Higher taxes on Canada's rich won't generate much new revenue - Macleans.ca

Higher taxes on Canada’s rich won’t generate much new revenue

Canada is different, says Stephen Gordon


Tomorrow’s Munk debate — “Be it resolved, tax the rich (more)” — features four well-known speakers: three Americans and a Greek. Notably, one of the Americans is Paul Krugman, the Nobel Prize winning Princeton economist and New York Times columnist.

The Canadians in the audience will no doubt appreciate what looks to be a lively debate, but going by Krugman’s prepared remarks, the discussion is likely to be based on U.S. data, and it should be noted that many of the conclusions will not apply to Canada.

Krugman refers readers to this survey, which is in turn largely based on this article by Peter Diamond, of the Massachusetts Institute of Technology and U.C. Berkeley’s Emmanuel Saez. The research received wide attention when it came out in 2011, because it suggested that the revenue-maximising tax rate for high earners in the U.S. is 73 per cent — much higher than the current rate. But it turns out that if you apply the same methodology to Canadian data, you get very different answers.

WARNING: This is going to be a wonkish post—there’s a certain amount of math involved. But it’s important to take the time every now and again to open up the hood of tax policy and get your hands dirty.

Here are three major differences that emerge when the debate on taxing high earners is adapted to the Canadian context.

1) Top earners in the U.S. earn much more than top earners in Canada. The popular image of the “one-percenter” may be a Wall Street financier, but it’s important to remember that Wall Street isn’t in Canada. The typical Canadian one-percenter earns roughly half what a one-percenter brings home in the US:

Top-end incomes: Canada and the US
United States
Lower bound Average income   Share
of total
Lower bound Average income   Share
of total
Top 1% $215,800 $488,600 11.7% $366,600 $1,048,200 19.8%
Top 0.5% $544,800 $1,660,800 15.7%
Top 0.1% $800,000 $1,792,200 4.3% $1,577,100 $4,977,000 9.4%
Top 0.01% $3,155,800 $6,060,500 1.5% $7,969,900 $23,679,500 4.5%

(U.S. data are from the updated data file available at Emmanuel Saez’ web page. Canadian data are from Cansim Table 204-0001.)

2) U.S. incomes are more highly concentrated at the top. Not only are U.S. top income shares consistently higher than in Canada, they are more concentrated. About one-third of the top one per cent income goes to the top 0.1 per cent in Canada, while in the U.S., the top 0.1 per cent receive half of the top one per cent. Going even higher, one-eighth goes to the top 0.01 per cent in Canada, compared to almost one-quarter in the U.S.

This increased concentration is important in calculating the tax rate that maximises revenue. Researchers have found that the Pareto distribution is a useful tool for modeling incomes above a certain (high) threshold. A key advantage of the Pareto distribution is its simplicity: it can be completely characterised by a single parameter, denoted by a in the literature. Smaller values of a mean that the distribution is more highly concentrated at the top.

A rough-and-ready way of finding the value of a that best fits the data is to make use of a very convenient property of the Pareto distribution:

a = Average/(Average – Lower threshold)

Applying this formula to the numbers in the table provides a good idea of what the appropriate values of a are for the problem at hand:

Implied values of a:
Canada and the US
United States
Top 1% 1.79 1.54
Top 0.5% 1.49
Top 0.1% 1.81 1.46
Top 0.01% 2.09 1.51

These numbers are typical of the range of estimates in the literature. In his recent survey of the topic (discussed in an earlier post here) McMaster University’s Mike Veall reported a range values between 1.7 and 2.0. The U.S. numbers are consistently smaller and concentrated around 1.5, which is the value used by Diamond and Saez.

3) Canadian taxable incomes are more sensitive to changes in tax rates. The other key parameter in determining the revenue-maximising tax rate is the elasticity of taxable income, which measures the extent to which tax filers are likely to go to minimize the impact of a hike in tax rates (or, vice versa, take maximum advantage of a reduction in tax rates). This parameter — denoted by e — is recovered from estimating models that look like this:

log of taxable income = e * log of (1 – tax rate) + controls

Diamond and Saez note that U.S. estimates for e range between 0.17 and 0.57, and their preferred value is 0.25. But as Mike Veall notes in his survey, estimates for e obtained from Canadian data are consistently larger and appear to be concentrated in the range 0.5-0.7, with some estimates going as high as 3.

