Statistical sour grapes -

Statistical sour grapes

So the rich are getting richer. What does it mean for the rest of us? Not much.


When the U of T Cities Centre announced a couple weeks ago that middle-class neighbourhoods are disappearing in Toronto, the Globe and Mail latched onto the study and squeezed it for all it was worth. Or, rather, what little it is worth and then some. The Globe used the study to craft a news article with a horror-movie lede, to order up a nostalgic Margaret Wente column, and to conduct a live online chat debating the issues raised. In the chat a user named “Paul” brought up a technical question for the study’s lead author, David Hulchanski:

I note that the maps drive off AVERAGE income. Do we know what they would look like if they drove off MEDIAN income? The published maps tell us that there is a growing class of people with super-high incomes. I think maps based on the median would be more informative about the middle class.

Let’s raise a glass to Paul. Even if you don’t understand why his point is important, you can see in the chat that Hulchanski’s answer is unsatisfactory: he says both that his team didn’t have median-income numbers going back far enough to make them the focus of the study and that he’s confident it wouldn’t make any difference. I think a criminal lawyer would call this “presenting an alibi and a justification at the same time.”

Hulchanski’s study found that the proportion of middle-income neighbourhoods in Toronto was 66% in 1970; it is now just 29%. Low-income neighbourhoods made up 19% of the city in 1970; that figure’s now 53%. Paul’s problem is that these types of neighbourhoods are defined relative to the mean individual income for the whole city ($88,400 in 2005). A middle-income neighbourhood is one whose residents are within 20% of the mean either way, while a low-income neighbourhood is 20%-40% below it. But a mean or average, unlike a median (i.e., the income that half the city makes more than and half makes less than), is sensitive to scale changes in individual outliers at the top of the distribution.

We can see the problem if we perform a thought experiment and imagine another city; we’ll call it Otnorot. In 1970, Otnorot had an unusual economic structure: it was divided into 100 equal-sized neighbourhoods numbered 1 to 100, each with an average real income corresponding (by total coincidence) to its number. In miserable Neighbourhood 1, the residents scrape by on 1 credit per year per person. In Neighbourhood 47, they make 47 credits on average. In Neighbourhood 100, they make 100 credits apiece, the filthy plutocratic bastards.

What would the Prof. Hulchanski of imaginary Otnorot report back to us about the economic structure of his city? The average income of the neighbourhoods (and the people in them) is, as the young Carl Friedrich Gauss could tell us instantly, the sum of the numbers 1 to 100 divided by 100: 50½ credits. Neighbourhoods 41 to 60, or 20 in all, are “middle-income” neighbourhoods within 20% of that mean. The “low-income” neighbourhoods are numbers 31 to 40; there are 10 low-income neighbourhoods.

By 2005, the vast majority of Otnorotians are living just as they and their forefathers always did. In Neighbourhoods 1-99, real incomes have not changed at all, nor have the relative population sizes changed. Neighbourhood 1 still earns 1 real credit per person, which buys exactly what it did in 1970. Neighbourhood 99 still earns 99. Only in Neighbourhood 100 has there been a change. Perhaps the residents held shares in the wildly successful Otnorotian version of Trivial Pursuit; perhaps they put their heads together and invented smell-o-vision. For whatever reason, they have gone from wealthy to superwealthy (at nobody else’s particular expense, or at least nobody’s in Otnorot), and they now earn a fantastic 8,000 credits per citizen every year.

For most Otnorotians, life hasn’t changed. The presence of the one new hyperrich neighbourhood would certainly have social effects, probably a mix of good and bad; you could, for example, almost certainly expect the Royal Otnorot Museum to acquire a hideous new glass mega-extrusion. But you wouldn’t say that the Otnorotian middle class had disappeared.

And yet—Shock! Concern!—that is exactly what Otnorot’s version of Prof. Hulchanski finds, unwisely using average incomes as his baseline. The overall average income for Otnorot is now a whopping 129½ credits a year, so no group at all outside lucky Neighbourhood 100 reaches the lower middle-income cutoff (103.6). The lower bound for a “low-income” neighbourhood, however, is now 77.7 credits. Where we once had just 10 low-income neighbourhoods out of 100, now everybody from 78 to 99 is defined as low-income, so we have 22.

