Income tax

Question 1

Laroque (2005) result

Answer 1

1. Assume preferences are separable between consumption and leisure
2. Whatever the tax structure, it can be improved by setting commodity taxes to zero and changing income tax to compensate

Question 2

Atkinson and Stiglitz (1976) result

Answer 2

1. Assume preferences are separable between consumption and leisure
2. Optimal to have commodity taxes = 0 and redistribute via income tax

Question 3

What does the assumption that preferences are separable between consumption and leisure mean?

Answer 3

All goods equally complementary with leisure

Question 4

A tax scheme is progressive if…

Answer 4

the effective marginal rate increases with income

Question 5

What does a flatter slope indicate on a graph in net/gross income space?

Answer 5

Higher marginal tax rate

Question 6

Optimal linear marginal tax rate higher if:

Answer 6

1. Avg. elasticity of labour supply (weighted by income) = lower
2. SWF more concave (inequality aversion higher, so low-income earners more ‘deserving’)
3. Income distribution more skewed

Question 7

Diamond (1998) proposition

Answer 7

1. Marginal tax rates increasing above modal skill level if, above this level:
   (i) Elasticity of labour supply constant
   (ii) Distribution of skills = Pareto (or fatter)

Question 8

Key underlying assumption that Diamond (1998) makes

Answer 8

No income effects

Question 9

Diamond (1998) - A(n) formula interpretation

Answer 9

1. Standard inverse elasticity term (not weighted, just elasticity for that particular person)
2. Lower marginal tax rate if labour supply more elastic

Question 10

Diamond (1998) B(n) formula interpretation

Answer 10

1. Average ‘relative deservingness’ for people above skill level n
2. Higher marginal tax rate if average relative deservingness is lower

Question 11

Diamond (1998) C(n) formula interpretation

Answer 11

1. How many people tax will affect
2. Higher marginal tax rate on skill n if:
   (i) There are more people ABOVE skill level n
   (ii) There are fewer AT skill level n
   (iii) Skill level n is lower

Question 12

What sort of distribution does Saez (2001) show empirically that the income distribution is close to? Implications of this for taxing the rich?

Answer 12

1. Income distribution v. close to Pareto distribution

2. Suggests constant marginal tax rate at top end (see Diamond)

Question 13

Why do indifference curves slope upwards in gross income/consumption space?

Answer 13

Labour is a bad and so, if individual is to work more, must be able to consume more in order to maintain utility

Question 14

Assumption Mirrlees makes when proving result that optimal marginal rate can never be below zero?

Answer 14

1. Assumes behaviour only focuses on intensive margin of response
2. i.e. all participate, but if tax rates affect participation decisions (extensive margin), then optimal rates may be negative

Question 15

1. General assumption Mirrlees makes in income tax model?

2. Implications?

Answer 15

1. Single-crossing property (agent monotonicity):

2a. Indifference curves only cross once
2b. Agent w/higher skill has lower slope at crossing point

Question 16

1. Practical problems with Mirrlees result that the optimal marginal income tax rate on the top earner = 0?
2. Consequence?

Answer 16

1a. Can’t identify who precise top earner is and what their earnings will be
1b. Can’t predict ahead of time (+ cannot design tax schedule after the event)
1c. Likely to change each year

2a. Example - incorrectly identify top earner and set zero marginal rate for all skill levels equal to/above this person person (but there’s actually a higher earner we failed to predict)
2b. Problem - not getting as much tax revenue as we could out of the top earner because we’ve accidentally set a zero marginal rate on some/much of his income

Question 17

1. Empirical evidence on the shape of the income distribution
2. Implication?

Answer 17

1. Saez (2001) - income distribution v. close to Pareto distribution
2. Diamond (1998) proposition v. relevant

Question 18

1. How does a Pareto income distribution link to the Diamond optimal marginal tax rate formula?
2. Implication?

Answer 18

1. Pareto income distribution means the factor C(n) is constant
2. Implication - suggests constant marginal tax rate at top end

Question 19

1. In terms of the Diamond model, what is the implication of an income distribution that’s even fatter than Pareto?
2. Policy implication?

