A worker’s tax year budget constraint

My model of the U.K. worker features a consumption tax, payroll taxes (by both employer and employee; hereafter, NICs or “National Insurance Contributions,” as they are called in the U.K.), personal income taxes, benefits based on personal income (such as working tax credits, child tax credits, and the child benefit), and benefits for the unemployed (including, but not necessarily limited to, jobless and housing allowances).Footnote 4 The weekly employer cost of worker i, y i , is the sum of weekly earnings w i and employer payroll taxes (w i − ST)τ f :

$$ {y}_i={w}_i+\left({w}_i-ST\right){\tau}_f, $$ (1)

where τ f denotes the marginal employer NICs rate and ST < y denotes the earnings threshold for weekly employer NICs.

The personal income tax and personal-income-related benefits are based on tax-year income (the tax year begins in April), but the NICs and unemployment benefits are weekly. The link between consumption c i and weekly earnings w i therefore depends on the number of weeks worked n i ∈ [0, 52]Footnote 5:

$$ {c}_i=\left(52-{n}_i\right)U{B}_i+{w}_i{n}_i-\left({w}_i-PT\right){n}_i{\tau}_e- PIT\left(\left(52-{n}_i\right)U{B}_i+{w}_i{n}_i\right)-{\tau}_c{c}_i, $$ (2)

where τ e is the marginal employee NICs rate, UB denotes the weekly unemployment benefit,Footnote 6 and PIT(⋅) denotes the combined schedules for personal income taxes, working tax credits, child tax credits, and the child benefit.Footnote 7 PT < y denotes the earnings threshold for weekly employee NICs. PT is known as the “primary threshold,” as distinct from the “secondary threshold” ST applicable to employers.Footnote 8 Equation (2)’s last term refers to indirect or consumption taxes (primarily VAT, but also important contributions from excise taxes: see Appendix I), which are levied as a fixed fraction τ c of consumption before tax. Combining (1) and (2), we have consumption as a function of weekly employer cost and weeks worked:

$$ \begin{array}{l}\left(1+{\tau}_c\right){c}_i=52U{B}_i+\left[\frac{1-{\tau}_e}{1+{\tau}_f}{y}_i+\frac{\tau_ePT+{\tau}_fST}{1+{\tau}_f}-U{B}_i\right]{n}_i\\ {}- PIT\left(52U{B}_i+\left[\frac{y_i}{1+{\tau}_f}+\frac{\tau_f}{1+{\tau}_f}ST-U{B}_i\right]{n}_i\right)\end{array} $$ (3)

The consumption tax rate is assumed to be constant across workers, but UB varies across workers due to family composition and housing expenses.

As indicated in equations (1) and (2), a fixed amount of earnings — the “primary” and “secondary” thresholds (PT and ST, respectively) — can be earned without any NICs owed by employee or employer.Footnote 9 The NICs system is therefore equivalent to a truly flat-rate payroll tax (specifically, without any PT or ST) plus a refund of a fixed amount to each employee and employer equal to the flat-rate tax that accrued on the first PT (or ST) of earnings. Equation (3) separates the “flat-rate” component from the PT-ST-refund component, with the former represented by the y i terms and the latter by the ratio with PT and ST in the numerator.

The U.K. personal income tax is a function of personal income above the “personal allowance.” There are multiple tax brackets, some of which are created by the phaseout of the personal allowance. All of these are represented by my PIT notation.

Unlike U.S. Social Security contributions, the NICs thresholds and rates are administered each pay period (e.g., weekly) without regard for earnings accumulated so far during the tax year. As a result, equation (3)’s PT and ST terms enter the budget constraint in the same way that the UB term does, except with the opposite sign. In effect, the PT-ST-refund component of my two-part representation of the NICs is, by itself, a weekly employment subsidy.

