LABOR ECONOMICS

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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

Author: János Köllő Supervised by: János Köllő

January 2011

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2

LABOR ECONOMICS

Week 2

Labor supply – Topics

János Köllő

The benchmark model of static labor supply Household production and labor supply Labor supply over the life-cycle

Added workers and discouraged workers

Taxes, benefits and labor supply

Household production: the presentation follows Gary Becker’s seminal paper (A Theory of the Allocation of Time, Economic Journal, September 1965) with major simplifications.

Labor supply over the life-cycle: the presentation follows a hand-out by Peter Kuhn (UCSB), downloadable at: www.econ.ucsb.edu/~pjkuhn /Ec250A

/Class%20Notes/C_DynamicLS.pdf.

Other topics: based on various sources as indicated in the text.

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3

Static labor supply

The problem:

where X is consumption, T is total time available for work and leisure, L is leisure, w is hourly wage and y is non-wage income. X and L are normal goods. Working time (H) is given by H=T–L

The Lagrangian:

First-order conditions:

In optimum the marginal rate of transformation equals the wage:

Rearranging terms yields MUL= wMUX – the marginal utility of consumption induced by a unit increase in the wage equals the marginal utility from an additional unit of leisure à w is the price of leisure, „time is money”.

In order to see the comparative static properties we introduce the concept of total income or endowment (I). Rearranging the budget constraint yields:

Total income (endowment) comprises non-wage income and total time available for work and leisure, evaluated at the hourly wage.

Demand for leisure depends on the price of leisure and income:

As far as leisure is a normal good, we have:

L y L T w L

X U

L

( , ) max ( ) ,

max

y L T w X L

X

U , ( )

max L

0 ,

0 U w

U

_X _L

U w U

X L

I y wT wL

X y

L T w

X ( )

Total consumption Total income

I y wT wL

X y

L T w

X ( )

Total consumption Total income

)) , ( ,

( w I w y L

L

I 0

L

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4 Which effect is stronger?

For people out of work (T–L)=0 only the substitution effect is at work. If wages rise the demand for leisure increases and, therefore, labor supply falls. This is why we expect that – on the level of the market as a whole – labor supply will be an increasing function of the wage upward sloping supply curve.

For people at work (T–L)>0 we have a substitution effect and an income effect. If w is high and (therefore) L is short the income effect may dominate the substitution effect: a further rise in w may decrease the individual’s supply of labor backward bending supply curve.

Effect of a change in the wage

)) , ( ,

( w I w y L

L

Demand for leisure is given by:

Differentiation by wyields:

I T L w

L w

I I L w

L dw

dL

const I const

I

I L L w

L w

L

const U const

I

We know from the Slutsky equation that for any good:

Substitution yields:

I L L w T

L dw dL

const

U

( )

(–) (+,0) (+)

• The Hicksian (compensated) substitution effect is negative.

• The income effect is positive.

•T–Lis non-negative

• The sign of the total effect is a priori

indeterminate.

Effect of a change in the wage

)) , ( ,

( w I w y L

L

Demand for leisure is given by:

Differentiation by wyields:

I T L w

L w

I I L w

L dw

dL

const I const

I

I L L w

L w

L

const U const

I

We know from the Slutsky equation that for any good:

Substitution yields:

I L L w T

L dw dL

const

U

( )

(–) (+,0) (+)

• The Hicksian (compensated) substitution effect is negative.

• The income effect is positive.

•T–Lis non-negative

• The sign of the total effect is a priori

indeterminate.

I L L w T

L dw dL

const

U

( )

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5

Household production

In the benchmark model of labor supply time is composed of working time and leisure.

Utility is a function of consumption (goods purchased using labor income w(T–L) and non-wage income y) and leisure, For any given T we have:

This a major simplification since:

a) A substantial part of time out of work is in fact devoted to household production, and people attach lower utility to these activities than they do to rest and

entertainment.We need to transform most goods purchased on the market in order to consume them. Utility is increased by final goods like prepared food, a clean flat, or getting from A to B and not by material inputs like raw food, a vacuum cleaner or a car. Transformation requires time. Final goods entering the utility function (z) are produced using purchased inputs (x) (including the services of durable goods) and time (T):

Comments

The focus of this approach is not joint optimization by household members. The model applies to single households as well. On joint decisions and specialization within the family see Ch 7 of the Ehrenberg–Smith textbook

In the classic model of household production (Becker 1965), followed here with major simplifications, leisure plays no distinguished role. The consumption of final goods requires purchased inputs and time and, unlike in the benchmark model of labor supply, we make no sharp distinction between ‘work’ and ‘leisure’.

