergence speed to the longrun equilibrium.

U1 = α0 + α1U0

U2 = α0 + α1U1 = α0 + α1(α0 + α1U0)

...

Ut = α0[1 + α1 + α21 + . . .+ αt−1

1 ] + αt1U0




Then if we calculate the sum of geometric series (convergence isguaranteed by |α1| < 1) and use the definition of U , we can write:

Ut = α01− αt

1

1− α1+ αt

1U0

Ut = U(1− αt1) + αt

1U0

Ut − U = αt1(U0 − U)

Suppose U0 is not equal U . How many periods of time (T ) will ittake to eliminate half of the difference between U0 and U?




We can treat this T as a measure of convergence speed (half-life):

UT − U ≡ αT1 (U0 − U) =

1

2(U0 − U) ⇒ αT

1 =1

2

Then by taking logs for both sides we get:

T = −ln 2

lnα1

For both UK and US is takes about 4.5 years!



Unemployment is countercyclical

Correlation = −0.844***

−2

0

2

4

6

1970 1975 1980 1985 1990 1995 2000 2005 2008

GDP growth rate U change

Figure 2. Change in unemployment rate and GDP growth, USA 1970-2008.



Unemployment is different among countries. . .

Figure 3. Unemployment rates across countries, 1980-2006.



. . . and age and sex groups

Table 1. Unemployment by sex and age.

Sex Men Women

Age 15 to 24 25 to 64 Total 15 to 24 25 to 64 Total

France 22.4 7.6 9.0 25.8 9.3 10.7

Germany 14.2 9.9 10.3 12.6 10.0 10.2

Japan 8.8 4.0 4.3 7.2 3.6 3.8

Norway 8.6 2.7 3.5 8.7 2.5 3.4

Poland 28.3 11.1 13.0 31.6 12.9 14.9

UK 15.8 4.1 5.7 11.8 3.6 4.9

US 11.2 3.5 4.6 9.7 3.8 4.6

EU 15 15.8 6.2 7.2 16.4 7.8 8.7

G7 12.9 4.9 5.8 11.3 5.3 6.0

OECD 12.6 5.0 5.9 12.3 5.6 6.4



Unemployment durations might be quite long

Figure 4. Unemployment duration (months) across countries, 1970-2007.



Unemployment durations might be quite long

Figure 5. Long term unemployment (over 12 months) across countries, 1970-2007.


Basic model of the neoclassical theory of labour supply 18/54

Basic modelof the neoclassical theory of labour supply



Choice between consumption and leisure


◮ It is assumed that consumer derives utility from two sources:the quantity of consumed goods (aggregated to C with pricenormalized to unity) and the amount of leisure (time devotedto other activities than work, denoted by L) – U(C,L)

◮ Total time available – T (number of hours per day, month,year, etc.)

◮ Labour supply: h = T − L

◮ Market wage – w

◮ Non-wage income – R





The properties of utility function:

UC > 0, UL > 0, UCC < 0, ULL < 0, UCL > 0.

Budget constraint:

C 6 w(T − L) +R ⇔ C + wL 6 wT +R︸︷︷︸

R0

(1)

Maximization problem:

MaxC,L

U(C,L) s.t. C + wL 6 R0





Lagrangean:

L(C,L, λ) = U(C,L) + λ(R0 − C − wL)

F.O.C.:

Lλ = 0 : R0 − C − wL = 0

LC = 0 : UC(C,L) − λ = 0

LL = 0 : UL(C,L)− λw = 0




Solution

If we denote optimal values by C∗, L∗ and λ∗, from F.O.C. we get:

UL(C∗, L∗)

UC(C∗, L∗)= w with C∗ + wL∗ = R0 (2)

Intuition: optimal choice lies on the budget constraint and theslope of the indifference curve equals (for interior solution) theslope of the budget constraint. L∗ is defined implicitly by (2), so:

L∗ = µ(w,R0). (3)





Figure 6. Trade-off between consumption and leisure and optimal choice.




Reservation wage

How can we guarantee the interior solution? When will theindividual be willing to supply any labour to the market? Clearly,when the market wage is high enough to provide appropriateincentives to give up some leisure. The opportunity cost of leisureincreases with market wage. In terms of our graphicalrepresentation, we can infer the minimum wage, at which theindividual will be indifferent between entering the labour market orstaying outside. This is called the reservation wage.




Reservation wage

The point E has to lie to the left of point A, otherwise L = T andh = 0. With convexity of utility curves, the MRSCL = UL

UCis

decreasing to the south-east along the indifference curve.

h > 0 ⇔ wA ≡UL

UC

∣∣∣∣L=T

< w

wA =UL(R,T )

UC(R,T )

The reservation wage depends on the value of R and the shape ofutility function. It determines the labour market participation.



