I'm going to answer in French.
You are saying that it's very difficult to quantify because it's illegal. It is even more difficult to quantify when people abuse largesse or profit from gaps or grey areas in the law. No, we don't have data, because practically no one has any yet.
The Canada Revenue Agency, the CRA, has since 2016 been conducting a major study on the tax gap. It deserves to be congratulated, as few countries are doing that. We are waiting for the completion of that examination, whose last report will be about the private sector. If I remember the figures contained in the most recent CRA report on this correctly, for 2014 alone, we are talking about an amount of $1billion to $3 billion for wealthy Canadian taxpayers who do not comply with tax rules. We don't have precise data on that, but the CRA data alone is enough to prove that the problem is real.
The CRA's methodology and some of the choices it made for its analysis could be criticized. You were talking for instance about illegal activities. For our part, we are interested in cases where the law does not provide a sufficiently rigorous framework, one which makes tax evasion possible, through abuse or aggressive tax planning. One example would be a precautionary agreement between Canada and a tax haven to prevent double taxation. Tax avoidance is legal in that case, but is it morally desirable? We think not. However the CRA does not take those financial transactions into account in its analysis, and it it did so, it would come up with even bigger numbers.