In this post on Ed Broadbent's suggestion for a 6 ppt increase in the income tax rates faced by people earning $250k or more, I mentioned that some serious econometric work had to be done before this could be treated as a meaningful proposal. It soon occurred to me that there very likely had been some work done on this topic, and that I should try to track down some of the literature. It turns out that prospects of using the tax system to counter the trend towards higher concentration of incomes at the top end of the income distribution are limited, and the chances of generating perverse outcomes are large.

The best place to start is this delightful paper written by Alan Blinder back in 1981, when the expression "Laffer curve" was still relatively new in public policy circles. Blinder makes it clear that the notion predates the famous table napkin, and indeed follows from Rolle's Theorem of calculus. If 100% tax rates generate zero revenues (and this doesn't seem to be a point anyone seriously disputes) then there must be a point where tax revenues are maximised, after which increasing tax rates results in lower total revenues.

Suppose for now that an increase in taxes has no effect on wages. A bit of manipulation (Blinder's equation 3 without the last term) yields that the tax rate that maximises revenues is τ* = 1/(1 + η), where η is the elasticity of the supply of labour. As the labour supply elasticity increases, the value of τ* declines.

So the debate is not whether or not the Laffer curve exists; it does. The question is an empirical one: what is the elasticity of the supply of labour? More specifically for the case at hand, what is the elasticity of the supply of labour for people with high incomes?

There are two recent studies that address this question. In a study using US data, Jon Gruber and Emmanuel Saez summarise their results as follows:

[T]axpayers who have incomes above $100 000 per year … have an elasticity of 0.57, while for those with incomes below $100 000 per year the elasticity is less than one-third as large. Moreover, high income taxpayers who itemize are particularly responsive to taxation. Our estimates suggest that optimal tax structures may feature tightly targeted transfers to lower income taxpayers and a flat or even declining marginal rate structure for middle and high income taxpayers.

The finding that high-income earners are most sensitive to changes in taxes is probably not surprising. In a study using Canadian data, Mary-Anne Sillamaa and Mike Veall also find that people at the top of the income distribution have higher elasticities. Moreover, they find that the elasticities are higher than those found in other studies: 1.32 for those earning more than $75,000 in 1986, and 1.67 for those with incomes higher than $100,000 (this corresponds roughly to the top 1% of the 1986 income distribution). An elasticity of 1.32 corresponds to a value of τ* = 0.43, and the revenue-maximising tax rate for the top 1% would be 0.37.

Sillamaa and Veall take care to note possible explanations for why their results are so much larger than in other studies, and suggest that "it is possible the estimation is picking up at least in some degree an intertemporal response that is larger in the short run than in the long run."

Long-run effects may offer a partial explanation for the differences between the Sillamaa-Veall and the Gruber-Saez results, but that's not a reason to discount them. Indeed, the long-run effects are precisely what matter most for tax policy. In the short run, workers are stuck with the human capital they've accumulated. But in the long run, human capital is endogenous, and higher tax rates reduce the returns on education. In a recent blog post, the never-to-be-sufficiently-praised Chris Dillow puts it this way:

[P]ut yourself in the shoes of someone on, say, £100,000 a year facing
[a] higher tax. He might well figure: "I’ve got an ex-wife and
kids to support: I’ve got to keep  earning. And I’m not qualified to do
anything else anyway. But I hear that some senior partners are thinking
of retiring now they have to pay more tax. If I work hard, I might be
able to get one of the jobs they leave."

But now, think of a
university student. He figures: "I was toying with the idea of going
into the City. But why should I work 80 hour weeks in a dullish job to
hand over most of my money to the government? I’ll do a less well-paid
job that I enjoy instead."

Now, in the short-run – which might be
many years – the £100,000 a year man’s response is the most important
one. But in the very long-run – decades – it’s the student’s response
that determines our macroeconomic fate.

See also this paper for some evidence on how students' education choices depend crucially on their perceived prospects in future labour markets.

If we interpret the Sillamaa-Veall estimate of 1.67 as a (possibly conservative) estimate for high earners' long-run elasticity, then the peak of the Laffer curve occurs at a tax rate of 37% – which is lower than the top marginal tax rate in all Canadian provinces. In other words, available evidence suggests that we are already on the wrong side of the Laffer curve. Increasing tax rates at the top end to finance a transfers to low-income households will actually reduce the amount of money available for redistribution.

Now let's relax the assumption that wages don't react after a change in the tax rates. If workers reduce their supply of labour after a tax increase, then wages will increase as we move up the demand curve for labour. The new tax rates will now be applied to these higher wages, and Blinder notes that this effect pushes the peak of the Laffer curve well to the right:

[U]nless the elasticities are quite high, we can only be over the Laffer hill only when marginal tax rates are extremely high… [I]t is very unlikely (though not totally impossible) that the peak in the Laffer curve comes at a tax rate that anyone might seriously entertain.

This condition is unlikely to be met: labour demand elasticities are generally very small. Indeed, part of the story behind the concentration of incomes at the very top end of the income distribution almost certainly involves labour demand elasticities that are extremely inelastic. Workers who face perfectly inelastic labour demand curves are pretty much asked to name their price. Instead of withdrawing their labour, top-end workers are more likely to obtain increases to their gross wages that keep after-tax incomes at their previous levels.

An interesting example of this sort of phenomenon is being played out in the market for soccer players in Europe. Elite soccer players in both France and Spain pay lower taxes than do other employees, and the governments of both countries want to eliminate this special treatment. Probably the most disinterested people in this story are the players themselves, who know that their take-home pay won't be affected no matter what happens. If they have to pay higher taxes, they know that market forces being what they are, they will be able to extract the appropriate pay increases to compensate.

This would seem to be a happy ending, then: high-income workers keep working, and they pay higher taxes on their (increased) wages. But the analysis doesn't end there. Once we introduce both supply and demand effects, we have to look at the incidence of the increased tax on high earners. The burden of the tax does not necessarily fall on the people who actually pay the tax.

We can be pretty sure that if there's one group of people who won't be paying the tax, it is the high-income earners themselves – the reason for the increase in wages is to compensate them for the higher tax bill. And if we're talking about a small open economy whose capital markets are highly integrated with the rest of the world – and in the case of Canada, we are – then we also know that the tax will not be borne by owners of capital.

If neither high-income earners nor investors are paying those increased taxes, then they must be being taken from workers further down the income distribution. And as we move down the income distribution, workers' bargaining power diminishes: demand for labour becomes more elastic, and supply becomes less elastic. We could even have the perverse result of a tax on high incomes having regressive effects.

(Note also that imposing a wage cap just puts us back to being on the wrong side of the Laffer curve.)

So here are the possible outcomes:

1. If wages don't adjust after the tax change, then we are very likely already on the wrong side of the Laffer curve for high-income earners: increasing the tax rates on high-income earners will reduce total revenues.
2. If wages do adjust, the gross incomes of high-income will rise so that their after-tax incomes are the same. Extra revenues will be generated, but the burden of the tax increase will be borne by those below the top end of the income distribution.

The reality is likely to be more nuanced,  but we can pretty much rule out the naive scenario in which there are no behavioural responses. And the existing literature suggests that those responses will generate effects that are almost exactly the opposite of the what we want to see happen.

Once again, we're back to the main message of my previous post. The tax system is at best a clumsy instrument for redistributing income, and there are simply too many possibilities for generating unintended perverse outcomes. If you want to reduce poverty and inequality, focus attention instead on setting up a well-designed system of transfers. It's effective, and it's also the strategy used by all successful social democracies.