The properties of labour supply

The properties of labour supply – substitution and income effects

We are now in position to analyse some interesting comparativestatics results. Primarily, we are interested in the influence ofa non-wage increase impact on the labour supply and the wageincrease impact on the labour supply. In order to do it, we cantotally differentiate the F.O.C.:

dR+ dw T − dC − dL w − dw L = 0

dC UCC + dL UCL − dλ = 0

dC UCL + dL ULL − dλ w − dwλ = 0




Comparative statics

We can rewrite it more conveniently as:

−dC −dL w = −(T − L)dw − dR−dλ +dC UCC +dL UCL = 0−dλ w +dC UCL +dL ULL = λdw

If we are now interested in the effect of a rise in a non-wageincome R on L, we can simply take dw = 0, and divide all threeequations by dR. This yields the following:

0 −1 −w−1 UCC UCL

−w UCL ULL

∂λ/∂R∂C/∂R∂L/∂R

=

−100




Comparative statics

Now we can use the Cramer’s theorem to solve for ∂L/∂R:

∂L

∂R=

1

|H |

∣∣∣∣∣∣

0 −1 −1−1 UCC 0−w UCL 0

∣∣∣∣∣∣

=−1

|H |

∣∣∣∣

−1 UCC

−w UCL

∣∣∣∣

=(−1) · (−UCL + wUCC)

|H|




Comparative statics

Let’s check the value of the determinant of the bordered HessianH:

detH = −w2UCC + 2wUCL − ULL > 0.

This means that:

∂L

∂R> 0.

Of course this result rests on the assumption that UCL > 0,meaning that L is treated as a normal good. Our result suggeststhat an increase of non-wage income is a disincetive to work, sincethe individual will opt for more leisure.




Comparative statics: effect of a rise in non-wage income

Figure 7. Effect of a rise in non-wage income.




Comparative statics: effect of a wage increase

In order to grasp the effect of a wage increase on labour supply weneed to repeat our procedure once again, and divide all threeequations by dw. The system becomes:

0 −1 −w−1 UCC UCL

−w UCL ULL

∂λ/∂w∂C/∂w∂L/∂w

=

−(T − L)0λ





∂L

∂w=

1

|H|

∣∣∣∣∣∣

0 −1 −(T − L)−1 UCC 0−w UCL λ

∣∣∣∣∣∣

=

=1

|H|

∣∣∣∣

−1 0−w λ

∣∣∣∣+

−(T − L)

|H|

∣∣∣∣

−1 UCC

−w UCL

∣∣∣∣=

=−λ− (T − L)(−UCL + wUCC)

|H |=

=−UC − (T − L)(−UCL + wUCC)

|H |≷ 0





The influence of a wage increase on the labour supply can beambiguous:

◮ higher wage will increase labour supply (decrease demand forleisure) if substitution effect is stronger than income effect:i.e. when (T − L) is small or when UC is large – somebodyworked relatively small or had relatively low wage;

◮ higher wage will decrease labour supply (increase demand forleisure) if income effect is stronger than substitution effect:i.e. when when (T − L) is large or when UC is small –somebody worked already for long or had high wage.





Figure 8. Effect of a wage increase.




Individual labour supply

Figure 9. Individual labour supply.




Supplementary constraints

Our analysis of labour supply is limited in a number of ways:

◮ it divides time only into two activities: work and leisure. It ispossible that household production is a substitute to marketproduction and time devoted to it could also play a rolei determining labour supply

◮ more sophisticated models will emphasize the role of thelabour supply being decided at a household level – bargainingpower and comparative advantage issues (with the same ordifferentiated utility functions for household members)

◮ intertemporal issues (life cycle and retirement decisions)

◮ other costs of participation (transport costs, child care, etc.)

◮ discrete time choices (time of work offered is in most casesnot a continuous variable)





Reality of life is far from flexible number of hours devoted to work:

◮ Assume that an individual has a choice of working duringT − Lf hours or not working at all

◮ Let point E represent the unconstrained optimum. If E lies tothe left of Ef the individual will agree to work for T − Lf

hours – he or she would even have liked to work more

◮ If point E is to the right of Ef , then the individual will takeup the job only if the point EA – the intersection ofindifference curve passing through A and the budget line – liesto the left of Ef : in this case he or she would obtain higherutility from work than from not participating

◮ If point EA lies to the right of Ef then individual will notparticipate (involuntary nonparticipation) – he or she wouldlike to work for T − L∗ hours at current wage, but facesconstraints that keep them from doing so





Figure 10. Constraints on hours of work.



Aggregate labour supply and Labour Force participation rate

Aggregate labour supply and Labour Force participation rate

◮ Given constraints on the number of hours devoted for work,each individual has choice to work for h = T − Lf hours ornot work at all

◮ In a large population, reservation wages are probably differentdue to utility differences and different non-wage incomes;wA ∈ [0,+∞)

◮ Distribution of reservation wages is represented bya cumulative distribution function Φ(·). By definition, Φ(w)shows the proportion of population for which reservation wageis lower than current wage w – it is the participation rate.

