henrik jacobsen kleven london school of economics lecture...
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LABOR SUPPLY RESPONSESTO TAXES AND TRANSFERS
Henrik Jacobsen Kleven
London School of Economics
Lecture Notes for MSc Public Economics (EC426)
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AGENDA
Efficiency cost of labor supply responses.
Theoretical models of labor supply.
Empirical approaches andmethodological issues in labor supply estimation.
Quasi-experiments:
— Tax-transfer reforms and difference-in-differences
— Kinks, notches, and bunching
Optimization frictions and observed vs. structural elasticities.
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WHY CARE ABOUT LABOR SUPPLY RESPONSES?
When the government levies income taxes to finance transfer programs
and public goods, individuals respond by changing labor supply.
By revealed preference, each individual prefers the new labor supply to
the old one at the tax-inclusive prices. So, everyone is better off because
of the labor supply adjustments?
No, the revealed preference argument applies to each individual alone,
not to the population as a whole.
Behavioral responses affect gov’t revenue and create a fiscal externality–
the deadweight loss of taxation.
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THE TOTAL DEADWEIGHT LOSS OF TAXATION
net-of-taxwage rate
labor supply functionfunction
tax revenue
Aw
TDWL
A
τ·w
(1- τ)w deadweight loss
CSB
consumer surplus
hours workedh*B h*A
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THE MARGINAL DEADWEIGHT LOSS OF TAXATION
net-of-tax
labor supply functionBehavioral revenue
wage rate
functione a o a e e ueeffect dB (≈ dDWL)
w
T DWLτ·w
(1- τ)wCS C
B
Mechanical revenue
hours worked
effect dM
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THE DEADWEIGHT LOSS OF TAXATION
The deadweight loss is given by =− , where is the utility
loss from taxation (in monetary units) and is collected tax revenue.
The marginal DWL is given by = − .
We have = + where is themechanical revenue effectand is the behavioral revenue effect. We have = using
the envelope theorem.
⇒ = − ( + ) = −.
General insight: In a model with efficient markets, the marginalefficiency cost of taxation is given by the behavioral revenue loss.
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DWL FROM LABOR SUPPLY RESPONSES
We have
= − = − · · =
1− · · ·
where ≡ (1− )(1− ) is the elasticity of hours worked with respect
to the net-of-tax rate.
Compensated vs uncompensated elasticity? For DWL, we want the
compensated elasticity (see Auerbach, 1985, for a rigorous treatment).
Empirical literature estimates compensated and uncompensated elas-
ticities.
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DIMENSIONS OF LABOR SUPPLY RESPONSE
1. Quantitative dimensions:
(a) Hours worked for those who are working (intensive margin)
(b) Labor force participation (extensive margin)
2. Qualitative dimensions:
(a) Effort on the job
(b) Type of job (occupation, industry, etc.)
(c) Education and on-the-job training
(d) Location and migration
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THE BASIC STATIC MODEL WITHOUT TAXES
Utility maximization:
max
= ( x) st. = +
where is the wage rate, is non-labor income, and x is a vector of
individual characteristics.
Optimal labor supply satisfies−00 = along with a non-negativity
constraint→ labor supply function = ( x) ≥ 0.
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substitution effect
incomeeffect
INCOME AND SUBSTITUTION EFFECTS
consumption c
hours worked h
slope w1
slope w0
u0
u1
y
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ELASTICITIES AND SLUTSKY DECOMPOSITION
Uncompensated wage elasticity =
. Can be either positive
or negative.
Income elasticity =
. Negative if leisure is normal.
Compensated wage elasticity captures the response at a con-
stant utility level. This elasticity is always positive.
The Slutsky Equation links elasticities:
= −
where ≡ − · is the income effect.
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BASIC CROSS-SECTIONAL ESTIMATION
Based on the model above, early work considered a regression specifi-
cation such as
= 0 + 1 · + 2 · + 3 · x +
where x is a vector of observable controls and is the error term.
OLS is consistent if explanatory variables and are uncorrelated.
Results:
•Male labor supply (see Pencavel, 1986): ' 0 and ' 01 ⇒ ' 01.
• Female labor supply (Heckman-Killingsworth, 1986): Much largerelasticities on average, but enormous variation across studies.
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PROBLEMS WITH BASIC APPROACH
1. Identification: may be positively correlated with taste for work,
which is unobserved and captured by → positive correlation be-
tween and → upward bias [omitted variable bias].
2.Measurement error as is measured as earnings/hours from
surveys.
3. Functional form sensitivity.
4. Ignores the impact of taxes on the central explanatory variables.
5.Non-participation: sample is selected so that 0, because
otherwise no wage rate is observed. Extensive responses ignored.
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ACCOUNTING FOR (NON-LINEAR) TAXES
-bracket piecewise linear schedule () with marginal tax rates
1
The budget constraint:
= − () + = (1− )+
where ≡ − () + is virtual income in bracket .
Within each bracket, optimal labor supply can be written on the form
= ((1− )).
We must deal explicitly with the possibility of a kink solution at thethreshold between two brackets.
