Taxpayer Responses over the Cycle: Evidence from Irish Notches Enda Patrick Hargaden

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Taxpayer Responses over the Cycle: Evidence from
Irish Notches
Enda Patrick Hargaden
Department of Economics
University of Michigan
IFS Labour Market Conference
March 1, 2016
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Introduction and Motivation
Why would cyclical variation be interesting?
Standard theory shows that the behavioral response optimally determines:
1
Tax rates
2
Extent of redistribution
3
Enforcement levels
Should these vary over the cycle?
Some have argued a Keynesian cyclicality story on the expenditure side.
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Introduction and Motivation
Why would cyclical variation be interesting?
Standard theory shows that the behavioral response optimally determines:
1
Tax rates
2
Extent of redistribution
3
Enforcement levels
Should these vary over the cycle?
Some have argued a Keynesian cyclicality story on the expenditure side.
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Introduction and Motivation
Which way does cyclical variation swing?
Arguments for increase in responsiveness during a recession:
If firms are struggling to survive, they may search harder for cost
savings
With income effects, employees may value a euro more during a
recession
Arguments for decrease:
There may be fewer opportunities to hide income when GDP is smaller
It is harder to adjust hours during a recession, by e.g. switching jobs
Wage rigidity could be a factor in downturns
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Introduction and Motivation
Which way does cyclical variation swing?
Arguments for increase in responsiveness during a recession:
If firms are struggling to survive, they may search harder for cost
savings
With income effects, employees may value a euro more during a
recession
Arguments for decrease:
There may be fewer opportunities to hide income when GDP is smaller
It is harder to adjust hours during a recession, by e.g. switching jobs
Wage rigidity could be a factor in downturns
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Introduction and Motivation
What does this paper have?
Administrative employee tax return data, and a set of notches
Unprecedentedly volatile developed economy
Insight into “frictions”, i.e. the determinants of reporting tax
disadvantaged incomes
Focus on the inter-temporal component of taxpayer response
A new method (bunching in differences) to investigate the
responsiveness
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Introduction and Motivation
Preview of Results
The evidence of taxpayer response is much weaker during the
recession.
Pre-2008 ‘treatment effects’ are about three times as large as
post-2008.
Much of the difference reflects non-random attrition from labor force.
I
Reduced employment in sectors (e.g. construction) that exhibit
above-average ability to report tax-advantaged incomes creates
composition effect/composition bias.
However, it’s more than just a composition effect.
I
Holding the labor force constant, people are less responsive to the
incentives.
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Introduction and Motivation
Overview of Talk
1
The theory of notches
2
Taxpayer responses and the elasticity of taxable income
3
Data description and introduction to methods
4
Empirical evidence of cyclical variation
5
Determinants of tax avoidance
6
Inverse probability weighting estimates?
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Theory of Notches
Question: What exactly are notches?
Post-tax
income
Y1
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Y2
Irish Tax Notches
Pre-tax
income
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Theory of Notches
Question: What exactly are notches?
Post-tax
income
Y1
Hargaden (University of Michigan)
Y2
Irish Tax Notches
Pre-tax
income
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Theory of Notches
Question: What exactly are notches?
Post-tax
income
Y1
Hargaden (University of Michigan)
Y2
Irish Tax Notches
Pre-tax
income
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Theory of Notches
Question: What exactly are notches?
Post-tax
income
Y1
Hargaden (University of Michigan)
Yl
Irish Tax Notches
Y2
Yu Pre-tax
income
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Theory of Notches
Question: What exactly are notches?
Post-tax
income
Strictly dominated region
Y1
Hargaden (University of Michigan)
Yl
Irish Tax Notches
Y2
Yu Pre-tax
income
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Understanding Taxpayer Responses
Understanding Taxpayer Responses
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Understanding Taxpayer Responses
Taxpayer Response and Taxable Income
Debate over which margin of adjustment: hours, gross income,
evasion/avoidance?
Feldstein (1995) shifted the focus to taxable income (ETI). Many
margins of adjustment, all captured by taxable income.
Under certain circumstances, this measures the welfare costs of
taxation.
Readily available empirical source.
