The role of aggregate
preferences for labour supply evidence from small jobs
Luke Haywood & Michael Neumann
DIW Berlin
ORA Project meeting, 29th February 2016
Equilibrium earnings
Earnings depend on individual incentives:
Bunching as result of SSC exemption for earnings below 325
euros/month
Figure: Daily gross earnings of main jobs in 2002
Equilibrium earnings II
...but other workers’ preferences also matter.
No bunching incentives for second jobs (before 2003)
Figure: Daily gross earnings of second jobs in 2002
Population labour supply effect
Firms offer jobs with fixed earnings that average workers
want → Job offers reflect aggregate preferences of workers
Unintended effects of tax incentives
Constraints for less dominant groups in the labour market
Population labour supply effect II
Differences between individual-level and market-level
labour supply elasticities
Bunching method might overestimate individual labour
supply elasticities (Chetty et al., 2011)
Contribute to explain differences in micro and macro
estimates
This study
This paper: Structurally estimate this population labour
supply effect within an equilibrium job search model
Endogenous job offer distribution reflects aggregate
preferences of workers
Research Question
Identify population labour supply effect generated by German
lower earnings threshold for SSC
Comparable to LEL in the UK
Welfare effects
Policy evaluations
Counterfactual policy simulations
location of threshold
group of affected workers
Large German reform of lower earnings threshold in 2003
Outline
1
Institutions
2
A simple model of the market for small jobs
3
Simulation
4
Estimation (no results, sorry!)
5
Outlook
Institutions (1999-2003)
Up to 325 e/month SSC-free (and potentially less income
taxes) for employees, but no social security
Earnings > 325 e/month full SSC → notch
∆tssc ≈ 20pp.; ∆tinc depends on household char.
Total earnings relevant: Not applicable for second jobs
At most 15 hours
Employers pay similar taxes below and above the threshold
A simple model of the market for small jobs
Focus on market for small jobs only (monthly earnings below
800 e) sectors
Simple equilibrium job search model following Burdett and
Mortensen (1998)
Continuum of firms
Identical (no heterogeneity in productivity)
Firms post earnings z
Facilitates population labour supply effect
Profit-maximizing: max π = [p − z]l(z)
z
Workers
Workers have main job (s) or not (f )
Type s: Search for small job as second job (first job
earnings exogenous)
Type f : Search for small job as first job
Both types draw from earnings offer distribution F (z) at
rate λs and λf
On-the-job-search for better small jobs
Utility increases by earnings: homogeneous hours or
workers do not care (will be relaxed)
Workers II
SSC exemption for z < z ∗ only applies to type f workers
Simplifying approximation instead of using taxes directly
θ̃: fraction of workers that only enter the market due to tax
exemption below z ∗ (extensive margin)
θ̃nf type f only accept offers with z ∈ (zr , z∗ ] with z r being
homogeneous reservation earnings
(1 − θ̃)nf type f workers and ns type s workers accept all
jobs with z > zr
Exogenous job destruction rate δ
Equilibrium earnings in the market for small jobs
Free entry and identical firms: equal profits [π = (p − z) l(z)]
for diff. earnings z.
Lower z: more profits per worker
Higher z: larger firm size ( equations )
but for z > z ∗ : θ nf individuals drop out
Equilibrium earnings II
Proposition (I) If we observe offers above z ∗ , there must be a
mass point of job offers at z ∗ . ( equations )
Proposition (II) If there is a mass point at z ∗ , there will be a
gap in the offer distribution just below the threshold.
Proposition (III) There may or may not exist wage offers below
the threshold z ∗ in equilibrium. The wage offer distribution will
then be continuous between z ∈ [z, z 00 ] for z 00 < z ∗ .
Simulation
Parameters: p = 800, z ∗ = 325, z r = 10, λs = 0.3, λf = 0.5,
δ = 0.2, θ = 0.1, ns = 0.5, nf = 0.7
Figure: Distribution of earnings, all types
Figure: Distribution of earnings, type f, θnf
Figure: Distribution of earnings, type s
Figure: Distribution of earnings, type s, counterfactual
Identification
Unemployment duration of type f workers
1
λf
1
λf
for z > z ∗
or λf F1(z ∗ ) for z ≤ z ∗ (depending on θ)
Size of mass point informative about θ
Type s workers identify F (.)
Estimation - Maximum Likelihood
Likelihood contributions are functions of F (.)
No simple analytical expression for F (.) (subject to
structural parameters)
Get F (.) by numerically solving system of equal profit
conditions
Estimation is work in progress
Outlook 1: Heterogeneous hours
So far: utility increases with earnings → homogeneous
hours
Now: Firms draw from continuous distribution of weekly
hours and set wage rates w
Workers care about w, h: reservation utility
w(z ∗ ) and u(z ∗ ) differ between firms
Outlook 1: Heterogeneous hours II
No mass point in the utility offer distribution (although
there might be one in the earnings distribution)
Mass below threshold:
l(v (z ∗ − , h), h) = l(v (z ∗ , h), h) if → 0
Mass above threshold possible as
∂l(.)
∂z
> 0 for z > z ∗
Outlook 2: Reform of 2003
SSC exemption also applies for second jobs
Incentive to start new second job with z < z ∗ (θns )
More potential workers lost if z > z ∗
Earnings threshold increased to z ∗ = 400
Distribution of second job earnings: 2002 vs 2005
Outlook 2: Reform of 2003 II
Validate our model
Evaluate reform with focus on population labour supply
effect
Relax assumptions (E.g. θ(z ∗ ))
Conclusion
Equilibrium job search model of market for small jobs
Rationalize mass point in earnings distribution due to
non-linearities in the tax schedule
Structurally estimate population labour supply effect
Unique setting where we observe bunching for workers for
which the threshold is not relevant
Perform (counterfactual) policy evaluations and welfare
analysis
Thank you.
References
Burdett, Kenneth and Dale T Mortensen, “Wage Differentials,
Employer Size, and Unemployment,” International Economic
Review, May 1998, 39 (2), 257–73.
Chetty, Raj, John N. Friedman, Tore Olsen, and Luigi
Pistaferri, “Adjustment Costs, Firm Responses, and Micro
vs. Macro Labor Supply Elasticities: Evidence from Danish
Tax Records,” The Quarterly Journal of Economics, 2011,
126 (2), 749–804.
Table: Distribution of sectors, 2000-2002
Sector
2 Primary production, prod. of goods
3 Facture of structural metal products
4 Steel deformation, vehicle constr.
5 Consumer goods industry
9 Wholesale trade
10 Retail industry
11 Transport and communication
12 Other services
13 Household services
14 Education, social and health-care
15 (Street)Cleaning, organisations
16 Public admin., social security
back
z ≤ 325
1st job 2nd job
1
1
2
2
2
2
2
3
6
6
18
7
3
6
22
30
12
14
7
8
12
12
2
3
1st jobs
if 2nd job
5
7
7
5
5
8
5
14
4
15
8
8
Equilibrium flows in the market of small jobs
Steady-state flows (
equations
) determine firm size l(z):
l(z) = l s (z) + l f (z)