An additional week of employment creates value y i , some of which goes to the employee (to finance additional consumption) and the rest of which goes to the public treasury in the forms of additional taxes, credits not paid, and other benefits not paid. The employment tax wedge q i is the public-treasury portion of this value, expressed as a share of weekly employer costFootnote 10:

$$ {q}_i\equiv \frac{y_i-\frac{\partial {c}_i}{\partial {n}_i}}{y_i}=\frac{1}{1+{\tau}_c}\left({\tau}_c+\frac{\tau_i+{\tau}_e+{\tau}_f}{1+{\tau}_f}+\left(1-{\tau}_i\right)\frac{U{B}_i}{y_i}-\frac{\tau_ePT+\left(1-{\tau}_i\right){\tau}_fST}{\left(1+{\tau}_f\right){y}_i}\right), $$ (4)

where τ i denotes worker i’s PIT bracket. The PIT brackets vary across workers according to the amount they earn for the year, although a majority of workers are in the “basic rate” bracket of 20 or 22 percent (depending on the year) plus, for some of the basic-rate workers, a phaseout of tax credits.Footnote 11

Equation (4) has a consumption-tax term multiplying the UB, PT, and ST terms (as well as the others), thereby giving the impression that a consumption tax increase would reduce the contribution of the UB, PT, and ST terms to the tax wedge. However, because jobless allowances and the NICs thresholds are automatically indexed to consumer-price inflation, and employer cost y is not, the contribution of these two terms to the wedge is independent of the consumption tax as long as the consumption tax is passed through one-for-one into consumer prices.Footnote 12 To put it another way, the consumption tax rate is expected to increase each ratio UB/y, PT/y, and ST/y in the same proportion that it reduces the ratio 1/(1 + τ c ).

Legislative changes since 2007: wage income tax brackets

Each of equation (4)’s statutory parameters changed after 2007. Moreover, real employer costs y were changing relative to the sterling-denominated and inflation-adjusted statutory parameters such as the jobless allowance and the PT. As I show below, many of the parameter changes are offsetting — perhaps by design — in terms of their effects on the employment tax wedge q. Because of the various offsets, the VAT (value-added tax) and tax credit changes ultimately drive most of the changes in the tax wedge.

Beginning at 17.5 percent, the standard VAT rate was temporarily cut to 15.0 percent for the last month of 2008 and the entire calendar year of 2009.Footnote 13 It was 17.5 percent again in 2010. On January 4, 2011, the rate was permanently increased to 20 percent where it is now. The UK VAT increases are especially interesting for the purposes of labor market analysis because a VAT reduces the purchasing power of wages without reducing the purchasing power of jobless benefits because the latter are indexed to the consumer price index (CPI).

The UK made several adjustments to its personal income tax on earnings, which has been a three or four-bracket system (plus implicit brackets for the phaseouts of tax credits and the personal allowance). Effective April 2008, the bottom two non-zero brackets of 10 percent and 22 percent were combined into a single 20 percent bracket, as it is today. Effective April 2010, the personal allowance was phased out beginning at £100,000, and the upper bracket of 40 percent was split in two brackets: 40 percent and 50 percent. A year later, the income threshold separating the 20 and 40 percent bracket was cut by three percent in nominal terms (seven percent in real terms), thereby creating a group of taxpayers who experienced a twenty percentage point increase in their bracket. The 50 percent bracket rate was cut to 45 percent effective April 2013.Footnote 14

The 2010 income tax changes helped harmonize the PIT with the NICs and thereby produce a more uniform combined marginal tax rate schedule among most full-year workers. Figure 2 shows those combined rates (excluding tax credit phaseouts – more on these below) as summarized on the vertical axis by the first ratio term inside equation (4)’s parentheses. The horizontal axis shows employer cost, which is the sum of the worker’s annual earnings and the employer NICs. The black-dotted schedule is from tax year 2007. The schedule dips sharply between about £42,000 and £49,000 because those workers had exceeded the upper earnings limit for the NICs but still had low enough income that their PIT bracket had not jumped from 20 to 40 percent.Footnote 15 By 2009, these two thresholds were, up to rounding error, identical for a full-year worker.Footnote 16 These rounding errors are seen as the thin spikes in the red and blue series.Footnote 17

Fig. 2 UK Income Tax Brackets, Combining PIT & NICs Full size image

One result of the ongoing threshold changes is that the 2010 and 2011 cuts to the real-income threshold between the 20 and 40-percent PIT brackets only increased overall marginal rates by about 10 percentage points for taxpayers with incomes between the old and new thresholds because much of their 20-point PIT marginal rate increase was offset by being moved into a lesser marginal NICs rate.

Effective April 2011, one percentage point was added to both the employer NICs and the employee NICs (HM Revenue and Customs 2014a). For the workers (they are a majority of taxpayers and have annual employer cost between £7,000 and £43,000) that would have been in the 22 percent personal income bracket under 2007 law, the additions to the marginal NICs rate almost exactly offset the 2-percentage point PIT cut after 2007. As a result, the solid-blue and black-dotted schedules almost coincide in that range, with the blue 2011 schedule located just 0.4 percentage points below the 2007 schedule.

Among the relatively few high-income taxpayers, the combined contribution of the PIT and NICs changes has been to increase the employment tax wedge. The contribution of these PIT and NICs changes to the overall average employment tax wedge is essentially zero.

In order to highlight the harmonization of the PIT and NICs brackets, Fig. 2 excludes the phaseout of “tax credits.” Two main tax credits are paid to households: working tax credits (WTCs) and child tax credits (CTCs). Both credits are a function of annual household income and prorated according to the beneficiary’s payment period (weekly or every four weeks).Footnote 18 In 2014, the full credits apply for annual household incomes between £0 and £6,420 (HM Treasury 2013). The WTC is phased out between £6,420 and about £18,000, depending on household circumstances, and at the same rate as the CTCs. Without beginning to count spousal income or income from job seekers allowances, someone earning the median wage in a full-time full-year job (hereafter “the median”) would earn about £23,000 and therefore not receive any WTC on the weekly employment margin (4) unless he was out of work much of the year and did not have significant income from other sources.Footnote 19 For this reason, this paper gives more attention to the CTCs, which are phased out above annual household income of £18,000 (or so, depending on circumstances) until about £26,000 for one child and £33,000 for two children.Footnote 20

Figure 3 shows the income ranges over which CTCs were phased out, in selected years. Relative to the median wage, the phase-out range widened somewhat between 2007 and 2013. By 2013, a household with 2 children could have an income of up to £32,400 (at the median wage, an individual’s 2013 full-time full-year earnings would be only about £22,000) and still be receiving some CTC.Footnote 21 But the more significant change has been in the increase in the phase-out rate from 37 percent to 41 percent. As I show below, these four percentage points are a large part of the work incentive because already in 2007 workers paying the basic rate and receiving CTC were keeping only 20 percent of their employer’s cost at the margin.

Fig. 3 U.K. Child Tax Credit phaseout ranges and rates Full size image

In summary, VAT rates, NICs parameters, personal income tax rules, and tax credit rules all changed after 2007. The next step is to use equation (4) to determine the direction and quantitative importance of the changes for incentives to be employed.

Changes since 2007: overall employment tax rates

Employment during a week creates income for the tax year and for this reason alone creates income and payroll tax liabilities — at the rates displayed in the previous section. In addition, employment is implicitly subsidized by the threshold amounts in the NICs rules and implicitly taxed by the opportunity for unemployment benefits during weeks not working. The economic importance of these three policy parameters, represented as UB, PT, and ST in equations (3) and (4), varies inversely with employer cost y. Table 1 displays each of these parameters for tax years 2010 and 2011, when some of the larger changes went into effect.

Table 1 Implicit Employment Taxes from NICs and the JSA, 2010 and 2011 Full size table

The top three rows are the NICs parameters. Both employer and employee rates increased between 2010 and 2011, which made each pound of primary and secondary threshold more valuable. Moreover, the two thresholds were increased by more than £25 per week. As shown in the table’s third row, the combination of these changes resulted in a 5.9-pound increase in the value (in terms of tax savings) of the primary threshold between 2010 and 2011, adjusted for inflation.

The next row is the job seekers allowance (JSA). Adjusted for inflation, it fell about one pound. The difference between the fourth and third rows is the net implicit weekly employment tax created by the JSA and NICs, holding annual income constant. It fell about seven pounds per week, adjusted for inflation. Both the JSA and ST values are adjusted for personal income taxes as specified by equation (4).

As with any employment tax, the economic importance of the employment taxes shown in Table 1 depends on their magnitudes relative to the value created by a week of work, which I measure as employer cost for a 40-h week at the median of the hourly wage distribution for full-time workers.Footnote 22 The next two rows in the Table therefore express the employment taxes as a percentage of the 2010–11 average employer cost. By this measure of change, which is entirely a function of the inflation-adjusted statutory parameters, employment tax rates fell more than one percentage point between 2010 and 2011.

Real wages and real employer cost were falling during this period, which means that each pound of implicit employment tax became economically more important over time. I account for this change by using the variable-weight measures shown in the final row of the table, which use year-specific employer cost for the ratios PT/y and UB/y. By comparison with the previous row, we see that falling real employer cost partly, but not fully, offsets the contribution of the growing value of the NICs thresholds to the weekly employment tax.

The tax-wedge equation (4) features the sum of four terms inside the parentheses. Figure 4 displays the three non-consumption-tax terms as red, blue, and green, respectively.Footnote 23 For the purpose of calculating the JSA and PT/ST terms, y is taken to be the weekly employer cost of the median worker (the same as in Table 1). Thirty percentage points are added to the JSA term so that it can be plotted on the same scale as the PIT-NIC term. The policy parameter changes noted above are readily seen in the figure: the PIT’s basic rate reduction in 2008 (red series), the 2011 addition to the NICs rates (red series), and the 2011 enhancement of the value of the PT (green series). The PIT-NIC series ends the time period essentially where it began, which leaves the net effect of the other two terms. The JSA term rises because employer costs grow less than the CPI (likely the VAT hike had something to do with that).

As with the other tax calculations in this paper, Fig. 4 does not include housing allowances for the unemployed. The changes over time would be the same if housing allowances had been included and stayed in a fixed proportion with the weekly employer cost of the median worker. See Adam and Browne (2013) for discussion of housing allowance policy changes and Appendix II for list of tax and benefit programs that are included in this paper’s calculations.

Table 2’s first column lists all of the tax and benefit programs that contribute to my calculation of the U.K. employment tax wedge according to equation (4). Among basic rate payers (of the personal income tax), the only reasons that the results of equation (4) vary across U.K. workers are: (a) some are having their credits phased out while others are not, (b) they have different employer cost y, and (c) persons who are both married and long-term unemployed may receive more JSA than the others do. Of these, only the credit phaseouts are quantitatively important for determining incentive changes over time.Footnote 24 Figure 5 puts all of equation (4)’s pieces together and shows the log change in the after tax share (1-q) among married basic-rate payers, separately by employer cost and credit-phaseout status.Footnote 25 A low-wage (high-wage) worker refers to one with weekly employer cost 0.4 below (above) the median worker, respectively.Footnote 26

Table 2 Tax and benefit programs included the rate calculations Full size table

Among those with credits fully phased out (dashed series in Fig. 5), the changes are essentially the same for low- and high-wage workers. The dashed series end in 2013 about where they began because the consumption tax increase (driven by the VAT change) tends to offset the combined reduction represented as the sum of Fig. 4’s three series. The low-wage dashed series finished slightly above the high-wage series because the £5 weekly reduction in the tax value of (JSA − tax value of PT and ST) is a somewhat greater percentage of employer cost for low-wage employees. Both series have a temporary increase in 2008 and 2009 because of the temporary VAT cut and because the PIT’s basic rate cut was sudden, and sooner, compared with the changes in employer cost and the higher NICs rates that would come later.

