31E00700 Labor Economics:
Lecture 3
Matti Sarvimäki
5 Nov 2012
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
First Part of the Course: Outline
1 Supply of labor
1 static labor supply: basics
2 static labor supply: benefits and taxes
3 intertemporal labor supply (today)
2 Demand for labor
3 Labor market equilibrium
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Intertemporal Models
What parameters of interest do reduced-form regressions on
labor supplyon wages identify (like the ones covered in lect 1&2)?
MaCurdy (1981): None. These estimates are a mix of income
effects, intertemporal substitution effects, and (compensated)
wage elasticies. “An Empirical Model of Labor Supply in a Life-Cycle
Setting.” Journal of Political Economy, 89(6), 1059-1085.
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Intertemporal Models
What parameters of interest do reduced-form regressions on
labor supplyon wages identify (like the ones covered in lect 1&2)?
MaCurdy (1981): None. These estimates are a mix of income
effects, intertemporal substitution effects, and (compensated)
wage elasticies. “An Empirical Model of Labor Supply in a Life-Cycle
Setting.” Journal of Political Economy, 89(6), 1059-1085.
Life cycle models differentiate between wage changes that are
Evolutionary (movements along profile)
“Parametric” (e.g. temporary tax cut)
Profile shifts (changing wage rate for every period)
Basic idea: workers shift hours between low-wage and
high-wage periods
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Why Does Intertemporal Labor Supply Matter?
Business cycles
an extreme view: recessions reflect fluctuations in the rate of
technological progress → sometimes wages low due to exogenous
reasons → people choose to consume more leisure [so, the Great
Depression was really the Great Vacation...]
Retirement decisions
Lifetime income affected by the timing of retirement
Wage changes have a substitution and income effect
(if pension benefits constant)
An increase in pension benefits reduces the price of retirement
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Today
Stylized Facts
Brief overview of alternative approaches
Three models and a field experiment
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Wage Profiles (1977-1989, U.S.)
54 David Card
2.61-
2.2 - / ^ ^ ^ *
& / ^/
| 1.8 - / /
j6 _ ^ ^ Wages in real 1983 $
/ Age 16 in 1976 Age 20 in 1976 Age 25 in 1976
1.4 - / Age 30 in 1976 Age 40 in 1976 Age 50 in 1976
1.21 I I I I I I I I I L
15 20 25 30 35 40 45 50 55 60 65
Annual averages of log wages for six cohortsAgeusing the 1977-1989 March CPS data.
Each line tracks the wage profile of a single cohort over the 13 year sample period.
Source: Card (1994):
Figure “Intertemporal
2.1 Life-cycle Labor Supply:
wage profiles for six An Assessment”
cohorts
Wage Profiles: Finnish manufacturing workers
(1990-2002)
Men Women
2.9
2.9
2.7
2.7
2.1 2.3 2.5
2.1 2.3 2.5
Log hourly earnings
Log hourly earnings
1.9
1.9
1.7
1.7
1.5
1.5
20 30 40 50 60 20 30 40 50 60
Age Age
Time rate, pr==0 Piece rate Time rate, pr==0 Piece rate
Time rate, pr==1 Time rate, pr==1
Age profiles of hourly piece-rate and time-rate earnings for men and women in the
Figuremanufacturing
Finnish 1: Age profiles of time
worker rates and
population piece
during rates. Source: Pekkarinen,
1990-2002.
Uusitalo (2012):
Predicted Aging
values fromandanProductivity: Evidence
OLS regression from Piece
of hourly Rates.
earnings on IZA
yearDP 6909
and firm
dumies, and piece-rate indicators interacted with the age dummies.
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Hours of Work over Life Cycle (2005, U.S.)
2,500
Male
Annual hours of work
2,000
Female
1,500
1,000
500
15 25 35 45 55 65
Age
Annual hours of work among those who are working.
Source: Borjas Figure 2-21
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Labor Force Participation over Life Cycle (2005, U.S.)
