The accuracy of the bunching method under
optimization frictions:
Students’ labor market frictions
Tuomas Kosonen (Labour Institute for Economic Research)
Tuomas Matikka (VATT Institute for Economic Research)
IFS Workshop, March 1, 2016
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
1 / 29
Motivation
Motivation
Bunching method is used to discover earnings elasticities from
behavioral responses to kinks and notches (Saez AEJ:EP 2010,
Bastani and Selin JPubE 2014, Kleven 2015)
Relate the size of the excess mass in the income distribution to the size
of tax incentives
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
2 / 29
Motivation
Motivation
The importance of optimization frictions in attenuating responses
(Chetty et al. QJE 2011, Chetty Ecta 2012, Kleven and Waseem QJE
2013)
Mitigated observed bunching responses
Frictions are defined as factors that affect behavior but outside of the
standard labor-leisure framework
Types of optimization frictions:
Labor market and search frictions: imprecise control of (annual)
income (Chetty et al. QJE 2011)
Awareness of rules and optimization ability: lack of these attenuate
responses (Chetty et al. AER 2009, Chetty et al. AER 2013, Currie
and Grogger 2001 and Kleven and Kopczuk AEJ:EP 2008)
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
3 / 29
Introduction
Introduction
Key question: How different optimization frictions affect
optimization behavior and the bunching estimator?
Study subsidy in Finland
Applies to all higher education students (university, polytechnic)
Eligibility depends on earnings: exceeding an income limit results in
losing disposable income → the notch
Notches create dominated regions where no one should willingly
locate under any standard preferences
A reform shifted out income limits
Global vs. local effects of the limit
Potential to disentangle different optimization frictions
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
4 / 29
Introduction
Introduction
We find both large excess bunching and a mass of students in the
dominated region
Students are aware of the notch, but frictions seem to matter too
The reform shifts out the whole income distribution → a global
response
The income limit appears to affect behavior further away from the
notch (in addition to the local response)
Bunching at the old notch disappears → students in general aware of
the income limits
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
5 / 29
Introduction
Introduction
Divided sample results
Optimization failures and ability explain some of the nonstandard
responses
Suggestively, these types of frictions only attenuate local responses
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
6 / 29
Institutions
Marginal income tax rate schedule
Marginal income tax rate schedule
.2
.3
Marginal tax rate
.4
.5
.6
Year 2007
0
40000
60000
80000
Taxable income
Note: Marginal tax rates include the average flat municipal tax rate
and average social security contributions
Tuomas Matikka (VATT)
20000
Students and optimization frictions
100000
IFS Workshop 2016
7 / 29
Institutions
Study subsidy
Study subsidy approx. 500e per month when studying at a university
or polytechnic
Default: 9 subsidy months per year
Max. 55 months per degree (in 2007)
Eligibility depends on
annual gross income: Default limit 11,800e
income limit depends inversely on the number of study subsidy months
applied
credit points (5pts/month)
In Finland, students typically work part-time during their studies
Effective third-party reporting of wage income
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
8 / 29
Institutions
Study subsidy
The notch: Exceeding the income limit results in reclaiming the
subsidy of one month (with interest)
Carefully monitored by the Social Insurance Institution
Additional subsidy month is reclaimed per every 1,300e over the limit
The reform: Income limits increased by 30% in 2008
Default 9 subsidy months: 9,200e→11,800e
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
9 / 29
Institutions
Study subsidy notch
9 months of study subsidy, year 2007
11100 11200 11300 11400 11500 11600 11700
Disposable income, euros
Disposable income around the study subsidy notch
-400
-300
-200
-100
0
100
200
300
400
Gross income relative to notch point
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
10 / 29
Methods
Behavioral responses to kinks and notches
Under standard labor-leisure preferences, some individuals should
respond to local discontinuities in their budget sets if average
elasticity is significant
If these responses occur, we should see individuals clustering around
kinks and notches
However, frictions might eliminate or mitigate observed responses
In theory, frictions can be thought of as adjustment costs or fixed costs
Example: small structural elasticity and large frictions → no observed
responses
Different (set of) frictions might lead to different patterns of
responding
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
11 / 29
Methods
Bunching at a kink point
Indiff. curves
for type H
(1- d;njͿ)z
Indiff. curve
for type L
Slope 1-τ2
Slope 1-τ1
k
Tuomas Matikka (VATT)
k+dz