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BUDGET SET AND VIRTUAL INCOME WITHA 2-BRACKET NONLINEAR TAX SCHEDULE
consumption c
hours worked h
slope (1- )�2
w
R1
R2
h
slope (1- )�1
w
u
kink
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ESTIMATION WITH NONLINEAR TAXES
Based on the model, consider an empirical specification such as
= 0 + 1 · (1− ) + 2 · + 3 · x +
which can be estimated by e.g. OLS.
Problems with this approach:
1. Identification:(a) is correlated with [omitted variable bias]
(b) are endogenous to and hence correlated with [reverse
causality].
2. Bunching: the model predicts bunching at kink points, but wetypically do not observe much bunching in the data.
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THE CONVEXITY ASSUMPTION
So far, we have assumed that workers supply labor where the indiffer-
ence curve is tangent to the budget set.
If this point of tangency occurred at negative hours, a non-negativity
constraint implied a corner solution at zero hours (non-participation).
In this model, marginal changes in taxes lead to marginal changes in
hours worked. Even participation responses are smooth in this way.
This analysis is fine as long as the budget and preferences are convex.
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THE CONVEX MODEL:INTENSIVE VS EXTENSIVE LABOR SUPPLY RESPONSES
hours worked h
consumption c
uA
slope w0
y
uB
hAhB
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THE CONVEX MODEL:INTENSIVE VS EXTENSIVE LABOR SUPPLY RESPONSES
hours worked h
consumption c
slope w0
y
slope w1
hAhB
uA
uB
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THE REAL WORLD IS NON-CONVEX
Fixed costs of working due to child care, commuting, etc.
Fixed costs of employing due to hiring costs, technological con-straints, etc.
Means-tested transfers creating higher marginal tax rates at thebottom than further up the distribution.
Non-convexities bring discrete participation responses into playeven with small changes in wages or taxes.
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�yF
A MODEL WITH FIXED WORK COSTS:INTENSIVE VS EXTENSIVE LABOR SUPPLY RESPONSES
hours worked h
consumption c
slope w0
y
�hF
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�yF
A MODEL WITH FIXED WORK COSTS:INTENSIVE VS EXTENSIVE LABOR SUPPLY RESPONSES
hours worked h
consumption c
slope w0
y
�hF
slope w1
small intensiveresponse
large extensiveresponse
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IndifferenceCurve
NonconvexBudget
High-TaxBracket
TransferPhase-Out
BUDGET SET WITH MEANS-TESTED TRANSFERS
hours worked h
consumption c
Low-TaxBracket
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MODERN LABOR SUPPLY LITERATURE
• Early phase (around 1990s):
— Focus on the evaluation problem in previous work
— Search for identification takes center stage
— Focus on experimental evidence
• Later phase (2000s onwards):
— From survey data to large administrative datasets
— Sharper identification and graphical evidence
— Sufficient statistics approach as a bridge between reduced-form and structural estimation
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SOURCES OF EXPERIMENTAL VARIATION
•Randomized experiments
— Truly exogenous variation
—Not very common in public finance
•Quasi-experiments [variation created by actual policy]
— Tax-transfer reforms and difference-in-differences
—Discontinuities in tax-transfer schedules and bunching approaches
—Regression Discontinuity Design
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THE EVALUATION PROBLEM
Counterfactual question: what would person ’s labor supply be if
taxes were different?
= person ’s labor supply if taxes are high (‘treatment’), =
person ’s labor supply if taxes are low (‘control’). We don’t observe
both and at the same time. What we do observe is
[ | ]−[ | ] = [ − | ]| {z }treatment effect
+³[ | ]−[ | ]
´| {z }
selection bias
The selection bias reflects systematic differences between treatments
and controls. Randomized experiments solve this problem.
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RANDOMIZED EXPERIMENTS
A sample of agents is divided randomly into treatments and controls
. Group is treated by a policy while group is not.
The treatment effect on outcome is measured by[ | ]−[ | ].
Random assignment⇒ [ | ] = [ | ]. Then,[ | ]−[ | ] = [ − | ] = true treatment effect.
Applications:
1.NIT experiments in the U.S. in the 60s and 70s. Many studies(e.g., Ashenfelter-Plant, JLE 1990).
2.Canadian Self Sufficiency Programme (SSP) in the 90s.Michalopoulos-Robins-Card (JPubE 2005).
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QUASI-EXPERIMENTS & DIF-IN-DIF
Tax reforms create natural experiments that may resemble true exper-
iments.
Compare a group affected by the reform ( ) to a group not affected
(). Let and denote before and after the reform.
The effect on can be estimated by the difference-in-differences
∆ −∆ = [ − ]− [ − ]
A before-after estimator ∆ is biased by time effects. A group
comparison − is biased by group effects. The dif-in-dif removes
common (group-invariant) time effects and time-invariant group effects.
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REGRESSION FORMULATION OF DIF-IN-DIF
Time dummy = 1 if is after the reform. Treatment dummy
= 1 if individual belongs to the treatment group.
Regression framework:
= 0+1+2+3·+4x+
Without covariates x, 3 is the basic dif-in-dif estimate. Including
covariates can improve the basic dif-in-dif.
