Econ 551 Government Finance: Revenues Fall 2019 Given by Kevin - - PowerPoint PPT Presentation

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Econ 551 Government Finance: Revenues Fall 2019

Given by Kevin Milligan Vancouver School of Economics University of British Columbia Lecture 8a: Taxing Labour Income

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Agenda

• 1. Overview
• 2. Basic model
• 3. Hausman vs. MaCurdy et al.
• 4. Estimation based on policy variation

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Overview

We are going to look at theory and evidence on the taxation of labour income. Most reliable estimates of male labour supply suggest that it is fairly inelastic—with elasticities around 0.1 (if not zero…) This has two implications for us:

• Suggests that taxing labour income may be efficient, since quantity doesn’t vary much with

price and we know that efficient taxes are characterized in terms of quantity.

• Studying the labour market behaviour of men is quite boring. They just work. You could put

very high tax rates on them and it doesn’t do too much.

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Overview

If the labour supply of men is unresponsive, where might we look for more interesting action?

• Second earners.
• Single parents with children.
• Retirement decisions.
• Participation margin for low earners. (Next time…)

For the above groups, consensus estimates suggest a more substantial response of labour supply to tax incentives.

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Single males and females: Employment rates

Source: Labour Force Survey

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Overview

We’re going to do three things:

• Review the basic theory.
• Enter the Hausman vs. MaCurdy et al. zone.
• Discuss recent evidence.

In future lectures we will extend our study of taxing labour incomes

• Look at low incomes in detail.
• Study high incomes in detail.

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Agenda

• 1. Overview
• 2. Basic model
• 3. Hausman vs. MaCurdy et al.
• 4. Estimation based on policy variation

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Basic model:

Nothing special here—just standard labour supply vs leisure choices.

• One period static model of labour supply.
• Get utility from leisure and consumption.
• Wage w, fixed tax rate t.
• 24 hours in a day; working hours are 24-l.
• Get transfer income y0 even if you don’t work at all.
• Let’s denote after tax wage as 𝑥0 = 𝑥(1 − 𝑢0).

max

𝑚

𝑉(𝑑, 𝑚) 𝑡. 𝑢. 𝑑 = 𝑥0(24 − 𝑚) + 𝑧0

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Basic static labour supply diagram:

leisure income l=24 A U0 Slope w0 E

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Basic diagram:

The story in this diagram:

• Choice is between hours worked and income/consumption.
• If work 0 hours, then you get to be at point A.
• Find tangency point—in this case E, but could be at point A.
• Slope of budget line is the after tax wage w(1-t).

Now, what happens if the tax rate t0 goes up to t1 > t0? Well, w0 goes down to w1. This makes the slope of the budget constraint flatter:

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Basic diagram:

leisure income l=24 A U0 Slope w0 E Slope w1

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Comments on this diagram:

• Slope is now flatter.
• We pivot at point A because our original nonlabour income y0 didn’t change.
• We will clearly be at a lower level of utility.
• Whether labour supply moves up or down depends on strengths of income and substitution

effects.

• Subs effect: we get less consumption for our labour, so we work less.
• Inc effect: we have less income so we demand less leisure; will work more.

Now let’s move a step closer to reality.

• Imagine that we have three tax brackets leading to after-tax wage rates w1, w2, and w3.
• What does this look like in our diagram?

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Convex budget sets:

leisure income l=24 Y1 U0 Segment 3 Segment 1 Segment 2 Y2 Y3

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Comments

• Three segments, each with their own after-tax wage.
• If you extend the budget constraint on each segment back to the l=24 line, you get what we

call the ‘virtual income’ associated with that segment of the budget constraint.

• ‘Virtual income’ depends on how high the previous tax rates were. Think of someone

currently on segment 3. If tax rates t1 and t2 were to change, the location of segment 3 would shift up and down. This generates income effects.

• If you were to run regressions on people’s current after tax wage and current non-wage

income, you would get a different answer than if you account for their virtual income instead.

• What happens if you’re on segment 3 and tax rates change?
• If a small change, you might just have an income and substitution effect and stay on

segment 3.

• If a larger change you might move to segment 1 or 2.
• Also, you might end up at a kink point.

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Agenda

• 1. Overview
• 2. Basic model
• 3. Hausman vs. MaCurdy et al.
• 4. Estimation based on policy variation

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Basic estimation equation

The equation you should have in mind for this kind of estimation looks like this: ℎ𝑗 = 𝛾0 + 𝑌𝑗𝛾1 + 𝑥𝑗𝛾2 + 𝑍

𝑗 𝑂𝑋𝛾3 + 𝜁𝑗

Where:

• i indexes individuals
• h is hours
• X is vector of individual characteristics (education marital status age etc.)
• w is wage after tax
• Ynw is nonwage income
• Epsilon is an error.

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What does this get us?

Note that the coefficient β2 gives us the Marshallian uncompensated elasticity.

• In order to get to the compensated elasticity we need to use the β3 coefficient on nonwage

income through the Slutsky equation: 𝜖ℎ 𝜖𝑥 = 𝜖ℎ𝑑 𝜖𝑥 + ℎ 𝜖ℎ 𝜖𝑧

• To get compensated elasticity, you must subtract off a term based on income elasticity.

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Hausman’s methodology

Hausman (1981) was very influential, both in methodology and results.

• Made sure the emphasis was on the compensated
• response. Why do we care about the compensated elasticity?

Because that’s what matters for figuring out the excess burden of taxation.

• Developed the ‘virtual income’ methodology to properly

account for tax rates in other tax brackets. This had the effect of making income effects larger.

• Because of the possibility of shifting around segments and kinks, you really have to

characterize the complete budget set and preferences. He used duality to help get the preference side. He used the virtual income methodology to get the budget set side.

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Hausman’s results

• Found a fairly small Marshallian uncompensated elasticity. Similar to other researchers.
• Found a much larger income response than other papers. This lead to much larger

compensated elasticities and then to larger welfare costs.

• Estimated the marginal excess burden of taxation in the US using 1975 data was 29% of

revenue – much larger than others had previously thought.

• This had large influence on tax policy in the 1980s and ERTRA 1983 and TRA 1986,

which saw top marginal rates fall from 70% down to 28%.

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Challenges to the Hausman analysis

• Hausman used data from the 1975 PSID. Exactly how variables for wages, hours, and

nonlabour income were constructed are not clear; different interpretations are available.

• MaCurdy, Green, and Paarsch (1990) use the same data but find essentially no compensated

supply response.

• Imposed Slutsky symmetry; imposed negative income effect.
• See Eklöf and Sacklén (2000) for attempted reconciliation.
• What is the variation that is identifying the parameters of interest? What’s a tax effect; what’s

an income effect?

• In general, the failure of this literature to converge is just a small part of the bigger labour

supply literature in the 1980s that produced widely varying results. (See Mroz 1987, for example).

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How seriously to take budget sets?

BC marginal tax rate schedule, 2019

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Where literature has gone

Using one year of data with opaque identification is hard to sell these days. (For good reason!) Instead, there has been a rise in other approaches:

• In the 90s and 00s: using policy variation to identify policy impact (e.g. Blundell and Meghir

1998)

• Using big admin data sets; looking at kinks and RDs.

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Agenda

• 1. Overview
• 2. Basic model
• 3. Hausman vs. MaCurdy et al.
• 4. Estimation based on policy variation

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Estimation using tax policy variation

In part as a reaction against the deadlock in the structural labour supply literature, a new approach emerged in the early 1990s.

• The idea was to use policy variation to estimate labour supply parameters.
• By taking very similar sets of people first in one tax regime and then in another, you can

potentially have greater confidence that what you are measuring is a pure tax effect and not driven by something else.

• Even better, you might have different groups that either a) had no ‘treatment’ or b) had

differing levels of treatment. So, you can econometrically see if those who got a ‘half dose’ had a ‘half response’.