100
90
Labor force participation rate
Male
80
70
Female
60
50
40
30
15 25 35 45 55 65
Age
Source: Borjas Figure 2-20
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Hours ofIntertemporal
Work labouroversupply:
Life Cycle (1977-1989, U.S.)55
an assessment
2200 r
1800- rf\/^^ ^°9\
g 1600 - / / \
I 1400 - 11 \
11200 - r*f w*
11000- / \
^ 800 - / \
600 - / Age 16 in 1976 Age 20 in 1976 Age 25 in 1976
I A g e 30 in 1 9 7 6 A g e 4 0 in 1976 A g e 5 0 in 197 6
400-/ I >
2001 I I I I I I I I I I
15 20 25 30 35 40 45 50 55 60 65
Age
Annual averages hours. Source: Card (1994): “Intertemporal Labor Supply: An
Figure 2.2 Life-cycle hours profiles for six cohorts
Assessment”
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Wage and Hours Profiles
Wages and hours of work (conditional on participation)
increase until roughly mid-30s
remain quite constant until early-50s
decline afterwards
A simple explanation
lifetime income determined by the entire wage profile
price of leisure determined by the current wage
→ leisure is cheap when young/old
Note that the decline of participation rates after mid-50s (and
thus average hours including zeros) is much more rapid than
the decline of wages.
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Alternative Approaches
Dominant: dynamic labor supply with perfect capital markets
Friedman (1957), Lucas and Rapping (1970), MaCurdy (1981)...
Keane, 2011. "Labor Supply and Taxes: A Survey," Journal of Economic
Literature 49(4): 961-1075
Examples of alternative approaches
Contracting (e.g. Abowd and Card 1987, 1989)
“Behavioral” (e.g. Camerer at al. 1997)
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Alternative Approaches
Dominant: dynamic labor supply with perfect capital markets
Friedman (1957), Lucas and Rapping (1970), MaCurdy (1981)...
Keane, 2011. "Labor Supply and Taxes: A Survey," Journal of Economic
Literature 49(4): 961-1075
Examples of alternative approaches
Contracting (e.g. Abowd and Card 1987, 1989)
“Behavioral” (e.g. Camerer at al. 1997)
Challenges for empirical work
Theory about transitory and anticipated changes in wages (but
real shocks tend to affect lifetime income and may not be anticipated)
Wages determined by supply and demand (endogeneity problems)
Institutional constraints (workers not free to adjust working hours)
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Empirical Strategies
Structural life-cycle models
e.g. Eckstein and Wolpin (1989), French (2005)
advantages: solves everything
critisism: requires a lot of assumptions & simplifications,
identification not transparent
“Reduced form” models testing implications of frictions
e.g. Beadry and Dinardo (1995), Ham and Reilley (2002), Chetty (2010)
High frequency studies
e.g. Camerer et al. (1997), Faber (2005), Fehr and Goette (2007)
advantages: transparent identification
critisism: external validity
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
The Experiment (Fehr and Goette, 2007)
Fehr and Goette study the intertemporal labor supply among
42 bicycle messengers working in a firm where
earnings a fixed percentage of daily revenues (no fixed-wage)
5-hour shifts (and no-one works two shifts per day)
workers commit to some shifts, but can flexibly add more
within a shift, workers can choose their effort
(how fast to ride, whether to accept delivery offers)
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
The Experiment (Fehr and Goette, 2007)
Fehr and Goette study the intertemporal labor supply among
42 bicycle messengers working in a firm where
earnings a fixed percentage of daily revenues (no fixed-wage)
5-hour shifts (and no-one works two shifts per day)
workers commit to some shifts, but can flexibly add more
within a shift, workers can choose their effort
(how fast to ride, whether to accept delivery offers)
The experiment
Participants randomly allocated to groups A and B
Sept ’00: A paid 25% more of daily revenues, B paid as usual
Nov ’00: A paid as usual, B paid 25% more of daily revenues
Fehr and Goette discuss the results of this experiment in the
light of three alternative models
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
The Baseline Neoclassical Model
Individuals maximize lifetime utility
T
�
U0 = δ t u (ct , et , xt )
t=0
1
where δ = 1+ρ
< 1 is the discount factor, ct is consumption, et is the amount
of work (effort) provided and xt a variable affecting preferences at period t.