The solid series shows incentive changes for “on-credits” individuals with a decision to work one week more (or less) during the year that affects the amount of their child tax credit. Specifically, on-credits individuals receive a credit if they work more, but less credit than they would receive if working less. For them, the reward to working falls significantly because the benefit reduction rate after 2010 was four points greater than it was in 2007 when their after-tax share was already as low as 20 percent. The increase in 2008 and 2009 is less than it is for those “off credits” because the benefit reduction rate increase in 2008 was offsetting the contemporaneous cut in the basic rate. Lesser employment disincentives emerge for low-wage workers because the combined value of the NICs thresholds is a nontrivial incentive for them to work and this value increased after 2007 (recall Fig. 4’s green PT/ST series).

As shown in Fig. 3, the threshold for CTCs did not change in exact proportions with the median wage, which means that even a worker whose wage tracked the median might receive credits in later years but not in earlier years, or vice versa. Figure 5 omits such workers, but their incentive changes would be massive because equation (4) evaluated without credit phaseout is about 55 percent whereas the value with credit phaseout exceeds 80 percent. These two situations are relatively rare, though, because the thresholds did not change much relative to the median wage.

Although payroll taxes, sales taxes, and personal income taxes do not combine the income of spouses in order to determine the rate that applies, tax credits do. This by itself tends to increase the likelihood of unmarried workers to be on credits. However, because cohabiting unmarried persons are treated as married for tax credit purposes, and couples are more likely to have children, single workers are not more likely to be on credits. For example, in the tax year beginning April 2011, workers claiming tax credits as singles were only 23 percent of all adults in working families with credits (HM Revenue and Customs 2013a, Table 2.1, counting husband and wife separately). By comparison, 42 percent of adults in the U.K. were neither married nor cohabiting.Footnote 27

Comparison with previous studies

Adam and Browne (2013) also look at changes in work incentives between 2010 and (their forecast for) 2015. Our studies have two major differences — the baseline against which policies are compared and the types of individuals considered — as well as a more subtle difference in the type of incentive(s) that we measure. On the first point, both their paper and mine note that “earnings have increased less quickly than benefit rates, which tends to make working less attractive” (Adam and Browne (2013), p. 1). Equivalently, benefit rates have increased more than wage rates: is that a policy change or not? This is merely a question of definition, and I refer to any change in benefit rates relative to wages as a policy change even if prior law would have it that way. Moreover, because benefit rates have increased relative to wages but decreased relative to the Retail Price Index (RPI, which prior law had used for indexing benefits), policy reduced the reward to work by my definition (ignoring the other statutory changes noted above).

The second difference from Adam and Browne (2013) is that my sample excludes persons not working at all during the year, whereas Adam and Browne’s include them. The difference is important because “The majority of the welfare reforms involve changing the maximum amount of means-tested support that can be received by those with no other income” (Adam and Browne (2013), p. 10). Persons not working at all during a tax year may not be close to the margin for working in the short run and are thereby less interesting for short-run behavioral analysis, although excluding them altogether (as I do) errs in the opposite direction.Footnote 28 I look at a variety of skill levels, but, unlike Adam and Browne, not deviations from the median wage that are so large that some of the workers are still receiving working tax credits.

The reward to working an additional week examined in this paper has a lot in common with the reward to earning more per week, which Adam and Browne (2013) call the EMTR, except that the latter does not reflect foregone unemployment benefits or the value of the NICs’ thresholds. As a result, they find the EMTR to be essentially constant after 2010, whereas my reward measure falls somewhat, in part because of the contribution of foregone unemployment benefits.Footnote 29

Because the labor market features a rich variety of circumstances and alternative work situations, all of the tax rate measures are relevant for behavioral analysis. The additional-week measure deserves some attention for the purpose of understanding employee and employer decisions of how long to maintain a job or to endure a period of joblessness, which are decisions that are relevant for business cycle purposes. My paper is also unique in its display of year-to-year tax-wedge dynamics after 2007.

The overall level of disincentives is not a focus of this paper or Adam and Browne’s. I report comparatively higher levels (80+ percent is not uncommon) because of my focus on the weekly employment margin (e.g., including JSA as an implicit tax) and perhaps because of my treatment of indirect taxes. Appendix I details my measurement of, and economic assumptions about, various indirect taxes.