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1. Suppose all assets are infinitely-lived, and yield $1 (inflation-adjusted) rent per year. If real interest rates halve, then the prices of those assets will double. But they still pay an income of the same $1 per asset per year. If people are infinitely-lived, this has no effect on the distribution of permanent consumption across the population. If people have finite lives, in an OLG model, this increases the permanent consumption of the old, on a one-time basis, but has no obvious (to me) effect on the distribution of consumption across a given cohort. This matters, because we have seen a big decline in real interest rates since 1982 (when they were very high).

2 and 3. From the CANSIM table 204-0001 you link to, I see a small decline in the share of income going to the top 1%, from 11.5% in 2008 to 10.3% in 2012 (if I'm reading it right). But I can't see data going back to 1982. Am I reading it wrong, or not clicking on the right thing??

@Nick Rowe: if you go to the tab for Add/Remove Data there is a selection for Time Frame (Step 5) which gives the option of going back to 1982.

Ah! Thanks Kathleen! (I just tried it, but couldn't connect, maybe because hundreds of other people are doing the same thing.)

" If people have finite lives, in an OLG model, this increases the permanent consumption of the old, on a one-time basis, but has no obvious (to me) effect on the distribution of consumption across a given cohort."

I think this is only true if there are no bequests and so no dynasties. If there are bequests, there can be a permanent gain (assuming a permanent fall in rates) to the dynasty, even though the gain to each individual member of the dynasty lasts only for their (2 period) lifetime.

Nick: With respect to your first point, I can see the argument to exclude capital gains and often do so in my own work, depending upon what I am studying. But if you going to exclude capital gains and you are looking at after-tax income, my point is that you should worry that deducting all personal income taxes means deducting taxes paid on the capital gains. If something is not in pre-tax income variable you are using, the taxes on it should not be deducted as you move to the after-tax income variable. If the authors of this study wanted to go with after-tax income without capital gains despite this difficulty, they should at least have discussed the issue and, I believe, done some calculations to try to bound the problem. For example for a high-income individual, federal plus provincial personal income tax on capital gains is going to be pretty close to a quarter of the value of the capital gain so an approximate adjustment of that sort might be made as a check. BTW, I believe the SLID coverage problem to be the more serious one.

Going to CANSIM, here is Canada, after-tax income shares including capital gains, 1982 to 2012, individual taxfilers. (The calculations I report in my piece are from the same table and series, except they are average incomes adjusted to 2015 dollars using the Bank of Canada inflation calculator, which is based on the all-items CPI to date.)

Top 0.1% Top 1%
1982 1.8 6.3
1983 1.7 6.2
1984 1.8 6.3
1985 1.9 6.5
1986 1.9 6.8
1987 2.2 7.7
1988 2.7 8.2
1989 3.7 9.5
1990 2.4 7.6
1991 2.3 7.4
1992 2.3 7.5
1993 2.6 8.3
1994 2.4 8.9
1995 2.4 7.5
1996 2.6 7.9
1997 3 8.6
1998 3.2 9
1999 3.4 9.3
2000 4.1 10.6
2001 3.8 10.1
2002 3.5 9.6
2003 3.4 9.6
2004 3.9 10.3
2005 4.3 10.9
2006 4.6 11.6
2007 4.7 11.7
2008 4.1 10.6
2009 3.4 9.6
2010 3.6 9.9
2011 3.7 10
2012 3.4 9.6

Managed to connect now. Thanks Kathleen. The share of the top 1% was 7.1% in 1982, then slowly rose to about 2006, then levelled off. I wonder why?

rsj: with full bequests and dynasties, it's like the infinitely-lived agent model.


Stock prices and capital gains are a huge portion of income for top earners.