Students and optimization frictions
z
IFS Workshop 2016
12 / 29
Methods
Bunching at a notch point
(1- d;njͿ)z
Indiff. curve
for type L
Indiff. curves
for type H
∆τ
Slope 1-τ
j
Tuomas Matikka (VATT)
j+∆zD j+ ∆z
Students and optimization frictions
z
IFS Workshop 2016
13 / 29
Methods
Empirical methods
Bunching estimation
Calculate elasticity by comparing behavioral responses from the size of
the excess mass (bunching) to the incentives (Saez AEJ:EP 2010,
Kleven and Waseem QJE 2013, Chetty et al. QJE 2011)
Even if ETI is not correctly estimated, the bunching response is
informative about behavioral responses
Optimization frictions
bunching response smaller than in a frictionless world → Kleven and
Waseem (QJE 2013) correct for this by utilizing the mass in the
dominated region
True response to a notch could be more global
Frictions not only attenuating bunching → We present new thoughts
on extending the bunching method
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
14 / 29
Methods
Data
Register-based data on the universe of taxpayers in Finland in
1999-2011 (at the moment student data up to 2009)
Based on linked employer-employee database (FLEED) provided by
Statistics Finland
Data include detailed income tax and income transfer variables from
official registers (Tax Administration, Social Insurance Institution)
Allows for accurate analysis of bunching around different kinks and
notches
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
15 / 29
Results
Study subsidy notch
Study subsidy notch, all students
Study subsidy notch, students with default subsidy (9 months)
6000
Excess mass: 1.903 (.269), Share in the dominated region: .881 (.039)
Upper limit: 23 (3.24)
0
2000
4000
Frequency
2000
4000
Frequency
6000 8000 10000 12000
Excess mass: 2.046 (.227), Share in the dominated region: .906 (.032)
Upper limit: 26 (4.613)
-50
-40
-30
-20
-10
0
10
20
Distance from the notch
Observed
Tuomas Matikka (VATT)
30
40
50
-50
-40
Counterfactual
Students and optimization frictions
-30
-20
-10
0
10
20
Distance from the notch
Observed
30
40
50
Counterfactual
IFS Workshop 2016
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Results
First MTR kink, all students
Last MTR kink, university/polytechnic graduates
Excess mass: -.09 (.107), Elasticity: -.006(.007)
Excess mass: -.106 (.084), Elasticity: -.001(.001)
2500
3000
Frequency
3500 4000
4500
5000
Frequency
5000 10000 15000 20000 25000 30000
MTR bunching for current and former students
-50
-40
-30
-20
-10
0
10
Distance from the kink
Observed
20
30
40
50
-50
-40
-30
Counterfactual
-20
-10
0
10
Distance from the kink
Observed
20
30
40
50
Counterfactual
First MTR kink, students who previously bunch at the notch
1000
Frequency
2000
3000
4000
Excess mass: -.656 (.183), Elasticity: -.044(.012)
-50
-40
-30
-20
-10
0
10
Distance from the kink
Observed
Tuomas Matikka (VATT)
20
30
40
50
Counterfactual
Students and optimization frictions
IFS Workshop 2016
17 / 29
Results
Road map
We showed that notches create behavioral responses and that
optimization frictions tend to attenuate these responses
Next: Global vs. local responses
Utilize the reform to study the extent and shape of behavioral responses
Alternative counterfactuals
Divided sample results
Divide students according to study credits, correlated with optimization
ability
Compare new and old students and rules, look into awareness about
the rules more carefully
Position relative to the notch prior to the reform (bunchers, dominated
region)
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
18 / 29
Global vs. local responses
Students with 9 subsidy months in different years
Income distribution in different years
0
Frequency
200
400
600
Students with 9 subsidy months and 9 subsidy months in base year
0
5000
10000
Income
2004−2005
2008−2009
Tuomas Matikka (VATT)
Students and optimization frictions
15000
20000
2006−2007
IFS Workshop 2016
19 / 29
Global vs. local responses
Students with 9 subsidy months in 2007 - 2008
Income distribution in different years
0
100
Frequency
200
300
400
Students with 9 subsidy months in year t and t−1
0
2000
4000
6000
8000 10000 12000 14000 16000 18000
Income
2007
Tuomas Matikka (VATT)
Students and optimization frictions
2008
IFS Workshop 2016
20 / 29
Global vs. local responses
Alternative shape of distribution
Income distributions for students and non−students
0
1000
1500
3000
4500
Students
Non−students
2500
4000
5500
6000
7000
Students: 9 subsidy months
Non−students: part−time workers, aged 19−24
1500
4500
7500
Students
Tuomas Matikka (VATT)
10500
Income
13500
16500
19500
Non−students
Students and optimization frictions
IFS Workshop 2016
21 / 29
Global vs. local responses
Alternative shape of distribution: Dif-in-dif-style
Income distributions for students and non−students
0
Density
.00005
.0001
.00015
Students with 9 subsidy months
Non−students: part−time workers aged 19−24
1500
4500
7500
10500
Labor income
13500
Students 04−05
Non−students 04−05
Tuomas Matikka (VATT)
Students and optimization frictions
16500
19500
Students 08−09
Non−students 08−09
IFS Workshop 2016
22 / 29
Divided sample results
Room for optimization errors?