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PARALLEL TRENDS ASSUMPTION
Identification assumption of dif-in-dif:
All non-reform time effects must be the same for and , i.e. if not
for the reform the two groups would have been on parallel trends.
(When both and experience a policy change but of different size,
dif-in-dif is still possible. But this requires an extra assumption.)
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EISSA (1995)
Never published but a good example for teaching.
The Tax Reform Act of 1986 (TRA86) cut marginal tax rates atthe top much more than further down the distribution.
The jointness of the US income tax implies that wives of rich husbandsexperienced larger tax cuts than wives of not-so-rich husbands.
Treatment/control assignment based on (husband’s earnings + family
non-labor income). -group = wives at the 99th percentile, -group =
wives at the 75th percentile.
Uses a dif-in-dif comparing changes in labor supply for and frombefore the reform (1985) until after the reform (1989).
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THE TAX REFORM ACT OF 1986
Source: Eissa (1995)( )
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MARGINAL TAX RATESFOR TREATMENTS AND CONTROLSFOR TREATMENTS AND CONTROLS
Source: Eissa (1995)
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DIFFERENCE-IN-DIFFERENCES:LABOR FORCE PARTICIPATIONLABOR FORCE PARTICIPATION
Source: Eissa (1995)
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DIFFERENCE-IN-DIFFERENCES:HOURS WORKED CONDITIONAL ON PARTICIPATIONHOURS WORKED CONDITIONAL ON PARTICIPATION
Source: Eissa (1995)
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LABOR SUPPLY ELASTICITIES
Relate dif-in-dif for labor supply to dif-in-dif for (1− ):
∆ −∆
∆(1− )(1− )−∆(1− )(1− )
Elasticity of labor force participation is 0.5. Elasticity of hours worked
is 0.4. Total elasticity is 0.9.
Large elasticities but also large standard errors → effects not statisti-
cally significant.
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ISSUES WITH EISSA’S APPROACH
1. The parallel trends assumption:
(a) -group starts from a lower level than the -group ⇒ -group
less able to absorb an upward trend in female labor supply.
(b) Alternative story: trend towards "power couples" in late 80s.
2. / assignment is not clean as TRA86 affected both groups
→ dif-in-dif requires homogeneous responsiveness for and .
3. Identification strategy requires no cross-substitutability in spousalleisures, which is very strong.
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NON-PARALLEL TRENDS?
1. Use data from periods prior and subsequent to the policy change:
(a) Do a placebo dif-in-dif for non-reform periods. If it is non-zero,then dif-in-dif is tenuous.
(b) Do a triple-dif = dif-in-dif of interest — placebo dif-in-dif.
(c) Plot longer time series of outcomes for and to see if "some-thing different" happens around the reform.
2. Plotting the time-series from 1979-1998, Liebman and Saez (2006)
show that Eissa’s results are not robust.
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TRANSFERS AND LABOR SUPPLY:IN-WORK BENEFITS
Transfers which are conditional on labor force participation.
They are typicallymeans-tested [targeted to low earnings/assets] andcategorical [targeted to single mothers].
Examples:
1.Earned Income Tax Credit (EITC) in the U.S. A cash transferprovided through the tax system.
2.Working Families Tax Credit (WFTC) in the U.K. is broadlysimilar to the EITC.
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fixedcost
LABOR SUPPLY RESPONSES TO THE EITC
hours worked h
consumption c
Non-EITC budget
phase-in plateau phase-out
EITC
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fixedcost
LABOR SUPPLY RESPONSES TO THE EITC
hours worked h
consumption c
Non-EITC budget
phase-in plateau phase-out
EITC
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fixedcost
LABOR SUPPLY RESPONSES TO THE EITC
hours worked h
consumption c
Non-EITC budget
phase-in plateau phase-out
EITC
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fixedcost
LABOR SUPPLY RESPONSES TO THE EITC
hours worked h
consumption c
Non-EITC budget
phase-in plateau phase-out
EITC
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EISSA & LIEBMAN (1996)
Use a dif-in-dif to estimate the effect of the EITC expansion in TRA86
on labor force participation and hours worked for single mothers.
Assignment to treatments and controls:
1. T= single women with children, C= single women without children.
2. T = single women with children and low education, C = single
women without children and low education.
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EITC BEFORE AND AFTER TRA86
Source: Eissa and Liebman (1996)
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DIFFERENCE-IN-DIFFERENCES:LABOR FORCE PARTICIPATION RATES OF SINGLE WOMENLABOR FORCE PARTICIPATION RATES OF SINGLE WOMEN
Source: Eissa and Liebman (1996)
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PARTICIPATION RATES OF SINGLE WOMEN 1981-1992
All Unmarried Females
Source: Eissa and Liebman (1996)
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PARTICIPATION RATES OF SINGLE WOMEN 1981-1992
Unmarried Females With Less Than High School Education
Source: Eissa and Liebman (1996)
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FINDINGS AND ISSUES
EL96 find large participation effects, no significant hours-of-work effects.
Using single women without children as a control for single women with
children is problematic, especially with regards to the parallel trends
assumption.
