Public 3: Income Taxes Flashcards
What is a progressive income tax?
An income tax is progressive if the average tax rate rises with income.
What is the effective marginal tax rate? Does it equal the headline rate of income tax?
The effective marginal tax rate is the amount of additional take-home pay you receive from a £1 pay rise. This is not in general equal to the headline rate of income tax, as the effective marginal tax rate also includes National Insurance contributions and the taper of any benefits.
What is the participation tax rate?
The participation tax rate is the average cost of entering the labour market (T(z) - T(0))/z where z is the prospective earnings when entering the labour force.
How is the optimal linear marginal tax rate related to the degree of societal inequality aversion?
When the social marginal utility of income is strongly negatively correlated with income, the optimal linear tax rates is lower.
What is the setup of the Mirrlees (1971) model?
- Individuals differ in innate ability to earn income. This is set exogenously.
- Income depends on both ability and effort. Only income is observable.
- There is only one period and no saving.
- The government aims to set a tax schedule such that revenue can be raised and redistributive transfers can be made, but without incentivising those of high ability to ‘feign’ being of low ability.
Why, in the Mirrlees model, are tax rates never negative?
Suppose we have a section of the income distribution with T’(z)<0. We can find a 45º tax schedule through this region (T’(z)=0) that leaves the total tax bill unchanged, if agents do not alter their labour choice. This will entail gains for the poor and losses for the rich, which implies social welfare gains when we are inequality-averse. However, since agents optimise they will also change their labour supply choices, and make themselves better off, at no cost to the government because T’(z)=0 in this region.
Why, in the Mirrlees model, are tax rates never above 1?
Suppose we have a section of the income distribution with tax rates above 1. No rational optimiser will choose to earn in this section. Therefore, replacing it with T(z) = 1 will be a weak Pareto improvement.
Why do Sadka and Seade argue that the marginal tax rate for the highest earner should be zero? Does this result hold in practice?
Suppose the highest earner chooses to earn z(n1) and that T’(z(n_1))>0. If we change the tax schedule to T’(z)=0 for all z≥n_1, the highest-ability consumer will choose to earn more, and is therefore made better off by revealed preference. Total government revenue does not change. Therefore, everyone is at least as well off and there is more tax revenue.
This result relies on there be an identifiable top earner. In practice, skill distributions may be unbounded, top earners may be internationally mobile, or the top earner may simply be unidentifiable. It therefore has few practical implications.
What three effects are there from changing the top tax rate?
Top earners choose to work less, and are made worse off.
Total revenue increases mechanically from the increase in marginal taxes.
Total revenue decreases with the elasticity of labour supply.
Where in the income distribution should marginal tax rates be relatively highest?
- Where the number of people earning this amount is low relative to the number above it.
- Where elasticities are low
- Where social welfare weightings are low
What is a Pareto distribution? Why is it empirically important that the top end of income distributions often closely resembles one?
A Pareto distribution is a probability distribution with fatter tails than the normal or lognormal distributions. Importantly, z(z-zbar) is constant for Pareto distributions, allowing us to simplify expressions such as those derived above for optimal marginal tax rates.
How can we estimate the elasticities of income at the top of the income distribution?
- Try to quantify the effects of tax rises on top (taxable) incomes.
- Difficulty is to disentangle tax-rise changes to other changes in the economy.
- Difference-in-difference approach with people around the cutoff for the band. Eg use the top 5% earners as a control group for the top 1%.
- Think carefully about whether income is decreasing, or whether top earners are reducing their taxable income through changing their tax behaviour (eg taking capital income, pensions, dividends).
What are some reasonable estimates for elasticities of labour supply at the top of the income distribution in the UK?
The Mirrlees review estimate e=0.46.
Diamond and Saez suggest e could be as low as 0.17, with a conservative upper bound of 0.57.
There is little consensus over the ‘true’ value, or how it might change over time.
What is the difference between the ‘extensive margin’ and the ‘intensive margin’?
The ‘intensive margin’ is the response of hours worked when tax rates change.
The ‘extensive margin’ is the response of whether or not to work when tax rates change.
How does introducing extensive effects into models of optimal income tax change our recommendations?
The Mirrlees (1970) model does not include effects on the extensive margin. It therefore targets benefits at the lowest earners by setting high marginal tax rates on low earners who are not the lowest earners.
However, the extensive margin seems to be the empirically strongest effect at this point in the income distribution. This points us to introducing in-work benefits, encouraging some nonworkers into work, raising welfare at the bottom and increasing revenues. However, this effect must be traded off with the income effect on those already choosing to work this amount.
