Wednesday, January 12, 2011

Walks Like A Duck, Talks Like A Duck, Statistically: Chicken

I turned on The Agenda on TVO last night and saw U of T prof David Hulchanski talking about his much publicized report on what he perceives as a growing income disparity in Toronto. It reminded me personally of why I never pursued post-graduate work and also how much I disagree with his report. Dr. Hulchanski received a mandate from a poverty-activist type place to do a report on income disparity in Toronto. Shockingly, the report says there is a problem and its getting worse! AHHHH! Sound the alarms! Lou Dobbs was right! The middle class is dying... sorry... I forgot to disable the panic button.

The problem with Dr. Hulchanski's report is that the numbers are rigged in his favour. Every elementary school child is taught the difference between a median and a mean. That child could tell the Dr. Hulchanski that a bunch of very big numbers in a group can really throw off a mean. That's essentially what has happened in Toronto. It's not really that there are a whole host of poorer Torontonians, in fact if you ran the numbers a different way you might even say people are generally a lot more comfortable than they were forty years ago. No, the biggest difference is how much money is being at the made at the top. According to the report, the top 20% earned about 55k per capita in the 1970's and 104k per capita in the 2000's. That growth in the earnings of the top percentages of Canadians is not exactly news to anyone. It completely distorts the numbers on the rest of the report. For his 70's baseline, the top group, those earning more than 40% above mean wages, was about 13% of the total pie. For his sky is falling modern numbers, the same group represents 36% of the total pie. The number of people represented in this group has gone from 7% to 13%. In other words, this group has about a 50% larger disproportionate effect on the mean today vs the baseline.

If you look at the report, the middle class has primarily eroded into the group 20 to 40% below the mean. That group in 1970 when, remember, there was likely only one person working in the household, was $22,300 per person. The so called middle class number was $29,800. Now, when there are likely two people working in a household, the number is $28,000. The question is as a household, would you rather have 30k a year in 1970 or 55k a year in 2005? While the 30k forty years ago is probably preferable, it isn't as much as a slam dunk as the authors of the report would like you to think.

Taking percentages off a mean can do really strange things. For the final graphs, the ones plastered all over the newspapers, they took three groups: people within 20% of the mean, people 20% or more above the mean and people 20% or more below the mean. So what does that actually equate to in dollar-terms? Your average middle class household straddle the narrow band between $32,500 and $48,840. Anyone making more than 49k is sent into the upper class and anyone making less than $32,500 is all of a sudden a pauper. Remember: this is per capita. So, if you are a successful professional making $150,000/annum and you support a spouse and three children alone on that income: your household is in the dreaded "third city" because per capita your household only makes 30k. By the same count a single TTC driver making 50K is in the first city. When your statistics are yielding that kind of crazy result, it's time to consider changing your methodology. Maybe household income would have been a better measuring stick? Maybe a median would have proved more accurate? I am generally pretty down on modern academia and this report only emphasizes the problem. Any system where this kind of statistical manipulation can not only pass as legitimate but be promoted and celebrated is fundamentally broken.

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