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Understanding Taxpayer Responses
Bunching at notches to identify taxpayer response
Notches provide very strong incentives, and clean tests of ability to
avoid taxes.
Extent of level-bunching can identify ETI (Saez, 2010). The larger
the bunching, the larger the ETI.
Chetty et al (2011) and Kleven & Waseem (2013) bunching in
Denmark and Pakistan.
Almunia & Lopez-Rodriguez (2014), Auten & Carroll (1999), Bastani
& Selin (2014), Gruber & Saez (2002), Jenderny (2015), Kopczuk &
Munroe (2015), Marx (2012), Onji (2009), Ramnath (2013), Sallee &
Slemrod (2012), Slemrod et al (2015), Yelowitz (1995).
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Understanding Taxpayer Responses
Slemrod & Kopczuk: ETI as a policy choice
ETI is not an immutable parameter. For a cost, we can influence it.
Dependence on tax system: compare Denmark and Greece.
Increased enforcement will lower responsiveness — ETI can be
lowered (at a cost).
Subtle point: I find a very low responsiveness for Ireland.
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Understanding Taxpayer Responses
Policy and academic implications of the paper
Time-varying responsiveness affects:
1
Optimal enforcement varies with the phase of the cycle: fund HMRC
in good times.
2
Stimulus package identification bias.
Small aside: tax cuts likely less stimulating than hoped.
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Understanding Taxpayer Responses
Policy and academic implications of the paper
Time-varying responsiveness affects:
1
Optimal enforcement varies with the phase of the cycle: fund HMRC
in good times.
2
Stimulus package identification bias.
Small aside: tax cuts likely less stimulating than hoped.
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Data Description
Data and Empirics
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Data Description
Sample from Universe of Irish Tax Returns
I have access to an administrative panel of employee tax returns with
demographics and details on their employer.
Employers must file an income statement for each employee
Dataset is a panel (2006–2013) of 10% of all employees,
representative of full sample
Demographic information on employee (age, sex, nationality)
Some business information on employer (legal form, number of
employees, detailed sector)
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Data Description
Trends in the data
Earnings distribution in Ireland, 2006-2013
40,000
Frequency
30,000
20,000
10,000
0
Hargaden (University of Michigan)
20,000
40,000
60,000
Total Annual Pay (€)
Irish Tax Notches
80,000
100,000
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Data Description
Trends in the data
100
Real Output (2005 Q1=100)
105
110
115
120
Irish and US Business Cycles
2006
2008
2010
Year
Ireland
2012
2014
USA
Sources: Central Statistics Office, FRED
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Data Description
Trends in the data
12.5
10
7.5
5
2.5
Unemployment Rate (seasonally adjusted)
15
Irish and US Unemployment Rates
2005
2006
2007
2008
2009
2010
Ireland
2011
2012
2013
2014
USA
Sources: Central Statistics Office, BLS
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Data Description
Trends in the data
100
80
60
40
Employment by Sector (2006 Q2 = 100)
120
Employment in Ireland
2007
2008
Total
2009
2010
2011
Year
Non-construction
2012
2013
2014
Construction
Source: Central Statistics Office/QNHS
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Data Description
Trends in the data
Limitation of the data
The notches are not applicable to people who are (i) married; (ii) jointly
filing; and (iii) both spouses working.
Will attenuate results.
Likely becomes less of a problem over time.
Marriage rate
Employment rate
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Data Description
Experimental Design
A Tale of Three Notches
Health Levy — earmarked for contribution to public health service,
enacted in 1979
Income Levy — enacted by the Financial Emergency Measures in the
Public Interest Act, 2009
Universal Social Charge (USC) — enacted in 2011 to replace both
the Health and Income Levies.
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Data Description
Experimental Design
A Tale of Three Notches
Health Levy — earmarked for contribution to public health service,
enacted in 1979
Income Levy — enacted by the Financial Emergency Measures in the
Public Interest Act, 2009
Universal Social Charge (USC) — enacted in 2011 to replace both
the Health and Income Levies.
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Data Description
Experimental Design
A Tale of Three Notches
Health Levy — earmarked for contribution to public health service,
enacted in 1979
Income Levy — enacted by the Financial Emergency Measures in the
Public Interest Act, 2009
Universal Social Charge (USC) — enacted in 2011 to replace both
the Health and Income Levies.