ns κs

(1+κs (1−F (z)))(1+κs (1−F (z−)))



nf κf


+ (1+κf (1−F (z)))(1+κf (1−F (z−)))


+
θnf κf
(1+κf (F (z ∗ )−F (z)))(1+κf (F (z ∗ )−F (z−)))
=





ns κs


(1+κs (1−F (z)))(1+κs (1−F (z−)))



nf κf
+ (1+κf (1−F (z)))(1+κ
f (1−F (z−)))
κ≡
back
λ
δ
∀z ≤ z ∗
∀z > z ∗
π(z ∗ ) =(p − z ∗ )(
n s κs
(1 + κs (1 − F (z ∗ )))(1 + κs (1 − F (z ∗ ) + f (z ∗ )))
+
n f κf
(1 + κf (1 − F (z ∗ )))(1 + κf (1 − F (z ∗ ) + f (z ∗ )))
+
θnf κf
(1 + κf f (z ∗ )))
π(z ∗ + ) = (p − z ∗ )(
+
back
ns κs
(1 + κs (1 − F (z ∗ )))2
nf κf
)
(1 + κf (1 − F (z ∗ )))2
π(z ∗ − ) =(p − z ∗ )(
ns κs
(1 + κs (1 − F (z ∗ ) + f (z ∗ )))2
+
n f κf
(1 + κf (1 − F (z ∗ ) + f (z ∗ )))2
+
θnf κf
)
(1 + κf (f (z ∗ )))2
δ(nj − u j ) = λj u j for j ∈ (s, f 1)
δ(θnf − u f 2 ) = λf u f 2 F (z ∗ )
[δ + λj (1 − F (z))]Gj (z)(nj − u j ) = λj F (z)u j for j ∈ (s, f 1)
[δ + λf (F (z ∗ ) − F (z))]Gf 2 (z)(nf 2 − u f 2 ) = λf F (z)u f 2 for z ≤ z ∗
back
D j (w)gkj (qk (w))ekj =
λj fk (qk (w))(u j + G0j (q0 (w) − )e0j + G1j (w − )e1j )
with D j (w) = [δ + λj ((1 − F1 (w)) + (1 − F0 (q0 (w))))] for
j ∈ (s, f 1)
back