We found that some of the optimization frictions originate from the
labor market and could be more global in nature
Students also aware of the study subsidy system in general
Any room for learning / inattention / optimization error type of
frictions that attenuate behavior?
These issues can be studied utilizing the local approach
We next utilize study subsidy credits to investigate if some students
do not fully understand all rules (although aware of them)
The relevant income concept (annual gross income)
How to accurately calculate and predict annual income
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
23 / 29
Divided sample results
Divided sample results: study credits
Study subsidy notch, study credits 75−100th percentile
0
100
500
200
Frequency
300
Frequency
1000
1500
400
2000
500
2500
Study subsidy notch, study credits 0−25th percentile
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
Tuomas Matikka (VATT)
30
40
50
−50
−40
−30
Students and optimization frictions
−20
−10
0
10
20
Distance from the notch
30
40
IFS Workshop 2016
50
24 / 29
Divided sample results
Utilizing the reform: new and old students and rules
Study subsidy notch, new students after the reform
0
500
500
Frequency
1000
Frequency
1000
1500
2000
1500
Study subsidy notch, new students before the reform
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
Tuomas Matikka (VATT)
30
40
50
−50
−40
−30
Students and optimization frictions
−20
−10
0
10
20
Distance from the notch
30
40
IFS Workshop 2016
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25 / 29
Divided sample results
Utilizing the reform: new and old students and rules
Study subsidy notch, old students after the reform
200
500
400
Frequency
600
800
Frequency
1000
1500
1000
2000
1200
Study subsidy notch, old students before the reform
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
Tuomas Matikka (VATT)
30
40
50
−50
−40
−30
Students and optimization frictions
−20
−10
0
10
20
Distance from the notch
30
40
IFS Workshop 2016
50
26 / 29
Divided sample results
Bunching/dominated region before the reform
Study subsidy notch, students in the dominated region before
50
100
200
100
Frequency
150
Frequency
300
400
200
500
250
Study subsidy notch, students who bunched before the reform
−50
−40
−30
−20
−10
0
10
20
Distance from the notch
Tuomas Matikka (VATT)
30
40
50
−50
−40
−30
Students and optimization frictions
−20
−10
0
10
20
Distance from the notch
30
40
IFS Workshop 2016
50
27 / 29
Summary
Conclusions
Study subsidy evidence shows that incentives matter (bunching) and
at the same time optimization frictions attenuate behavior (many
students in dominated region)
The reform evidence shows that the notch does not only induce local
bunching, but also a more global shift in the income distribution
The notch appears to induce behavioral responses well below the
income limit
Presumably, ETI is not calculated correctly by just utilizing local
bunching estimates
This, and the disperse bunching, also indicate that taxpayers have
difficulties in controlling their income precisely
Optimization ability also prevalent in explaining behavioral responses
Correlation between study credits and optimization behavior
Use data on secondary school test scores in the future
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
28 / 29
Summary
Thank you for your attention!
Tuomas Matikka (VATT)
Students and optimization frictions
IFS Workshop 2016
29 / 29