It so happens that in Otnorot, lukewarm social science performed at public expense and promoted by newspaper editors is punished by means too horrendous to translate into English. Things are done differently in the real Toronto, a mercifully liberal-minded place. But the processes that so confused our alterna-Hulchanski are surely, in an oversimplified way, the same processes that have confused the real scholar. Observers of inequality have observed a genuine, dramatic numerical increase in it over the past two or three decades; one only need have been looking at business-magazine “rich lists” for a while to see that billionaires, all but unknown in the early 1980s, are now as common as seagulls.

There are real social and political dangers from this, to the degree that we allow economic power to translate into social and political power. But it does not mean that the “middle class” has really disappeared or dwindled. It only means that the logarithmic scale of possible incomes has stretched out at the top in a new Gilded Age, a realm of pervasively low marginal taxes and new deregulated industries.

Toronto might really, in some sense, have become bifurcated more arrestingly between rich and poor. But the Cities Centre’s measurement procedure cannot prove that this has really happened. Would it be a good thing for social conditions in Toronto if the Bridle Path were annihilated by a meteor? If that happened, Prof. Hulchanski (and the Globe) would probably be able to report several “low-income” neighbourhoods magically re-entering the “middle class”.

Respectable social science of this sort will ordinarily work with medians or with log-income (as the UN Human Development Index does), or it will approach inequality questions with the aid of the Gini coefficient—a metric totally absent from the Hulchanski study. No doubt Prof. Hulchanski would give the same sour-grapes defence he gave to our friend Paul: don’t have the numbers, don’t need the numbers. But there’s a further question. Why should we necessarily be concerned with between-neighbourhood inequality at all? The Cities Centre would use the same “average income” figure to describe and classify both Neighbourhood X, where everybody makes a healthy $100,000 a year, and Neighbourhood Y, where half the residents make $200,000 and half make nothing, bartering and stealing for their living. Funny sort of egalitarianism, if you ask me.


Statistical sour grapes

  1. I would like to visit Otnorot and observe the social science punishments first-hand. We can learn from those people.

  2. Until recently…with the advent of Harper's supposed 'Timmies crowd'… everyone in Canada was considered middle-class. I see we're now entering an era of class warfare.

    • Or at least the possibility for vertical social mobility.

      • We've always had social mobility, we just don't make a production out of it.

    • We entered yet another period of class warfare when the rest of the population bailed out failed industries and banks, only to see those who created the mess still get bonuses and retain their positions. We paid billions for their mistakes, they paid nothing but still live better than most and expect it to continue.
      Real class war has one real characteristic – Redistribution of wealth has very rarely gone from rich to poor, but it has very frequently gone the other way.

  3. Measuring poverty and/or prosperity continues to be a pain, and it doesn't help that almost everyone who does it has an axe to grind. How many times have the stats people warned us not to use LICO (StatsCan's "low-income cut off") as a poverty line, and how many times have journalists used it that way anyhow?

    • Add political parties as well. B.C, NDP use the child poverty stats as one of their main 'shame' platforms.

      "Statistics Canada has long complained that LICO should not be used as a poverty line, but in the absence of a viable alternative the LICO became the default poverty measure in Canada."

  4. So, Colby argues, there is more. It's just unevenly distributed. Waiting for the trickle-down.

    • I have a magic wand. This magic wand, when waved, can do one of two things:

      1) It will double the real incomes of households in the bottom quintile, treble those in the second-to-lowest, quintuple those in the middle quintile, increase those in the second-highest quintile by a factor of 10, and increase those in the uppermost quintile by a factor of 100 . . . except the uppermost percentile, who get a factor of 1000 increase. There will be no trickle-down whatsoever; the increase in inequality will be permanent.

      2) It will move everybody to the income at the border of the lowest and second-lowest quintiles.

      Which effect should I use, sir?

      • False Dilemna

        • No, just a hypothetical.

          Surely you have some opinion whether, in principle, it would be better for the average person to be poorer but society more equal than it currently is, or it would be better for the average person to be better off but inequality to be much greater.

          If economists sat down with the data, churned it, and actually proved, to the point where all economists agreed it was as indisputable as heliocentrism, that there was a direct tradeoff between prosperity and equality, which would you choose?

          Or would you just stick your fingers in your ears and shout because reality didn't conform to your demands, like the fundamentalists who deny evolution?

          • I sense this is an argument for the rich getting richer. Which is fine, but the poor are getting poorer (in the sense that they are falling further behind the 'standard' of living). One thing the parents always said about the Great Depression was that while they didn't have the Nike shoes or the Spider-Man backpack, it was fine because nobody else had them, either.