Robustness checks:
• Treatment-control assignment that exploits EITC means-testing:single mothers with low vs. high education→ no significant effect.
• Longer time series plot of participation rates across treatment andcontrol groups→ only moderately convincing.
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OVERVIEW OF EITC LABOR SUPPLY STUDIES
• Eissa-Liebman (1996): effect on single mothers using TRA86 as aquasi-experiment. Large participation effect, no hours-of-work effect.
•Meyer-Rosenbaum (2001): effect on single mothers using the 86, 90,and 93 reforms as quasi-experiments. More variation than EL96, but
complications due to welfare reform. Large participation effect.
• Eissa-Hoynes (2004): effect on married couples with low earnings.Jointness of EITC discourages participation of married women.
⇒ consensus that extensive responses aremore important than intensive
responses. But this view might need revision in light of recent work.
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CURRENT RESEARCH FRONTIER
Survey data are out; large administrative datasets are in.
Quasi-experimental work based on clear and sharp identification.Effects should be visible in graphs!
Combines reduced-form strategies (credible identification) with more
structural approaches (link to theory and welfare analysis). Estimation
of sufficient statistics for welfare analysis.
Distinction between observed and structural elasticities due tooptimization frictions (adjustment costs, inattention, etc.).
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RECENT QUASI-EXPERIMENTAL APPROACHES
Difference-in-differences using administrative data over long timeperiods allowing for graphical identification.
Bunching approaches that exploit discontinuous jumps in marginaltax rates (kinks) or discontinuous jumps in tax liability (notches).
Regression Discontinuity Design (RDD) andRegression KinkDesign (RKD).
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RECENT PAPERS
•Bunching approaches:— Saez (AEJ-Pol 2010)— Chetty, Friedman, Olsen, and Pistaferri (QJE 2011)—Kleven and Waseem (QJE 2013)— Chetty, Friedman, Saez (AER 2013)
—Kleven (ARE 2016)
•Difference-in-differences:—Kleven, Landais, and Saez (AER 2013)—Kleven, Landais, Saez, and Schultz (QJE 2014)
•Regression Discontinuity Design:— Saez, Matsaganis, and Tsakloglou (QJE 2012)
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BUNCHING AT KINK POINTS
In the old debate (Hausman vs. Heckman), bunching was seen as a
purely technical issue in the estimation of labor supply responses.
But bunching provides direct and compelling evidence of a labor supply
response to the marginal tax rate.
To detect bunching precisely, administrative data are crucial.
Saez (2010) shows that excess bunching around kinks can be used toidentify the compensated elasticity of labor supply/earnings.
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SAEZ (2010): KINK ANALYSIS
Utility ¡ − ()
¢where is before-tax earnings and is ability.
Linear tax system () = · ; smooth ability distribution⇒ smooth earnings distribution with density 0 ().
Introduce a (small) kink by increasing the MTR from to + at the
cutoff ∗.
This kink produces bunching at ∗ by all individuals who had incomes inthe interval [∗ ∗ + ∗] prior to the kink. Individual H is the marginalbuncher who reduces his income by ∗ in response to the kink.
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INDIFFERENCE CURVES AND BUNCHING
Source: Saez (2010)
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DENSITY DISTRIBUTIONS AND BUNCHING
Source: Saez (2010)
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SAEZ (2010): KINK ANALYSIS
The elasticity of earnings with respect to the marginal net-of-tax rate
can be inferred from the marginal buncher H.
For this individual, the income cutoff ∗ represents a tangency pointbetween the indifference curve and the upper part of the budget set
⇒ response ∗ is like an interior response.
For a small kink, the earnings elasticity is given by
=∗∗
(1− )= [0 (
∗) · ∗] (1− )
where = 0 (∗) ∗ is the total number of bunchers.
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WHICH ELASTICITY CONCEPT?
A kink does not change the tax burden on inframarginal units of income
below ∗
⇒ a small kink does not change the average tax rate over the range
[∗ ∗ + ∗]
⇒ the response ∗ is driven by a change in the marginal tax rate withno change in the average tax rate (i.e., no income effect), and therefore
is the compensated elasticity.
Very large kinks may have income effects in which case will be a mix
of the compensated and uncompensated elasticities.
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ESTIMATING EXCESS BUNCHINGUSING AN EMPIRICAL DENSITY DISTRIBUTIONUSING AN EMPIRICAL DENSITY DISTRIBUTION
Source: Saez (2010)
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EMPIRICAL IMPLEMENTATION
Counterfactual density 0 (∗) and bunching is estimated from the
observed density, dropping observations right around the bunch.
Basic method by Saez (2010) assumes a uniform counterfactual density
in a small interval around the kink.
Refinement by Chetty et al. (2011) allows for curvature by fitting a
flexible polynomium to the observed distribution.
Standard errors can be obtained using the delta method or a bootstrap
method.
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BUNCHING AND THE EITC
Source: Saez (2010)
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BUNCHING AND THE EITC
Source: Saez (2010)
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BUNCHING AND THE EITC:WAGE EARNERS VS. SELF-EMPLOYED
Source: Saez (2010)
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BUNCHING AND THE EITC:WAGE EARNERS VS. SELF-EMPLOYED
Source: Saez (2010)
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SAEZ (2010): RESULTS AND IMPLICATIONS
Clear bunching at the first EITC kink (for the self-employed) and the
first kink of the income tax. Both kinks are large and salient.
Otherwise, no evidence of bunching. Why?
Two potential explanations:
1. True structural elasticity is small.
2. True structural elasticity is not small, but the observed elasticity is
attenuated by optimization frictions.
Optimization frictions: (a) imperfect information, inattention, in-ertia, (b) adjustment costs and hours constraints.
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CHETTY ET AL. (2011): BASIC IDEA
Micro elasticity estimates are small, macro elasticity estimates are large:
•Micro estimates are attenuated by frictions that prevent workers fromre-optimizing in response to small tax changes in the short run.
•Macro estimates are not attenuated by frictions, but they suffer fromidentification problems.
For welfare analysis and optimal policy, we are interested in the long-run
structural elasticity that is not attenuated by frictions.
Micro approach (ensuring identification) to analyze the role of frictions
for elasticity estimates.
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CHETTY ET AL. (2011): SETUP
• Firms offer jobs with fixed wage-hours packages
•Workers draw jobs from a distribution of wage-hours packages and
must pay search costs to re-optimize
• Not all workers are located at their individual optimum (without
search frictions)
• Two types of equilibrium: (i) competitive markets, (ii) collectivebargaining
• In both cases, the distribution of hours offered by firms must equalthe distribution of hours selected by workers after search is complete
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CHETTY ET AL. (2011): BUNCHING
With hours contraints, there are two ways to locate at the kink:
1. Individual bunching: workers search for jobs at the kink
2.Aggregate bunching: workers draw jobs at kink to begin with
• Such bunching may be generated by firms/unions tailoring joboffers to aggregrate worker preferences
• Signature of aggregate bunching: even workers who do not facethe kink bunch there
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CHETTY ET AL. (2011): PREDICTIONS
1. [Size] Larger kinks generate larger observed elasticities
• Larger kinks induce more workers to pay searchs cost and relocateto the kink
2. [Scope] Kinks that affect a larger number of workers generate largerobserved elasticities
• Firms/unions tailor jobs to aggregate preferences → more aggre-
grate bunching at common kinks
3. [Correlation] More aggregrate bunching in sectors with greaterindividual bunching
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CHETTY ET AL. (2011): DATA & VARIATION
Matched employer-employee administrative panel data for the full pop-
ulation of Denmark.
Very detailed tax return, labor market, and socio-demographic infor-
mation.
Sample restriction: wage earners aged 15-70, fully tax liable, years 1994-
2001→ about 20 million observations.
Quasi-experimental variation from large vs. small kinks in the Danish
income tax [and using tax reforms that move bracket cutoffs over time].
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Marginal Tax Rates in Denmark in 200060
020
4080
100 200 300 40050 150150 250 350Taxable Income (1000s DKR)
Mar
gina
l Tax
Rat
e (%
)
log(NTR) = -11%
log(NTR) = -33%
Note: $1
6 DKr
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Income Distribution for Wage Earners Around Top Kink (1994-2001)20
000
4000
060
000
8000
010
0000
-50 -40 -30 -20 -10 0 10 20 30 40 50
Taxable Income Relative to Top Bracket Cutoff (1000s DKr)
Freq
uenc
y
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Income Distribution for Wage Earners Around Top Kink (1994-2001)20
000
4000
060
000
8000
010
0000
-50 -40 -30 -20 -10 0 10 20 30 40 50
Taxable Income Relative to Top Bracket Cutoff (1000s DKr)
Freq
uenc
y
Excess mass BΔ
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Income Distribution for Wage Earners Around Top Kink (1994-2001)20
000
4000
060
000
8000
010
0000
-50 -40 -30 -20 -10 0 10 20 30 40 50
Taxable Income Relative to Top Bracket Cutoff (1000s DKr)
Freq
uenc
y
Excess mass (b) = 0.81 Standard error = 0.05
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1000
020
000
3000
0
1000
020
000
3000
0
-50 -40 -30 -20 -10 0 10 20 30 40 50
0Fr
eque
ncy
(mar
ried
wom
en)
Freq
uenc
y (s
ingl
e m
en)
(a) Married Women vs. Single Men
Taxable Income Relative to Top Bracket Cutoff (1000s DKr)
Married WomenExcess mass (b)= 1.79Standard error = 0.10
Single MenExcess mass (b) = 0.25Standard error = 0.04