Hargaden (University of Michigan)
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Data Description
Experimental Design
A Tale of Three Notches
Health Levy — earmarked for contribution to public health service,
enacted in 1979
Income Levy — enacted by the Financial Emergency Measures in the
Public Interest Act, 2009
Universal Social Charge (USC) — enacted in 2011 to replace both
the Health and Income Levies.
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Data Description
Experimental Design
List of Quasi-Experimental Variation
Year
Health Levy
2005
2006
2007
2008
2009
2010
2011
2012
2013
20,800
22,880
24,960
26,000
26,000
26,000
Hargaden (University of Michigan)
Income Levy
USC
15,028
15,028
4,004
10,036
10,036
Irish Tax Notches
Tax Penalty
(416)
(458)
(499)
(520)
(867)
(1,040)
(80)
(201)
(201)
(200)
(301)
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Data Description
Experimental Design
Order of the Game
1
December of Year T − 1: government announces annual budget.
2
January 1 of Year T : tax changes take effect. Wages are paid and
100% of taxes are deducted by employers at source.
3
Early in Year T + 1: employers send tax forms to Revenue detailing
total annual pay.
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Bunching Estimates
Empirical Design
Estimation
The literature’s standard estimation technique measures excess mass
(“bunching”) near the threshold.
1
Plot histogram of earnings near the threshold.
2
Fit high-order polynomial to these data.
3
Compare actual mass to the predicted mass.
Identification requires the level of the income distribution to be flat at the
notch threshold.
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Bunching Estimates
An Illustrative Example
Bunching (Levels) in 2008
200
0
100
Frequency
300
400
Extent of excess bunching b= 7.5 (0.6)
25,490
25,690
25,890
26,090
26,290
26,490
Income
2005
2006
2007
Hargaden (University of Michigan)
2008
2009
2010
Irish Tax Notches
2009 IL
2010 IL
2012
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2013
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Bunching Estimates
Round-number problem: spurious bunching
600
500
300
400
Frequency
700
800
Earnings Distribution, 2006-2007
20,000 21,000 22,000 23,000 24,000 25,000 26,000 27,000 28,000 29,000 30,000
Annual Income
Clear round-number bunching for multiples of e1,000.
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Bunching Estimates
Changes in bunching as an alternative strategy
Rather than look at the bunching in levels, we can look at the bunching in
differences.
Identification is valid if the change in the income distribution is flat at
the notch threshold.
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Bunching Estimates
Difference Bunching
Bunching Clear in Early Years: 2006
Bunching (Differences) in 2006
100
0
50
Frequency
150
200
Extent of excess bunching b=72.3 (21.7)
22,370
22,570
22,770
22,970
23,170
23,370
Income
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Bunching Estimates
Difference Bunching
Bunching Clear in Early Years: 2007
Bunching (Differences) in 2007
100
0
50
Frequency
150
200
Extent of excess bunching b=146.5 (24.4)
24,450
24,650
24,850
25,050
25,250
25,450
Income
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Bunching Estimates
Difference Bunching
Bunching Clear in Early Years: 2008
Bunching (Differences) in 2008
50
-50
0
Frequency
100
150
Extent of excess bunching b=153.6 (18.8)
25,490
25,690
25,890
26,090
26,290
26,490
Income
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Bunching Estimates
Difference Bunching
No Bunching: 2009
Bunching (Differences) in 2009
50
-50
0
Frequency
100
150
Extent of excess bunching b=15.6 (10.2)
14,520
14,720
14,920
15,120
15,320
15,520
Income
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Bunching Estimates
Difference Bunching
No Bunching: 2009
Bunching (Differences) in 2009
50
-50
0
Frequency
100
150
Extent of excess bunching b=-20.3 (10.0)
25,490
25,690
25,890
26,090
26,290
26,490
Income
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Bunching Estimates
Difference Bunching
No Bunching: 2010
Bunching (Differences) in 2010
50
-50
0
Frequency
100
150
Extent of excess bunching b=-2.0 (9.5)
14,520
14,720
14,920
15,120
15,320
15,520
Income
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Bunching Estimates
Difference Bunching
No Bunching: 2012
Bunching (Differences) in 2012
50
-50
0
Frequency
100
150
Extent of excess bunching b= 9.4 (8.3)
9,530
9,730
9,930
10,130
10,330
10,530
Income
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Declining Responsiveness
Salience?
Could this be a salience story?
One plausible explanation is that people knew about the tax in the initial
years and, in the midst of a recession, lost sight of their personal finances.
This seems quite unlikely.
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Declining Responsiveness
Salience?
Could this be a salience story?
One plausible explanation is that people knew about the tax in the initial
years and, in the midst of a recession, lost sight of their personal finances.
This seems quite unlikely.
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Declining Responsiveness
Salience?
Public attention of USC
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Declining Responsiveness
Salience?
Public attention of USC
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Declining Responsiveness
Salience?
Public attention of USC
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Declining Responsiveness
Salience?
Public attention of USC
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Declining Responsiveness
Salience?
Public attention of USC
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Declining Responsiveness
Salience?
Public attention of USC
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Declining Responsiveness
Salience?
Public attention of USC
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Declining Responsiveness
Salience?
Public attention of USC
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Declining Responsiveness
Salience?
Public attention of USC
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Declining Responsiveness
Salience?
Public attention of USC
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Determinants of Bunching
Who bunches?
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Determinants of Bunching
Who bunches?
If it’s not a salience story, what sort of people place themselves in the
tax-advantaged portion of the income distribution?
To address this, consider
( a dummy variable:
1 if income in dominated region
Dominated Region =
0 if income ∈ (Threshold-e100, Threshold]
This permits estimating probits on the determinants of tax-reporting
behavior.
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Determinants of Bunching
Regression Results
Self-employed construction workers avoid taxes
Table: Selected determinants of reporting tax-disadvantaged income
Avg. Marginal Effects
Personal Characteristics
Firm Characteristics
Industry
Hargaden (University of Michigan)
Number of Employers
EU 2004
Fifty-two weeks
Self-employment
Partnership
Private Limited
Foreign Branch
Public Limited
Firm-size
Construction
Retail
Hotel & restaurants
Public admin
Utilities
Irish Tax Notches
1.9???
2.0??
-3.7???
-16.0???
3.7??
5.4???
10.0???
10.2???
0.02???
-3.0???
-2.0??
-3.2??
3.2??
4.2
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Determinants of Bunching
Regression Results
Discussion of regression results
Bunchers share traits.
They are younger, are employed primarily in small enterprises, typically for
52 weeks of the year, in certain industries.
Perhaps these covariates are changing over time, and this is affecting
bunching.
What happens when we reweight the pre- and post-recession samples to
look like each other?
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Counterfactual Estimation
VAT Notch in Japan
Figure: Onji (JPubEc, 2009)
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Counterfactual Estimation
DiNardo, Fortin, Lemieux approach
DFL Density Estimates 2006-2007
.00055
Density
.0005
.00045
.0004
24,500
25,000
Annual Pay (€)
Actual (pre)
Actual (post)
25,500
Counterfactual
Controls: male age irish emp_size legal_form sector fiftytwo
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Counterfactual Estimation
DiNardo, Fortin, Lemieux approach
DFL Density Estimates 2007-2008
.0005
Density
.00048
.00046
.00044
.00042
25,500
26,000
Annual Pay (€)
Actual (pre)
Actual (post)
26,500
Counterfactual
Controls: male age irish emp_size legal_form sector fiftytwo
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Counterfactual Estimation
DiNardo, Fortin, Lemieux approach
DFL Density Estimates 2008-2009
.00055
Density
.0005
.00045
.0004
25,500
26,000
Annual Pay (€)
Actual (pre)
Actual (post)
26,500
Counterfactual
Controls: male age irish emp_size legal_form sector fiftytwo
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Counterfactual Estimation
DiNardo, Fortin, Lemieux approach
DFL Density Estimates 2009-2010
.00046
Density
.00044
.00042
.0004
.00038
14,500
15,000
Annual Pay (€)
Actual (pre)
Actual (post)
15,500
Counterfactual
Controls: male age irish emp_size legal_form sector fiftytwo
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Controlling for composition
It’s not just composition bias
Table: Changes in wage dynamics for job-stayers
Year
2005-06
2006-07
2007-08
2008-09
2009-10
2010-11
2011-12
2012-13
Proportion Freezes
Proportion Cuts
Proportion Increases
2.5%
2.5%
2.8%
3.3%
4.4%
6.8%
10.3%
10.0%
17.2%
17.6%
22.9%
52.7%
55.2%
39.3%
34.2%
34.3%
80.4%
79.9%
74.2%
44.0%
40.3%
53.9%
55.5%
55.7%
Job-stayers are defined as employees who remain with the same employer over
multiple years. Table shows the proportion of job-stayers whose pay was frozen
within ±0.1% of previous year’s pay, cut, or increased. Source: Doris et al. (2013)
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Controlling for composition
Inverse Probability Weighting
I use weights to match the pre- and post-recession samples
One way to disentangle composition bias from additional constraints on
behavior is to use inverse probability weighting (IPW).