            It is, I suppose, wonderful to have the choice between nutritious food and hydro. But if you have to make that choice, I'm betting you aren't focussed on how much better you have it than those who came a century before you.

          • No, it isn't an argument for the rich getting richer. It's an attempt to extract assumptions.

            To poke at this from another direction, which country would you rather live in? One where a household in the bottom quintile has $100,000 in real income (that is, can buy everything that a current family with $100,000 in after-tax income could buy), one in the second has $1,000,000, in the third $10,000,000; in the fourth $100,000,000, and in the uppermost $1,000,000,000? Or one in which every household had $50,000 in real income?

            Doesn't one or the other strike you as a better society to live in? Maybe you think that high inequality hurts society more than relative non-prosperity, because it fuels stratification, envy, and social disharmony. That's a perfectly valid answer, isn't it?

            Doug Rogers is apparently afraid to answer that, however. He demands to cling to a world where the only possible answer is that equality and prosperity are linked, to the point where he refuses to even play with the idea that you might have to pick one as a higher priority than the other.

          • Okay, good. So, it's just another way to say my ensuite bathroom example. I personally don't have an ensuite bathroom. It would be nice to have one, but I don't think my life is without merit or that I'm tremendously handicapped without one. But it is absolutely AMAZING to me how many people–buying a house with NOTHING down–expect an ensuite bathroom! Won't even look at a house without one. There is something seriously wrong with that kind of expectation when you are relying on other people's money to fund it.

            So, obviously, there is a point for me at which prosperity tips the scales over equality. And under which equality wins. Now to determine what that point is, and then have everyone agree with me!

          • It is not an either/ or question of one extreme against another.

          • no, it is both hypothetical, and still a false dilemna, followed up by ad hominem and straw man.

  5. The right-wingers will be always quick to cast doubts on issue of income inequality. They don't care about income inequality. As long as the rich can continue to grow wealthier without encumbrances , then the Conservatives would have done their job well and make their shawdowy masters happy.

    • It does seem strange, but unsurprising, that the Harper government seems not to care about a lot of Canadians convicted of crimes abroad at the same time that it expresses serious concerns about the conviction of a Russian billionaire. If I ever become an oil tycoon in an eastern European petro-state, I want Lawrence Cannon in my corner.

    • Surely it is the actual conditions that poor Canadians live in, and not "inequality," that ought to be the concern here. Living within 10 miles of Larry Tanenbaum might not make life easier for people in Scarborough housing projects, but it doesn't make things harder, either, and their lot won't suddenly get better if he gets less rich.

      • Maybe not just one Larry Tanenbaum, but many Larry Tanenbaums could raise the cost of living.

  6. Not surprised to see a couple of "I don't care whether pisspoor measures of inequality or good ones are used, I just want a reason to be mad that rich people exist" comments here. Pray for that meteor, guys.

    • You should have put your prediction in your original post. That would have made you appear extremely clever instead of extremely grumpy that more people aren't commenting about how extremely clever you are.


        • You forgot the [irony] tags,[/irony]

        • For such a clever fellow, you assume a great deal about how unaware of irony I am.

        • What I found ironic is Macleans getting all hissy about others research. 'Most corrupt' , 'Too Asian' – hello?

          • Look, over there! Quebec!

    • Rather, it matters little whether the methods were faulty – averages or medians, the conclusion is the same: the middle class is being squeezed out of Toronto.

      • So, even if the method being used to arrive at the conclusion are WRONG, you still accept the conclusion?

        You've done the same thing the professor did. You're ASSUMING that the results would show the same discrepancies if one used value X instead of using value Y, despite NOT EVEN KNOWING WHAT THE VALUE OF Y IS. Saying that using the median would lead researchers to the same overall conclusion as using the mean did is like saying that because we've shown that 2+2=4, therefore we know that 2+X will ALSO equal 4, and that this holds true even if we don't know what the value of X is!!!

        • There is other evidence that the middle class is leaving Toronto: the growth of the suburbs. And speaking of not having numbers, what is the median income?

          • Umm, the fact that suburbs are growing does not necessarily mean that the middle class is leaving Toronto. There could be lots of other reasons for the growth of suburbs, e.g., overall economic growth, immigration, in-migration from other provinces, etc.

          • Didnt say it was proof. Said it was evidence. Like bloody gloves.

