Are stagnant incomes a statistical artifact?

The American middle class hasn't got a raise in 15 years. Median household incomes aren't moving.

Canadian numbers tell a similar story. The market income (earnings, private pensions, investment income) of the median Canadian household is lower now, in real terms, than it was in 1976:

But what happens if we break apart that median household, and see how various types of families are faring? To make the comparisons easier, I've normalized so that 1976=100 for all family types.

 

Every type of couple family has done better than the typical family, with married "elderly" (Statistics Canada's term for the 65 and over) couples experiencing spectacular gains in market incomes.

The next diagram shows trends in median market incomes for various uncoupled demographics. Elderly singles are enjoying four times the market incomes their counterparts received in 1976. (Note that this is before factoring in Canada and Quebec Pensions and Old Age Security). Another group that has done well is  single moms: the market income of the median female lone parent has almost doubled, real terms, since 1976. Yes, the income of unattached women under 65 has decreased in constant dollars - but by basically the same amount as the median incomes of all household units have decreased. Only one major demographic - unattached non-elderly men - has seen their median income fall by more than that of the "typical" household. Even there, the difference is not large - median incomes, overall, have fallen 7 percent in real terms since 1976; median incomes of single non-elderly men have fallen 10 percent. 

 But it's a puzzle: how can the median incomes of just about every demographic rise by more than overall median incomes? Shouldn't we expect to see a number of groups doing less well than the population average?

Actually, no. The next diagram shows the evolution of median incomes for all household types, in constant 2011 dollars:

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As Canada's population ages, there are more and more elderly households. Yes, market incomes have grown among the elderly - but that growth is on a very small base. The elderly still have much lower market incomes than those under 65. There are also relatively more singles and relatively fewer families with children now than there once were - in 2011, for the first time, there were more one-person households than there were couples with children - and singles, on average, have lower incomes than families with children. In 1976, couples with children outnumbered couples without; in 2006, that changed, and couples without children became the majority - yet couples with children earn, on average, more than those without.  

Household incomes in Canada have stagnated in part because - whether by choice or the force or circumstance -  people are living in smaller households, and fewer potential earners means lower incomes.  

Yet the fact that people move between demographic groups means that one has to be very careful with claims that one group or another is experiencing rapid income growth (or conversely, falling incomes). Someone who was 76 in 1976 came of age during the first world war, then lived through the depression and the second world war. When would he or she have had an opportunity to set aside money for retirement? Someone who was 76 in 2011, on the other hand, would have been born in 1935, hit the labour market in the 1950s, might have bought into Vancouver or Toronto real estate in the 1950s or 1960s, seen their mortgage debt erased by the inflation of the 70s and 80s, invested during the stock market boom of the 1990s... The rapid growth in the median income of the elderly doesn't necessarily translate into income growth for any given elderly person. It might simply reflects people who had relatively poor lifetime income and investment opportunities being replaced by people who had relatively good lifetime income and investment opportunities. The same goes for every other demographic.

I'm not the first to observe that changing demographics can account for part of the trends in median household income - this issue has discussed on Tyler Cowen's blog, and Ben Casselman takes apart the trends here. 

It's easy just to focus on a single number, and track that number over time. But to really understand what's going on, one needs to take a cohort approach - think of the population as a whole collection of people of different ages, and think about what is happening to each one of those cohorts as they age over time. Yet this is an order of magnitude more difficult than tracking a single number over time, because it involves thinking in three dimensions, not two. 

The truth is out there. Unfortunately, it's complicated.

Comments

[Squeeky Wheel]

"yet couples with children earn, on average, more than those without"

So we should all go have children so that our incomes go up?? I suspect it might be better to say that fewer couples are having children because they feel budget constrained (definitely the case in Singapore - a mix of cost of children increasing faster than incomes, and preference for bling going up relative to preference for children).

[Bob Smith]

Frances,

Great post. I've seen this point made in the US context before, but hadn't seen in done in the Canadian context. I think the key take-away is that comparing median family income in 1976 to that in 2012 is only meaningful if the median family has stayed the same. If it hasn't (and it hasn't) then you're comparing apples and oranges.

The one interesting thing, once you go through the exercise of comparing like to like, is that there seems to be a very real disconnect in the mid 1990s (say, 1996). Before that incomes of most groups (other than single mothers and the elderly) do seem to have stagnated or declined, while after that we seem to see fairly healthy rebound/growth in market income. What happened in 1996 to cause this disconnect?

[Nick Rowe]

Yep. Good post. Reminds me of "inequality has increased in every country, but world inequality has fallen" (because some of the poor countries got richer).

"because it involves thinking in three dimensions, not two."

Income, age, household composition?

[Frances Woolley]

Nick, income over time makes two. People, I.e. cross sectional data, adds a third.

[Michael Bishop]

Good post. But didn't you want to mention the name of the phenomena: Simpson's Paradox

[Avon Barksdale]

Yes, this is just the parallelogram law for inner product spaces. Given the heterogeneity of the sample, I would be surprised if we didn't see this effect.

[Frances Woolley]

Michael - it's actually quite hard to figure out how much of the change in median household incomes over time is due to Simpson's Paradox-type composition effects, because medians are harder to work with than means, and because the information about the number of households in each type isn't readily available - I tried to derive it from the Census PUMFs but gave up.

Do econometricians talk about Simpson's Paradox a lot? Honestly, I don't remember encountering the term before.

Bob "What happened in 1996" - I really don't know. Part of it is that it took that long to recover from the oil price shock of 1973, the job market absorbing the last of the baby boomers in the early 80s, and the hangover of inflation and government debt in the 1980s. Also 1996 was the end of the "Echo Boom" - when the last of the baby boomers had their kids, more or less - and so the beginning of a very sweet demographic spot with few old people and few kids. But probably one of the macro guys has much more to say on this than I do!

Squeeky wheel: " I suspect it might be better to say that fewer couples are having children "

True. If you take a typical parent, his or her earnings aren't growing at the same rate as the incomes of two-parent families with children. