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Finally. There is good news about income inequality in Canada. Statistics Canada's recently released income data reveals that we are a much more equal society than we were a few years ago.

For almost three decades, we've heard only bad news: growing inequality (the gap between the rich and poor) and greater income polarization (a dramatic decline in middle-income groups), resulting in greater income segregation and inequality among neighbourhoods in Canada's cities.

It seems the income-inequality deniers may have been right all along. They just didn't have the "correct" data from the most recent census to convince us with.

We have to thank Prime Minister Stephen Harper's voluntary National Household Survey (NHS), which replaced the mandatory long-form census, for this good news.

According to the NHS, many of the census tracts where low-income people live have seen their average incomes rise, while the highest-income census tracts in the country have lower average incomes. If true, this means we are now a more equal society with a much larger middle-income group. The rich are not so rich; the poor are not so poor.

According to the standard statistical measurement of inequality, the Gini coefficient, neighbourhood income inequality within Canadian cities has dropped significantly (a lower "Gini number" means less inequality or income segregation). In the Toronto and Calgary metropolitan areas, for example, income inequality among neighbourhoods fell by 12 per cent, from a Gini of about 0.22 in the 2006 Census to 0.19 in the 2011 NHS. Impressive.

But … maybe too impressive. Could the good news be too good to be true?

Fortunately, we can check these NHS income results. Our Neighbourhood Change Research Partnership based at the University of Toronto compared the income information from the NHS with the income data collected by the Canada Revenue Agency (CRA) from all tax filers in 2010. The CRA income tax filer data is neither a survey, nor is it voluntary. If you have an income, you must file. You must tell the truth. Or else.

We have been studying income inequality and income polarization in Canada's metropolitan areas since 2005. As soon as the NHS income data was released in early September we began a detailed comparison of the two sets of 2010 income data, the NHS and the CRA, at various levels of geography.

At the highest level, that of the nation, the provinces, and metropolitan areas, the two sets of income match fairly well – within 2 per cent on average for most metropolitan areas. However, the NHS was likely "adjusted" at that level to roughly match the CRA income data. Such an adjustment for very big geographies is easy enough to do.

But the national level of aggregation is not helpful for people in business and marketing, in social services, in government planning and budgeting agencies, and in research in general who need to know in detail, at the local level, people's family, socioeconomic, and ethno-cultural status.

The problem is that the voluntary survey has, as predicted, widely varying non-response rates. The response rates vary by location, socioeconomic status, ethno-cultural origin, family status, and so on. The non-response rate for Montreal was 20 per cent, for Vancouver and Toronto about 25 per cent, and in 18 metropolitan areas it was near or above 30 per cent. Peterborough, at 36 per cent, was the highest for a metropolitan area.

People with higher levels of education, higher-status jobs, higher (but not the highest) incomes and older people had higher response rates. Single parents and one-person households as well as renters had lower response rates. So did those living in the richest and poorest census tracts.

These missing responses explain why the Prime Minister's NHS paints a rosy picture of a country with a growing middle-income group and fewer low-income areas. The fact is, fewer low-income people filled in the voluntary long form.

When we compare the NHS to the CRA results for all census tracts in eight of the largest metropolitan areas, 6.3 per cent of the census tracts (about 200) strangely show up in the NHS as middle-income, tracts that were once either high-income or low-income.

The Gini coefficient of neighbourhood income inequality for Canada's major metropolitan areas in the 2011 CRA and the 2006 Census are about the same, but not in the 2011 NHS. Inequality can increase or decrease in measurable ways over five years, but rarely by the amount claimed in the NHS.

In short, all the good news from the NHS is nonsense.

The sad thing is that the news is now "official." It comes from official government of Canada statistics. It will, no doubt, be used in partisan ways. It will be used to confuse the debate about the growing gap between rich and poor. It will be used to make it appear that Canada is becoming more equal, when the opposite is happening.

The voluntary nature of the NHS was controversial from the start. Can a voluntary survey ever substitute for a mandatory census? In July 2010 the head of Statistics Canada, Munir Sheikh, who was appointed to that position in 2008 by Mr. Harper, issued a short answer with his resignation: "It can not."

Mr. Sheikh noted that he had no choice but to resign because he "always honoured" his "oath and responsibilities as a public servant as well as those specific to the Statistics Act." It turns out that he is the one in the debate with the Prime Minister who was 'right' and the one who acted 'honourably' on our behalf.

The income data in the National Household Survey is not valid. It should not be used or cited. It should be withdrawn. The 2016 census should be restored to the non-politicized, non-partisan scientific methodology that existed prior to the flawed 2011 National Household Survey.

The authors are professors who direct the data analysis of the Neighbourhood Change Research Partnership based at the University of Toronto, a multi-year national research initiative funded by the Social Sciences and Humanities Research Council of Canada.

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