Frictions and the elasticity of taxable income: evidence from
bunching at tax thresholds in the UKI
Stuart Adama , James Brownea , David Phillipsa , Barra Roantreea
a
The Institute for Fiscal Studies, 7 Ridgmount Street, London WC1E 7AE
Abstract
The standard neoclassical model of labour supply predicts that individuals should bunch at
discontinuities and convex kink-points in the budget set, such as those created by progressive
tax systems. Saez (2010) showed that the extent of this bunching can be used to estimate
the elasticity of taxable income, a parameter that under certain conditions measures the
efficiency costs of taxation. However, optimising frictions might attenuate reduced-form
estimates of the ETI (or the elasticity of labour supply) away from the parameter relevant
for responses in other settings (e.g. for a smaller tax change). This paper provides evidence
from bunching at tax thresholds in the UK that such frictions are substantial, and could
help reconcile macro and micro estimates of the elasticity of labour supply. We also find
significant heterogeneity in frictions that corresponds closely to well-documented differences
in elasticity estimates, raising the question whether the literature identifies differences in
preferences or frictions between men and women.
Keywords: Social security, income tax, elasticity of taxable income, optimising frictions
JEL: H21, H24, J22, J23
DRAFT WORKING PAPER: DO NOT CITE WITHOUT PERMISSION
I
The authors would like to thank Richard Blundell, Raj Chetty, Julien Grenet, Luke Haywood, Henrik
Kleven, Ian Preston, and Emmanuel Saez for their helpful comments, but in particular colleagues at the
IFS, DIW Berlin, CPB and IPP. The authors gratefully acknowledge funding from the ESRC Centre for
the Microeconomic Analysis of Public Policy based at the Institute for Fiscal Studies (ES/M010147/1) and
ESRC Research Grant ES/K006185/1. Data from the New Earnings Survey is produced by the Office for
National Statistics and supplied by the Secure Data Service at the UK Data Archive. Data from the Survey
of Personal Incomes is Crown Copyright material and has been used with the permission of the Controller
of HMSO and the Queens Printer for Scotland.
Preprint submitted to IFS working paper series
February 26, 2016
1. Introduction
Income tax and social security contributions are major sources of government revenue in
advanced economies, with the two combined raising just over half of total tax revenues in
2013.1 How individuals respond to such taxes on personal income is of enormous importance
for policy making: the efficiency costs of taxation are highly dependent on the magnitude of
these responses, as is the revenue yield from tax reforms. For example, the UK government’s
central estimate of the yield from increasing the top rate of income tax from 40 to 50
percent in 2010-11 fell from £6.5 billion to £2.7 billion once it allowed for a modest degree
of behavioural response (Brewer et al., 2012).
There is a vast literature estimating the responsiveness of agents to taxes on personal
income, as indicated by reference to any of the numerous survey papers on labour supply
(Blundell and Macurdy, 1999; Blundell et al., 2007; Keane, 2011; Meghir and Phillips, 2011).
The elasticity of taxable income (ETI) - how taxable income changes in response to a change
in the (net-of) tax rate - has come to hold particular importance in the public economics
literature as, under certain conditions, it is a sufficient statistic that measures the excess
burden of taxes on income (Feldstein, 1999; Chetty, 2009). While most of the literature has
sought to estimate the ETI using aggregated time-series data (Feldstein, 1995) or individuallevel panel data (Auten and Carroll, 1999; Gruber and Saez, 2002), Saez (2010) showed
that the amount of bunching at convex kink-points in individuals’ budget set - such as
those created by a progressive tax schedule - can also be used. This approach exploits the
growing availability of administrative data (which is subject to less measurement error than
household surveys) and does not require parametric controls for mean reversion or secular
income trends to which estimates are quite sensitive (Saez et al., 2012).
This paper investigates the responsiveness of individuals to taxes on personal income
exploiting variation induced by the UK tax schedule, which creates strong incentives for
individuals to adjust their taxable income, building on the literature in a number of ways.
Firstly, whereas the existing literature is focused on the earnings responses of high earners
1
See OECD Revenue Statistics at http://dx.doi.org/10.1787/888933276537
2
(Auten and Carroll, 1999; Gruber and Saez, 2002; Slemrod and Kopczuk, 2002; Brewer et
al., 2012; Kleven and Waseem, 2013) and those filling tax returns (Saez, 2010; Chetty and
Saez, 2013; le Maire and Schjerning, 2013), we investigate responses to taxes for a broad
range of taxpayers at various points across the earnings distribution, whose behaviour is less
well understood despite constituting an important group for welfare analysis of tax policy.
In line with the literature, we find that company owner-managers (who can easily control
the timing of their dividend income) and the self-employed (whose tax returns are subject
to audit with low probability) are particularly responsive to taxes. However, the majority
of taxpayers that we consider have limited ability to manipulate their incomes, as their tax
liabilities are reported to authorities and deducted from income at source by employers. Of
these, we find that only part-time employees, particularly those in the retail and hospitality
sectors, respond to taxes.
The reason for this is our second contribution: we show that most workers face substantial frictions in adjusting their taxable income which are likely to significantly attenuate
elasticities obtained from the reduced-form estimation of hours or taxable income functions,
as suggested by Chetty (2012). Frictions of the magnitude we identify (in excess of 2 percent
of gross earnings for full-time employees at median earnings) could play an important role
in reconciling micro and macro elasticities of labour supply, as suggested by Chetty (2012).
We also find significant heterogeneity in frictions that corresponds with well-documented
differences in estimates of the elasticity of labour supply between men and women. This
raises the questions whether the larger elasticities found in the literature for women is due
to differences in underlying preferences or frictions. Increases in the share of women working
full rather than part-time (and so facing higher optimising frictions) might then help explain
why Blau and Kahn (2007) (among others) find declines in the elasticity of women’s labour
supply over time.
Finally, the pattern of results we document - with much less bunching at new and nontransparent tax thresholds than at long established ones - is suggestive of a role for salience
and learning costs in determining the responsiveness of agents to taxes. This adds to a
growing literature which finds that individuals react differently to salient and non-salient
3
taxes, with consequences for the optimal design of taxes (Chetty et al., 2009; Reck, 2014).
The rest of this paper proceeds as follows. Section 2 sets out the theoretical framework
that leads to the prediction that agents should bunch at tax thresholds. Section 3 discusses
the institutional setting, namely the kinks and discontinuities in the UK tax schedule that
we exploit. Section 4 describes our data before we set out the results of our analysis in
Section 5. Section 6 concludes.
2. The Bunching Framework
The basic neoclassical model of labour supply predicts that, if preferences are convex and
smoothly distributed in the population, individuals will bunch at convex kink-points and
notches in the budget set. A convex kink is defined by an increase in the effective marginal
rate of tax at some threshold, a feature typical of progressive systems of taxation (and some
in-work benefits) where those with higher levels of income face higher marginal rates. A
notch is defined by a change in the effective average rate of tax at a threshold (which may
or may not be accompanied by a change in the marginal rate), most commonly found where
individuals face a discrete jump in tax liabilities (or benefit withdrawal) at some level of
income. Although not explored in this paper, notches are also a feature of benefit systems
where individuals receive a higher payment above some threshold: e.g. couples in the UK
claiming Working Families Tax Credit (an in-work benefit similar to the EITC claimed by
low-income workers in the US) receive a premium for working more than 30 hours per week.
We now outline an approach that exploits bunching at convex kink-points and notches
to estimate an elasticity of taxable income.
2.1. Bunching at kink-points
Consider a simple frictionless world where individuals have preferences decreasing in pretax income z (because earning income is costly in terms of leisure forgone) but increasing in
post-tax income z − T (z) which allows consumption, where T (z) is a tax function and there
is heterogeneity in ability (n), described by the density distribution f (n). If preferences, the
distribution of abilities and the tax schedule T (z) = T0 (z) are all smooth then the income
4
distribution h0 (z) will also be smooth, as depicted by the dotted black line in Figure 1a.
This is as each individual of ability n will work such that their indifference curve is at a
tangent to their budget set, as for individual H in Figure 1b who has pre-tax income of
z0 = k + ∆z.
If instead of being smooth, the tax schedule is kinked such that T (z) = T1 (z) = τl ∗
z + (τh − τl )(z − k)1[z > k] for τh > τl , the income distribution h1 (z) will exhibit a spike
at and a lower density above the kink-point k. This is as individuals who would otherwise
have located above k reduce their incomes in response to the higher tax rate τh . Specifically,
letting individual H be the person who bunches at the kink point (z1 = k) with the highest
level of income under the smooth tax schedule (z0 = k + ∆z), all individuals who under
the smooth tax schedule T0 (z) located on the interval (k, k + ∆z) will instead bunch at the
kink point k while all individuals with income above k + ∆z will reduce their earnings but
remain in the upper tax bracket. This leftwards shift in the density above k is shown by the
blue line in Figure 1a, with the number of individuals choosing to locate at the kink-point
k given by:
k+∆Z
Z
B=
h0 (z)dz
(1)
k
We call individual H the ‘marginal buncher’, whose earnings response ∆z is an interior
response between two tangency points, as shown in Figure 1b: the indifference curves H 1
and H 2 are tangent to the budget set at earnings levels k + ∆z and k respectively. By the
definition of the elasticity of income with respect to the net-of-tax rate (the ETI), we have
a relationship between this earnings response and known parameters of the tax system:
e≡
∆z 1 − τ
∆z (1 − τl )
=
z ∆τ
k τh − τl
(2)
The bunching approach exploits the fact that - as shown by Saez (2010) - this earnings
response ∆z is also proportional to the mass observed at k. That is, we have:
Z
k+∆z
h0 (z)dz ≈ h0 (k)∆z
B=
k
5
(3)
Figure 1: Effect of a kinked tax schedule on:
(a) the distribution of gross earnings
B
With kinked tax schedule
Density distribution
With smooth tax schedule
k
k + Δz
Before-tax income z
(b) individuals’ budget sets
After--tax income, c
H1 H2
Kinked tax schedule
Smooth tax schedule
0
k
k + Δz
Before-tax income , z
6
an approximation that links the ETI to the unknown, but estimable, entity
B
h0 (k)
via the
earnings response ∆z.2 The next step in the approach is to estimate the unobserved counterfactual density h0 (k) and so B̂ ≡
B
,
ĥ0 (k)
the excess mass or bunching at the kink-point,
which we then substitute for ∆z in equation 2.
2.2. Estimating the counterfactual density
We estimate the counterfactual density following Chetty et al. (2011), fitting a flexible
polynomial to the observed distribution of earnings, excluding observations in a window
[−R, Ru ] around the threshold k. To account for the fact that individuals come from above
the kink-point, we impose the integration constraint that the area under the counterfactual
distribution of earnings must equal the area under the empirical distribution, by increasing
the excluded area above the threshold and repeatedly estimating the polynomial. An estimate of bunching at the kink-point is then obtained by subtracting the counterfactual from
the empirical distribution over the interval [−R, R].
Formally, the counterfactual distribution Ĉj is defined as the fitted values from the
regression:



BˆN

Cj 1 + 1[j > R] R
P CˆJ

j=−R
2R+1
q
R
 X
X

i
γi 1[zj = i] + j
βi (zj ) +
=
 i=0
k=−R
(4)
P
where zj is the number of individuals in a small bin of earnings, and BˆN = R
j=−R Cj −
PR
Ĉj = k=−R γˆk is the predicted excess mass at the threshold. This regression is iteratively
estimated as the dependent variable is a function of BˆN , which is in turn a function of the
estimated β̂i , recomputing βˆN using the estimated β̂i until a fixed point is reached. Standard
errors for the estimated bunching mass b̂ =
βˆN
Cˆj
j=−R 2R+1
PR
are obtained by using a parametric
bootstrap procedure, where a large number of draws from the estimated vector of errors j
in equation 4 are made (with replacement) to generate a distribution of b̂ estimates: the
2
This approximation assumes that the density h0 (z) is constant on the interval (k, k + ∆z) and simplifies
the analysis, but is unnecessary in general. See Saez (2010) for a fuller discussion.
7
standard error is then defined as the standard deviation of this distribution. Since the ETI
is just a function of b̂ and other parameters that we know with certainty (namely the width
of the bins, the kink point and the tax rates either side of the kink), if b̂ is statistically
significantly different from zero, the taxable income elasticity will be also.
2.3. Hetrogenous elasticities, income effects and optimisation frictions
The simple case outlined above describes a situation where all individuals have homogeneous preferences over consumption and leisure, implying there exists a single ETI in
the region of the kink-point. In reality, there will be heterogeneity in preferences and so a
distribution of ETIs. The bunching approach is easily generalisable to the case of heterogeneous elasticities: instead of a distribution of abilities f (n) and a distribution of earnings
h0 (z), consider a joint distribution of abilities and elasticities fˆ(n, e) and a joint distribution
of earnings and elasticities ĥ0 (z, e). We then have the earnings response of the marginal
buncher at each elasticity level (∆ze ) and an expression that links the observed bunching
mass B to the average earnings response E[∆ze ] and so the local average earnings elasticity:
Z Z
k+∆z
ĥ0 (z, e)dzde ≈ h0 (k)E[∆ze ]
B=
e
(5)
k
For both homogeneous and heterogeneous preferences, equation 2 holds only at a small
kink and assumes there are no income effects on the bunching interval (k, k + ∆z). In
such cases, the elasticity estimated is a compensated one, but at larger kinks it is necessary
to specify a parametric form for preferences. This provides a relationship between the
ETI and the earnings response of the marginal buncher, which as before is derived from
the amount of bunching observed at the kink-point and an estimate of the counterfactual
earnings distribution.
However, Chetty et al. (2011) argue that in the presence of optimising frictions, the
estimated elasticity does not coincide with any ‘structural’ elasticity related to individuals’
preferences. If, for example, workers face a fixed search cost to adjusting their earnings,
there will be some for whom the net utility gain from bunching is not positive. This will
8
serve to dampen the degree of bunching at the threshold, and so attenuate estimates of the
elasticity below the true parameter that explains how individuals respond to tax changes.
The estimated parameter is of limited interest as it understates responses to taxation in the
longer run when frictions dissipate or in a different setting: in the example above, as the set
of workers willing to incur the fixed adjustment cost and bunch at a kink-point is increasing
with the size of the kink, the presence of adjustment costs will mean that larger kinks will
generate larger estimates of the ETI even if the underlying preferences are identical.
More generally, there are many sources of frictions that can induce agents to deviate
from optimal choices besides adjustment costs: for example, constraints on hour choices,
inattention and inertia. These all drive a wedge between the ‘structural’ parameter and
the estimated elasticity derived from the amount of bunching at kink-points in the tax
schedule. Given an estimate of the elasticity from observed bunching at a kink-point and an
assumption about the optimising frictions people face, one could bound the unattenuated
structural elasticity. However, as Chetty (2012) shows, small frictions are sufficient to explain
the absence of or negligible bunching at kink-points in the US tax schedule. This limits the
usefulness of such bounds, as a small (reasonable) range of frictions can reconcile the observed
bunching at kink-points with a wide range of underlying structural elasticities.
2.4. Bunching at notches
Notches provide a more promising source of variation for the identification of structural
elasticities. This is because an upward jump in tax liabilities at a threshold creates a region
that no-one should choose to locate in save for frictions: an individual can increase both
consumption and leisure by reducing their earnings below the threshold. Kleven and Waseem
(2013) develop a framework for identifying the unattenuated structural elasticity, exploiting
variation created by notches to estimate the extent of frictions directly.
As before, the fundamental idea underlying this approach is to combine an estimate of
the earnings response of the marginal buncher with known parameters of the tax system
(here, the location and size of the notch) to identify the ETI. The dashed black line Panel (a)
in Figure 2 shows that in a frictionless world, a notch should result in sharp bunching below
9
the threshold N and zero-density in the dominated region (D) above N . The density should
then gradually converge back to the no-notch distribution (shown in blue), as heterogeneity
in elasticities means that there will be some less responsive individuals for whom bunching is
not optimal. The bunching mass is as before proportional to the average earnings response
across all elasticity levels E[∆z ] ≡ ∆z ∗ .
This earnings response can be linked to the local average earnings elasticity in two ways.
The first specifies a functional form for preferences, and then exploits the identity provided
by indifference of the marginal buncher between earnings levels N and N + ∆z ∗ . We follow
Kleven and Waseem (2013)3 in using an iso-elastic specification for utility
U (z, e, n) = z − T (z) −
n
z
.( )1+1/e
1 + 1/e n
1+1/e
1
∆T /N
1
1
1
=0
=⇒
1+
−
−
∗
∗
1 + ∆z /N
1−t
1 + 1/e 1 + ∆z /N
1+e
(6)
(7)
which characterises the relationship between the elasticity (e), the percentage earnings re∗
sponse ( ∆z
), and the percentage change in the average net-of-tax rate created by the notch
N
/N
). A consequence of adopting this iso-elastic specification for utility is that we assume
( ∆T
1−t
away income effects, which is unlikely to hold in the case of a notch (where average tax rates
jump up above the threshold). This biases the estimated elasticity downwards.
The second method uses a reduced-form approximation between the average earnings
response and the implicit marginal tax rate (τ ∗ ) that a notch creates between earnings
levels N and N + ∆z ∗ .4 In this paper, we use a similar approximation, specifically:
τ∗ =
T (k + ∆z ∗ ) − T (k)
∆t.(k + ∆z ∗ )
∆t.z ∗
=
t
+
≈
t
+
∆z ∗
δz ∗
∆z ∗
∗
∗
∗
∆z /z
(∆z /z ∗ )2
ˆR F =
≈
∆t∗ /(1 − t∗ )
∆t/(1 − t)
(8)
(9)
Because a notch will induce a larger earnings response than the implicit kink would, by
3
See pp. 672–676 of Kleven and Waseem (2013).
As Kleven (2016) notes, this will induce a form of aggregation bias as the average earnings elasticity
will in general differ from the elasticity at the average earnings response.
4
10
Figure 2: Bunching at a notch
(a) Frictionless model
Density with notch
Density distribution
No-notch density
N
N+D
Before tax income
(b) With optimising frictions
Density with notch
Density distribution
No-notch density
N
N+D
Before tax income
11
treating the earnings response as if it were generated by a kink we will overstate the ETI
using this method.
What notches provide that kinks do not is an additional empirical moment - the observed
density in the strictly dominated region above the notch - which we can use to measure the
attenuation bias from frictions. Specifically, if (1) the share of individuals at earnings level
z and elasticity level e who do not respond to the notch because of frictions φ (call this
a(z, e, φ)) and (2) the counterfactual density are both locally constant across the bunching
segment N + ∆z ∗ , then we have:
Z Z
N +∆z
B=
e
[1 − a(z, e, φ)].ĥ0 (z, e)dzde ≈ h0 (N ).[1 − a∗ (φ)].∆z ∗
(10)
N
This can be used to identify the average earnings response across all elasticity levels given an
estimate of the bunching mass B̂ ≡
B
ĥ0 (N )
(as before) and the share of constrained individuals
a∗ (φ) (from the mass observed in the strictly dominated region D above the notch). Kleven
and Waseem (2013) call this the ‘bunching-hole’ method, which will deliver a downwardly
biased estimate of the marginal buncher’s earnings response. This is because rather than
being locally constant (as assumed), the share of individuals prevented from bunching by
frictions is likely to be higher the further above the notch one goes (as the gain to bunching
is smaller). Our estimate â∗ (φ) used to scale the estimated bunching mass B̂ is taken from
the dominated region immediately above the notch (where the gain to bunching is largest)
and is therefore likely smaller than the ‘true’ a∗ (φ), biasing
B̂
(1−â∗ (φ))ĥ0 (N )
downwards.
Kleven and Waseem (2013) also propose a ‘convergence’ method for estimating the crucial
earnings response of the marginal buncher. This involves assuming all of the observed
mass in the interval [N, N + ∆z ∗ ] arises because of frictions, and none because of low
underlying elasticities. The unattenuated earnings response is then given by the point of
convergence between the counterfactual and empirical distributions. As this estimates the
average unattenuated earnings response with that of the most responsive individual, it can
be seen as an upper bound on the structural earnings response.
In summary, we have four ways of estimating the ETI from bunching at notches: the
12
bunching-hole or convergence method for estimating the local average earnings response,
which is then linked to the local average earnings elasticity using either the structural or
reduced-form approaches outlined above. We present estimates for each of these combinations in section 5.
3. Institutional Setting
The UK has two main personal direct taxes: income tax, paid by individuals on their
earned and unearned income, and National Insurance contributions (NICs), payable by employees, employers and the self-employed on earned income only. NICs notionally entitle
individuals to certain ‘contributory’ social security benefits. In practice, however, contributions paid and benefits received bear little relation to each other for any individual
contributor, so we treat NICs as an additional tax.
In fiscal year 2015–16, both income and NICs had piecewise linear schedules, and applied
above ‘tax free’ allowances at standard rates to a common annual upper limit of £42,380 per
year.5 However, the historic design of the two taxes differs significantly and provide multiple
non-linearities that we can exploit using the methods outlined in the previous section.
3.1. Income Tax
In 1973 a complicated array of surtaxes, reliefs, and allowances were consolidated to
form a unified income tax, which applied at a starting, a basic, and several higher rates to
income above a tax-free allowance, assessed - since 1990 - at the individual level. Successive
governments reduced these rates so that in 1992–93 there was a relatively simple regime with
four effective rates in operation: zero up to the tax allowance, 20% on the first £2,000-3,000
of income, 25% over a range that covered the majority of taxpayers and 40% for a small
group of those with high incomes.
5
Until 2009–10 - when the two thresholds were aligned - the threshold for NICs was set at a level just
below the threshold for income tax threshold, meaning that there was a short range of earned income
between these thresholds that was subject to a lower marginal tax rate than slightly lower or higher levels
of earnings.
13
Table 1: Income tax rates on earned income, 197879 to 201516
Fiscal year
1992–93 to
1996–97
1997–98 to
1999–2000
2000–01 to
2008–09 to
2010–11 to
2013–14 to
1995–96
1998–99
2007–08
2009–10
2012–13
2015–16
Starting rate
20
20
20
10
10
Basic rate
25
24
23
23
22
20
20
20
Higher rates
40
40
40
40
40
40
40–50
40–45
Note: Different tax rates have applied to dividends since 1993–94 and to savings income since 1996–97. The
basic rate of tax on savings income has been 20% since 1996–97, while the 10% starting rate (which was
largely abolished in 2008–09) continued to apply to some savings income until April 2015. The basic rate
of tax on dividends was 20% from 1993–94 to 1998–99 and has been 10% since 1999–2000, when the higher
rate of tax on dividends became 32.5%. However, an offsetting dividend tax credit means that the effective
tax rates on dividends have been constant at zero (basic rate) and 25% (higher rate) since 1993–94. The
additional tax rate on dividend income has been 37.5% since 2014–15, which is an effective rate of 30.56%
once the dividend tax credit is taken into account. When calculating which tax band different income sources
fall into, dividend income is treated as the top slice of income, followed by savings and then by other income.
Source: Tolleys Income Tax, various years.
The system was simplified further by the abolition of the starting rate in 2008–09 (to pay
for a cut in the basic rate) but reforms have since complicated the rate structure for those
with the highest incomes: from 2010–11, the tax-free personal allowance has been withdrawn
from those with incomes greater than £100,000, creating a band of income in which income
tax liability increases by 60 pence for each additional pound of income, while incomes above
£150,000 have been subject to an ‘additional’ rate (50% in the years we examine).
In short, the structure of income tax in the UK provides a number of non-linearities
which we can exploit using the methods outlined in section 2:
• A (convex) kink at the higher-rate threshold
• A (convex) kink at the personal allowance
• A (convex) kink at the starting-rate limit 1992–93 to 2007-08
• A (convex) kink at £100,000 since 2010-11
• A (convex) kink at £150,000 since 2010-11
14
• A (non-convex) kink where the tax-free personal allowance is fully withdrawn (around
£115,000) since 2010-11
3.2. National Insurance
NICs operated as a system of fixed-amount contributions until 1961, when they were
supplemented by earnings-related contributions for some employees. In 1975 this system was
replaced by flat-rate earnings related contributions (at a standard employee and a standard
employer rate) that applied to the entirety of earnings up to a ceiling called the Upper
Earnings Limit (UEL) once earnings exceeded a lower threshold called the Lower Earnings
Limit (LEL). This created a discontinuous jump in NICs liabilities (a notch) at the LEL,
and a strictly-dominated range of earnings above. The dashed grey line in Figure 3 shows
the NICs schedule for both employee (panel A) and employer (panel B) contributions as the
system stood in April 1984.
Reforms taking effect in October 1985 changed the system substantially. As shown by
the solid grey lines in Figure 3, the flat rate of employee and employer NICs were replaced
by a system of graduated contributions, where higher (marginal and average) rates applied
to the entirety of earnings once earnings exceeded higher thresholds.
Once earnings exceeded the LEL, employee NICs were levied at a rate of 5% on all
earnings, rather than at 9% as under the April 1984 system; in other words the size of
the notch at the LEL was reduced. However, two additional notches were introduced at
higher thresholds, so that the rates of employee NICs jumped to 7% and then 9%, with
the highest rate applying to all earnings up to the UEL. Likewise, once earnings exceeded
the LEL employer NICs were levied at 5% (on all earnings) rather lower than the 9 % rate
under the April 1984 system. In addition, three additional notches were introduced at higher
thresholds (at rates of 7%, 9% and 10.45%), and the cap was abolished so that the highest
rate of employer NICs applied even above the UEL.
Another reform, in October 1989, replaced the system of graduated employee contributions with a small entry fee at the LEL (equivalent to 2% of the LEL) and a single rate
that applied to earnings between the LEL and the UEL. However, the graduated system of
15
Figure 3: National Insurance contribution schedules, April 2014 prices
(a) Employee contributions
£100
1984-85
1986-87
1997-98
2014-15
£90
£80
NICs, £ per week
£70
£60
£50
£40
£30
£20
£10
£0
£0
£200
£400
£600
Gross weekly earnings
£800
£1,000
£800
£1,000
(b) Employer contributions
£100
1984-85
1986-87
1997-98
2014-15
£90
£80
NICs, £ per week
£70
£60
£50
£40
£30
£20
£10
£0
£0
£200
£400
£600
Gross weekly earnings
Note: Previous years’ thresholds have been uprated to April 2014 prices using the RPI. Assumes employee
contracted into State Earnings-Related Pension Scheme (SERPS) or State Second Pension (S2P). The 198485 schedule excludes the 1% National Insurance surcharge abolished in September 1984.
Source: HM Treasury, Financial Statement and Budget Report, various years; Tolleys National Insurance
Contributions, various years.
16
employer NICs with four notches remained in place, as shown by the dashed black lines in
Figure 3b.
The structure of NICs in place today (shown by the solid black line in Figure 3) is
the legacy of reforms that took effect between 1998 and 2003. This removed the remaining
notches from both employer and employee NICs, and now contains only kinks; that is changes
in marginal contribution rates. A main employee NICs rate (now 12%) applies on earnings
between a new Primary Threshold and the UEL, with a reduced rate (now 2%) applying to
earnings above this level. A single employer NICs rate (now 13.8%) applies on all earning
above a new Secondary Threshold, including earnings above the UEL.
To summarise, the design of NICs in the UK provides a number of kinks and notches
that create incentives for individuals to bunch at thresholds:
• A notch at the LEL from 1975–76 to 1998–99
• Multiple notches above the LEL from 1985–86 to 1988–89
• Multiple notches in the employer NICs schedule above the LEL: 1989–90 to 1998–99
• Kinks at the Primary and Secondary thresholds from 1999-2000
4. Data
This paper uses both administrative and survey data: respectively the Survey of Personal
Incomes (SPI) - a sample of UK income tax records held by HM Revenue and Customs
(HMRC) - and the New Earnings Survey (NES) - a mandatory employer survey carried out
annually since 1970.
The SPI includes information from the vast majority of taxpayers: those whose affairs
are dealt with exclusively through the Pay As You Earn (PAYE) system that deducts income
tax from earnings at source; those who submit a self-assessment tax return; and a few other
individuals who come into contact with HMRC because they have to claim back tax that
17
has been incorrectly deducted at source.6 Those with very high incomes are oversampled in
the data: the sampling fraction ranges from 1 in 100 for those with very high incomes to
1 in 200 for employees and pensioners with lower incomes. Around 680,000 individuals are
included each year from 1995–96 to 2010–11, though as the data are a repeated cross-section
of the taxpaying population, it is not possible to track the same individuals over time.7
The target sample frame of the NES is employees whose National Insurance number
(NIno) ends with a specific pair of digits.8 In principle, this should deliver a 1% random
sample of employees. In practice, it delivers a sample of around 0.7% of employees per year,
due to employer non-response and the exclusion of non-civilian employees. This is a much
larger sample than is available in other datasets (such as the Labour Force Survey or the
Family Resources Survey) and does not suffer from the same degree of measurement error,
as responses are provided by employers with reference to their payroll records (rather than
a household member by recall). Furthermore, it covers the period when the NICs schedule
contained the non-linearities that we are interested in exploiting, and captures pay over the
same horizon that NICs are assessed on (the employee’s pay-period, rather than annually
as for income tax).
However, some features of these data affect their use in our analysis. Firstly, the definition
of earnings that NICs is levied on is (slightly) broader than the earnings variable collected
in the NES: for example, the NICs base has included most benefits-in-kind since 1991 while
only gross earnings are recorded by the NES. This is unlikely to be a significant problem as
the differences between these bases is quite small in aggregate terms.9
Second, NICs (and income tax) are not the only deductions from earnings that people
6
Unusually by international standards, most employees in the UK have their exact tax liability deducted
from their earnings at source and never have to submit a tax return. HMRC estimates that out of around
30 million income taxpayers, 10.74 million taxpayers had to fill in a self-assessment tax return for 2012–13:
primarily the self-employed, those with significant unearned income and those with incomes over £100,000.
7
Data for 2008–09 are currently unavailable.
8
The use of a fixed pair of digits from 1975 onwards means that panel data covering up to 38 years of
individuals earnings can be constructed. As our focus in this paper is what we can learn from the crosssectional distribution of earnings around tax thresholds in particular years, we do not exploit the panel
dimension, but do so in ongoing work.
9
Class 1A NICs revenues in 2011-12, for instance were just 2% of class 1 employer NICs, which implies
that only a very small fraction of remuneration takes the form of benefits-in-kind liable to Class 1A NICs.
18
face. Most benefits in the UK are means-tested and depend on family circumstances - which
neither the NES or SPI contain information on - meaning that we do not know for sure
the effective marginal rates individuals in receipt of benefit face. We therefore calculate the
average tax rate due to other deductions (such as income tax and benefit withdrawal) faced
by people around the NICs thresholds using data from surveys with the requisite income
and socio-demographic data (such as the Family Expenditure Survey) and the Institute for
Fiscal Studies tax-benefit microsimulation model TAXBEN.
Two further issues related to the sampling frame used by the NES and are potentially
more problematic. First, individuals falling within the scope of the sample frame are identified using HMRC’s PAYE records.10 As it is not mandatory to operate PAYE on the
earnings of employees below the LEL (the threshold at which there was a discontinuous
jump in NICs liabilities), those with earnings below this threshold are less likely to be sampled. This could have the effect of reducing the amount of bunching that we observe at
the LEL and biasing estimated elasticities downwards. However, this does not appear to be
a significant problem in practice: employers seem to include all employees on their PAYE
scheme, even if they have earnings below the LEL. When we compare the distribution below
this threshold to that of a representative household survey (the Family Resources Survey)
which does not suffer from the same potential selection issues, we find that the two densities
look very similar.
Finally, the NES records earnings during the pay period covering a specified date in April
each year. The start of the fiscal year (when NICs thresholds and other parameters are by
default uprated with inflation) is April 6th, and hence there is little time for workers and
employers to adjust earnings in response to the NICs system in place.11
10
12
For this reason
Prior to 2004, individuals were identified from these records in late February or March, meaning those
who were not in employment at this time, or had changed jobs by April, were not captured in the sample.
Computerisation of PAYE records has resolved this problem in recent years, making it possible to extract .
11
In 4 years (1974, 1979, 1990 and 1990), the specified date is April 5th or earlier and so the NICs schedule
in place is that of the previous tax year (i.e. 1973–74, 1978–79, 1989–90 and 1994-95).
12
For a small group of people who are paid irregularly, it is also possible that pay periods span
more than one tax year. Those paid regularly (whether weekly, monthly or on some other basis) always have their first pay period of the tax year aligned to the start of the tax year. See
http://www.hmrc.gov.uk/manuals/nimmanual/nim08002.htm.
19
Figure 4: Simulated bunching with 2010–11 income tax schedule: no frictions
(b) ETI = 0.10
80
80
70
70
60
60
50
50
Density
Density
(a) ETI = 0.01
40
40
30
30
20
20
10
10
0
0
90
100
110
120 130 140 150 160 170
Annual taxable income (£000s)
180
190
200
90
100
110
120 130 140 150 160 170
Annual taxable income (£000s)
180
190
200
Note: In panel b), density is 217 at £100,000 and 45 at £150,000.
Source: Authors simulations based on 2009–10 SPI data and tax schedule for earned income.
we examine bunching at both the contemporaneous and previous year’s NICs thresholds.
5. Results
Figure 4 shows what we would expect the density distribution of taxpayers to look like in a
frictionless model around the kink points higher earnings faced under the 2010-11 income tax
schedule, given two small values for the ETI. These calculations are made using the 2009-10
SPI and assuming a quasi-linear utility function. It is clear that even very small elasticities
(as in panel A) should lead to quite marked bunching in the distribution. Furthermore, the
drop in the marginal tax rate at the end of the personal allowance taper (around £113,000
in 2010-11) should lead to a hole in the distribution. This is as individuals whose income
would previously have been just below the end of the taper reduce their incomes in response
to a higher marginal tax rate but those whose incomes are just above the end of the taper
do not. The extent of bunching, and the size of the hole, are increasing in the size of the
ETI, as shown by panel B for a (still small) ETI of 0.10.
Notches should lead to more bunching below the threshold than kinks, since individuals
face a sharp increase in their tax liability if they have earnings slightly above the threshold.
20
In a frictionless model, a notch also leads to a hole (zero mass) in the distribution above the
threshold, due to the dominated region in which no one should locate.
5.1. Bunching at kink-points
Figure 5 shows the distribution of taxable income in small bins around kink-points in
the income tax schedule.13 While there is some bunching at the higher-rate (Panel A) and
£100,000 thresholds (Panel B), where the rate of income tax increases from 20 to 40 and
from 40 to 60 percent respectively, it is nowhere near as strong as in the simulations shown
in Figure 4. No hole is observable at the end of the personal allowance taper, and it is hard
to identify any bunching whatsoever at the £150,000 threshold. Figure 6 shows that we also
do not observe any bunching at the convex kink-points in the NICs schedule - the Primary
and Secondary Thresholds - that existed after 1999.14
What bunching there does seem to be at these income tax thresholds is driven by the
responses of company owner-mangers and - to a much lesser extent - the self-employed, as
shown in panels (a-b) and (c-d) respectively of Figure 7. Both these groups of taxpayers
will pay tax through self-assessment, which is subject (with low probability) to audit but
not third-party reporting, while company owner-managers draw much of their income in
the form of dividends, over which they have considerable flexibility in terms of timing. The
same cannot be said for other taxpayers - mostly employees who have income tax deducted
at source by employers - who as Panels (e-f) show, do not seem to bunch at all.15
Unsurprisingly, this meagre bunching translates into very small elasticities: Table 2
shows that with the exception of company owner-managers at the higher-rate threshold,
the estimated elasticities are below 0.10, with most estimates less than 0.05.16 These are
13
We use £100 bins around the higher-rate threshold and £250 bins around the £100,000 and £150,000
thresholds, where our sample size is smaller.
14
Here, data from the New Earnings Survey between 2000 and 2010 are pooled together and normalised
around the threshold, with bins showing the number of observations in £1 bins of real earnings (April 2012
prices) around the threshold in red. Observations located at ‘round-numbers’ are dropped from the sample.
15
This group also includes a few individuals with very high levels of savings income.
16
We obtain similar - though less precisely estimated - elasticities using the method of Saez (2010) to
construct the counterfactual density. This estimates the amount of bunching by comparing the number of
individuals in a £2,000 window around the threshold with the number of individuals in a similar sized band
either side, and is somewhat sensitive to the choice of bunching window.
21
Figure 5: Bunching at kink-points in the income tax schedule
(b) £100,000-£150,000 thresholds
(a) Higher-rate threshold: 2003–04 to 2007–2008
3000
25
20
Observations in £250 bins
Observations in £100 bins
2500
2000
1500
1000
500
0
-10000 -7500 -5000 -2500
0
2500 5000 7500
Distance from kink point (in 2007-08 £s)
15
10
5
0
10000
90
100
110
120
130
140
Annual taxable income (£000s)
150
160
Notes: Panel A shows the distribution of taxable income (2007–08 prices) in £100 bins around the higherrate threshold. Panel B shows the distribution of annual taxable income in 2010–11, with the kinks at
£100,000 £112,950 and £150,000 shown by the vertical red lines. Panel C shows the distribution of taxable
income in £100 bins around the higher-rate threshold in 1985.
Source: authors’ calculations using 2003–04 to 2007–2008 (Panel A) and 2010–11 SPI data (Panel B).
Figure 6: Distribution of earnings around kink-points in the NICs schedule: 2000-2010
Observations in 1ppt bins
1000
1500
2000
500
0
0
500
Observations in 1ppt bins
1000
1500
2000
2500
(b) Secondary Threshold
2500
(a) Primary Threshold
-50
-40
-30
-20
-10
0
10
20
30
40
Distance from NICs Primary Threshold (in Apr 2012 prices)
50
-50
-40
-30
-20
-10
0
10
20
30
40
Distance from NICs Secondary Threshold (in Apr 2012 prices)
Notes: Figures show the distribution of weekly gross earnings in £1 bins around the Primary and Secondary
thresholds. Observations with ‘round-number’ earnings dropped from the sample.
Source: Authors calculations using microdata from the New Earnings Survey 2000–2010
22
50
Figure 7: Bunching at income tax thesholds: by group
(a) HRT: owner-managers
(b) £100-150k: owner-managers
400
6
350
Observations in £100 bins
Observations in £100 bins
5
300
250
200
150
4
3
2
100
1
50
0
-£5,000
-£2,500
£0
£2,500
Distance from higher-rate threshold
0
£90,000
£5,000
(c) HRT: self-employed
£100,000
£110,000
£120,000 £130,000 £140,000
Annual taxable income
£150,000
£160,000
(d) £100-150k: self-employed
400
6
350
Observations in £100 bins
Observations in £100 bins
5
300
250
200
150
4
3
2
100
1
50
0
-£5,000
-£2,500
£0
£2,500
Distance from higher-rate threshold
0
£90,000
£5,000
(e) HRT: other taxpayers
£100,000
£110,000
£120,000 £130,000 £140,000
Annual taxable income
£150,000
£160,000
(f) £100-150k: other taxpayers
2000
14
1800
12
Observations in £100 bins
Observations in £100 bins
1600
1400
1200
1000
800
600
10
8
6
4
400
2
200
0
-£5,000
-£2,500
£0
£2,500
Distance from higher-rate threshold
0
£90,000
£5,000
£100,000
£110,000
£120,000 £130,000 £140,000
Annual taxable income
£150,000
£160,000
Note: Figures show number of individuals in bins of income for company owner-managers; those with some
self-employment income who are not also company owner-managers; and those who do not fit into either of
these categories.
Source: authors’ calculations using 2003–04 to 2000–08 (left-hand panels) and 2010–11 SPI data (Right-hand
panels).
23
Table 2: Elasticity estimates from bunching at income tax kink points
Kink point
Higher-rate threshold:
Bunching mass
s.e.
£100,000 threshold:
Bunching mass
s.e.
£150,000 threshold:
Bunching mass
s.e.
All
Selfemployed
Ownermanagers
Others
0.032
3.395***
-0.313
0.058
6.164***
-0.557
0.246
26.25***
-0.717
0.015
1.620***
-0.362
0.014
2.332***
-0.402
0.02
3.309***
-0.922
0.039
6.435***
-0.987
0.007
1.168**
-0.548
0.022
2.486***
-0.507
0.011
1.225
-1.06
0.07
7.726***
-1.413
0.015
1.748***
-0.621
Note: Standard errors shown in italics refer to the estimate of the bunching mass, with the stars showing
statistical significance at the 10% (*), 5% (**) and 1% (***) levels.
Source: Authors calculations using 2003-04 to 2007-08 and 2010-11 SPI data.
much smaller than previous estimates found for high earners in the UK (Brewer et al., 2011;
HMRC, 2012), and toward the lower end of the range of elasticities that have been estimated
in the wider literature (Saez et al., 2012). However, as already discussed, optimisation
frictions will drive a wedge between the estimated and the ‘structural’ elasticity related to
individuals’ preferences. Allowing for such frictions could reconcile these estimates with
much larger elasticities, as the utility loss from not bunching at kink-points can be small:
assuming a quasi-linear utility function, the loss from not bunching at these thresholds is
between 0.4 and 0.8 of consumption at the higher-rate and £150,000 thresholds, and 1.6
percent of consumption at the £100,000 threshold.
We follow Chetty (2012) and calculate bounds on the underlying structural elasticity
allowing for a fixed adjustment cost of 1 percent of utility. Our elasticity estimate for all
taxpayers at the £100,000 threshold of 0.014 is then consistent with an underlying structural
elasticity of between 0.00 and 0.50, while our estimates from the other kink-points are
consistent with elasticities of between 0.00 and 2.35.17 This serves to highlight the limited
17
Bounds computed using the calculator of Chetty (2012), available online at http://www.rajchetty.
24
usefulness of ETI estimates obtained from bunching at kink points: they are consistent with
either very low underlying elasticities or the presence of non-trivial adjustment costs.
5.2. Bunching at notches
We now turn to look at bunching at notches, where the presence of a dominated region
that no one should locate in - regardless of how unresponsive they might be - allows us to
distinguish high frictions from low underlying elasticities. Figure 8 shows the distribution of
earnings from the New Earnings Survey in each year between 1978 and 1998 in real £1 bins
(April 2012 prices) around the point where NICs became payable (the LEL). Bunching is
clearly visible below the threshold from 1985, and seems to get sharper over the late-1980s
and early-1990s. As we’ve already seen in Figure 6, this bunching dissipated once the notch
at the LEL was replaced by kinks at the Primary and Secondary thresholds in 1999.
To boost the size of our sample, Figure 9 pools observations across three sets of years:
1978–1985 (when there was a large notch at the LEL), 1986–1989 (when there was a smaller
notch) and 1990-98 (when there was an even smaller notch). The left-hand panels show the
earnings distribution normalised around the LEL in the tax years beginning 6 April, and the
right-hand panels in the tax years ending 5 April. Observations whose weekly, monthly, or
annual earnings are integer amounts are dropped from the sample to avoid conflating bunching in the earnings distribution at ‘round-number’ amounts from behavioural responses.18
Also shown in the figures is the dominated region in which no one should locate save frictions
(between the solid and the dashed-red lines) and an estimate of the counterfactual density,
constructed using a flexible (12-15 order) polynomial.
Between 1978 and 1985 (panel A) we see some bunching at the LEL, though there is
substantial mass in the dominated region to the right of this threshold. This implies that
optimisation frictions are large enough to prevent those in the dominated region (between
the solid and the dashed vertical red lines) from relocating below the threshold, where
com/chettyfiles/bounds_calculator.xls. The change in net-of-tax rates at the higher-rate, £100,000
and £150,000 thresholds are 0.41, 0.19, and 0.27 respectively.
18
Our results are not sensitive to whether or not these individuals are included along with a more flexible
polynomial that can account for bunching at ‘round-number’ amounts.
25
-50
0
1978: LEL = 17.5 GBP
50
-50
0
1981: LEL = 27 GBP
50
-50
0
1984: LEL = 34 GBP
50
-50
0
1987: LEL = 39 GBP
50
-50
0
1990: LEL = 46 GBP
50
-50
0
1993: LEL = 56 GBP
50
-50
0
1976: LEL = 13 GBP
50
-50
0
1979: LEL = 19.5 GBP
50
-50
0
1982: LEL = 29.5 GBP
50
-50
0
1985: LEL = 35.5 GBP
50
-50
0
1988: LEL = 41 GBP
50
-50
0
1991: LEL = 52 GBP
50
-50
0
1994: LEL = 57 GBP
50
50
50
-50
0
1980: LEL = 23 GBP
50
-50
0
1983: LEL = 32.5 GBP
50
-50
0
1986: LEL = 38 GBP
50
-50
0
1989: LEL = 43 GBP
50
-50
0
1992: LEL = 54 GBP
50
-50
0
1995: LEL = 58 GBP
50
-50
0
1998: LEL = 64 GBP
50
Observations
0 .01 .02 .03 .04
Observations
.01 .02 .03
0
Observations
.01 .02 .03
0
Observations
.01 .02 .03
0
Observations
.01 .02 .03
0
26
0
0
1996: LEL = 61 GBP
0
1977: LEL = 15 GBP
Observations
0 .01 .02 .03 .04
Observations
0 .01 .02 .03 .04
Observations
.01 .02 .03
0
Observations
.01 .02 .03
0
Observations
.01 .02 .03
0
Observations
.01 .02 .03
Observations
0 .01 .02 .03 .04
Observations
0 .01 .02 .03 .04
Observations
0 .01 .02 .03 .04
Observations
.01 .02 .03
0
Observations
.01 .02 .03
0
Observations
.01 .02 .03
0
Observations
.01 .02 .03
0
-50
-50
Observations
0 .01 .02 .03 .04
50
Observations
0 .01 .02 .03 .04
0
1975: LEL = 11 GBP
Observations
0 .01 .02 .03 .04
-50
Observations
0 .01 .02 .03 .04
Observations
0 .01 .02 .03 .04
Observations
0 .01 .02 .03 .04
Figure 8: Distribution of earnings around the LEL (Apr 2012 prices)
-50
0
1997: LEL = 62 GBP
50
Note: Figures show the number of observations in real £1 bins of earnings around the LEL.
Source: Authors calculations using microdata from the New Earnings Survey 1978-1998.
Figure 9: Bunching at the LEL
1500
1000
500
0
0
500
1000
1500
2000
(b) Previous year: 1978–85
2000
(a) Current year: 1978–85
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70
Distance from current year's LEL (as % LEL)
80
90 100
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70
Distance from previous year's LEL (as % LEL)
90 100
80
90 100
80
90 100
1000
500
0
0
500
1000
1500
(d) Previous year: 1986–89
1500
(c) Current year: 1986–89
80
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70
Distance from current year's LEL (as % LEL)
80
90 100
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70
Distance from previous year's LEL (as % LEL)
(f) Previous year: 1990–99
0
0
500
500
1000
1000
1500
1500
(e) Current year: 1990–99
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70
Distance from current year's LEL (as % LEL)
80
90 100
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70
Distance from previous year's LEL (as % LEL)
Pooled data with earnings normalised around annual threshold at 0, dropping individuals at round numbers.
Dark vertical lines show estimated earnings response using convergence and bunching-hole methods as
described in Section 4.
Source: Authors calculations using microdata from the New Earnings Survey 1978-1998
27
they would see a rise in net-of-tax earnings of around 7%, and employers a similarly sized
reduction in employer NICs. Bunching is sharper over the period 1986–89 (panel B), with
the estimate of the excess mass rising even though the size of the notch at the threshold was
smaller: the total average tax rate (including income tax and benefit withdrawal) jumped
from 11 to 19 percent at the threshold over this period on average, compared with from 12
to 29 percent over the period 1978–85. Bunching continued throughout the 1990s (panel C)
despite an even smaller jump in the total average tax rate (from 0.16 to 0.25), though was
not as sharp as between 1986 and 1989.
Table 3 contains estimates of the unattenuated elaticities for the bunching shown in
panels a, c and e of Figure 9, accounting for the large optimisation frictions that are present.19
Panel A shows reduced-form estimates using the convergence and bunching-hole methods
of Kleven and Waseem (2013), with the next Panel showing estimates using the structural
(indifference-relation based) approach that assumes a quasi-linear utility function and so
rules out income effects (biasing estimates of the ETI downwards). The table also shows,
in Panel C, estimates of the bunching mass B̂, share of constrained individuals a∗ (φ), and
earnings responses
∆zc ∆zbh
, N ,
N
along with the order of the polynomial fitted to the distribution
and the range of earnings below the threshold excluded in fitting the counterfactual.
We estimate an unattenuated ETI of between 0 and 0.10 for the period 1978–1985,
and - as one would expect given the sharper bunching we observe at smaller notches - larger
estimates for the period after: 0.07-32 for the period 1986–1989, and 0.30-0.70 for the period
1990-99. Although the ‘structural approach’ estimates are much lower than the reducedform approach estimates, all are quite tightly estimated, as indicated by the bootstrapped
standard errors in italics.
The large increase in the estimated elasticities between the 1985–89 and 1990–99 periods
is due to both an increase in our measure of frictions (from 0.83 to 0.89) and a similar
amount of excess mass (0.149 compared to 0.147) at the threshold despite a significantly
19
We do not estimate elasticities for bunching at the LEL in the tax year ending 5 April (i.e. panels b, d
and f of Figure 9), as the dominated region contains those bunching at the LEL in the tax year beginning
6 April, biasing estimates upwards by dramatically overstating â∗ (φ).
28
Table 3: Elasticity estimates from bunching at the LEL
1978–85
1986–89
1990–99
Panel A: Reduced-form approach
Convergence method
s.e.
Bunching-hole method
s.e.
0.0428
0.0002
0.0965
0.0014
0.1203
0.0013
0.3210
0.0046
0.4350
0.0032
0.6891
0.021
Panel B: structural approach
Convergence method
s.e.
Bunching-hole method
s.e.
0.0000
0.0001
0.0430
0.0009
0.0670
0.0010
0.2221
0.0036
0.3051
0.0026
0.5403
0.0186
B̂
â∗ (φ)
∆zconvergence /N
∆zbunching-hole /N
Excluded range below threshold
Polynomial order
0.0904
0.8737
14.50%
23.00%
0.2
12
0.1468
0.8257
16.00%
28.25%
0.2
12
0.1493
0.8932
38.50%
52.25%
0.2
15
Note: Bootstrap standard errors in italics are calculated by repeating the estimation procedure 200 times,
each time fitting a polynomial to the earnings distribution of a bootstrap sample drawn (with replacement)
from the empirical distribution.
Source: New Earnings Survey, 1978-1999
29
lower jump in tax rates. Indeed across all three periods, our estimates suggest that between
80 and 90 percent of individuals are subject to frictions large enough to prevent them from
moving out of the dominated region. The total tax wedge for those who located in this
region was up to 17% of gross earnings higher than for those who located just below the
threshold, suggesting that - on average - the frictions faced by employees in this time period
were really quite large, even at this low level of earnings.
So too does what we observe at the notches in the NICs schedule that existed between
1986 and 1999 further up the earnings distribution, shown in Figure 10. At these thresholds,
the combined employee and employer average NICs rate jumped up by between 1 and 4
percentage points, implying substantial losses from not bunching below the threshold: for
example, locating in the dominated region in 1989 meant an additional tax wedge between
employer cost and net take-home pay of about £500 on earnings of £17,700 per year (both
in April 2012 prices). Yet there is no evidence whatsoever of bunching below or missing
mass above these thresholds, meaning frictions must have been sufficient to dominate any
bunching response for all workers in the region of these thresholds corresponding to around
4/5, 1 and 2 times median earnings over the 1980s and 1990s.
If, as we’ve seen earlier, a fixed adjustment cost equal to 1% of net-income can reconcile
elasticities of between 0 and 0.50 at the £100,000 income tax threshold, frictions of the order
implied above could easily explain why we see no bunching by employees at the higher-rate
(or indeed any other) kink-point. But so far we have treated frictions as a ‘black box’ of
sorts. The nature of these frictions could be of considerable importance in assessing over
what time period attenuated elasticities converge towards their unattenuated counterparts.
