Frictions and the elasticity of taxable income: evidence from bunching at tax thresholds in the UK

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1 Frictions and the elasticity of taxable income: evidence from bunching at tax thresholds in the UK Stuart Adam a, James Browne a, David Phillips a, Barra Roantree a 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security, income tax, elasticity of taxable income, optimising frictions JEL: H21, H24, J22, J23 DRAFT WORKING PAPER: DO NOT CITE WITHOUT PERMISSION The authors would like to thank Richard Blundell, Raj Chetty, Julien Grenet, Luke Haywood, Henrik Kleven, Ian Preston, and Emmanuel Saez for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

2 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 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 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 2

3 (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

4 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 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) = T 0 (z) are all smooth then the income 4

5 distribution h 0 (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 z 0 = k + z. If instead of being smooth, the tax schedule is kinked such that T (z) = T 1 (z) = τ l z + (τ h τ l )(z k)1[z > k] for τ h > τ l, the income distribution h 1 (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 τ h. Specifically, letting individual H be the person who bunches at the kink point (z 1 = k) with the highest level of income under the smooth tax schedule (z 0 = k + z), all individuals who under the smooth tax schedule T 0 (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: B = k+ Z k h 0 (z)dz (1) 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 z 1 τ τ = z k (1 τ l ) τ h τ l (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: B = k+ z k h 0 (z)dz h 0 (k) z (3) 5

6 Figure 1: Effect of a kinked tax schedule on: (a) the distribution of gross earnings B With kinked tax schedule With smooth tax schedule Density distribution k k + Δz Before-tax income z (b) individuals budget sets H 1 H 2 -tax income, c After- Kinked tax schedule Smooth tax schedule 0 k k + Δz Before-tax income, z 6

7 an approximation that links the ETI to the unknown, but estimable, entity earnings response z. 2 B h 0 (k) via the The next step in the approach is to estimate the unobserved counterfactual density h 0 (k) and so ˆB B, the excess mass or bunching at the kink-point, ĥ 0 (k) which we then substitute for z in equation 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, R u ] 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: C j ˆ 1 + 1[j > R] R j= R BN ˆ C J 2R+1 = q β i (z j ) i + i=0 R k= R where z j is the number of individuals in a small bin of earnings, and γ i 1[z j = i] + ɛ j (4) ˆ B N = R j= R C j Ĉ j = R k= R ˆγ k is the predicted excess mass at the threshold. This regression is iteratively estimated as the dependent variable is a function of ˆ BN, which is in turn a function of the estimated ˆβ i, recomputing ˆ β N using the estimated ˆβ i until a fixed point is reached. Standard errors for the estimated bunching mass ˆb = βˆ N R Cˆ j j= R 2R+1 are obtained by using a parametric bootstrap procedure, where a large number of draws from the estimated vector of errors ɛ j in equation 4 are made (with replacement) to generate a distribution of ˆb estimates: the 2 This approximation assumes that the density h 0 (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

8 standard error is then defined as the standard deviation of this distribution. Since the ETI is just a function of ˆb 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 ˆb is statistically significantly different from zero, the taxable income elasticity will be also 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 h 0 (z), consider a joint distribution of abilities and elasticities ˆf(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 ( z e ) and an expression that links the observed bunching mass B to the average earnings response E[ z e ] and so the local average earnings elasticity: B = k+ z e k ĥ 0 (z, e)dzde h 0 (k)e[ z e ] (5) 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

9 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 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

10 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 ɛ ] 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 1 + 1/e.( z n )1+1/e (6) = [ T/N ] 1 + z /N 1 t [ /e z /N ] 1+1/e e = 0 (7) which characterises the relationship between the elasticity (e), the percentage earnings response ( z ), and the percentage change in the average net-of-tax rate created by the notch N ( T/N ). A consequence of adopting this iso-elastic specification for utility is that we assume 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 + t.(k + z ) z δz ˆɛ R F = z /z t /(1 t ) ( z /z ) 2 t/(1 t) t + t.z z (8) Because a notch will induce a larger earnings response than the implicit kink would, by 3 See pp of Kleven and Waseem (2013). 4 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. 10 (9)

11 Figure 2: Bunching at a notch (a) Frictionless model No-notch density Density with notch Densi ity distribution N N+D Before tax income (b) With optimising frictions No-notch density Density with notch Densi ity distribution N N+D Before tax income 11

12 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: B = e N+ z N [1 a(z, e, φ)].ĥ0(z, e)dzde h 0 (N).[1 a (φ)]. z (10) This can be used to identify the average earnings response across all elasticity levels given an estimate of the bunching mass ˆB B (as before) and the share of constrained individuals ĥ 0 (N) 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 ˆB 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 ˆB (φ), biasing downwards. (1 â (φ))ĥ0(n) 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

13 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 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 , 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 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 at the individual level. Successive governments reduced these rates so that in 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 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

14 Table 1: Income tax rates on earned income, to Fiscal year Starting rate Basic rate Higher rates to to to to to to Note: Different tax rates have applied to dividends since and to savings income since The basic rate of tax on savings income has been 20% since , while the 10% starting rate (which was largely abolished in ) continued to apply to some savings income until April The basic rate of tax on dividends was 20% from to and has been 10% since , 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 The additional tax rate on dividend income has been 37.5% since , 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 (to pay for a cut in the basic rate) but reforms have since complicated the rate structure for those with the highest incomes: from , 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 to A (convex) kink at 100,000 since A (convex) kink at 150,000 since

15 A (non-convex) kink where the tax-free personal allowance is fully withdrawn (around 115,000) since 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 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

16 Figure 3: National Insurance contribution schedules, April 2014 prices (a) Employee contributions NICs, per week ,000 Gross weekly earnings (b) Employer contributions NICs, per week ,000 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 schedule excludes the 1% National Insurance surcharge abolished in September Source: HM Treasury, Financial Statement and Budget Report, various years; Tolleys National Insurance Contributions, various years. 16

17 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 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 to Multiple notches above the LEL from to Multiple notches in the employer NICs schedule above the LEL: to Kinks at the Primary and Secondary thresholds from 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 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

18 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 to , 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, million taxpayers had to fill in a self-assessment tax return for : primarily the self-employed, those with significant unearned income and those with incomes over 100, Data for 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 , 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

19 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 For this reason 10 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 , , and ). 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 19

20 Figure 4: Simulated bunching with income tax schedule: no frictions (a) ETI = 0.01 (b) ETI = Density 40 ensity De Annual taxable income ( 000s) Annual taxable income ( 000s) Note: In panel b), density is 217 at 100,000 and 45 at 150,000. Source: Authors simulations based on 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 income tax schedule, given two small values for the ETI. These calculations are made using the 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 ) 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 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

21 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 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 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 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. 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

22 Figure 5: Bunching at kink-points in the income tax schedule (a) Higher-rate threshold: to (b) 100, ,000 thresholds ns in 100 bins Observation ns in 250 bins Observation Distance from kink point (in s) Annual taxable income ( 000s) Notes: Panel A shows the distribution of taxable income ( prices) in 100 bins around the higherrate threshold. Panel B shows the distribution of annual taxable income in , with the kinks at 100, ,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 Source: authors calculations using to (Panel A) and SPI data (Panel B). Figure 6: Distribution of earnings around kink-points in the NICs schedule: (a) Primary Threshold (b) Secondary Threshold in 1ppt bins Distance from NICs Primary Threshold (in Apr 2012 prices) in 1ppt bins 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. with round-number earnings dropped from the sample. Source: Authors calculations using microdata from the New Earnings Survey

23 Figure 7: Bunching at income tax thesholds: by group (a) HRT: owner-managers (b) k: owner-managers Observa ations in 100 bins Observa ations in 100 bins ,000-2, ,500 5,000 Distance from higher-rate threshold 0 90, , , , , , , ,000 Annual taxable income (c) HRT: self-employed (d) k: self-employed Observa ations in 100 bins Observa ations in 100 bins ,000-2, ,500 5,000 Distance from higher-rate threshold 0 90, , , , , , , ,000 Annual taxable income (e) HRT: other taxpayers (f) k: other taxpayers Observa ations in 100 bins Observa ations in 100 bins ,000-2, ,500 5,000 Distance from higher-rate threshold 0 90, , , , , , , ,000 Annual taxable income 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 to (left-hand panels) and SPI data (Right-hand panels). 23

24 Table 2: Elasticity estimates from bunching at income tax kink points Kink point All Selfemployemanagers Owner- Others Higher-rate threshold: ɛ Bunching mass 3.395*** 6.164*** 26.25*** 1.620*** s.e ,000 threshold: ɛ Bunching mass 2.332*** 3.309*** 6.435*** 1.168** s.e ,000 threshold: ɛ Bunching mass 2.486*** *** 1.748*** s.e 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 to and 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 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 This serves to highlight the limited 17 Bounds computed using the calculator of Chetty (2012), available online at 24

25 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 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 To boost the size of our sample, Figure 9 pools observations across three sets of years: (when there was a large notch at the LEL), (when there was a smaller notch) and (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. 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

26 Figure 8: Distribution of earnings around the LEL (Apr 2012 prices) : LEL = 11 GBP : LEL = 13 GBP : LEL = 15 GBP : LEL = 17.5 GBP : LEL = 19.5 GBP : LEL = 23 GBP : LEL = 27 GBP : LEL = 29.5 GBP : LEL = 32.5 GBP : LEL = 34 GBP : LEL = 35.5 GBP : LEL = 38 GBP : LEL = 39 GBP : LEL = 41 GBP : LEL = 43 GBP : LEL = 46 GBP : LEL = 52 GBP : LEL = 54 GBP : LEL = 56 GBP : LEL = 57 GBP : LEL = 58 GBP : LEL = 61 GBP : LEL = 62 GBP : LEL = 64 GBP 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