Answer 19

1. Factor C(n) is increasing

2. Implication - suggests increasing marginal tax rates at top

Question 20

What question does Saez (2001) seek to answer?

Answer 20

If top marginal tax rate is some constant, what should that rate be?

Question 21

Gruber and Saez (2002)

Answer 21

US LABOUR SUPPLY ELASTICITY EVIDENCE

1. Estimates for elasticity of labour supply suggest elasticity increases w/income
2. Taxable income of very high earners may be esp. elastic
3. Could indicate declining marginal rates at the top

Question 22

1. Saez (2001) - findings from numerical simulations

2. Reason for findings

Answer 22

1. Numerical simulations indicated that marginal rates should increase between middle/high earners, w/rates for high earners “not lower than 50% and maybe as high as 80%”
2. Reason – right tail of income distribution better described by Pareto distribution w/thick tails

Question 23

Saez et al (2010) - Mirrlees Review

Answer 23

TOP UK TAX RATE

1. Based on estimates of labour supply elasticity of rich, UK government would maximise revenue w/overall marginal rate on highest earners = 57%
2. Similar to current rate of 53% (incl. income tax, NI contributions and indirect taxes)
3. NO strong case for significantly increasing top marginal rates in the UK

MARGINAL RATES FOR LOW EARNERS

1. EXTENSIVE MARGIN - v. high marginal rate (close to 100% pre-working tax credit and v. high after it) for those entering work at low earnings due to taxes + withdrawal of benefits, harming incentives to enter labour force
2. INTENSIVE MARGIN - 73% marginal rate for low/moderate earners as tax credits withdrawn
3. RECOMMENDATION - increase amount people can earn before benefits withdrawn to improve incentives to enter work

LABOUR SUPPLY ELASTICITY

1. Responsiveness of hours worked to tax system is v. low for most groups, perhaps zero
2. Responsiveness of taxable earnings = bigger, which rises for high-earners

Question 24

Based on estimates of labour supply elasticity of rich, UK government would maximise revenue w/overall marginal rate on highest earners = 57%

Answer 24

Saez et al (2010) - Mirrlees Review

Question 25

..... (.....) Based on estimates of labour supply elasticity of rich, UK government would maximise revenue w/overall marginal rate on highest earners = .....%

Answer 25

Saez et al (2010) - Mirrlees Review Based on estimates of labour supply elasticity of rich, UK government would maximise revenue w/overall marginal rate on highest earners = 57%

Question 26

..... (.....) 1. Numerical simulations indicated that marginal rates should increase between middle/high earners, w/rates for high earners “not lower than .....% and maybe as high as .....%” 2. Reason – right tail of income distribution better described by .....

Answer 26

Saez (2001) 1. Numerical simulations indicated that marginal rates should increase between middle/high earners, w/rates for high earners “not lower than 50% and maybe as high as 80%” 2. Reason – right tail of income distribution better described by Pareto distribution w/thick tails

Question 27

1. What does Saez (2001) mean by an unbounded distribution? | 2. What implication does this have for the top marginal tax rate?

Answer 27

1. Top earnings not known in advance, but can instead think that potential earnings drawn randomly from Pareto distribution 2. Mirrlees' zero top rate result has no policy relevance

Question 28

If participation effects are important, what is the implication for optimal income transfers to the poor?

Answer 28

1. Optimal to give higher transfers to low-income than non-workers 2. Reason - encourages people to work, given evidence of importance of extensive margin for low-earners

Question 29

3 key recommendations of Diamond and Saez (2011)

Answer 29

1. Very high earnings should be subject to rising and high marginal rates 2. Policy toward low earners should include subsidy to earnings and phase out subsidisation at relatively high rate 3. Capital income should be taxed

Question 30

Evidence that labour supply responses along extensive (participation) margin are important

Answer 30

Diamond and Saez (2011) 1. Compelling evidence of substantial labour supply responses to transfers along extensive margin (participation, whether/not to work) 2. Extensive elasticity of choosing whether to participate large for those w/low incomes, relative to intensive elasticity of choosing no. hours to work

Question 31

Compelling evidence of substantial labour supply responses to transfers along extensive margin (participation, whether/not to work)

Answer 31

Diamond and Saez (2011)