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
The Baseline Neoclassical Model
Individuals maximize lifetime utility
T
�
U0 = δ t u (ct , et , xt )
t=0
1
where δ = 1+ρ
< 1 is the discount factor, ct is consumption, et is the amount
of work (effort) provided and xt a variable affecting preferences at period t.
... subject to a lifetime budget constraint
T
� T
� ŵt et + yt
p̂t ct
t =
t=0
(1 + r ) t=0
(1 + r )t
where p̂t is price of the consumption good at period t, r is the interest rate
(assumed constant), ŵt is the wage rate at time t and yt is non-labor income.
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
The Baseline Neoclassical Model
First-Order-Conditions
� �t
1+ρ
uct (ct , et , xt ) = λ p̂t
1+r
� �t
1+ρ
−uet (ct , et , xt ) = λ ŵt
1+r
where uz is the derivative of u (�) with respect to z. To derive these FOCs, note that
� �T
the Lagrangian is L = T t
t=0 δ u (ct , et , xt ) − λ t=0 (ŵt et + yt − p̂t ct ) (1 + r )
−t
1
and δ = 1+ρ .
The Baseline Neoclassical Model
First-Order-Conditions
� �t
1+ρ
uct (ct , et , xt ) = λ p̂t
1+r
� �t
1+ρ
−uet (ct , et , xt ) = λ ŵt
1+r
where uz is the derivative of u (�) with respect to z. To derive these FOCs, note that
� �T
the Lagrangian is L = T t
t=0 δ u (ct , et , xt ) − λ t=0 (ŵt et + yt − p̂t ct ) (1 + r )
−t
1
and δ = 1+ρ .
In words, consumption and effort at period t are determined by
the marginal utility of litetime wealth (λ),
discount (ρ) and interest (r ) rates
and the current price of consumption (p̂t ) and effort (ŵt )
The Baseline Neoclassical Model
Useful thing to note: The intertemporal maximization problem corresponds to
the static problem of maximizing
v (et , xt ) = λwt et − g (et , xt )
� �t
1+ρ
where wt = 1+r
ŵt is the discounted wage in period t and g (�) is strictly convex
(in et ) function measuring the discounted disutility of effort
The Baseline Neoclassical Model
Useful thing to note: The intertemporal maximization problem corresponds to
the static problem of maximizing
v (et , xt ) = λwt et − g (et , xt )
� �t
1+ρ
where wt = 1+r
ŵt is the discounted wage in period t and g (�) is strictly convex
(in et ) function measuring the discounted disutility of effort
Participation decision can be introduced in two ways
Minimum effort (work only if et∗ > �e )
Fixed costs (work only if utility of working exceeds the fixed cost)
The Baseline Neoclassical Model
Useful thing to note: The intertemporal maximization problem corresponds to
the static problem of maximizing
v (et , xt ) = λwt et − g (et , xt )
� �t
1+ρ
where wt = 1+r
ŵt is the discounted wage in period t and g (�) is strictly convex
(in et ) function measuring the discounted disutility of effort
Participation decision can be introduced in two ways
Minimum effort (work only if et∗ > �e )
Fixed costs (work only if utility of working exceeds the fixed cost)
Predictions: Increase in ŵt
increases the number of shifts
increases effort within a shift
Neoclassical Model with Nonseparable Utility
The predictions of the baseline model rely on the assumption
of time-separable utility (only current consumption and effort matter).
Neoclassical Model with Nonseparable Utility
The predictions of the baseline model rely on the assumption
of time-separable utility (only current consumption and effort matter).
Suppose instead that workers maximize
v (et , et−1 ) = λet wt − g (et (1 + αet−1 ))
i.e. effort in the last period increases the disutility of effort in
the current period (for simplicity, xt is now dropped)
Neoclassical Model with Nonseparable Utility
The predictions of the baseline model rely on the assumption
of time-separable utility (only current consumption and effort matter).