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Compare cell means

Consider some outcome 𝑧𝑢𝑕 which we observe in two time periods t=0 and t=1. All observations are from either a treatment group (g=A), or a control group (g=B). How should we measure the impact of treatment on y? An obvious way is to take the mean difference between the treatment and the control group: 𝜀 ̂ = (𝑧1𝐵 − 𝑧0𝐵) − (𝑧1𝐶 − 𝑧0𝐶) Where 𝜀 ̂is a difference-in-differences estimator. Why is this useful?

• Having control group B useful if there are other things affecting 𝑧1𝐵 independent of the

policy.

• We use the control group to account for any common trends before and after treatment can be

removed from the estimate of the impact of treatment.

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Regression implementation

There is an obvious regression analogue to the cell-mean differences formulation. Here it is: 𝑧 = 𝛾0 + 𝐵𝑒𝑣𝑛𝛾1 + 𝐵𝐺𝑈𝐹𝑆𝛾2 + 𝜀𝐵𝑒𝑣𝑛 × 𝐵𝐺𝑈𝐹𝑆 + 𝑣 Where: Adum: dummy variable taking the value 1 for members of the treatment group. AFTER: dummy variable taking the value 1 for observations in the ‘after’ period. 𝜀: estimate of policy impact.

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Advantages and Disadvantages

The advantages of using policy variation are:

• Transparency in identification – we know where the variation is coming from. We don’t have

to rely on functional form assumptions. (At least, not in the same way.) We might not know what it is that we are estimating, but we can do it robustly.

• Ease of computation. (At the extreme, it can be very easy. How much should this matter?)

Some disadvantages of this method are:

• Requires additively separable errors.
• Requires trends common to treatment and control groups to have a special structure.
• Produces results specific to a given ‘experiment’. This makes it hard to generalize, hard to

compare across studies, and hard to use as policy advice.

• Produces results that may not directly relate to parameters from an economic model.

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Example - Eissa 1995/96

Looked at effect of TRA 86 on hours worked.

• Top tax rates went from 50% down to 28%.
• Looked specifically at women, using the 99th percentile
• f the earnings distribution as a treatment group and the 75th

and 90th as a control group.

• Average MTR for the 99 group dropped 13.9 pps,

while for the 90 group it dropped 7 pps.

• Hours worked for group 99 went up 206 hours from

595.7

• Hours worked for group 90 went up 128.8 hours from

876.4

• This leads to elasticities in the range of 0.8.
• Note that she cannot do compensated elasticities. What is being estimating?
• How to interpret this result outside this experiment? 99 vs 90? What does that tell us?

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Example: Blundell, Duncan, and Meghir (1998)

• Blundell and coauthors use a host of tax changes in the UK in the 1980s to study the effect of

taxes on the labour supply of married women.

• They use UK data and exploit tax reforms through the 1980s.
• Define different groups by cohort and education level – much better than the endogenous

income used by Eissa to define the groups.

• The tax reforms generally saw taxes go down – from a high of 83% pre-Thatcher to 40% by

1988.

• Ideally, you would have some ups and downs, so that you would not be as susceptible to

picking up long run trends that are coincidentally moving along.

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Comments:

• You can see that there is some decent – although not huge – variation across education and

cohort groups through time. The text says that about 33% of the variation is explained by edu-cohort-time interactions, with 67% explained by the main effects.

• Tax rates are coming down much more in the low education group than the high education

group.

• They estimate the labour supply equations with some structure, so that they are able to

estimate income effects as well, facilitating the calculation of compensated elasticities.

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• You can see that elasticities in Table 4 are in the range of .140 to .439. These imply

substantial welfare costs, but are quite a bit lower than some other estimates that are out there.

• Note that income elasticities are not huge – not a large difference between uncompensated and

compensated elasticities.

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Next time:

Looking at taxes / transfers for low income individuals. Saez, Emmanuel (2002), “Optimal Income Transfer Programs: Intensive Versus Extensive Labor Supply Responses,” Quarterly Journal of Economics, Vol. 117, No. 3, pp. 1039-1073. Available

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