] ), , , (

[ X w L y L U

U

) , (

_i _i

i

f x T

z

The presentation follows Becker, Gary: A Theory of the Allocation of Time (Economic Journal, September 1965) with major simplifications

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6 We shall see that the predictions of the benchmark model continue to hold: the income effect is negative, the compensated substitution effect is positive and the total effect of a change in the wage is theoretically indeterminate.

It can be easily shown that the benchmark model is a special case of the more general model of labor supply with household production.

Example with two final goods. If we have two final goods (z1, z2), the optimal choice is p for a given level of total income (wT+y). At p, the MRS between the two goods equals the ratio of relative prices.

We shall assume from now on that z1 is a time-intensive good while z2 is

product-intensive.

The utility function is:

) ,..., , ( ) ,..., ,

( z

₁

z

₂

z

_n

U f

₁

f

₂

f

_n

U

Subject to the constraint:

Tw y w T x

p

_i _i _i

where pstands for the price of purchased inputs, wdenotes the wage (assumed to be independent of working time)*, Tis total time available and yis non-wage income.

Writing the production functions in equivalent form (T_i t_iz_i, x_i b_iz_i)and substituting them to the constraint yields:

Tw y z z

w t b

p

_i _i _i

)

_i _i _i

(

wheret_iand b_i are the time intensity and product intensity of the i-th „final good”, respectively.

The utility function is:

) ,..., , ( ) ,..., ,

( z

₁

z

₂

z

_n

U f

₁

f

₂

f

_n

U

Subject to the constraint:

Tw y w T x

p

_i _i _i

where pstands for the price of purchased inputs, wdenotes the wage (assumed to be independent of working time)*, Tis total time available and yis non-wage income.

Writing the production functions in equivalent form (T_i t_iz_i, x_i b_iz_i)and substituting them to the constraint yields:

Tw y z z

w t b

p

_i _i _i

)

_i _i _i

(

wheret_iand b_i are the time intensity and product intensity of the i-th „final good”, respectively.

z

₁

z

₂

p

z

₁

z

₂

p

*) We ignore the difference between average and marginal wage discussed at length in Becker (1965)

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7 Effect of an increase in non-wage income

Relative prices (p, w) do not change so the opportunity set shifts outward. In the new optimum (p*) the consumpítion of both final goods will be higher.

This implies that total time allocated to household production increases the supply of market work falls*.

Impact of an increase in the wage if its income effect is fully compensated by a fall in non-wage income (Hicksian substitution).

Relative prices change, shifting the opportunity curve at p. A rise in the wage increases the full price of the time- intensive good (z1) more than the price of the product-intensive good (z2) so the curve shifts clockwise.

The consumption of z1 falls and the consumption of z2 increases as we move to the new optimum (p**).

Since consumption shifts toward less time-intensive final goods, time devoted to household production falls the supply of market work increases.

z₁ z₂

p

p^*

z₁ z₂

p

p^*

*) Unless time-intensive final goods are strongly inferior (Becker, op. cit. 501).

z

₁

z

₂

p p^**

z

₁

z

₂

p p^**

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8 The total effect of a change in the wage depends on the relative magnitude of the compensated substitution and income effects the sign of the effect is a priori indeterminate.

The benchmark model as a special case

The only cost of the good called ‘leisure’ in the benchmark model (z2=L) is foregone earnings. The only cost of consumer goods (z1=X) is the market price to be paid for them. The FOCs in this special case are given by:

Labor supply over the life-cycle

1 ,

0 ,

1 since

₁ ₁

1

p t

b z U

U

X

1 ,

0 since

₂ ₂

2

t b

w z U

U

L

n i

w t b z p

U

i i i i

,..., 1 )

(

Hence we arrive at the well- known optimum condition:

U w U

X L

1 ,

0 ,

1 since

₁ ₁

1

p t

b z U

U

X

1 ,

0 since

₂ ₂

2

t b

w z U

U

L

n i

w t b z p

U

i i i i

,..., 1 )

(

Hence we arrive at the well- known optimum condition:

U w U

X L

Differences in labor force participation over the life cycle are large – often larger than those between countries and social groups at a given point in time.