I am just a worker bee, but even I got shares of stock and early exercised at a low price (pre IPO price), and then sold at much higher price. On my tax form this was a capitl gain, but it was understood that this was part of my compensation. Now from the point of view of the angel investors, they made an initial investment at price X and sold at price 10X. That's how venture capitalists make money -- by capital gains, but it is income for them. There really is no plausible definition of income that doesn't include capital gains, at least realized capital gains. These types of arrangements are a large portion of income realized by executives, investors, and other top earners.

One consequence is that when there is a stock market crash, such as in 2008, the income of these groups falls.

Mike: thanks.

"But if you going to exclude capital gains and you are looking at after-tax income, my point is that you should worry that deducting all personal income taxes means deducting taxes paid on the capital gains."

I look at it the other way around (or I might be misunderstanding you).

Suppose part of my income is purely fictitious, and shouldn't be taxed, but they tax it nevertheless. We should either look at my before tax income minus the fictitious income. Or else look at my after tax income, which equals total income, minus fictitious income, minus *all* taxes (including taxes on my fictitious income), because that's what I have left over to finance my permanent consumption.

(Of course, some "capital gains" really are income proper.)

The exercise of in-the-money stock options results in income that is taxed like capital gains but not classified as capital gains.

I assume that is included?

(The issuance of stock options, often with a 10 year life, expanded starting in the early 90's. Perhaps that shows up a bit in the data above as you move into the 2000's.)

Taxes paid on Capital Gains are typically due because the gain has been triggered through an actual disposition. That means cash has changed hands and the capital gain has been realized. There are exceptions in the form of deemed dispositions (taxes are levied on market value obtained through estimates, not through a sale) that occur in situations such as family trusts, but I have to think those are somewhat unusual/rare. Capital Gains are not fictious if they have been realized. Cash is paid to the income earner and that cash can then be used for current consumption or saving - just like any other source of income.

Looking at the study in question, the authors declare their preferred definition of income excludes capital gains:

"Capital gains are excluded because they are not by their nature regular and recurring. It is further assumed that they are less likely to
be fully spent in the period in which they are received, unlike income that is regular and recurring."

Anyone who lives off their investment income will find this a very puzzling characterization of Capital Gains. For example, mutual funds and REITs routinely designate a portion of their pay-outs as capital gains. There are even mutual funds designed specifically to transform income into capital gains.

Nick: As Kathleen says, realized capital gains are not fictitous.

Let me re-make the point in terms of your first post where you write: "Suppose all assets are infinitely-lived, and yield $1 (inflation-adjusted) rent per year. If real interest rates halve, then the prices of those assets will double. But they still pay an income of the same $1 per asset per year." I agree that if the infinitely-lived individual just keeps taking the $1 per asset year, the capital gain may not mean mean much. But then the capital gain isn't realized so it doesn't show up in current income and it is not taxed. So using the words of your second post, there is no "fictitious income" to tax. If individuals realize some of that capital gain, perhaps because they are finitely-lived, there is income, but it is not fictitious: holders of those assets can now use their capital gains to attain a higher consumption path until their deaths.

Still your second post is a neat way to think about some fictious capital gains which do get taxed: the fictitious capital gains due to inflation. (A common argument for the special tax treatment of capital gains is that it very roughly offsets the inflation effect.) I have never done it but one could try a rough fix to try to take out the inflation component of capital income. This would almost surely lower the level of measured inequality. However such a fix would probably do more in 1982, when inflation was comparatively high, and not so much in 2010, when inflation was low. So one would expect that it would increase the rate of increase of measured inequality between 1982 and 2010.

To repeat what I wrote above, I imagine the bigger issue with the Fraser Institute study is the SLID coverage problem. Much of the increase in income inequality over the 1982 to 2010 period comes from higher-income individuals getting more labour income (or at least what is called labour income for tax purposes).

JKH: The Stats Can taxfiler data includes stock option income. The SLID data did in principle by 2010 because by then most SLID respopndents had the option of allowing their income tax data to be used and that income includes stock option data. However some respondents supply their own numbers and I just checked the questionnaire: it doesn't ask for option income explicitly, although it does ask for "other income".