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010
0020
0030
0040
00
020
0040
0060
0080
00
-50 -40 -30 -20 -10 0 10 20 30 40 50
(b) Teachers vs. MilitaryFr
eque
ncy
(teac
hers
)
Freq
uenc
y (m
ilita
ry)
Taxable Income Relative to Top Bracket Cutoff (1000s DKr)
TeachersExcess mass (b)= 3.54Standard error = 0.25
MilitaryExcess mass (b) = -0.12Standard error = 0.21
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Freq
uenc
y (a
ll w
age
earn
ers)
Freq
uenc
y (m
arrie
d w
omen
)0
1000
2000
3000
4000
6000
8000
1000
012
000
1400
0
210 220 230 240 250 260 270 280 290 300Taxable Income (1000s DKR)
All Wage Earners
Married Women
Taxable Income Distributions in 1994
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1000
2000
3000
0
4000
8000
1200
01995
210 220 230 240 250 260 270 280 290 300Taxable Income (1000s DKR)
Freq
uenc
y (a
ll w
age
earn
ers)
Freq
uenc
y (m
arrie
d w
omen
)
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1000
2000
3000
0
4000
8000
1200
01996
210 220 230 240 250 260 270 280 290 300Taxable Income (1000s DKR)
Freq
uenc
y (a
ll w
age
earn
ers)
Freq
uenc
y (m
arrie
d w
omen
)
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010
0020
0030
00
5000
1000
015
000
1997
210 220 230 240 250 260 270 280 290 300Taxable Income (1000s DKR)
Freq
uenc
y (a
ll w
age
earn
ers)
Freq
uenc
y (m
arrie
d w
omen
)
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010
0020
0030
00
4000
8000
1200
01998
210 220 230 240 250 260 270 280 290 300Taxable Income (1000s DKR)
Freq
uenc
y (a
ll w
age
earn
ers)
Freq
uenc
y (m
arrie
d w
omen
)
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010
0020
0030
0040
00
4000
8000
1200
01999
210 220 230 240 250 260 270 280 290 300Taxable Income (1000s DKR)
Freq
uenc
y (a
ll w
age
earn
ers)
Freq
uenc
y (m
arrie
d w
omen
)
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1000
2000
3000
4000
0
6000
1000
014
000
2000
210 220 230 240 250 260 270 280 290 300Taxable Income (1000s DKR)
Freq
uenc
y (a
ll w
age
earn
ers)
Freq
uenc
y (m
arrie
d w
omen
)
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1000
2000
3000
4000
6000
1000
014
000
2001
210 220 230 240 250 260 270 280 290 300Taxable Income (1000s DKR)
Freq
uenc
y (a
ll w
age
earn
ers)
Freq
uenc
y (m
arrie
d w
omen
)
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Distribution of Wage Earnings20
000
4000
060
000
8000
0
-50 -40 -30 -20 -10 0 10 20 30 40 50
Freq
uenc
y
Income Measure Relative to Top Bracket Cutoff (1000s DKR)
Excess mass (b) = 0.68Standard error = 0.05
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PREDICTION 1: SIZE OF TAX CHANGE
Larger kinks generate larger observed elasticities, because they induce
more workers to pay searchs cost and relocate to the kink.
Compare observed elasticities from bunching at the large top tax kink
and the small middle tax kink.
Auxiliary tests to make sure that a difference in observed elasticities is
indeed driven by differences in the size of the tax change rather than
heterogeneity in elasticities by income level or tax rate level.
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4000
060
000
8000
010
0000
1200
00
-50 -40 -30 -20 -10 0 10 20 30 40 50
Middle Tax Kink: All Wage Earners, Taxable Income Distribution
Excess mass (b) = 0.06Standard error = 0.03
Predicted excess mass = 0.16Standard error = 0.01
Taxable Income Relative to Middle Bracket Cutoff
Freq
uenc
y
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5000
060
000
7000
080
000
9000
010
0000
-50 -40 -30 -20 -10 0 10 20 30 40 50
Middle Tax Kink: All Wage Earners, Wage Earnings Distribution
Wage Earnings Relative to Middle Bracket Cutoff
Freq
uenc
y
Excess mass (b) = -0.06Standard error = 0.03
Predicted excess mass = 0.14 Standard error = 0.01
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1000
020
000
3000
040
000
-50 -40 -30 -20 -10 0 10 20 30 40 50
Middle Tax Kink: Married Women, Taxable Income Distribution
Taxable Income Relative to Middle Bracket Cutoff
Freq
uenc
y
Excess mass (b) = 0.06Standard error = 0.03
Predicted excess mass = 0.35Standard error = 0.02
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Switchers from Top Tax to Middle TaxFr
eque
ncy
(Mid
dle
Tax)
Taxable Income Relative to Bracket Cutoff
Freq
uenc
y (T
op T
ax)
050
0010
000
1500
020
000
5000
1000
015
000
2000
0
-25 -15 -5 5 15 25
Excess mass (b) = 0.54Standard error = 0.08
Excess mass (b) = 0.06Standard error = 0.07
Middle Tax, year t+2Top Tax, year t
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Observed Elasticity vs. Size of Tax Change
Log Change in Net-of-Tax Rate
Obs
erve
d E
last
iciti
es
0 10% 20% 30%5% 15% 25%
0
0.005
0.01
-0.005
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PREDICTION 2: SCOPE OF TAX CHANGE
Kinks that affect a larger group of workers generate larger observed
elasticities as firms/unions tailor jobs to aggregate worker preferences.
Variation in the size of the group affected by a kink:
Variation in deductions and non-wage income across workers creates
variation in the effective location of the top bracket cutoff [i.e., the
wage income needed to locate at the kink].