010203040

15 25 35 45 55 65 75

Életkor

Férfiak Nõk

KSH Munkaerõ-felmérés, 2008 január-március

A nappali tagozaton tanulók kizárásával

Az adott korosztály tagjai által átlagosan ledolgozott heti munkaórák száma

20406080100

1970 1980 1990 2000 2010

Az 1955-59-ben születettek foglalkoztatási rátája 1969-2006-ban

Forrás: KSH-ONYF adatfelvétel 2008

3. Individuals over the life cycle

The cohort followed in Figure 2 worked 278 days a year in 1970-2008, on average, with a

standard deviation of 113 days withinindividual careers.

1. Cohorts at a given point in time

Average weekly working hours by age in 2008, Hungary

2. One cohort followed in calendar time

Employment rate of those born in 1955-59, Hungary

We obviously do not claim that the patterns observed in the above charts are explained by supply-side factors.

(+) women, (–) men

Differences in labor force participation over the life cycle are large – often larger than those between countries and social groups at a given point in time.

010203040

15 25 35 45 55 65 75

Életkor

Férfiak Nõk

20406080100

1970 1980 1990 2000 2010

010203040

15 25 35 45 55 65 75

Életkor

Férfiak Nõk

20406080100

1970 1980 1990 2000 2010

3. Individuals over the life cycle

The cohort followed in Figure 2 worked 278 days a year in 1970-2008, on average, with a

standard deviation of 113 days withinindividual careers.

1. Cohorts at a given point in time

Average weekly working hours by age in 2008, Hungary

2. One cohort followed in calendar time

Employment rate of those born in 1955-59, Hungary

We obviously do not claim that the patterns observed in the above charts are explained by supply-side factors.

(+) women, (–) men

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9

• In the static model individuals seek an optimal allocation of time year by year within the constraints of their total annual income (wT+y). Workers do not save and can not borrow.

• In the life-cycle model individuals seek an optimum subject to a single life-time constraint (zero debt at the end of their career). Thanks to savings and borrowing they can spend more or less than their current income in any year.We shall see that the effect of a change in the wage strongly depends on how that particular change affects lifetime earnings. à figure on the next slideIn modern

macroeconomics, unforeseen transitory wage changes bear special importance.

Changes of this type are expected to have strong intertemporal substitution effect on labor supply. If this effect is strong, it can provide an explanation of why

employment fluctuates in a wider range over the business cycle than the real wage does (Lucas-Rapping 1969).

Types of wage changes

A → B: unpredicted, permanent B → C: predictable, „evolutionary”

C → D: unpredicted, transitory

Age

w

A B

C D

Age

w

A B

C D

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10 Assumptions

Perfect capital market, unique, time-invarying interest rate (r) A single constraint*: no debt at the end of one’s career

Time-invarying subjective discount factor ( ) Time-invarying preferences: U(.)

The marginal utility of lifetime income:

*) How we come to this constraint? Savings at t are given by St=wt(1-Lt) + yt – Xt .

Net wealth at t is given by:

The lifetime constraint is: AT 0. Writing net wealth for t=T we immediately arrive at the above formula.

The problem

Choose X1,…, XT –t and L1 , …, LT –t so as to maximise

Since the problem is empirically untractable in this form, most approaches assume additive separable utility. The problem can be re-written as a decision to maximise V:

We have 2T first-order conditions:

T

t

t t t t

T

t

t i

r y L w

r X

1

1 (1 )

) 1 ( )

1 (

t t

t

t S r

A (1 )

1

) ,..., ,

,...,

; ,..., ( ) ,...,

; ,...,

( X

₁

X

_T

L

₁

L

_T

U w

₁

w

_T

y

₁

y

_T

L

₁

L

_T

U U

T

t

T

t

t t

t t t

t t

t

L w L y X r

X U V

1 1

) 1 )(

) 1 ( ( )

1 )(

, (

T t

r L

X

U_X( _t, _t)(1 ) ^t (1 ) ^t 0, 1,...,

T t

r w L

X

U_L( _t, _t)(1 ) ^t _t(1 ) ^t 0, 1,..., T t

r L

X

U_X( _t, _t)(1 ) ^t (1 ) ^t 0, 1,...,

T t

r w L

X

U_L( _t, _t)(1 ) ^t _t(1 ) ^t 0, 1,...,

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11 In this form, the problem is manageable. We have 2T+1 equations including the

constraint, 2T+1 endogeneous variables (Xt, Lt, i=1,…,T and ), and 2T+2 exogeneous parameters (wt, yt, i=1,…T, r and ).