Question 32

Extensive elasticity of choosing whether to participate large for those w/low incomes, relative to intensive elasticity of choosing no. hours to work

Answer 32

Diamond and Saez (2011)

Question 33

Diamond and Saez (2011)

Answer 33

EXTENSIVE LABOUR SUPPLY ELASTICITY 1. Compelling evidence of substantial labour supply responses to transfers along extensive margin (participation, whether/not to work) 2. Extensive elasticity of choosing whether to participate large for those w/low incomes, relative to intensive elasticity of choosing no. hours to work TOP-END ELASTICITY ESTIMATES 1. Considerable uncertainty about long-run behavioural responses to top tax rates 2. Estimates of high labour supply elasticities for top earners (e.g. Gruber and Saez 2002) may be over-estimates due to importance of tax avoidance responses, which often involves shifting timing of taxes paid 3. Tax avoidance component of elasticity response can be reduced by broadening base/reducing deductions POLICY RECOMMENDATIONS 1. Very high earnings should be subject to rising and high marginal rates 2. Policy toward low earners should include subsidy to earnings and phase out subsidisation at relatively high rate 3. Capital income should be taxed

Question 34

1. State the Chamley-Judd result of zero capital taxation 2. Explain 3. Key assumption?

Answer 34

1. In model w/infinitely-lived agents, optimal tax on capital income = 0 2a. Constant capital income tax creates growing wedge between current and future consumption as time horizon grows 2b. To avoid tax compounding that grows w/o limit as time horizon extends, optimal average rate must be zero 3. Key assumption – individuals make rational decision about savings across v. long horizons

Question 35

1. Key assumptions of Chamley-Judd result of zero capital taxation 2. Evaluate these

Answer 35

1a. Infinitely-lived agents 1b. Individuals make rational decision about savings across v. long horizons 2a. Savings decisions not 100% rational, but influenced by psychology (e.g. self-control) or small transaction costs (e.g. default options) 2b. Empirical evidence shows concern for heirs, but not sufficient to support rigorous dynasty model required by Chamley and Judd

Question 36

Reasons to tax capital income

Answer 36

1. DIFFICULT TO DISTINGUISH CAPITAL AND LABOUR INCOME (i) After 1993 Finnish tax reform to lower rate on capital income, significant shifts of labour to capital income among self-employed 2. EASE TAX BURDEN ON BORROWING CONSTRAINED (i) Capital income taxes fall on those not borrowing constrained (they have capital) (ii) raising revenue from capital income tax allows for lower earned income tax (incl. on poorer, borrowing constrained) 3. POSITIVE CORRELATION BETWEEN EARNINGS OPPORTUNITIES AND SAVING PROPENSITIES (i) Taxing savings might contribute to efficient redistributive taxation by indirectly identifying those w/higher earnings abilities

Question 37

Intuition for why it is not optimal to have a marginal tax rate below zero

Answer 37

1. Negative marginal tax rate = subsidy to work | 2. If subsidise work, then high-skilled (who gain more from working) gain relative to low-skilled

Question 38

1. Marginal tax rates increasing above modal skill level if, above this level: (i) Elasticity of labour supply constant (ii) Distribution of skills = Pareto (or fatter)

Answer 38

Diamond (1998)

Question 39

Under what conditions is the marginal tax rate increasing above the modal skill level, according to Diamond (1998)?

Answer 39

(i) Elasticity of labour supply constant | ii) Distribution of skills = Pareto (or fatter

Question 40

Saez (2001)

Answer 40

1a. Income distribution v. close to Pareto distribution 1b. Suggests constant marginal tax rate at top end (see Diamond) 2a. Numerical simulations indicated that marginal rates should increase between middle/high earners, w/rates for high earners “not lower than 50% and maybe as high as 80%” 2b. Reason – right tail of income distribution better described by Pareto distribution w/thick tails

Question 41

US LABOUR SUPPLY ELASTICITY EVIDENCE 1. Estimates for elasticity of labour supply suggest elasticity increases w/income 2. Taxable income of very high earners may be esp. elastic 3. Could indicate declining marginal rates at the top

Answer 41

Gruber and Saez (2002)

Question 42

TOP-END ELASTICITY ESTIMATES 1. Considerable uncertainty about long-run behavioural responses to top tax rates 2. Estimates of high labour supply elasticities for top earners (e.g. Gruber and Saez 2002) may be over-estimates due to importance of tax avoidance responses, which often involves shifting timing of taxes paid 3. Tax avoidance component of elasticity response can be reduced by broadening base/reducing deductions

Answer 42

Saez and Diamond (2011)

Question 43

Possible reasons that very long-run elasticity of labour supply responses might be higher, esp. for top-earners?

