LABOR ECONOMICS

LABOR ECONOMICS

LABOR ECONOMICS

Sponsored by a Grant TÁMOP-4.1.2-08/2/A/KMR-2009-0041 Course Material Developed by Department of Economics,

Faculty of Social Sciences, Eötvös Loránd University Budapest (ELTE) Department of Economics, Eötvös Loránd University Budapest

Institute of Economics, Hungarian Academy of Sciences

Balassi Kiadó, Budapest

LABOR ECONOMICS

Author: János Köllő

Supervised by: János Köllő January 2011

ELTE Faculty of Social Sciences, Department of Economics

LABOR ECONOMICS

Week 11

Equilibrium in a competitive labor market

János Köllő

• Marshallian equilibrium

• Delays of adjustment: cobweb cycle

• Frictions: job search and unemployment

• Frictions: equilibrium with job destruction and job creation

• Supply or demand?

Equlibrium in a perfectly competitive

labor market with no frictions

Excess demand

Shortages tend to push wages upward.

Demand falls and supply rises in

response to growing wages.

E is the only point, where the number of people willing to

work and the number of jobs offered are equal.

D,S

w S

D

Labor shortage

E

Marshallian equilibrium

Excess supply

Wages fall under the pressure of

unemployment

Demand rises and supply falls in response to falling wages

E is the only point, where the number of people willing to

work and the number of jobs offered are equal

D,S

w S

D

unemployment

E

Marshallian equilibrium

Cobweb cycle

Delays in adjustment

Cobweb cycle: conditions

Closed occupational labor market

Entry only from the school system. Skills are not convertible.

Naive expectations

Expectations concerning the future returns to education are based on current returns.

Cost-based planning in education

Quotas are determined on the basis of current social costs and returns.

Labor demand is more elastic than labor supply.

D⁰

D¹ w

S

Let the demand for an occupation rise, shifting the

demand curve from D

to D

.

The market can not move immediately to the new equilibrium point because labor supply reacts with a delay.

D⁰

D¹ w

S

?

D⁰

D¹ w

D,S A

B

Step 1

Wages and enrolment rise but it takes time until students

graduate and enter the labor market.

Step 2

Students graduate  supply rises

D⁰

D¹ w

D,S A

B

Step 3

Growing supply puts a pressure on wages. Increased supply is absorbed only at lower wages.

D⁰

D¹ w

D,S A

B

Step 4

Since wages are now lower, enrolment falls. After a while the number of graduates falls, too.

D⁰

D¹ w

D,S A

B

Step 5

A smaller cohort of students graduate. Falling supply pushes wages upward and leads to an increase in enrolment.

And so on …

D⁰

D¹ w

D,S A

B

D⁰

D¹ w

D,S A

B

… and on

D⁰

D¹ w

D,S A

B

… and on

D⁰

D¹ w

D,S A

B

… and on

D⁰

D¹ w

D,S A

B

Until the market finds the new equilibrium.

Note that if supply is more elastic than demand the process does not

converge.

Factors working against a cobweb cycle

• Skills are convertible to some extent.

Workers can leave and enter the market.

• Adult training can further increase mobility.

• Future changes are predictable to some

extent.

Frictions

Job search

• In practice, markets never reach the equlibrium point.

• Even in tight markets, many workers remain unemployed. In mature market economies

unemployment seldom fell below 3 per cent in the last few decades.

• A part of this problem arises because job

seekers may be interested in searching further rather than accepting the job offers they meet.

• Let us examine how job seekers make their

decisions.

The costs (and benefits) of searching

Shall we search further in a short period t after meeting a wage offer w*?

Consider an unemployed job seeker, who has information (or beliefs) on the distribution of wages but not on actual wage offers.

Unemployed workers can receive benefits, produce goods in the household and has to cover search costs.

b = unemployment benefit

h = value of household production c = direct costs of job search

F(w) = the distribution of wage offers

< 1 = the probability of an offer in period t

r = discount rate measuring risk aversion

The costs of searching further

) ( c b h w

I have to cover the costs of further

search (+)

I can work further in the household

(–)

I continue to receive unemployment benefit

(–) I lose wage w* by refusing

the offer (+)

w* = opportunity cost, c–b–h = direct costs

w r w

w w E w

F 1

( 1 1

Probability that the offer is higher than w*

Expected gain

Risk aversion

Probability of an offer

Recall that Pr(w>w*)=1–F(w*)

The benefit from further search

The asking wage* (w ^R )

c h

b r w

w w

w w E w

F ^{R R R R}

1 ( 1

1

w r w w w E w

F 1

( 1 1

c h b w

c h

b w*

Gains

w^R

(gain if w* is accepted)

(gain if w* is rejected)

The wage, at which the job seeker is neutral between accepting and refusing an offer:

It is also called the reservation wage. We follow Borjas (2008) in calling it differently from the concept discussed in Labor supply

If the offer is lower than the asking wage further search Further search implies further (search) unemployment

w r w w w E w

F 1

( 1 1

c h b w

c h b

w*

Gains

w^R

(gain if w* is accepted)

(gain if w* is rejected)

If the offer is higher than the asking wage stopping

w r w w w E w

F 1

( 1 1

c h b w

c h b

w*

Gains

w^R

(gain if w* is accepted)

(gain if w* is rejected)

The probability that a random offer is accepted

(a is exogeneous):

• Benefits, household production  decrease

• Search costs: increase

Lower costs make further search more attractive.