@Nick - "If people have finite lives, in an OLG model, this increases the permanent consumption of the old, on a one-time basis, but has no obvious (to me) effect on the distribution of consumption across a given cohort".

Isn't it going to have a distributional impact across the cohort of old people, because they hold different amounts of the asset?

Mike: sometimes capital gains get realised because people rebalance their portfolios (or are noise traders, or fundamentalists, or technical analysts) and sell and buy at the micro level. Not sure how big this effect is, but I doubt many people are "buy and hold till I want to consume".

(Yep, the inflation case was at the back of my mind when I was writing that comment.)

What are some examples of fictitious income?

Miami: examples are capital gains and interest income that are really just inflation. Like if you earn 2% interest (or capital gains), but inflation is also 2%, so in real terms you earn nothing, but you still pay tax on that 2%.

Unfortunately, I, and likely many others, have long disregarded anything produced by the Fraser Institute. The findings of its studies are all too predictable. Furthermore, I have lower regard for those who associate themselves with the Fraser Institute, including Livio Di Matteo, who writes for this blog. Why would someone risk their reputation by working for such an outfit?

Nonetheless, my thanks to Professor Veall for his detective work in this case.

It's pretty hard to name a more completely self-discredited voice in Canadian life than the Fraser Institute; self-parody, but still with an edge of naked malice, that, like a mad dog, might just go for you next. (And if you've known an actual mad dog, I have, too, and I intend the analogy.) It's not entirely unapposite given Simon Fraser's own unattractive personality, but at least the man accomplished something in his life, so he can take care of his own reputation by association. At this point, as a Vancouverite, I'm afraid that there's a danger of ruining the river's reputation by association.

"In sum, the Fraser Institute study uses a flawed income variable and a data set that lacks coverage in the tails, both in ways that lead to underestimated inequality."
What!? The Fraser Institute selected a nonsensical methodology in order to give them the results they were looking for. Preposterous, I say.

(Note sarcasm.)

I'm interested in the argument about whether family inequality of individual inequality is the more useful measure, if only because addressing family inequality seems kind of impractical.

Policies to address family inequality would focus on things like reducing divorce (more two income families), and encouraging marriage across economic classes. Which requires some serious social engineering, and is probably the kind of problem that governments would be hard-pressed to address in any meaningful way. How do you make university-educated people less likely to marry other university-educated people? Another approach is more incentives for one parent to stay home, but again, is this a desirable thing for governments to do?

Inequality between individuals can be addressed on the income side by bringing down the high earners through higher personal tax rates, limits on the CIT deductibility of executive pay, that sort of thing. The bottom can be boosted with skill development incentives, a minimum guaranteed income, and arguably minimum wage increases. It's a bit clearer what kind of government policies can pull on these levers than the ones on the family side, and they're not as intrusive into people's personal lives.


I'm not sure it's correct to say that it's easier to address individual taxation than family taxation. We could, after all, adopt a policy of family taxation, rather than individual taxation, and tax the bejesus out of high income families. Granted, some of my law and feminism colleagues would have a few thoughts on that (the usual thinking being that such policies encourage woman to leave the workplace), but it's certaintly a feasible strategy. Or we could provide tax credits to low income families (which, in practice, is what we do). And presumably, many of the policies targetted at individual level inequality would reduced family level inequality as well.

As an aside, note how using state power to encourage some results, such as reducing divorce or encouraging marriage (both, objectively, highly desirable results) constitutes "social engineer", but using the same state power to distort the economy isn't "serious social engineering". I'd argue both are a form of social engineering. And while you ask the question "is this a desirable thing for governments to do" with respect to the first set of policies, you don't for the second. Why is the desirability of state manipulation of social outcomes questions in the first instance but presumed in the second?

Nick: "Managed to connect now. Thanks Kathleen. The share of the top 1% was 7.1% in 1982, then slowly rose to about 2006, then levelled off. I wonder why?"

