Econ 551 Government Finance: Revenues Fall 2019 Given by Kevin Milligan Vancouver School of Economics University of British Columbia Lecture 8a: Taxing Labour Income ECON 551: Lecture 8a 1 of 33
Agenda 1. Overview 2. Basic model 3. Hausman vs. MaCurdy et al. 4. Estimation based on policy variation ECON 551: Lecture 8a 2 of 33
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 zer o…) 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. ECON 551: Lecture 8a 3 of 33
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. ECON 551: Lecture 8a 4 of 33
Single males and females: Employment rates Source: Labour Force Survey ECON 551: Lecture 8a 5 of 33
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. ECON 551: Lecture 8a 6 of 33
Agenda 1. Overview 2. Basic model 3. Hausman vs. MaCurdy et al. 4. Estimation based on policy variation ECON 551: Lecture 8a 7 of 33
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 y 0 even if you don’t work at all. • Let’s denote after tax wage as 𝑥 0 = 𝑥(1 − 𝑢 0 ) . 𝑉(𝑑, 𝑚) 𝑡. 𝑢. 𝑑 = 𝑥 0 (24 − 𝑚) + 𝑧 0 max 𝑚 ECON 551: Lecture 8a 8 of 33
Basic static labour supply diagram: income U 0 E Slope w 0 A l=24 leisure ECON 551: Lecture 8a 9 of 33
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 t 0 goes up to t 1 > t 0 ? Well, w 0 goes down to w 1 . This makes the slope of the budget constraint flatter: ECON 551: Lecture 8a 10 of 33
Basic diagram: income E U 0 Slope w 0 Slope w 1 A l=24 leisure ECON 551: Lecture 8a 11 of 33
Comments on this diagram: • Slope is now flatter. • We pivot at point A because our original nonlabour income y 0 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. o Subs effect: we get less consumption for our labour, so we work less. o Inc effect: we have less income so we demand less leisure; will work more. Now let’s move a step close r to reality. • Imagine that we have three tax brackets leading to after-tax wage rates w 1 , w 2 , and w 3 . • What does this look like in our diagram? ECON 551: Lecture 8a 12 of 33
Convex budget sets: income Segment 2 Y 3 Segment 3 U 0 Segment 1 Y 2 Y 1 l=24 leisure ECON 551: Lecture 8a 13 of 33
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 t 1 and t 2 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? o If a small change, you might just have an income and substitution effect and stay on segment 3. o If a larger change you might move to segment 1 or 2. o Also, you might end up at a kink point. ECON 551: Lecture 8a 14 of 33
Agenda 1. Overview 2. Basic model 3. Hausman vs. MaCurdy et al. 4. Estimation based on policy variation ECON 551: Lecture 8a 15 of 33
Basic estimation equation The equation you should have in mind for this kind of estimation looks like this: 𝑂𝑋 𝛾 3 + 𝜁 𝑗 ℎ 𝑗 = 𝛾 0 + 𝑌 𝑗 𝛾 1 + 𝑥 𝑗 𝛾 2 + 𝑍 𝑗 Where: • i indexes individuals • h is hours • X is vector of individual characteristics (education marital status age etc.) • w is wage after tax • Y nw is nonwage income • Epsilon is an error. ECON 551: Lecture 8a 16 of 33
What does this get us? Note that the coefficient β 2 gives us the Marshallian uncompensated elasticity. • In order to get to the compensated elasticity we need to use the β 3 coefficient on nonwage income through the Slutsky equation: 𝜖𝑥 = 𝜖ℎ 𝑑 𝜖ℎ 𝜖𝑥 + ℎ 𝜖ℎ 𝜖𝑧 • To get compensated elasticity, you must subtract off a term based on income elasticity. ECON 551: Lecture 8a 17 of 33
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. ECON 551: Lecture 8a 18 of 33
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. o 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%. ECON 551: Lecture 8a 19 of 33
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. o Imposed Slutsky symmetry; imposed negative income effect. o 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). ECON 551: Lecture 8a 20 of 33
How seriously to take budget sets? BC marginal tax rate schedule, 2019 ECON 551: Lecture 8a 21 of 33
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. ECON 551: Lecture 8a 22 of 33
Agenda 1. Overview 2. Basic model 3. Hausman vs. MaCurdy et al. 4. Estimation based on policy variation ECON 551: Lecture 8a 23 of 33
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 diffe rent 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’. ECON 551: Lecture 8a 24 of 33
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