    • Damn Colby, just when you make it through a (very good) piece without stopping to punch a hippie strawman, you show up in the comments and do just that.

  7. Great article CC, one of your best. Once again the adage "the figures don't lie, it's the liars that figure" stands true.

    And kudos to "Paul" for asking the kind of question that should be asked in Question Period instead of the rhetorical BS we hear so often. Hope he runs in the next election.

  8. Dude from the "Cities Centre" has no clue as to the importance of actually getting the centre measured properly. Wow.

    Not quite the dumb objectification of subjectivity you rightfully blasted social sciences research for previously. But, indeed, this is dangerously dumb improper objectification of alleged objectivity.

    Lemme guess: the taxpayer funded this garbage somehow?

  9. I don't know anything about social science, but I do know that whoever had the bright idea to have most if not all neighbourhoods as "mixed" was a genius. And I fear that we're moving away from that, at least judging by recent subdivision construction. I live in a non-subsidized unit in a subsidized housing complex. One street over is a golf course, with the golf-course mansions. In between are fairly large family homes as well as smaller homes and townhouse/semis. Whether I was from Toronto or Otnorot, my neighbourhood would completely screw with the narrative.

  10. How many rich Torontonians are, in reality, ice-footed Detroiters in canuck garb? And how many poor?

  11. The median/average lesson is one it would be just as important for the Fraser Institute to start using.

    Far moreso, probably.

    • Release Date: December 6, 2010
      VANCOUVER, BC—Canadians seeking surgical or other therapeutic treatment faced a median wait time of 18.2 weeks in 2010, the first increase since 2007 and the second-longest wait time recorded, according to a new report from the Fraser Institute, Canada's leading public policy think-tank.

    • Government-run Pharmacare Will Not Help Patients or Taxpayers
      Between 1997 and 2002, only three per cent of Canadian households spent more than five per cent of their annual income on prescription drugs. Looking specifically at seniors, an analysis of the province of Saskatchewan shows that, in 2006, elderly families (65 years of age or older) only spent 1.4 per cent of their median after-tax income on prescription drugs.

      • ….elderly families…spent 1.4 per cent of their median after-tax income on prescription drugs.

        Side note….that strikes me as a somewhat garbled statement on the part of the FI.

        I wonder if the FI really meant that the median amount spent by elderly families was 1.4% of their after-tax income.

    • Search "median" in Fraser Institute website:

      Total results: 409

      Good news: they've heard of the term.

      • Your time would have been better spent looking at the methodologies for TAx Freedom Day than writing three posts.

        A little knowledge is a dangerous thing indeed.

        • …except you didn't include that little nugget in your little cryptic lament, now did you?

          Suppose you enlighten us on your statistical objection to Tax Freedom Day? There is a decent chance that I will agree with you.

          • Oh oh…i know ; that's where they include all of the taxes paid since the good lord threw the rascals out of the temple, but don't include all of the income…odd that! Seems they confused average and median too – MT's point.

          • While I should not presume to make Mike T's point for him, I suspect he objects to AVERAGE taxpayer contributions being used to compute Tax Freedom Day, rather than MEDIAN taxpayer contributions. Why? Because, obviously, MEDIAN portion of income spent on taxes would have led to an earlier date, given the large number of Canadians who pay (no or) very little in tax. The super-duper taxpayers will pull up the average waaay more than they could pull up the median, because, well, they can't pull up the median.

  12. Statistics may inflame some people who feel others have too much and should be forced to hand it over to them, but for the vast majority of Canadians the amount of wealth other people have is irrelevant, we're all better off than we were. Even the 'poor' have cellphones and cable TV, only the stupid go to bed hungry in Canada.

    • Anyone who is hungry can always eat cake, right Marie?

      • They could if they bought some cake with the charity we are forced to give them, but if they're hungry they're obviously too stupid to have purchased a cake. They spent the welfare money we gave them on luxuries instead of necessities. It would be difficult to explain it more simply for you, perhaps you know an adult who could?

    • The difference is that when the wealthy are stupid they reach for the phone to call their bankruptcy lawer rather then go to bed hungry. The poor pay for their stupidity or bad choices one way or the other, the wealthy seem to feel everyone else should share their pain.

      • If politicians bail them out, that's our fault, we should not elect such idiots and throw them out when they do. Nor should we pay through the nose to provide the 'poor' with luxuries, politicians who buy votes from the 'poor' lobby should also be thrown out.