Suppose instead that workers maximize
v (et , et−1 ) = λet wt − g (et (1 + αet−1 ))
i.e. effort in the last period increases the disutility of effort in
the current period (for simplicity, xt is now dropped)
Rational workers take this into account when deciding today’s
effort → higher wages may decrease � effort within a shift
Nevertheless, overall labor supply, et , within the high wage
period will increase
Predictions: Increase in ŵt
increases shifts
may increase or decrease effort within shifts
A Model with Reference Dependent Utility
Suppose that one-period utility is
�
λ (wt et − ỹ ) − g (et , xt ) if wt et ≥ ỹ
v (et )=
γλ (wt et − ỹ ) − g (et , xt ) if wt et < ỹ
where ỹ is a daily income target and γ > 1 measures the degree of loss aversion
A Model with Reference Dependent Utility
Suppose that one-period utility is
�
λ (wt et − ỹ ) − g (et , xt ) if wt et ≥ ỹ
v (et )=
γλ (wt et − ỹ ) − g (et , xt ) if wt et < ỹ
where ỹ is a daily income target and γ > 1 measures the degree of loss aversion
This is an alternative to the expected utility theory, first
proposed by Kahneman and Tversky (1979)
The idea is that individuals set a reference point, ỹ , and
consider lower outcomes as losses and larger as gains →
discontinuous drop in the marginal utility of daily earnings at ỹ
A Model with Reference Dependent Utility
Suppose that one-period utility is
�
λ (wt et − ỹ ) − g (et , xt ) if wt et ≥ ỹ
v (et )=
γλ (wt et − ỹ ) − g (et , xt ) if wt et < ỹ
where ỹ is a daily income target and γ > 1 measures the degree of loss aversion
This is an alternative to the expected utility theory, first
proposed by Kahneman and Tversky (1979)
The idea is that individuals set a reference point, ỹ , and
consider lower outcomes as losses and larger as gains →
discontinuous drop in the marginal utility of daily earnings at ỹ
Predictions: Increase in ŵt
increases shifts (utility of working in a given day increases)
reduces effort within shifts (easier to cross the reference point)
the magnitude of effort reduction depends on γ
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Results
Effect on total revenue (Tables 1–3)
Increase of CHF1,000 (from the baseline level of roughly
CHF3,500) → intertemporal elasticity of substitution roughly
1000/3500
0.25 = 1.14
consistent with all three models
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Results
Effect on total revenue (Tables 1–3)
Increase of CHF1,000 (from the baseline level of roughly
CHF3,500) → intertemporal elasticity of substitution roughly
1000/3500
0.25 = 1.14
consistent with all three models
Effect on the number of shifts (Tables 1–4)
Increase of roughly four shifts (from the baseline of roughly
11) → wage elasticity of shifts roughly 4/11
0.25 = 1.45
consistent with all three models
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Results
Effect on total revenue (Tables 1–3)
Increase of CHF1,000 (from the baseline level of roughly
CHF3,500) → intertemporal elasticity of substitution roughly
1000/3500
0.25 = 1.14
consistent with all three models
Effect on the number of shifts (Tables 1–4)
Increase of roughly four shifts (from the baseline of roughly
11) → wage elasticity of shifts roughly 4/11
0.25 = 1.45
consistent with all three models
Effect on effort (Figure 1, Table 5)
Reduction of revenue per shift of roughly 6 percent → wage
elasticity of revenue per shift roughly −0.06
0.25 = −0.24
inconsistent with the baseline model; consistent with
nonseparable utility and reference dependent utility models
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Distinguishing between the Neoclassical and
Reference Dependent Utility Models
Fehr and Goette suggest a test based on a measurement of γi
(individual-level loss aversion parameter)
Neoclassical model: this does not matter
RDU model: results driven by workers with high γi
Measure of γi obtained by revealed preferences to participate
in two lotteries (Appendix A and B)
according to this measure 2/3 of the messangers are loss averse
Only loss averse messengers reduce their effort (Figure 2, Table 6)
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
Introduction Stylized Facts Alternative Approaches Models and a Field Experiment
Summary (of Fehr and Goette, 2007)
Intertemporal substitution large
Results most consistent with the reference dependent utility
model (but: 1/3 of the messengers do not exhibit loss aversion
External validity: how representative are bicycle messengers?
31E00700 Labor Economics: Lecture 3 Matti Sarvimäki