Election of the Harper Conservatives? :)

I'm actually surprised they haven't grabbed this dataset and run a series of ads with it.

Bob: I really didn't see *that* one coming!!

Some out of this world civic migration analysis:
People earned a little too much in the 80's (in pulp towns before the internet ruined their incomes).
To make more for less work, people went to University. The complacency garnered by too much income was bad as people blamed outsiders for ruining their income. The winners of globalization are the educated and the resourceful (enough to make time to read).
The University graduates didn't return to the bitterness of people unworthy of a wage of an educated man, woman, or transsexual.
My personal lost-role model doesn't apparently work because most people use parents. I figure enough immigration will change things around in a generation or two. This also explains the bitterness of Halifax, but certainly the 3 universities could've formed a service sector base.

Mike, your criticisms seem to make sense to me, but only if I fixate on the absolute difference between the bottom-most data point and the top-most data point. Are you suggesting that this is the best way to measure the income gap?

Suppose that the distance between the tails has indeed grown, but the population within a single standard deviation of the mean has grown dramatically. Would you argue that the income gap had worsened in that scenario?

At best you seem to have lent greater credence to the notion that "it depends on who you measure."

re: the downturn in inequality, the series I provided above and pretty much all the others show the downturn in 2008. The incomes of high earners, including the labour incomes of high labour income earners, fell proportionately more during the 2008 crisis than those incomes below the very top. But top share inequality is still well above its 1980s level. In the United States the recent evidence is clear that top share inequality has begun to increase again but in Canada the evidence is a lot weaker.

re: family income vs. individual income. In my own research about earnings processes, the ultimate cause of the increase of inequality, I look at pre-tax-and-transfer individual income. But if the research topic is comparing standards of living (i.e. the consequences of inequality), then I look at after-tax-and-transfer family income, ideally converted to adult equivalents. I agree with the Fraser Institute study there.

to RPLong: My main point is that if you are studying anything, you would like to use data that has complete coverage. The Fraser Institute study isn't very good at covering the top end of the income distribution. If nothing happened at the top end of the income distribution, then that might not be so serious in studying trends in inequality. But as is well known in the field, other data that do cover the top end show that the top end got a big increase, so that the coverage problem in the Fraser Institute study made them find a smaller increase in inequality than actually occurred.

I absolutely agree that it depends who you measure and, as you point out, it is difficult to get simple, single measures of inequality that are always reliable. My own very rough characterization from 1982 to 2010 is that not that much happened to the income distribution except the right tail stretched out. That is pretty clearly an increase in inequality.

Mike - So, in shorter form, your view is that the best measurement of inequality is the absolute difference between the tails, regardless of what's happening in the middle? I apologize if I'm mischaracterizing your position, but that is the impression I am getting of it.

RPLong: No. The middle matters. The problem is that you can't summarize a general distribution with a single statistic. I can go along with the Gini, largely because that is what seems to have made it into the public arena. (I would have preferred Theil/Atkinson.) These measures all put significant weight on what is happening in the middle.

Top shares are interesting because (a) they have changed much more than the rest of the distribution (b) they can be estimated historically back to 1920 for Canada, unlike other measures and (c) there is some research that suggests in practice that when we can estimate the whole distribution, there are seldom important pre-tax-and-transfer income distribution trends that differ much from the pre-tax-and-transfer top share trends.

Mike -

If you know the Fraser numbers, and you know that the Fraser numbers underestimate the top tier, and you can estimate the approximate size of the top tier using historical data back to 1920, then isn't it a trivial extrapolation exercise to arrive at a better estimate of what the "real" inequality numbers are?

From the Globe and Mail article, I see that the Gini coefficient estimates a 24% increase in income inequality, while the Fraser Institute is suggesting a 10% increase. Your blog post above leads me to conclude that the lion's share of the discrepancy is due to an underrepresentation of the top income tier.

