Payroll taxes and employment subsidies

A payroll tax is levied on each hour, or each dollar, of labour a firm employs. It drives a wedge of exactly the tax between the cost of an hour to the firm and the wage the worker takes home. Who bears it depends on the elasticities of labour supply and demand, not on who remits it.

The wedge

The tax separates two prices that are equal without it:

• the cost of an hour to the firm, $w_{\text{firm}}$, which includes the tax, and
• the wage the worker takes home, $w_{\text{worker}}$, which does not.

With a tax of $$t$ per hour, $w_{\text{firm}} - w_{\text{worker}} = t$. The model determines where the wedge sits relative to the old wage: how much of the $$t$ comes out of take-home pay and how much is added to the firm’s cost.

In Canada the rules split the bill on paper. Employers pay the same Canada Pension Plan contribution rate as their employees, and they pay 1.4 times the Employment Insurance premium their employees pay.¹ That legal division is the statutory incidence of the tax. The division of the burden after markets adjust is the economic incidence, and the two need not match.

The model

Start with a competitive labour market: many firms and many workers, all taking the wage as given. Labour demand is the value of the marginal product of labour, the most a firm will pay for each hour. Labour supply shows the lowest wage at which workers will offer each hour.

Now charge firms $$t$ for every hour they employ. For any number of hours, the most a firm will now pay the worker is its value of the marginal product minus the tax, so the labour demand curve shifts down by exactly $$t$. The new equilibrium is where the shifted demand curve $D_1$ meets supply.

Payroll tax per hour

$4.00

Worker gets

$14.67

Firm pays

$18.67

Employment

41.7k hrs

Deadweight loss

$16.7k

Open in Graph Lab

Figure 1. A payroll tax of $t$ per hour collected from firms shifts labour demand down from $D_0$ to $D_1$. At $t = 4$, employment falls from 50 to 41.7 thousand hours, the wage workers receive falls from $17.00 to $14.67 and firms' cost rises to $18.67. The deadweight loss grows with the square of the tax.

Three things happen at once:

1. Employment falls, because hiring is now more expensive and the lower take-home wage draws out fewer hours.
2. The wage workers receive falls, but by less than the tax.
3. The cost of an hour to firms rises, also by less than the tax.

The tax revenue is the rectangle $t \times E_1$. The shaded triangle is the deadweight loss: hours between $E_1$ and $E_0$ that firms valued at more than workers needed to supply them, which are no longer worked. The revenue is a transfer from the market to the government; the triangle is value that simply disappears.

It does not matter who writes the cheque

Suppose the government instead collects the same $$t$ from workers. Now the lowest wage a worker will accept for each hour rises by $$t$, so the supply curve shifts up by $$t$ and demand stays put.

Payroll tax per hour

$4.00

Worker keeps

$14.67

Firm pays

$18.67

Employment

41.7k hrs

Open in Graph Lab

Figure 2. The same tax collected from workers shifts supply up by $t$. Employment, the wage firms pay and the wage workers keep are identical to Figure 1.

The equilibrium must again be the employment level at which the demand price exceeds the supply price by exactly $$t$. There is only one such level, so every outcome is the same as in Figure 1. This is the central result of tax incidence: statutory incidence does not determine economic incidence.

Key idea

A payroll tax drives a wedge of exactly $t$ between the firm’s cost and the worker’s wage. Where the wedge sits depends only on the elasticities of labour supply and demand, never on which side the law bills.

Who bears the burden

The burden falls mostly on whichever side of the market is less able to walk away. For a small tax, the share borne by workers is

$$\text{workers' share} = \frac{\varepsilon_D}{\varepsilon_D + \varepsilon_S},$$

where $\varepsilon_D$ and $\varepsilon_S$ are the wage elasticities of labour demand and labour supply, both in absolute value. If supply is the less elastic side ($\varepsilon_S < \varepsilon_D$), workers bear more than half.