Let us rewrite the FOCs in this way:

Note that marginal utilities in any year depend on X, L and w in that year while (.) depends only on time. If >r, is increasing in calendar time and vice versa. We have:

Implications: the demand for X and L only depend on the current wage and a set of time- invarying parameters.* Wages outside the current period only affect the demand for X and L through (the marginal utility of lifetime income). The income effect of a transitory change in the current wage cannot be very strong since it only marginally affects lifetime earnings.

Formally: how the optimum changes in response to a change in the wage? Totally differentiating the FOCs and writing the derivative in matrix form (while and are treated as constants) we get:

Applying Cramer’s rule we have:

T t

t r

L X

U t

t t

t

X ( ), 1,...,

) 1 (

) 1 ) (

, (

T t

t r w

w L

X

U _t

t t t

t t

L ( ), 1,...,

) 1 (

) 1 ) (

, (

T t

t r

L X

U t

t t

t

X ( ), 1,...,

) 1 (

) 1 ) (

, (

T t

t r w

w L

X

U _t

t t t

t t

L ( ), 1,...,

) 1 (

) 1 ) (

, (

)) ( , ,

( w t

X

_t

X ( w

_t

, , ( t )) L

_t

L ( w

_t

, , ( t )) X

_t _t

L

_t

L ( w

_t

, , ( t ))

*) The equations above are called ‘Frisch demand functions’ named after Norvegian economist Ragnar Frisch (Nobel prize in 1969)

0 /

/

t t LL

LX

XL XX

dw dL

dw dX U

U

U U

0 0

/ poz

U U

U

U U

U U dw

dL

^XX

LL LX

XL XX

LX XX

t t

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12 The determinant in the denominator is positive if the utility function is strictly concave.

UXX is negative by the fundamental assumption of decreasing marginal utility.

If the wage increases, the demand for leisure decreases and the supply of labor rises.

That said, let us come back to our chart showing different kinds of wage changes!

Importance of the intertemporal substitution effect

Labor supply can change substantially over the business cycle if the intertemporal substitution effect is strong. This can be one of the reasons why economic upturns and downturns exert strong influence on employment and weaker on the real wage (Lucas and Rapping 1969).

However, macro models should assume rather high intertemporal elasticities of

substitution (e) in order to explain the behavior of time series by means of the life-cycle model. Prescott (1986), for instance, assumes e=2.

Labor economists using micro data usually estimate much lower elasticities.

The consensus estimate is »e0.3. Some recent papers got higher elasticities

(see Pistaferri 2003 e=0.7, Kimball and Shapiro 2003, »e1, Ham and Reilly 2006, »e0.9- 1.0) but still way below what is ‘required’ to explain fluctuations in employment over the business cycle.

Labor supply over the life-cycle

Age

w

A

B C

D Types of wage changes

A B: unpredicted, permanent B C: predictable, „evolutionary”

C D: unpredicted, transitory

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13

Added and discouraged workers

A further reason why it is hard to predict the supply effects of business cycles is that changes in the demand for labor induce changes in the supply of labor per se.

Added worker effect: the jobloss of one family member reduces the non-wage income of other family members inducing them to enter the labor market. The effect, if exists, is counter-cyclical.

Discouraged worker effect: discouraged workers do not actively search for jobs because they think they have absolutely no chance to find one. In recessions, when job offers are scarce, many people give up search while during upturns they return to the labor market. The effect, which unambiguously exists, is pro-cyclical.Added worker effect (AWA)

The general agreement is that this effect is not very strong. At least, we lack a

‘consensus estimate’. Some results on AWA:

USA

No AWA: Pencavel (1982), Maloney (1987, 1991)

Weak AWA: Heckman – MaCurdy (1982), Lundberg (1985)

Strong AWA: Stephens (2001). AWA replaces ¼ of the husband’s lost earningsJuhn- Potter (2007).Wives of job losers have 5-6 per cent higher probability of entering the labor marketAustralia

Mixed results: Gong (2009). No AWA on employment but some effect on working hours and willingness to workDeveloping countries:

