# Tax Gap Estimate

Written by: Thomas Hirt, CPA, CGA

Mark Twain – “There are three types of lies:  lies, damned lies, and statistics.”

In June 2019, the Canada Revenue Agency (CRA) released a fifth report , “Tax Gap and Compliance Results for the Federal Corporate Income Tax System”, in its series of reports about the tax gap.

The tax gap is the difference between what the Canadian government believes it should have collected in taxes, and what was actually collected.

The usefulness of the tax gap estimate by CRA needs to be taken with a truckload of salt for a variety of reasons.

First is that this is the estimate of the tax gap for 2014.

Imagine taking a picture of a bird; the bird has its wings stretched and the only other element of the picture is the sky.  The picture of the bird has limited utility.  You cannot tell from a single picture whether the bird is ascending, descending, or flying levelly.

The same thing is true of the tax gap estimate for 2014.  This is an estimate of the tax gap for 2014, but without estimates for years before and after, you cannot tell if the tax gap is increasing, decreasing or level.

Hence, the snap shot of the 2014 tax estimate does not tell you what is going on with the tax gap.

Second, the total combined tax gap is based on the total of four different estimates.

Simply adding together estimates is problematic.

For example, let’s study Bill and Bob to estimate their annual incomes.

We are 90% certain that Bill’s income is \$50-60 thousand and 90% certain that Bob’s income is \$20-40 thousand (referred to as 90% confidence intervals).

The government’s tax gap estimate is the equivalent of saying that as a result of those studies, Bill and Bob’s combined income is estimated to be \$70-100 thousand.

However, because you have combined studies, the odds of the combined income being \$70-100 thousand is between 81% (= 90% x 90%) and 90% (it could be higher than 81% because there is the chance that the errors in Bill’s income and Bob’s income cancel each other out and the total is still in the \$70-100 thousand range).

If you combine four studies, each with a 95% confidence interval, the odds of the total range being correct is between 81.4% (=95% X 95% X 95% X 95%) and 95%.

Hence there is a problem with combining four estimates to estimate the total tax gap.

Lastly, the estimate is only good for 2014.

Changes in the situations underlying a study invalidate the study’s usefulness for examining other years.

For example, in 2016 the government began to require individual tax payers to disclose disposals of principal residences on their tax returns.  The purpose of this disclosure is to decrease the number of individuals inappropriately claiming that the gain made on the sale of a property was eligible for the principal residence exemption (and hence, tax free), when it should not be exempted.  As a result, starting in 2016, the tax gap resulting from the sale of residences will have decreased.

Hence the tax gap estimate for a given year cannot provide any information about the tax gap in other years.

After audit results, CRA’s statistics estimate the tax gap as \$15.7 billion to \$19.9 billion for the 2014 year.  We do not know if this estimate is: higher, lower or the same as prior years; the accuracy of the total; or anything about years other than 2014.  Hopefully, Canadians will look at this estimate with a suitably skeptical eye, and salt merchants will do a booming business.