Consider two different effective locations of the top tax kink:
• Statutory top tax kink [faced by 60% of population]
• “Pension kink” [faced by 2.5% of population]
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010
2030
40
-50000 0 50000
Distribution of Net Deductions
Net Deduction (DKr)
Freq
uenc
y
Indivs making pension contribs.Indivs with non-wage income
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05
1015
20
20000 30000 40000 50000
Distribution of Net Deductions Given Deductions > DKr 20,000
Net Deduction (DKr)
Freq
uenc
y
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050
010
0015
00
-50 -40 -30 -20 -10 0 10 20 30 40 50
Wage Earnings Relative to Statutory Kink (1000s DKR)
Freq
uenc
y
Wage Earnings Distribution: Teachers
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020
0040
0060
0080
0010
000
-50 -40 -30 -20 -10 0 10 20 30 40 50
Wage Earnings Relative to Statutory Kink (1000s DKR)
Freq
uenc
y Wage Earnings Distribution: Teachers with Deductions > DKr 20,000
This groupstarts paying top tax here
This groupstarts paying top tax here
This groupstarts paying top tax here
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Wage Earnings Relative to Pension Kink (1000s DKR)
Freq
uenc
y Wage Earnings Around Pension Kink: Deductions > 20,000
2000
2500
3000
3500
4000
4500
-50 -40 -30 -20 -10 0 10 20 30 40 50
Excess mass (b) = 0.70Standard error = 0.20
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Wage Earnings Relative to Pension Kink (1000s DKR)
Freq
uenc
y Wage Earnings Around Pension Kink: Deductions Between 7,500 and 25,000
2000
3000
4000
5000
-50 -40 -30 -20 -10 0 10 20 30 40 50
Excess mass (b)= -0.01Standard error = 0.15
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Wage Earnings Relative to Statutory Kink (1000s DKR)
Freq
uenc
y Wage Earnings Around Statutory Kink: Deductions Between 7,500 and 25,000
2500
3000
3500
4000
4500
5000
-50 -40 -30 -20 -10 0 10 20 30 40 50
Excess mass (b)= 0.56Standard error = 0.10
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0.0
05.0
1.0
15.0
2.0
25
.45 .5 .55 .6 .65 .7Fraction of Group with |Net Deductions| < 7500
Obs
erve
d E
last
icity
from
Bun
chin
g at
Top
Kin
kObserved Elasticities vs. Scope of Tax Kink
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SELF-EMPLOYED INDIVIDUALS
Thus far, we have looked only at wage earners
The self-employed do not face search frictions or hours constraints
• They can easily adjust reported earnings either by changing laborsupply or by avoidance/evasion
The self-employed serve as a “placebo test” for the findings
• Three predictions should not hold for the self-employed
• Size and scope of tax change should not matter
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020
000
4000
060
000
-50 -40 -30 -20 -10 0 10 20 30 40 50
Excess mass (b) = 18.42Standard error = 0.42
Freq
uenc
y Self-Employed: Taxable Income Distribution around Top Tax Cutoff
Taxable Income Relative to Top Bracket Cutoff (1000s DKr)
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4000
6000
8000
1000
012
000
-50 -40 -30 -20 -10 0 10 20 30 40 50
Excess mass (b)= 1.44Standard error = 0.10
Freq
uenc
y Self-Employed: Taxable Income Distribution around Middle Tax Cutoff
Taxable Income Relative to Top Bracket Cutoff (1000s DKr)
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800
1000
1200
1400
1600
1800
-50 -40 -30 -20 -10 0 10 20 30 40 50
Excess mass (b)= 0.22Standard error = 0.47
Self-Employment Income Relative to Statutory Top Tax Cutoff (1000s DKr)
Freq
uenc
y Self-Employment Income Around Statutory Kink: Deductions > 20,000
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0.1
.2.3
.4.5
.1 .2 .3 .4
Obs
erve
d E
last
icity
fro
m B
unch
ing
at T
op K
ink
Self-Employed: Observed Elasticities vs. Scope of Tax Changes
Fraction of Group with |Net Deductions| < 7500
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CHETTY ET AL. (2011): CONCLUSIONS
• Frictions due to search costs and hours constraints attenuate short-run behavioral responses to taxation
— Size and scope of tax variation matter for the observed elasticity
• Some notes and caveats:— For wage earners, the observed elasticity is tiny even at the largetop kink [size effect on elasticity is extremely small].
— For the self-employed, the small-kink elasticity is also smaller thanthe large-kink elasticity [size effect even when search costs and
hours constraints shouldn’t matter].
— Top and middle kinks differ in other dimensions than size.
—A broader view on frictions (inattention, inertia, etc.).
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KLEVEN & WASEEM (2013): NOTCHES
Previous papers: observed elasticity 6= structural elasticity due tofrictions, but the true structural parameter is not identified.
This paper develops a method to identify the amount of friction andthe structural elasticity using notches.
Notches = discontinuities in the choice sets of individuals or firms.
Notches are conceptually different from kinks = discontinuities in the
slope of choice sets.