No AWA: Ethiopia, Serneels (2004)

Strong AWA: Mexico, Parker – Skoufias (2004) Wives of job losers are more likely to enter the labor market (by 15-16 per cent during recessions and 8-9 per cent during upswings) than the spouses of continuously employed husbands

Discouraged worker effect (DWA)

Results are mixed but it seems that the cyclical fluctuations of labor supply are dominated by DWA rather than AWA: the activity rate of groups under examination typically falls when aggregate unemployment increases, and vice versa.DWA is clearly

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14 pro-cyclical. It is present all the time, introducing a wedge between ILO-OECD

unemployment and the total number of people who want a job but do not necessarily search. The wedge is wider in recessions and narrower at upswings.

An important implication is that, in upswings, more than one job should be created in order to reduce unemployment by one person.

Unemployment rates with different definitions of unemployment*

Blue: ILO-OECD definition

Red: wants a job but is not searching

*) European Labour Force Survey, 2005

0 .05 .1 .15 .2 .25

PLLV SKIT DEESBE HUDKEEFRCZATLT GRCYUKSEPTSIFI NONLLUIEIS

mean of u1 mean of difu2

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15 Unemployment rates with different definitions of unemployment*

Blue: ILO-OECD definition

Red: regards himself/herself as unemployed but is not searching

Benefits and labor supply

Unconditional benefits/subsidies

Benefits of this kind affect labor supply in the way discussed in the benchmark model: a flat rate benefit has negative effect while the impact of a wage subsidy is ambiguous.

0 .05 .1 .15

SKPLLVIT HUDEES GRDKCYBEFRCZEESEPTATLTSIIEFI NOUKNLLUIS

mean of u1 mean of difu2

*) European Labour Force Survey, 2005

Flat rate benefit

X

? L

Wage subsidy (increasing the net wage)

X

L Flat rate benefit

X

? L X

? L

Wage subsidy (increasing the net wage)

X

L X

L

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16 Conditional benefits 1

Work (of any kind) prohibited while recieving benefit

Strengths: prevents the misuse of benefits.

Weaknesses: Excludes casual work, reduces workers’ willingness to take up low-paid, short-term and temporary jobs. See the great classic of the sociology of unemployment (Jahoda–Zeisel–Lazarsfeld 1933 a.k.a the Marienthal study) on the devastating effect of a full ban on gainful employment.

Since then, several practices have been developed to make work possible for benefit recipients. In many countries the rules allow casual and part-time employment. In others, benefit payment is suspended (without the loss of eligibility) while the recipient is at work.

Conditional benefits 2

Means-tested flat rate benefit

Strengths: reduces the risk of ‘too high’

income from social transfers.

Weaknesses: high effective marginal tax rate at the critical income level. Net income may even fall in response to slightly longer working time (as shown in the chart). High risk of poverty trap.

Conditional benefits 3 X

L X

L

X

L X

L

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17 Guaranteed income

Benefits ensure that the recipients’ per capita household income reaches G0. Earnings implying income higher than G0 reduce the benefit one for one.

Strengths: reduces the risk of poverty, on the one hand, and ‘too high’ benefits levels, on the other

Weaknesses: zero effective marginal net wage in region A–B. Short-term, temporary employment is likely to imply loss of utility.

High risk of poverty trap.

Conditional benefits 4

Base income + high tax rate on labor income while recieving benefit

A more carefully designed version of guaranteed income.

Strengths: The effective net wage is positive albeit lower than the market wage.

Weaknesses: Compared to the regime of no benefit (point P), the introduction of the system implies negative income effect (P Q) and substitution effect (Q R).

X

A L B

G

G₀

X

A L B

G

G₀

X

L G A B

P Q

R

X

L G A B

P Q

R

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18 Conditional benefits 5

Transforming leisure to job search and training

The scheme takes away exactly as much utility from leisure as the value it provides in terms of utility from cash. This is achieved by monitoring job search activity, requiring

regular visits to the labor office and enrolment to active programs thereby reducing the scope for black work and sheer leisure.

Strengths: reduces the misuse of benefits, potentially prevents the erosion of human capital.

Weaknesses: much depends on the effectiveness of monitoring and quality of ALMP. There is a risk of taking away leisure and informal income in exchange of nothing.

X

Leisure reduced L by this amount P

X

Leisure reduced L by this amount P