Lies, damned lies and statistics — and your taxes

April 25, 2010

Last week, the Fraser Institute released its Consumer Tax Index report, which claims to show that the average Canadian family's tax bill has increased by a whopping 1,624 per cent since 1961. There are a lot of things wrong with the Fraser Institute's math. Here are just a few of them.

To begin with, the numbers should have been adjusted for inflation, something the Fraser Institute did not do.

A dollar in 1961 bought a lot more than a dollar buys today, so it doesn't make sense to compare the tax bill in 1961 dollars to the tax bill in 2009 dollars. Once adjusted for inflation, that 1,624-per-cent increase shrinks to just 137 per cent.

On top of inflation, we need to consider that incomes also grew over the last half century, so the tax bill would have grown even if we paid the same proportion of our income in taxes in 2009 as in 1961.

What we need to compare, then, is not the change in absolute dollars that families pay in taxes, but the change in the share of family income that goes to pay for taxes.

In 2009, the average family paid 41.7 per cent of their income in taxes — at least according to the Fraser Institute — but they count business taxes as part of the family tax bill, which grossly overstates average taxes.

According to the Fraser Institute, the average family pays $2,848 in corporate income tax and $397 in natural resource royalties. The argument that the average Canadian family pays for all business taxes is simply not convincing.

Even if individuals ultimately pay business taxes, it's not necessarily Canadians who pay them (think of all the stuff we export).

And it's certainly not the average family that pays them.

In fact, given how unequally distributed shareholder profits and investment earnings are these days, the average has become meaningless — it's artificially pulled up by those with higher incomes and does not represent the experience of most families.

The median family's tax bill would be a lot better metric in this case, meaning the family in the middle of the income spread.

When corporate income tax, natural resource royalties and other business taxes are excluded from the calculation, the average family's tax bill comes out to 36 per cent of family income. This includes personal income taxes, sales taxes, taxes on liquor, tobacco and fuel and payroll taxes.

But even using the Fraser Institute's own numbers, flawed as they are, we find the following.

In 1961, families paid 33.5 per cent of their income on taxes, but by 1969 they were paying 39 per cent and in 1974 they paid 43.4 per cent of their income.

So, if you compare the 41.7 per cent families spent on taxes in 2009 to 1961, you will find a 25-per-cent increase, but you will only find a seven-per-cent increase since 1969 — and an actual decrease since 1974.

Therein lies the peril of summary statistics — calculating the percentage change over time crucially depends on your starting and ending point.

A few years either way could result in completely different numbers.

And we wonder why people are so suspicious of statistics.

The best way to avoid this kind of statistical trick is to show as much of the underlying data as possible and let people see the patterns for themselves. The Fraser Institute's report contains a graph, Figure 4, that plots taxes as a share of income.

The report's conclusion that "the average Canadian family's tax burden has been rising steadily for the better part of 48 years" is clearly not supported by its own data.

The share of income going to taxes rose quite fast in the 1960s and in the decade between 1976 and 1985 but has hovered around 45 per cent ever since.

It seems that the Fraser Institute report is much ado about nothing — the effective tax rate as a share of average family income has been stable over the past quarter century.

The tax increases the institute is so concerned about capture the increases during 1960s, when many of Canada's core social programs, such as Medicare, were first established.

No news here, folks, unless you are interested in picking up some tricks on how to present statistics in a way that makes the growth of a spending item of your choice appear larger than it really is.