    • "Statistics may inflame some people who feel others have too much and should be forced to hand it over to them…"

      "…only the stupid go to bed hungry in Canada."

      Only the willfully stupid would have such a stunted view of poverty in Canada. Here – after 3 seconds on Google, I found this report from a Toronto foodbank. Lots of detail here about why some Canadians go to bed hungry:

      Warning: it opens a .pdf. I dare you to read it.

      • You must be kidding?

        The daily bread food bank is in the business of being a food bank, their self-preservation is their highest priority, of course they create reports that justify their existence and funding.

        The poverty industry is a well-oiled machine from which many people make a very comfortable living, don't be fooled.

        • Yup. Willfully stupid.

          Did you even open the document?

  13. Truly poor people aren't buying houses – they rent. That's what seems to be missing from all this.

  14. And, as predicted, now we have open class warfare on here.

  15. Those poor Otnorotians, having to put up with that hideous new glass mega-extrusion on their Royal Museum! Oh, wait…

  16. I think your first mistake was to read something written by Margaret Wente. She seems to always leave me wishing I could have my time back.

    Interesting piece on social science. I think the key point would be: "the very high causal densities that characterize human society guarantee that no matter how refined our predictive rules become, there will always be conditionals lurking undiscovered. "

    The piece gives few examples of failures in social policy derived from faulty social science. Ironically it spends time on criminology and economics as similarly unreliable fields attempting to study complex situations. Somehow I doubt the Manhattan Institute is about to call for a healthy skepticism of tough-on-crime policies or economics as a whole.

    On the other hand, the conclusions about social science seem pretty self-serving for a hard-right think tank: few social programs can be proven to work, the best ones provide incentives, and social programs can't magically fix things.

    In light of the long-term assault on the social safety net from the right, this product of a hard-right think tank should be viewed with skepticism.

  17. If only someone would invent a system of government that would confiscate all personal assets from it's citizens and distribute them amongst the population equally. Then, regardless of ability or contribution, pay each person an equal wage for whatever work they may do.

    I bet that would work great!

    • That's why the USSR is doing so well these days!

      • Oh dear lord…

  18. Hulchanski's reply could not have been summed up fairly in one sentence and reading his actual reply shows it wasn't.

    "We do not have median income going back to 1970. We did run tests using median income for shorter periods of time and end up with the same results. Only 2 or 3% of census tracts change depending on our use of household, or employment, or individual income. We are dealing with large numbers here: 2.5 million people in the City of Toronto. Those slightly different measures make very little difference — and no change in any of the trends. "

    He did attempt some statistical checking and made a statement based on what he had. If the median information doesn't exist, then it doesn't exist. His use of averages can cause slewed outcomes as you illustrated, but your refutation of his data failed to take into account the evidence he did present in his reply to Paul.

    One could accuse you of bending the figures to suit too.

    • I completely stand by my characterization of that answer.

      • I would be surprised if you didn't.
        Black and White very rarely accept shades of grey

  19. Ha ha ha ha, Or how about the trivial-pursuit inventing. smell-tv producing lucky people of Otnorot get tired of the envy from 20 credit bums, or maybe the lucky 4000 credit folk's offspring intelligence runs out – what to do?

    Move your game to hCina where the a 20 credits is a dream for some and those who don't dream in widgets,credits – this is what happens:

    But, then years later the formely creative wonder what happened?

    Not a big fan of statistics – more a big fan of systems theory

    • One correction to the altered scenario – everybody has a belief in widgets and credits of some sort.

  20. On Exactitude in Science . . . In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography. – Borges

  21. A lot of hypotheticals here. The money in that 100 sector had to come from somewhere and unless it's all Renminbi from those stupid Chinese, it's Canadian dollars, largesse sucked less through brilliance than monopoly (see Rogers/Shaw) and sucked from the totality of Canuckistan by the usual usurious loans on their houses, cars; ever expanding credit card, debit and ATM fees. Money, as long as the human race has had it, only flows – no less than water, and wasn't that a joke – in only one direction. If Smellovision is the best invention this John Galt can even imagine it speaks volumes for the lack of innovation that keeps this country hewers of wood and drawers of water for the planet. When the superrich pay the 90% rate again – as they did in the dirty fifties – we'll have money for free post secondary education, world class health care and infrastructure and we will be as comeptitive as Germany and Sweden and even the Filthy Few CEOs will be better off, free and possibly happy to occasionally leave their gaited community in safety on good roads. I know, lots of luck with that.