Elasticity of labour supply

1.20

Workers' share of the tax

59%

Firms' share

41%

Fall in employment

8.3k hrs

Open in Graph Lab

Figure 3. A $4 tax with labour supply pivoting through the original equilibrium. As labour supply becomes less elastic, workers' share of the tax rises toward 100 percent and the fall in employment shrinks.

Two limiting cases:

• Perfectly inelastic labour supply (a vertical supply curve). Hours do not respond to the wage, so the demand shift slides straight down the supply curve. Workers bear the entire tax through lower wages, employment does not change, and there is no deadweight loss.
• Perfectly elastic labour supply (a horizontal supply curve). Workers will not accept less than the going wage, so the wage they receive cannot fall. Firms bear the entire tax and employment falls the most.

Most evidence finds that labour supply, especially for prime-age men, responds little to the wage, while firms can adjust hiring and capital over time. That combination predicts that workers bear most of a payroll tax in the long run.

Employment subsidies

An employment subsidy is a payroll tax run in reverse. If the government pays firms $$s$ for each hour they hire, labour demand shifts up by $$s$. Employment rises, the wage workers receive rises, and the net cost of an hour to firms falls, with the two again exactly $$s$ apart.

Subsidy per hour

$3.00

Worker gets

$18.75

Firm pays (net)

$15.75

Employment

56.3k hrs

Cost to taxpayers

$168.8k

Deadweight loss

$9.4k

Open in Graph Lab

Figure 4. A subsidy of $s$ per hour shifts labour demand up from $D_0$ to $D_1$. The shaded triangle is the deadweight loss from hours whose output is worth less than the workers' time.

In a competitive market the extra jobs are not free. For each hour between $E_0$ and $E_1$, the value of what the worker produces (read off the original demand curve) is less than the value of the worker’s time outside the market (read off the supply curve). The triangle between them is a deadweight loss, and taxpayers pay $s \times E_1$ in total, which can be a large cost for each additional job.

Canada ran the largest employment subsidy in its history during the COVID-19 pandemic. The Canada Emergency Wage Subsidy initially covered 75 percent of an employee’s pay, up to $847 a week, for wages paid between March 15 and June 6, 2020, and was later extended.² The competitive model is a poor guide to that episode: the goal was to keep existing worker-firm matches alive through a temporary shock, not to create jobs that would not otherwise exist, and losing those matches would itself have destroyed value.

Worked example

Labour demand is $w = 27 - 0.2E$ and labour supply is $w = 3 + 0.28E$, with $E$ in thousands of hours a week. The government introduces a payroll tax of $4 per hour on employers.

1. Find the original equilibrium. Set demand equal to supply: $27 - 0.2E = 3 + 0.28E$, so $E_0 = 24 / 0.48 = 50$ and $w_0 = 3 + 0.28(50) = 17$.

2. Shift demand down by the tax. The new demand curve is $w = 23 - 0.2E$.

3. Find the new equilibrium. $23 - 0.2E = 3 + 0.28E$ gives $E_1 = 20 / 0.48 \approx 41.67$ thousand hours.

4. Read off the two wages. Workers receive the supply price, $3 + 0.28(41.67) \approx 14.67$. Firms pay that plus the tax, $18.67$.

5. Split the burden. Workers lose $17.00 - 14.67 = 2.33$ per hour, or 58 percent of the tax. Firms lose $18.67 - 17.00 = 1.67$, or 42 percent. With linear curves, workers’ share is the supply slope over the sum of the slopes, $0.28 / (0.2 + 0.28) = 0.58$.

6. Measure revenue and deadweight loss. Revenue is $4 \times 41.67 \approx 166.7$ thousand dollars a week. The deadweight loss is $\tfrac{1}{2} \times 4 \times (50 - 41.67) \approx 16.7$ thousand dollars a week.

