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.


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