◮ NΦ(w) – aggregate labour supply

◮ Since dΦ(w)/dw > 0, then the elasticity of aggregate laboursupply is also positive if N is constant

◮ Decision to participate is sensitive to many incentives, notnecessarily only wage


Labour demand in the neoclassical model 40/54





The demand for labour is a demand for factors of productionderived from demand for final goods. Firms in a perfectlycompetitive market use a short run production function (withpredetermined capital stock and given technology) to maximizeprofits:

Y = AF (L,K),

Y – real output, K – given capital stock, L – amount of labouremployed, A – technology. Standard assumptions about theproduction function F (·) are adopted:

FL > 0, FK > 0, FLL < 0, FKK < 0, FLK = FKL > 0.




Firms aim at maximizing short-run profits:

π = PY −WL

MaxL

π = PAF (L,K)−WL.

dπ

dL= 0, ⇒ AFL(L,K) = W/P. (4)

Demand for labour (LD) is defined implicitly by (4).




Let’s take w = W/P as a real wage. Then by totallydifferentiating (4) we get:

d(AFL(LD,K)) = dw

FL dA+A(FLL dLD + FLK dK) = dw

By rearranging terms we obtain:

dLD = −FL

AFLLdA−

FLK

AFLLdK +

1

AFLLdw




Properties of labour demand:

◮ since FLL < 0, then an increase of real wage reduces demandfor labour

◮ since FLK > 0, then an increase in capital stock increasesdemand for labour

◮ since FL > 0, then an improvement in technology increasesdemand for labour




Figure 11. Labour demand in the neoclassical model.


Unemployment in neoclassical model 46/54

Unemployment in neoclassical model



Neoclassical labour market

Neoclassical labour market is characterized by:

◮ Homogenous workers

◮ Perfect competition

◮ Market clearing, flexible wages

◮ Perfect information

◮ No involuntary unemployment

Is neoclassical model enough to explain the performance of thelabour market today?



Possible explanations for unemployment

Possible explanations for unemployment

If wages do not clear the market, so that there existsunemployment, why don’t they fall?

◮ There is no problem – some people just don’t want to workanyway

◮ Wage rigidity (especially downward) – minimum wagelegislation

◮ Efficiency wages – it may be profitable for the firms to payhigher wage in equilibrium than market-clearing wage

◮ Bargaining power of labor unions (insiders-outsiders)

◮ Heterogeneity of workers and jobs – search for jobs andmatching a worker with suitable job is costly and takes time



Difference in unemployment of skill groups in a neoclassical model

Can we still explain the difference in unemployment of skill groups usingneoclassical model?

Skilled and unskilled labor in the production function:

Y = G(Ls, Lu,K) = G(Ls, Lu, 1) ≡ F (Ls, Lu),

with Fu ≡ ∂F∂Lu

> 0, Fs ≡∂F∂Ls

> 0, Fuu ≡ ∂2F∂L2

u

< 0, and

Fss ≡∂2F∂L2

s

< 0

Representative firm chooses two types of labour:

maxLs,Lu

π ≡ PF (Ls, Lu)−WsLs −WuLu.




Maximization of profits yields standard condition for the value ofmarginal product of labour equal real wage (for skilled andunskilled labour):

Fu(Lu, Ls) =Wu

P≡ wu

Fs(Lu, Ls) =Ws

P≡ ws

These two conditions lead to labour demand functions, LDu and

LDs . By totally differentiating these two conditions, we get:

[dLs

dLu

]

=1

∆

[Fuu −Fsu

−Fsu Fss

] [dws

dwu

]

where ∆ ≡ FssFuu − F 2su > 0.




Therefore demand functions can be written as follows:

LDs = LD

s (ws, wu), LDu = LD

u (ws, wu).

Clearly, the „own” real wage effects are negative, because ofdiminishing marginal products:

LDss ≡

∂LDs

∂ws=

Fuu

∆< 0, LD

uu ≡∂LD

u

∂wu=

Fss

∆< 0.

What are the „cross” real wage effects? Additional assumption –skilled and unskilled labour are treated as (imperfect) grosssubstitutes, so that these cross effects are positive. If unskilledlabour becomes more expensive, the demand for skilled increasesand vice versa.




In order to close the model as simply as possible, supply curves ofthe two types of labour are both assumed to be inelastic:

LSs = Ls

LSu = Lu




Implications

◮ With flexible wages, both types are fully employed(equilibrium skill premium, ws/wu)

◮ With a binding, skill-independent, minimum wage w theunskilled will experience unemployment. How to cure it?

◮ abolish minimum wage (incomes distribution problems)◮ subsidize unskilled work◮ let government hire unskilled workers◮ train unskilled workers to become skilled (investment in humancapital may pay for itself)




Graphical representation

LDs (ws, w

∗

u)

LDs (ws, w)

LsLs

ws

w∗

s

w′

s

w

LDu (w

′

s, wu)

LDu (w

∗

s , wu)

LuLu

wu

w∗

u

w

Figure 12. Labour market equilibrium for skilled and unskilled

Documents

Leszek Wincenciak, Ph.D.coin.wne.uw.edu.pl/.../lecture_1.pdf · Lecture outline: Introduction Basic facts about the labour market performance Basic model of the neoclassical theory