Exercise: the same market with a $2 tax

Demand becomes $w = 25 - 0.2E$, so $E_1 = 22 / 0.48 \approx 45.83$. Workers receive $3 + 0.28(45.83) \approx 15.83$ and firms pay $17.83. Workers still bear 58 percent of the tax, because the split depends only on the slopes. The deadweight loss is $\tfrac{1}{2} \times 2 \times 4.17 \approx 4.2$ thousand dollars, a quarter of the loss from the $4 tax: halving a tax cuts its deadweight loss by about three quarters.

Evidence

Chile. In 1981 Chile replaced its pay-as-you-go social security system with individual retirement accounts. Over the following years the payroll tax burden on employers fell dramatically; in Jonathan Gruber’s sample of manufacturing plants the average rate fell from 30 percent to 5 percent. Gruber found the cut was passed through to workers as higher wages, essentially one for one, with no measurable effect on employment.³ That is the pattern the model predicts when labour supply is close to perfectly inelastic: workers had been bearing nearly all of the tax, so they captured nearly all of the cut.

Greece. A 1993 Greek reform sharply raised payroll taxes on high earners who entered the labour force from that year onward, while leaving earlier entrants under the old rules. Comparing workers on either side of the cut-off, Saez, Matsaganis and Tsakloglou found that employers compensated younger new-regime workers for the extra employer tax but not for the extra employee tax, so in this case the legal split did matter. For older new-regime workers, incidence matched the standard model: they bore both taxes.⁴ The authors point to seniority-based pay norms that keep wages from adjusting freely, a reminder that the clean equivalence result assumes wages can move.

Common mistakes

Traps on exams

• Shifting demand by less than the tax. The demand curve shifts down by the full tax. The partial pass-through shows up in the new equilibrium, not in the size of the shift.
• Assuming a 50/50 split. The split equals 50/50 only when the curves are equally steep. Read it off the graph or the elasticities.
• Calling the revenue rectangle a loss. Revenue is a transfer. Only the triangle is deadweight loss.
• Forgetting that a subsidy also creates a deadweight loss in a competitive market: the extra hours are worth less than they cost.

On the exam

Draw both wages on the vertical axis and label them ($w_{\text{firm}}$ above, $w_{\text{worker}}$ below) with the gap marked $t$. Label the original equilibrium, the new employment level, the revenue rectangle and the deadweight-loss triangle. Then state who bears more and why, in one sentence about elasticities.

Check yourself

1.

True or false: if a payroll tax is collected from workers instead of firms, employment falls by more.

1True2False

Check answer

2.

Labour supply in a market is perfectly inelastic. The government introduces a $2 per hour payroll tax on employers. Which outcome follows?

1The wage workers receive falls by $2, employment does not change, and there is no deadweight loss2The wage workers receive falls by $1 and firms' costs rise by $13Employment falls and a deadweight loss appears, but wages do not change4Firms' labour costs rise by $2 and the wage workers receive does not change

Check answer

3.

At the initial equilibrium the wage elasticity of labour demand is $-1.5$ and the wage elasticity of labour supply is $0.5$. Approximately what percentage of a small payroll tax do workers bear?

Your answer (percent)

Check answer

Practise more questions on this topic

Sources

1. Canada Revenue Agency, EI premium rates and maximums and CPP contribution rates, maximums and exemptions. ↩

2. Department of Finance Canada, The Canada Emergency Wage Subsidy (archived), and Canada Revenue Agency, Frequently asked questions: Canada emergency wage subsidy. ↩

3. Gruber, J. (1997). The incidence of payroll taxation: Evidence from Chile. Journal of Labor Economics, 15(3), S72 to S101. NBER working paper 5053. ↩

4. Saez, E., Matsaganis, M. and Tsakloglou, P. (2012). Earnings determination and taxes: Evidence from a cohort-based payroll tax reform in Greece. Quarterly Journal of Economics, 127(1), 493 to 533. NBER working paper 15745. ↩