One source of frictions that might be at play is constraints on hours choices, something
that has received considerable attention in the literature (Altonji and Paxson, 1988; Chetty
et al., 2011; Beffy et al., 2014). Whereas the majority of those in the region of the LEL were
part-time employees, most of those near these notches higher in the earnings distribution
were full-time employees. Indeed as Figure 11 shows, the bunching response at the LEL
was driven entirely by part-time workers, who are overwhelmingly women. Neither men
nor full-time employees seem to bunch below the LEL at all, while the missing-mass above
30
Figure 10: Bunching at notches above the LEL
0
0
500
Observations in 1ppt bins
2000
4000
Observations in 1ppt bins
1000
1500
2000
6000
(b) First notch: 1990-99
2500
(a) First notch: 1986-89
-50
-40
-30
-20
-10
0
10
20
Distance from notch (as % of notch)
30
40
50
-50
-40
-30
-20
-10
0
10
20
Distance from notch (as % of notch)
30
40
50
30
40
50
30
40
50
(d) Second notch: 1990-99
6000
0
0
500
Observations in 1ppt bins
2000
4000
Observations in 1ppt bins
1000
1500
2000
2500
(c) Second notch: 1986-89
-50
-40
-30
-20
-10
0
10
20
Distance from notch (as % of notch)
30
40
50
-50
-40
-20
-10
0
10
20
Distance from notch (as % of notch)
0
0
500
Observations in 1ppt bins
2000
4000
Observations in 1ppt bins
1000
1500
2000
6000
(f) Third notch: 1990-99
2500
(e) Third notch: 1986-89
-30
-50
-40
-30
-20
-10
0
10
20
Distance from notch (as % of notch)
30
40
50
-50
-40
-30
-20
-10
0
10
20
Distance from notch (as % of notch)
Note: Pooled data with earnings normalised around threshold (at 0), dropping individuals at round numbers.
Source: Authors calculations using microdata from the New Earnings Survey 1978-1998.
31
the threshold for these groups is substantially smaller than for women or part-time workers
(implying that, on average, full-time employees and men face much larger frictions at this
earnings level).
Figure 11 also shows that there is substantial heterogeneity in bunching responses and
missing mass across sectors. While there is no bunching or missing mass observable in the
distribution of public sector employees’ earnings, those employed in the hospitality or retail
sectors - where shift-work is common - bunch very sharply and with much less missing mass
above the threshold, implying far smaller frictions on average. We conclude by discussing
this, and other implications of our results in the final section.
6. Conclusion
This paper has used administrative and survey data to investigate the responsiveness of
agents to taxes, exploiting variation induced by kinks and notches in the UK tax schedule.
Taking our results as a whole, what can we say about optimising frictions and the elasticity
of taxable income? Firstly, we found evidence that the frictions faced by most workers are
substantial, and are likely to significantly attenuate estimates of elasticities. This seems to
particularly be the case for full-time employees, who may not be able to change their hours
in response to a change in tax rates as part-time employees can, nor adjust the timing,
composition or reporting of their income as company owner-managers and (to a lesser extent)
the self-employed can. This will attenuate estimates of elasticities obtained not only from
bunching at kink-points, but also from more traditional reduced-form estimates of hours
or taxable income functions. As a result, frictions of the order we identify could play an
important role in reconciling (very large) macroeconomic estimates of labour supply with
their (much smaller) microeconomic counterparts (Chetty, 2012; Keane and Rogerson, 2015).
Secondly, we found much less bunching at new (the £150,000) and non-transparent
(£100,000) income tax thresholds than the long-established higher-rate threshold, despite
the fact that the last of these was increased in line with a measure of prices every year. This
can be taken as (suggestive) evidence that individuals react differently to salient and nonsalient taxes, in line with a growing literature that has consequences for the optimal design
32
Figure 11: Bunching at the NICs entry threshold, 1978-1989: by group
(b) Men
1500
Observations in 0.5ppt bins
500
750
1000
1250
250
0
0
250
Observations in 0.5ppt bins
500
750
1000
1250
1500
(a) Women
-50
-40
-30
-20
-10
0
10
20
Distance from LEL (as % of threshold)
30
40
50
-50
-40
-20
-10
0
10
20
Distance from LEL (as % of threshold)
30
40
50
30
40
50
30
40
50
Observations in 0.5ppt bins
500
750
1000
1250
250
0
0
250
Observations in 0.5ppt bins
500
750
1000
1250
1500
(d) Full-time workers
1500
(c) Part-time workers
-30
-50
-40
-30
-20
-10
0
10
20
Distance from LEL (as % of threshold)
30
40
50
-50
-40
-30
Observations in 0.5ppt bins
500
750
1000
1250
250
0
0
250
Observations in 0.5ppt bins
500
750
1000
1250
1500
(f) Public sector
1500
(e) Retail and hospitality
-20
-10
0
10
20
Distance from LEL (as % of threshold)
-50
-40
-30
-20
-10
0
10
20
Distance from LEL (as % of threshold)
30
40
50
-50
-40
-30
-20
-10
0
10
20
Distance from LEL (as % of threshold)
Note: Pooled data with earnings normalised around annual threshold at 0. Y-axis shows the proportion of
the distribution observed in 1 percentage point bins.
Source: Authors calculations using microdata from the New Earnings Survey 1978-1989.
33
of tax policy (Chetty et al., 2009; Reck, 2014). However, as SPI data for more recent years
is not currently available, we cannot test this hypothesis by looking at whether bunching
gets stronger at the £100,000 and £150,000 thresholds over time (though we plan to do so
in future work).
We also saw that bunching below the LEL got considerably sharper from 1985 on, despite
the size of this notch being cut from a combined 17.6 percent to 9.5 percent of gross earnings.
This leads us to speculate whether then Chancellor Nigel Lawson contributed to a greater
awareness and salience of the notch at the LEL by - in his March 1985 Budget speech making a great deal of its detrimental effect on employment:
I have concluded that an effective response to [unemployment] must include direct action in
two related areas - to cut the costs of employing the young and unskilled, and to sharpen their
own incentive to work at wages which employers can afford to pay. I am therefore proposing,
in collaboration with my right hon. Friend the Secretary of State for Social Services, a radical
reform of the structure of national insurance contributions. ... The effect [of these reforms] on
job prospects will, over time, be substantial. The radical restructuring I have announced will
encourage employers to take on the young and unskilled and give them, in turn, an incentive
to seek work at wages that employers can afford. ... These are changes of a major order.
They amount to a direct and powerful attack on disincentives to employment. They tackle the
problem of unemployment where it is most acute. They complete my Budget for jobs.20
Thirdly, Figure 11 showed that there is substantial heterogeneity in the frictions faced
by different groups of workers, with men facing much higher frictions than women of similar
earnings levels. These differences correspond with well-documented heterogeneity in estimates of labour supply elasticities: for instance, in their survey of the effects of taxes on
labour supply, Meghir and Phillips (2011) conclude that hours of work are almost completely
unresponsive to tax rates for men but extremely responsive for women, particularly those
with young children. While our approach does not allow us to separately identify unattenuated elasticities for both these groups (as we see neither missing mass nor bunching around
notches for men), distinguishing whether the well-documented heterogeneity in observed
labour supply elasticities is due to differences in underlying preferences or frictions seems a
worthy topic for future research, given its importance for the optimal design of tax policy.
20
http://hansard.millbanksystems.com/commons/1985/mar/19/national-insurance-contributions
34
Finally, we also found substantial differences in bunching and missing mass across sectors
for workers of similar earnings levels. One possibility is that this is driven by aspects of
labour demand, such as hours constraints imposed by employers. This serves as a reminder
that what is identified from the estimation of a hours or taxable income function does not
necessarily correspond to a labour supply parameter, let alone a ‘deep’ preference parameter.
Pencavel (2015) recently noted that ‘a whole generation of researchers ... have forgotten the
need to address [this] fundamental identification problem’ in the estimation of parameters
describing the effects of taxes on labour supply. And while the methods used in this paper to
estimate these parameters accounting for frictions are modern, sometimes the most difficult
challenges to overcome are the oldest ones.
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