Week 3- Tax Evasion

Question 1

In the standard model, what do X, Y and t stand for?

Answer 1

Declared income level, real income level, marginal tax rate.

Question 2

What is income when not caught?

Answer 2

Ync= Y-tX

Question 3

What is income when caught?

Answer 3

Yc= Y[1-t] - Ft [Y-X]

Question 4

Is the fine based on undeclared tax or undeclared income?

Answer 4

The undeclared tax.

Question 5

Assuming the taxpayer behaves as if they maximise their expected utility-what does the optimal declaration X (the income declared) solve?

Answer 5

max(x) E[U(X)] = [1-p]U(Ync) + pU(Yc)

Question 6

According to the evasion decision graph, which line joins the points for X=0 and X=Y?

Answer 6

The opportunity line- which shows all the sets of possible payoffs.

Question 7

Give 3 statements about the opportunity line?

Answer 7

• Is on the 45° at the truthtelling point X=Y
• Is downward sloping, increasing X transfers income from the not-caught state to the caught state.
• Implies Ync>Yc for X

Question 8

At what point is the optimal level of income reporting during the evasion problem?

Answer 8

At X*, where the indifference curve meets the opportunity line.

Question 9

In the tax exasion graph, what is the difference between X=Y and X=0?

Answer 9

X*=Y means all income has been declared

X*=0 means that no income has been declared.

Question 10

When do taxpayers evade at least some of their income?

Answer 10

When indifference curve at X=Y is steeper than the opportunity line.

Question 11

What is the slope of the opportunity line?

Answer 11

-F

Question 12

When does evasion occur?

Answer 12

p[1+F] < 1

Question 13

How do you calculate the MRS (slope of the indifference curve) in the evasion decision?

Answer 13

dYc/dYnc = [1-p]/p

Question 14

What is the levels puzzle?

Answer 14

The idea that all taxpayers should engage in tax evasion as p[1+F] is far below 1.

Question 15

What happens when either p or F increases?

Answer 15

Evasion reduces.

Question 16

What happens when there is an increase in the Fine Rate?

Answer 16

The opportunity line pivots around X=Y, leading the optimal choice to move closer to the honest declaration; thus lowering evasion.

Question 17

What happens to the opportunity line when taxes increase?

Answer 17

The opportunity line shifts inward when taxes increase.

Question 18

What is the effect on declaration when taxes increase?

Answer 18

This is not clear cut.

Question 19

If absolute risk aversion decreases with income, what happens to evasion when taxes increase, and what is this called?

Answer 19

Evasion reduces- this is called the Yitzhaki puzzle.

Question 20

What happens to absolute risk aversion as income increases?

Answer 20

Absolute risk aversion decreases- ie rich people are more likely to take risks.

Question 21

Why does it seem strange that increasing taxes would reduce evasion?

Answer 21

As basic intuition would suggest that increasing taxes increases the inventive to avoid paying a higher tax- as most empirical evidence actually agrees with.

Question 22

Explain the theory behind the Yitzhaki puzzle.

Answer 22

An increase in taxes leaves households poorer, which increases their risk aversion- so they reduce their exposure to risk and evade less!

Question 23

Is there any substitution effect with the Yitzhaki puzzle?

Answer 23

No, as both the tax rate and the penalty rate increase proportionally with t, making the Yitzhaki puzzle arise purely from income effect.

Question 24

If we are choosing to replace EUT with PT, how can we write the problem facing the taxpayer?

Answer 24

V=w(p)v(Yc-R) + w(1-p)v(Ync-R)
where w() is a probability weighting function and v() as a payoff function that replaces U().

Question 25

Under PT reference level, how would reference income be calculated as the level of income if declared honestly?

Answer 25

R=[1-t]Y

Question 26

Under PT reference level, how would reference income be calculated as the expected value of the gamble.

Answer 26

R=w(p)Yc + w(1-p)Ync

Question 27

How do Piolatto and Rablin (2017) write R?

Answer 27

As a weighted average of Yc and Ync:
R=αYc+[1-α]Ync
where α doesn’t depend on X and is 0

Question 28

If you want to use the reference level w(p)Yc + w(1-p)Ync, what should you set α equal to?

Answer 28

w(p)

Question 29

If you want to use the reference level [1-t]Y, what should you set α equal to?

Answer 29

1/[1+F]

Question 30

What happens if both outcomes are gains?

Answer 30

The interesting parts of PT in the loss domain are lost.

Question 31

What happens to the objective function V if both outcomes are losses?

Answer 31

The objective function V becomes convex- the taxpayer will evade everything or nothing!!

Question 32

According to PT what is the payoff in the caught state?

Answer 32

Yc-R= -[1-α][Ync-Yc]<0

this is therefore a loss

Question 33

According to PT what is the payoff in the not caught state?

Answer 33

Ync-R= α[Ync-Yc]>0

this is therefore a gain

Question 34

When loss aversion is added to PT, what happens to evasion and why?

Answer 34

Evasion falls as aversion to a possible loss reduces the risk taking involved with evasion.

Question 35

When probability weighting is added to PT, what happens to evasion and why?

Answer 35

Evasion falls as taxpayers psychologically overweight the (small) probability of being caught.

Question 36

Why is the probability of audit not close to the naïve prediction of 1%?

Answer 36

As around 80% of people have zero chance of evading tax anyway as they are taxed through PAYE, it is only self employed people who could get audited, which then brings the realistic chance of audit for them up to around 20%.

Question 37

How does PT help solve the levels puzzle?

Answer 37

It predicts lower levels of tax evasion, which are more in line with those we see empirically.

Question 38

How does PT help solve the Yitzhaki puzzle?

Answer 38

It usually doesn’t, a tax rate rise still decreases evasion.

Question 39

Piolatto and Rablen show that the Yitzhaki puzzle always holds when…

Answer 39

α() does not depend upon t

Question 40

Can PT sometimes solve the Yitzhaki puzzle?

Answer 40

Yes, but those reversals typically rely on some peverse psychology!

Question 41

How can PT sometimes solve the Yitzhaki puzzle?

Answer 41

By reversing the income effect, ie making taxpayers feel richer after an increase in tax rate! However this is generally implausible can can only happen if you make R go down by more than Y.

Question 42

What can S sometimes be interpreted as?

Answer 42

The psychological cost of non-compliance with a social custom.

Question 43

What happens in countries with low compliance?

Answer 43

People feel less obligated to pay their taxes which in turn changes the social customs making people less guilty about not paying etc in a vicious circle.

Question 44

In the equation S=XiEi, will people with high Xi be more or less compliant and why?

Answer 44

People with high Xi will be more compliant as they have greater concern about social custom.