These differences matter, because the formula for the revenue-maximising tax rate T is

T = 1/(1 + a*e)

If you plug in Diamond and Saez’ preferred parameter values – a=1.5 and e=0.25 – the revenue-maximising rate is T = 1/(1 + 1.5*0.25) = 0.73. But if you use other estimates for a and e, you will of course get other answers. This table provides the revenue-maximising tax rates associated with various combinations of a and e:

Revenue-maximising tax rates
(per cent)
0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8
a 1.4 78 74 70 64 59 54 51 47
1.5 77 73 69 63 57 53 49 45
1.6 76 71 68 61 56 51 47 44
1.7 75 70 66 60 54 50 46 42
1.8 74 69 65 58 53 48 44 41
1.9 72 68 64 57 51 47 43 40
2.0 71 67 63 56 50 45 42 38
2.1 70 66 61 54 49 44 41 37

The range of parameter values consistent with Canadian data are in red; they are all much smaller than the 73 per cent rate obtained by Diamond and Saez using U.S. data. Note also that the marginal tax rates faced by high earners in Canada are already in this range: the top rates in Ontario and Quebec are just under 50 per cent.

This is how Mike Veall summarised matters in his brief to House of Commons Standing Committee on Finance:

I am not sure we have the evidentiary base to be sure that an increase in marginal tax rates at the top will raise tax revenue. A more promising approach is to eliminate those tax expenditures that tend to benefit the affluent. 

The thing about evidence-based policy analysis is that different countries face different sets of facts. Policy recommendations based on U.S. data should not be automatically applied to Canada without first checking to see if using Canadian data leads to the same conclusion. Canadians watching tomorrow’s Munk debate will probably learn a lot about what’s going on with inequality and tax rates in the United States. But they should know that the debate in Canada is based on a quite different set of facts.



Higher taxes on Canada’s rich won’t generate much new revenue

  1. If the inequality, or concentration of wealth in the US is socially undesirable, and this trend has been occurring for some time, is Canada on the same path, just delayed?

    If so, what measures could be taken to alleviate this problem in Canada now?

  2. Any idea why income elasticity is so much higher in Canada than in the US?

    • The US implemented the Alternative Minimum Tax a few years ago to limit this problem. A growing portion of Canadians earning over $90k are incorporating and thereby writing off their car and mortgage payments, paying themselves a minimum salary, and paying the cut rate business tax on the rest.

      • If the US AMT is so effective at limiting elasticity, we clearly need our own AMT except that we’ve had our own for several decades.

        As for a growing portion of Canadians earning over $90K incorporating in order to write off their car and mortgages, perhaps they should be told they can write off their car and (if they want to reduce the tax free capital gain they realize when they sell their principal residences) their mortgages relative to the extent they operate businesses from their home WITHOUT incorporating.

        They should also be told the “cut rate business tax” they pay on corporate net income, added to the tax rate they’ll pay when they take the after-tax earnings out of the corporation as a dividend, will come close to – or even exceed – the tax rate on the same income if they forget about incorporating and simply earn it as a proprietor.

        Otherwise – excellent points!

  3. Okay, what’s your alternative then? Tax their assets? Stock trades? Luxury goods? Austerity measures are disproportionately inflicted on poor people so we need to raise tax revenue from people who can afford it.

    • You seem to have missed the point entirely, which is that it is not possible to “raise tax revenue from people who can afford” it beyond the “revenue maximizing rate”, which arguably is the rate currently in place in many provinces.

      It really is not that hard a concept to grasp – think of taxable revenue as being the maple tree sap that can be tapped to produce delicious syrup. You can certainly increase the diameter of tapping holes to get more of the sap out now, but in doing so you risk killing the tree.

      • No you miss my point, which is that increasing taxation on low income earners isn’t productive either, it just siphons productive spending out of the marketplace.

        Mr. Gordon and others have argued against corporate taxation, too, so I’m asking where the revenue to run this place is going to come from. It’s a fair question.

        • There’s only so much government spending that can be supported via taxation. Maybe it’s time to recognize those limits and talk more about optimization of the spending rather than simply more spending.

          • uhm + 1,000,000 for this comment.

        • The point of Gordon’s post isn’t about finding other ways to generate more government revenue, it’s about the single, narrow issue of whether there is a rate beyond which raising personal income tax rates fails to generate greater revenue. There appears to be little controversy that this rate exists, just contention over whether that rate is “x %” or “y %”.

          Your point, if I understand it correctly, is to assert other alternatives to “tax the rich” have their own issues. This may in fact be true, but in no way changes the economic case made by Diamond/Siaz and embraced by Krugman, et al, that there is a tax point of diminishing return, albeit no consensus as to what that point is. That, in your view, other alternatives to “tax the rich” are problematic doesn’t change the futility of taxing the rich beyond this point, although I expect doing so anyway would make you and the occupy folk feel all warm and cuddly.