This calculates the determinants of bunching “as if” the composition of
the labor force were unchanged from previous years.
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Controlling for composition
Inverse Probability Weighting
Post-matching magnitudes vary
Table: Matched sample determinants
Fifty-two weeks
Firm Size (’000s)
Self-employment
Number of employers
Irish
Male
2006
2010 (match)
-3.18?
-0.01
-12.66???
1.03
1.72
-0.27
-7.58???
0.05??
-21.33???
2.14
0.50
2.58?
Table shows selected mean marginal effects from probit regression on the determinants of bunching. The first column shows the results for the notch at
e22,880 in 2006. The second column shows the results for the 2010 notch, but
with the results weighted so the covariates match those of the 2006 sample.
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Controlling for composition
Inverse Probability Weighting
Interpretation of recession in potential outcome framework
One interpretation of the results is to consider the recession as a treatment
with non-random assignment (e.g. construction).
If a recession imposes no additional constraints on behavior, then selection
into the treatment should explain the change in outcomes.
This is rejected by the data.
Regardless of the specification, the change in tax-reporting behavior is not
explained by the covariates. People are 4–5pp less likely to respond to
these tax incentives post-2008.
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Conclusion
Conclusions and contributions
This paper has three things really going for it:
1
Great variation: several changes in location and severity of notch
I
Motivation for the difference bunching strategy
2
Great data: third party-reported, administrative panel
3
Huge business cycle volatility
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Conclusion
Conclusions and contributions
Developed a new bunching strategy with more compelling
identification than existing approaches.
Tested the response to the ‘treatment’ of notch introduction.
Contributed to the literature on what covariates are consistent with
avoiding taxes.
Decomposed the total response into a labor composition effect, and a
change in behavior effect.
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Conclusion
Conclusions and contributions
Clear, unambiguous results in the initial period: people avoid taxes.
That evidence disappears.
The employer and employee characteristics are determinants of
reporting behavior.
Changes in the composition of the labor force can explain much of
the changes in reporting. . .
. . . but composition alone cannot explain the findings.
In a model of cyclical responsiveness, optimal tax rate and
enforcement vary over the cycle. People are less able to avoid taxes
during recessions: fund the tax authorities in good times.
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Conclusion
Conclusions and contributions
Clear, unambiguous results in the initial period: people avoid taxes.
That evidence disappears.
The employer and employee characteristics are determinants of
reporting behavior.
Changes in the composition of the labor force can explain much of
the changes in reporting. . .
. . . but composition alone cannot explain the findings.
In a model of cyclical responsiveness, optimal tax rate and
enforcement vary over the cycle. People are less able to avoid taxes
during recessions: fund the tax authorities in good times.
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Conclusion
Conclusions and contributions
Clear, unambiguous results in the initial period: people avoid taxes.
That evidence disappears.
The employer and employee characteristics are determinants of
reporting behavior.
Changes in the composition of the labor force can explain much of
the changes in reporting. . .
. . . but composition alone cannot explain the findings.
In a model of cyclical responsiveness, optimal tax rate and
enforcement vary over the cycle. People are less able to avoid taxes
during recessions: fund the tax authorities in good times.
