Week 3- Tax Evasion Flashcards
In the standard model, what do X, Y and t stand for?
Declared income level, real income level, marginal tax rate.
What is income when not caught?
Ync= Y-tX
What is income when caught?
Yc= Y[1-t] - Ft [Y-X]
Is the fine based on undeclared tax or undeclared income?
The undeclared tax.
Assuming the taxpayer behaves as if they maximise their expected utility-what does the optimal declaration X (the income declared) solve?
max(x) E[U(X)] = [1-p]U(Ync) + pU(Yc)
According to the evasion decision graph, which line joins the points for X=0 and X=Y?
The opportunity line- which shows all the sets of possible payoffs.
Give 3 statements about the opportunity line?
- 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
At what point is the optimal level of income reporting during the evasion problem?
At X*, where the indifference curve meets the opportunity line.
In the tax exasion graph, what is the difference between X=Y and X=0?
X*=Y means all income has been declared
X*=0 means that no income has been declared.
When do taxpayers evade at least some of their income?
When indifference curve at X=Y is steeper than the opportunity line.
What is the slope of the opportunity line?
-F
When does evasion occur?
p[1+F] < 1
How do you calculate the MRS (slope of the indifference curve) in the evasion decision?
dYc/dYnc = [1-p]/p
What is the levels puzzle?
The idea that all taxpayers should engage in tax evasion as p[1+F] is far below 1.
What happens when either p or F increases?
Evasion reduces.
What happens when there is an increase in the Fine Rate?
The opportunity line pivots around X=Y, leading the optimal choice to move closer to the honest declaration; thus lowering evasion.
What happens to the opportunity line when taxes increase?
The opportunity line shifts inward when taxes increase.
What is the effect on declaration when taxes increase?
This is not clear cut.
If absolute risk aversion decreases with income, what happens to evasion when taxes increase, and what is this called?
Evasion reduces- this is called the Yitzhaki puzzle.
What happens to absolute risk aversion as income increases?
Absolute risk aversion decreases- ie rich people are more likely to take risks.
Why does it seem strange that increasing taxes would reduce evasion?
As basic intuition would suggest that increasing taxes increases the inventive to avoid paying a higher tax- as most empirical evidence actually agrees with.
Explain the theory behind the Yitzhaki puzzle.
An increase in taxes leaves households poorer, which increases their risk aversion- so they reduce their exposure to risk and evade less!
Is there any substitution effect with the Yitzhaki puzzle?
No, as both the tax rate and the penalty rate increase proportionally with t, making the Yitzhaki puzzle arise purely from income effect.
If we are choosing to replace EUT with PT, how can we write the problem facing the taxpayer?
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().
Under PT reference level, how would reference income be calculated as the level of income if declared honestly?
R=[1-t]Y
Under PT reference level, how would reference income be calculated as the expected value of the gamble.
R=w(p)Yc + w(1-p)Ync
How do Piolatto and Rablin (2017) write R?
As a weighted average of Yc and Ync:
R=αYc+[1-α]Ync
where α doesn’t depend on X and is 0
If you want to use the reference level w(p)Yc + w(1-p)Ync, what should you set α equal to?
w(p)
If you want to use the reference level [1-t]Y, what should you set α equal to?
1/[1+F]
What happens if both outcomes are gains?
The interesting parts of PT in the loss domain are lost.
What happens to the objective function V if both outcomes are losses?
The objective function V becomes convex- the taxpayer will evade everything or nothing!!
According to PT what is the payoff in the caught state?
Yc-R= -[1-α][Ync-Yc]<0
this is therefore a loss
According to PT what is the payoff in the not caught state?
Ync-R= α[Ync-Yc]>0
this is therefore a gain
When loss aversion is added to PT, what happens to evasion and why?
Evasion falls as aversion to a possible loss reduces the risk taking involved with evasion.
When probability weighting is added to PT, what happens to evasion and why?
Evasion falls as taxpayers psychologically overweight the (small) probability of being caught.
Why is the probability of audit not close to the naïve prediction of 1%?
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%.
How does PT help solve the levels puzzle?
It predicts lower levels of tax evasion, which are more in line with those we see empirically.
How does PT help solve the Yitzhaki puzzle?
It usually doesn’t, a tax rate rise still decreases evasion.
Piolatto and Rablen show that the Yitzhaki puzzle always holds when…
α() does not depend upon t
Can PT sometimes solve the Yitzhaki puzzle?
Yes, but those reversals typically rely on some peverse psychology!
How can PT sometimes solve the Yitzhaki puzzle?
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.
What can S sometimes be interpreted as?
The psychological cost of non-compliance with a social custom.
What happens in countries with low compliance?
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.
In the equation S=XiEi, will people with high Xi be more or less compliant and why?
People with high Xi will be more compliant as they have greater concern about social custom.