          • The main factor in this analysis is tax elasticity, which could be mitigated through legislation to close many of the loopholes currently enjoyed by the wealthy.

          • You’re correct in this, but by limiting the debate to this specific point without looking at the alternatives creates a frame around the issue which leads to further problems.

            ie, we can’t just say, “Well we can’t tax the rich more” without addressing the issue of, “Well what do we need to do then?”

            It’s like looking at a guy with a knife in his chest and saying “Well, we can’t pull it out or he’ll bleed to death”, and then leaving the discussion there.

          • I didn’t set the terms of the debate.

          • Nor did you stick the knife in the guy. The point, pun not intended, remains.

    • I am not sure we have the evidentiary base to be sure that an increase in marginal tax rates at the top will raise tax revenue. A more promising approach is to eliminate those tax expenditures that tend to benefit the affluent.

      There are lots of tax expenditures that could be eliminated that affect mostly the affluent. Like subsidizing post secondary education for one thing. The vast majority of University students from well-off families, and why the poor are forced to subsidize their educations is beyond me, especially when the poor won’t be able to send their own kids.

      Allowing private healthcare would also reduce the burden on the healthcare system while only the rich would consider it an option.

      There are lots of ways for Canada to do more with less, the only problem is the politics involved.

      • I don’t think the poor are actually subsidizing post-secondary education so much as being subsidized in other areas by those post-secondary graduates. Low income Canadians don’t actually pay that much tax. On the other hand, they tend to have a higher demand for health care and income support. The degree to which post-secondary education should be funded is a fair question, but consideration is required for how much benefit the country receives in return for that initial support.

  4. Try telling that to the Occupy types. I’ve tried. This is the problem with these “global movements”. They start in the US and only apply to the US but all the NGO’s around the world pick up the same message and start to create their own movement out of it when it doesn’t really apply.

    • Marie Antoinette never said anything about cake either…..and the mob understood nothing about economic theory……however it seems the guillotine didn’t care.

      • That actually fits in with what wallhousewart is saying. The French Revolution began in emulation of the American Revolution, which was idealized by the revolutionaries.

        Of course the US was very different so instead of Liberté, égalité, fraternité, the French ended up with the Reign of Terror, Napoleon and more emperors.

        • Half the world’s population lives on less than $2.50 a day. One billion children live in poverty, and 22,000 of them die each day because of it. More than one billion people lack access to adequate drinking water, and 400 million of those are children. Almost a billion people go hungry every day.

          • So what does that have to do with what we’re talking about? Besides most of your stats are the phoney ones demagogues use.

          • ‘Occupy’ is all about wanting access to the system…..having a share in the pie….being able to eat, like other people. They may not understand economic theory, but they understand pitchforks and torches well enough. So perhaps it’s time to even up the system

            Mr Harper is a demagogue….I don’t support him, you do….and the stats are available online

          • And? How many of those people live in countries rued by corrupt governments who use public donations from the developed world as their personal bank accounts?

          • Half the world?? Be serious.

            India alone has 1.2B people and is a democracy

  5. “Tomorrow’s Munk debate – “Be it resolved, tax the rich (more)” …. ”

    “In May 2010 Greg Mankiw reported some data on tax revenue per person in some big economies. From that data I’d guess that the US and European tax systems raise roughly equal amounts of revenue per person, even though US taxes are slightly less than 30% of GDP, and European taxes are closer to 40% of GDP …. I’d argue that this data is strongly supportive of the view that both the US and Europe are near to tops of the Laffer Curve for total taxation. I did not say then, nor do I claim now, that we are precisely at the top …. The progressive response is that the Laffer Curve idea is far-fetched, and that higher tax rates don’t reduce GDP per capita. Instead they argue that the lower European GDP/person represents mysterious cultural differences … ”


    • Watch carefully between where they say “GDP” and “GDP per capita”. The two are very different concepts. One thing you can generally rely on is that when people are using two similar terms with very different meanings, they’re trying to hide something from you.

  6. Again I point out that the problem here is with the tax breaks available. If we reduce the amount of tax breaks available for the wealthy (such as the TFSA, the various boutique tax credits, the obscure shelters you need an accountant to find, and then increase our capital gains rate), we reduce the e which allows us, if needed, to continue to increase taxes.

    And the best part is, simply by doing so we may go some distance to levelling out the growing disparity.

  7. It’s all a red herring anyway, and Krugman is just rabble rousing.

    If the American government took every penny of income made by anyone who earned over $1 million a year, it would be $616 billion. That’s not even a third of the annual state and federal deficit. And the debt would still be skyrocketing, all their wealthy people would leave or go broke, and there would be no more money from them the next year.