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
51 / 51
Conclusion
Conclusions and contributions
Clear, unambiguous results in the initial period: people avoid taxes.
That evidence disappears.
The employer and employee characteristics are determinants of
reporting behavior.
Changes in the composition of the labor force can explain much of
the changes in reporting. . .
. . . but composition alone cannot explain the findings.
In a model of cyclical responsiveness, optimal tax rate and
enforcement vary over the cycle. People are less able to avoid taxes
during recessions: fund the tax authorities in good times.
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
51 / 51
Conclusion
Conclusions and contributions
Clear, unambiguous results in the initial period: people avoid taxes.
That evidence disappears.
The employer and employee characteristics are determinants of
reporting behavior.
Changes in the composition of the labor force can explain much of
the changes in reporting. . .
. . . but composition alone cannot explain the findings.
In a model of cyclical responsiveness, optimal tax rate and
enforcement vary over the cycle. People are less able to avoid taxes
during recessions: fund the tax authorities in good times.
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
51 / 51
Conclusion
Conclusions and contributions
Clear, unambiguous results in the initial period: people avoid taxes.
That evidence disappears.
The employer and employee characteristics are determinants of
reporting behavior.
Changes in the composition of the labor force can explain much of
the changes in reporting. . .
. . . but composition alone cannot explain the findings.
In a model of cyclical responsiveness, optimal tax rate and
enforcement vary over the cycle. People are less able to avoid taxes
during recessions: fund the tax authorities in good times.
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
51 / 51
95
Employment (2005 Q1=100)
105
100
110
115
Irish and US Employment Levels
2006
2008
2010
Year
Ireland
2012
2014
USA
Sources: Central Statistics Office, BLS
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
1 / 12
0
20
Weddings (2005=100)
40
60
80
100
120
Weddings Registered in Ireland
2005
2006
2007
2008
2009 2010
Year
2011
2012
2013
2014
Source: Central Statistics Office
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Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
2 / 12
Bunching (Levels) in 2005
150
100
0
50
Frequency
200
250
Extent of excess bunching b= 3.8 (1.2)
20,290
20,490
20,690
20,890
21,090
21,290
Income
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
3 / 12
Bunching (Levels) in 2006
150
100
50
Frequency
200
250
Extent of excess bunching b= 1.9 (0.8)
22,370
22,570
22,770
22,970
23,170
23,370
Income
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
4 / 12
Bunching (Levels) in 2007
0
100
Frequency
200
300
Extent of excess bunching b= 3.5 (1.0)
24,450
24,650
24,850
25,050
25,250
25,450
Income
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
5 / 12
Bunching (Levels) in 2008
200
0
100
Frequency
300
400
Extent of excess bunching b= 7.5 (0.6)
25,490
25,690
25,890
26,090
26,290
26,490
Income
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
6 / 12
Bunching (Levels) in 2009
100
0
50
Frequency
150
Extent of excess bunching b= 4.8 (0.9)
14,520
14,720
14,920
15,120
15,320
15,520
Income
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
7 / 12
Bunching (Levels) in 2009
200
0
100
Frequency
300
Extent of excess bunching b= 8.2 (1.0)
25,490
25,690
25,890
26,090
26,290
26,490
Income
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
8 / 12
Bunching (Levels) in 2010
100
0
50
Frequency
150
200
Extent of excess bunching b= 4.4 (0.9)
14,520
14,720
14,920
15,120
15,320
15,520
Income
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
9 / 12
Bunching (Levels) in 2010
200
0
100
Frequency
300
400
Extent of excess bunching b=10.0 (0.9)
25,490
25,690
25,890
26,090
26,290
26,490
Income
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
10 / 12
Bunching (Levels) in 2012
100
0
50
Frequency
150
200
Extent of excess bunching b= 3.3 (3.7)
9,530
9,730
9,930
10,130
10,330
10,530
Income
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
11 / 12
Bunching (Levels) in 2013
100
0
50
Frequency
150
200
Extent of excess bunching b= 3.2 (5.4)
9,530
9,730
9,930
10,130
10,330
10,530
Income
Back
Hargaden (University of Michigan)
Irish Tax Notches
March 1, 2016
12 / 12
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