• Risk aversion: increases

• Abundance of job offers: decreases

This relates to accepting a given offer. In the same time, abundance

increases the job offer arrival rate and thereby decreases unemployment.

• Wage distribution: depends

Job seekers often notice changes in the wage distribution with a delay

w

Offers accepted Density of wage

offers

Job seekers may not immediately notice changes in the wage distribution. Despite f

f

their asking wage may remain at w*

• Implications:

• Exit from unemployment falls since Prob(w>w^R) decreases.

• Since the condition for entry to employment is still w>w^R, accepted wages do not fall.

Wages are seemingly rigid.

Accepted offers

f

f

w

Frictions

With job destruction and job creation

• Markets are in motion: jobs are destroyed

and created, and workers are hired and fired, on a massive scale even when aggregate

employment is constant.

• We can speak of equilibrium (steady state), when the number of exits from and entries to employment are equal.

• Steady states can be achieved at different

levels of unemployment. This is what we try

to understand in the forthcoming section.

The UV curve

Let us keep the rate of job destruction constant. How many vacant jobs should be created in order to keep unemployment (U) constant?

U V

When unemployment is high, it is easier to fill vacancies. Therefore, less vacancies should be created in order to keep unemployment constant.

Along the UV curve s(1–u) = x(u,v), where s is the separation rate and x(u,v) is a matching function describing the number of entries to employment. Unemployment is u while v denotes vacancies.

In other words, along the UV curve the number of new matches keep

unemployment constant for a given rate of job destruction.

Different UV curves

Let us keep the rate of job destruction constant. How many vacant jobs should be created in order to keep unemployment (U) constant?

If matching is inefficient (because workers and firms are poorly informed, mobility is constrained, the demanded and supplied skills differ to a large extent)  more V is required at a given level of U.

U

V

The VS curve

VS=vacancy supply

How many jobs are created by firms? How job creation varies with U?

High U  falling wages and recruitment costs  it is now cheaper to create V.

U

V

Different VS curves

How many jobs are created by firms? How job creation varies with U?

If wages are rigid and recruitment costs do not fall with U (because the

unemployed live in remote areas, are unskilled, etc.)  firms create less V at a given level of U.

U

V

Steady state

Firms are interested in creating as many vacancies as required to keep unemployment constant for a given level of job destruction.

U V

UV

VS UV

VS

Right of the steady state

Firms create more vacancies than required for the equality of flows  U starts to fall.

u v

UV

VS UV

VS

Left of the steady state

Firms create less vacancies than required for the equality of flows  U starts to grow.

u v

UV

VS UV

VS

Different steady states

A: good equilibrium. Flexible wages, low mobility costs, low information costs, demanded and supplied skills are similar.

B: bad equilibrium. Rigid wages, high mobility costs, high information costs, severe skills mismatch.

U V

B

A

Supply or demand?

• How can we ascertain whether market changes are supply or demand driven?

• We shall see that there is no reassuring answer to the question. However, we can arrive at a second best answer by studying how changes of wages and employment

are related to each other.

• The forthcoming slides draw from L. F. Katz–D. H. Autor (1999):

Changes in the Wage Structure and Earnings Inequality, in: Orley

Ashenfelter and David Card, eds., Handbook of Labor Economics

(Amsterdam, North-Holland).

Supply or demand? In practice, we only see how the market moved from one point to another. We do not know if the market moved along a highly elastic demand curve (D*) or the supply and demand curves S,D were shifted by some external shocks.

w

L D*

D

S

The Katz-Murphy (1992) cross-products provide some insight. Let us use the following notation:

X_t – K 1 vector of factor demands in year t.

w_t = K 1 vector of wages (factor prices) in year t.

Z_t = m 1 vector of demand shifters in year t.

Factor demands depend on prices and the shifters:

) , ( ]

1

[ X

D w

Z

In terms of differentials:

t Z t

t w t

Z t

w

t

D dw D dZ D dw dX D dZ

dX ]

2 [

where D

is the matrix of cross price effects (Slutsky matrix)

3 2 1

3 2 2

2 1

2

3 1 2

1 1

1

2 1

2 2 1

2

2 1 1

1

2 1

dz dz dz

z x z

x z

x

z x z

x z

x dw

dw w

x w x

w x w

x dx

dx In case of two factors and three demand shifters, e.g.

Multiplying equation [2] with dw

from the left yields:

0 ) (

] 3

[ dw

D

dw

dw

dX

D

dZ

If demand is constant (dZ=0), the cross product of changes in wages and employment will be non-positive:

0 ]

4

[ dw

dX

In other words, positive cross products can not be reconciled with purely supply driven scenarios. This is less than a full answer but much more than nothing.

Why? Applying Shepard’s lemma we have:

j i j

i

w w

C w

x (w) ² (w)

.

It is easy to see that the Slutsky matrix is the Hessian of the cost function. If the cost function is concave its Hessian is negative semi-definite. If a matrix is negative semi-definite then

0 0

'Ax x

x .