Thus, if you are right, I have to conclude that most of the change in income inequality is due to an increase in the wealth of the top tier, not a decrease in the wealth of the bottom tiers. We might even be able to say that the middle has changed less than expected (based on the notion that the Fraser study is biased toward the middle tiers).

If so, I fail to see what the issue is. The Fraser study could be methodologically improved, leading to a conclusion that income inequality is not an issue for the middle class, and the wealthy are doing much better than in the past. Your blog post make it sound like the Fraser Institute did something nefarious, but if we use your corrections, we still reach the kind of conclusion that might be termed "Fraser-friendly."


Paragraph 1: I don't know that it is a trivial extrapolation but it is true that all other studies that I know of find higher estimates of inequality than the Fraser Institute study.

Paragraph 2: The Globe article by Professor Sarlo only cites Fraser Institute estimates, all of which share the problem with the sample undercoverage.

Paragraphs 3 and 4: For someone who thinks that the only change in inequality that matters is that within the middle of the distribution, then the undercoverage at the ends of the sample used by the Fraser Institute would not be a concern. (Existing studies had already concluded that not much was changing with respect to inequality in the middle of the distribution.) However, the focus of the policy debate is the increase in the inequality between the top and the middle. Given that the Fraser Institute study was trying to inform that debate, it should have stated that its sample had this coverage problem which would lead to underestimates of inequality. As I noted in the blog, the problem was well known in the literature.

BTW, even if we took the Fraser Institute estimates at face value, it is not clear whether a "10%" increase in the Gini coefficient is a "modest" increase as the study suggests. For example, for after-tax family income Gini coefficients, that is about the difference between the Netherlands and Canada and about half the difference between Canada and the U.S.

Mike, you said: "However, the focus of the policy debate is the increase in the inequality between the top and the middle."

There are two scenarios in which the gap would increase between the top and the middle:

(1) The top tier somehow exploits the middle tier, or gains at their expense.
(2) The top tier simply grows without impeding the other tiers.

I can see how your view of the Fraser study makes sense if we take view (1) by assumption, but I cannot see any grounds for taking (1) on assumption, and in fact your blog post gives me more reason to believe (2).

What am I missing? Should I rather believe (1), and if so, why?

RPLong: My criticisms of the Fraser Institute study are simpler. As I wrote, it does not use the entire income distribution in its calculations, but does not make that clear. Its income definition is flawed, but it does not make that clear.

Suppose there were a bunch of studies that said that there were large and rising speed differentials among vehicles driving on a highway. Then study F comes along and uses a data set that excludes a significant number of the very highest speeds and for the higher speed vehicles it does include, uses flawed radar gun measurements that are underestimates. The study does not point out these problems but concludes that speed differentials are not so large nor increasing so rapidly.

Speed differentials may or not be a serious problem for accidents or whatever. But that is not a defence of study F.

One strong point in their method was to focus on inequality after taxes and transfers. It would be nice for the poor to have the opportunities to earn their way into the middle class, but since that's not always the case, if we're focused on inequality of outcomes, then we should follow that outcome through to, well, the outcome, i.e., after taxes and transfers.

Another shortcoming I find in inequality measures is that they tend to ignore that people's income tends to increase with age. If we are concerned about inequality of opportunity, we should be looking at inequality of outcomes in age groups, and not comparing the income of teenagers and university students with that of people in their prime earning years.

Nathan W: I agree with both your points.

With respect to the first comment, while the Fraser Institute study press material implies otherwise, working with after-tax-and-transfer income is common if the data period is recent. For example, in my own top shares research there is Table 2 in this paper. Sometimes, however, the focus is on the determinants of the increase in inequality in which case it makes sense to look at before-tax-and-transfer incomes. And that is the only option if one is going to do historical work.

With respect to the second comment, I have done some work which showed that the trends in top shares for the senior population are those similar to the population as a whole. But that is far from a complete response to the issue that you raise.

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