    The problem is expenditures, but even with ferocious cuts (i.e. defunding the US military, it’s budget is smaller than the deficit) it would still be impossible to eliminate the deficit let alone touch their debt.

    The US is headed for a collapse no matter what it does or who’s in charge.

    Krugman knows this of course and is simply laying the groundwork for assigning blame like the proper little class warrior he is.

    • Good thing we don’t tax anyone at 100% then, isn’t it.

  8. I thought it was about the redistribution of wealth. the idea is to tax the rich more and the poor less. The rich will not spend more if they have more, but the poor will spend everything that they have. Add in the multiplier effect and you have more business in Canada, and consequently more tax revenue for the government.

    • “The rich will not spend more if they have more” do you have any evidence at all to backup that assertion?

      • It is logically impossible for spending to scale directly with income infinitely — a person has a limited amount of time for consumption, no matter how rich they are. Thus the argument, “the rich will not spend more if they have more” is certainly true, depending on what is meant by “rich”.

        Of course, this only matters at the very high levels, but if you add the words “on necessities” to that sentence, then the income level of “the rich” doesn’t need to be terribly high at all for it to be true, rich or poor need the same amount of milk, after all.

        And if we believe society and markets are to as efficiently distribute necessities as possible, this disparity causes market inefficiencies, in that the poor people can’t get the milk they need, while the rich don’t get more than they need, and the market signal received is that we don’t need as much milk as we actually do.

      • You do not become rich spending all your money. Poor people are poor because they do not have enough income to save, so they spend it all. You do not need a study for that.

  9. When conservatives advocate tax cuts, they talk about how those tax cuts will spur economic growth as people spend their tax savings. Yet we rarely hear the other side make the equally plausible argument that government spending spurs growth. Indeed, if you look at the BLS estimates of the multiplier effect for upper-income tax cuts vs. say, spending on infrastructure, the former is way higher.

    So even if raising taxes on the rich above current (low) levels wasn’t revenue-maximizing in itself, there might also be an increase in the tax base as that money was spent (or as the deficit was reduced).

    And of course, we can use tax gains from taxing the wealthy to target other taxes that more directly harm Canadian competitiveness and undermine job creation, like the corporate tax. Sadly though, there isn’t much of a market for a message of “tax the rich, not corporations.”

    • So you would reduce the government’s revenue’s because there “might also be an increase in the tax base as that money was spent”?

      I think it’s much wiser policy to have a tax rate that you know will maximize revenues. From there you can readjust spending to maximize ROI, if that’s the desire.

      • So you’re saying you want a government that increases GST and reduces payroll taxes like EI?

  10. A 45% tax rate on income over $200,000 yields roughly the same tax revenue as 3% tax on all income at $41,500 or below (Canadian 99% average income). Tax elasticity can be reduced by concrete legislation.

  11. There’s something to be said for the homeopathy option ..
    doing something that is not necessarily effective but will
    make me feel better …

  12. What are the mechanics of tax elasticity in Canada? In particular how much of it is due to the ability and willingness of rich people to move to the US? The debate may be about US policy and US numbers, but that doesn’t mean it will have no effect on Canada.

    More generally, how stable are those numbers? Has there been a secular change over time? What do we expect them to be in the future?

  13. It seems to me like the framing of this debate is at cross purposes.

    The motion “be it resolved, inequality should be reduced” and the motion “be it resolved, tax the rich” are separate.

    The real question that is not raised by Krugman AT ALL is how does inequality fit into the initial creation and distribution of money. Once you talk about channels of money creation/destruction, than the assumption that public spending should be financed by planned surpluses to begin with crumbles away.

    “Put in retrospect, the new orthodoxy was the ultimate achievement of what had been the fiscal counterrevolution unleashed in the late 1960s against the earlier post–World War II macroeconomic policies. Phase one of the fiscal counterrevolution targeted balanced budgets and implemented procyclical fiscal policies so as to suppress the impact of automatic stabilizers. The second phase began in the mid-1990s. Macroeconomic policy now targeted rising surpluses independently of the state of the economy. According to the prevailing ideology, rising surpluses were the sole source of funds for the cash-strapped state.”

    Alain Parguez (2004) “A Monetary Theory of Public Finance”


  14. Good post. I find it distressing that governments generally seek to bring in the most revenue possible, rather than attempt to bring in what is required for government services.
    Since Canada is close to the maximal marginal tax rate for the rich, this leaves little room to maneuver when government economic issues arise. For instance, the PIIGS in Europe have discovered they can no longer bring in more revenue when they need it most. The citizens are tapped out.

  15. I’m calling bullshit on this article. (Though I don’t have a degree on economics so what the fuck do I know.)

    • Too much math?

      • …Right.