Answer 43

In long-run, high marginal rates may impact: 1. Decisions about education and career choice (e.g. very high marginal rate might raise lots of money today, but discourage future earnings) 2. Decisions about location (e.g. banker might move to New York from London)

Question 44

If participation effects are important, what is the implication for optimal income transfers to the poor?

Answer 44

1. Optimal to give higher transfers to low-income than non-workers 2. Reason - encourages people to work, given evidence of importance of extensive margin for low-earners

Question 45

1. Based on estimates of labour supply elasticity of rich, UK government would maximise revenue w/overall marginal rate on highest earners = 57% 2. Similar to current rate of 53% (incl. income tax, NI contributions and indirect taxes) 3. NO strong case for significantly increasing top marginal rates in the UK

Answer 45

Saez et al (2010) - Mirrlees Review

Question 46

MARGINAL RATES FOR LOW EARNERS 1. EXTENSIVE MARGIN - v. high marginal rate (close to 100% pre-working tax credit and v. high after it) for those entering work at low earnings due to taxes + withdrawal of benefits, harming incentives to enter labour force 2. INTENSIVE MARGIN - 73% marginal rate for low/moderate earners as tax credits withdrawn 3. RECOMMENDATION - increase amount people can earn before benefits withdrawn to improve incentives to enter work

Answer 46

Saez et al (2010) - Mirrlees Review

Question 47

2 main dimensions of labour supply response to tax change?

Answer 47

1. 'Real' behavioural effect (on hours worked) | 2. Effect on taxable earnings (e.g. through tax avoidance, changing labour to capital income)

Question 48

..... (.....) - Mirrlees Review TOP UK TAX RATE 1. Based on estimates of labour supply elasticity of rich, UK government would maximise revenue w/overall marginal rate on highest earners = .....% 2. Similar to current rate of .....% (incl. income tax, NI contributions and indirect taxes) 3. Conclusion - .....

Answer 48

Saez et al (2010) - Mirrlees Review TOP UK TAX RATE 1. Based on estimates of labour supply elasticity of rich, UK government would maximise revenue w/overall marginal rate on highest earners = 57% 2. Similar to current rate of 53% (incl. income tax, NI contributions and indirect taxes) 3. Conclusion - NO strong case for significantly increasing top marginal rates in the UK

Question 49

..... (.....) - Mirrlees Review MARGINAL RATES FOR LOW EARNERS 1. EXTENSIVE MARGIN - v. high marginal rate (close to .....% pre-working tax credit and v. high after it) for those entering work at low earnings due to taxes + withdrawal of benefits, harming incentives to enter labour force 2. INTENSIVE MARGIN - .....% marginal rate for low/moderate earners as tax credits withdrawn 3. RECOMMENDATION - .....

Answer 49

Saez et al (2010) - Mirrlees Review MARGINAL RATES FOR LOW EARNERS 1. EXTENSIVE MARGIN - v. high marginal rate (close to 100% pre-working tax credit and v. high after it) for those entering work at low earnings due to taxes + withdrawal of benefits, harming incentives to enter labour force 2. INTENSIVE MARGIN - 73% marginal rate for low/moderate earners as tax credits withdrawn 3. RECOMMENDATION - increase amount people can earn before benefits withdrawn to improve incentives to enter work

Question 50

TOP UK TAX RATE 1. Based on estimates of labour supply elasticity of rich, UK government would maximise revenue w/overall marginal rate on highest earners = 57% 2. Similar to current rate of 53% (incl. income tax, NI contributions and indirect taxes) 3. Conclusion - NO strong case for significantly increasing top marginal rates in the UK

Answer 50

Saez et al (2010) - Mirrlees Review