Application to income tax notches in Pakistan.
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KLEVEN & WASEEM (2013): NOTCHES
Consider a notch where income tax liability increases discretely at an
earnings cutoff.
Prediction 1: excess bunching just below cutoff, hole above cutoff.
Prediction 2 (no frictions): strictly dominated region just abovethe cutoff should be empty in a frictionless world under any preferences.
Methodology:
1. Bunching identifies the observed elasticity
2. Density mass in dominated region identifies the amount of friction
3. Combination of (1)-(2) identifies the structural elasticity
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KLEVEN & WASEEM (2013): NOTCHES VS KINKS
Smallness of bunching at kinks has two possible interpretations:
1. Small structural elasticities and small frictions
2. Large structural elasticities and large frictions
Cases 1 & 2 are observationally equivalent for kinks (same bunching),
but not for notches (same bunching, different hole).
Notches separately identifies observed and structural elasticities by us-
ing two moments (bunching and hole), whereas kinks provide only one
moment (bunching) and identifies only the observed elasticity.
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PAKISTAN INCOME TAX SCHEDULES
05
1015
2025
Ave
rage
tax
rate
(%
)
100 200 300 400 500 600 700 800 900 1000 1100 1200 1300Taxable Income in PKR 000s
Wage Earners (2006−07)Self−Employed Individuals (2006−09)
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BEHAVIORAL RESPONSES TO A TAX NOTCH:BASELINE MODEL
Consumptionz - T(z)
Earnings z
Individual Lindiff. curve
Individual Hindiff. curves
slope 1-t
slope 1-t- tΔ
notcht·z*Δ
z* z*+ΔzD z*+Δz*zI
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EFFECT OF NOTCH ON EARNINGS DENSITY:BASELINE MODEL
Density
Earnings z
post-notch density
pre-notch density
bunching
densityhole
z* z*+Δz*zI
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EFFECT OF NOTCH ON EARNINGS DENSITY:BASELINE MODEL SIMPLIFIED
Density
Earnings
post-notch density
pre-notch density
bunching
z* z*+Δz*
dominatedregion
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EFFECT OF NOTCH ON EARNINGS DENSITY:HETEROGENEITY IN ELASTICITIES
Density
Earnings
post-notch density
pre-notch density
bunching
z*
dominatedregion
e is too lowfor bunching
z*+Δze*
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EFFECT OF NOTCH ON EARNINGS DENSITY:OPTIMIZATION FRICTIONS
Density
Earnings
post-notch density
pre-notch density
bunching
z*
dominatedregion
e is too lowfor bunching
z*+Δze*
frictions are toohigh for bunching
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EFFECT OF NOTCH ON EARNINGS DENSITY:MEASURING FRICTIONS
Density
Earnings
post-notch density
pre-notch density
bunching
z*
dominatedregion
z*+Δze*
share a*
share 1-a*
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OBSERVED VS. STRUCTURAL ELASTICITY
Assuming quasi-linear utility with constant elasticity , the indifference
condition for the marginal buncher implies
∆∗
∗=
µ
∆
1−
¶; lim
→0∆∗ = ∆
Observed elasticity based on ∆∗ = 0(∗)
.
Structural elasticity based on ∆∗ = (1−∗)0(∗)
.
(1− ∗) = bunching scaled by the hole in the dominated range= amount of bunching if individuals overcame adjustment costs.
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ESTIMATING THE COUNTERFACTUAL DENSITYUSING THE EMPIRICAL DENSITY
Density
Earnings zz*zL zU
exc uded rangel
dominatedrange
empiricaldensity h(z)
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ESTIMATING THE COUNTERFACTUAL DENSITYUSING THE EMPIRICAL DENSITY
Density
Earnings z
empiricaldensity h(z)
z*zL zU
exc uded rangel
dominatedrange
counterfactualdensity h (z)0
share a* ofcounterfactual(frictions)
bunching B
missing mass M = B
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BUNCHING, HOLE & FRICTIONS:SELF-EMPLOYED (500K NOTCH)
zUzL
b = 5.52(0.38)a* = 0.51(0.02)zU = 540.0(9.9)
dominatedrange
500
1000
1500
0N
umbe
r of
taxp
ayer
s
425 450 475 500 525 550 575Taxable income in PKR 000s
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BUNCHING, HOLE & FRICTIONS:WAGE EARNERS (600K NOTCH)
zUzL
b =0.80(0.09)a* =0.91(0.01)zU =633.0(16.4)
dominatedrange50
010
0015
000
Num
ber
of ta
xpay
ers
525 550 575 600 625 650 675Taxable income in PKR 000s
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KLEVEN-WASEEM (2013): EMPIRICAL RESULTS
1. Observed bunching at notches is large and sharp.
2. Optimization frictions are also very large (majority of taxpayers in
dominated ranges are unresponsive).
3. Combination of 1 & 2 implies that the frictionless earnings response
to notches is extremely large.
4. But the structural elasticity driving this response is nevertheless
modest.
5. This highlights the inefficiency of notches: by creating extremely
strong price distortions, they induce large behavioral responses even
when structural elasticities are small.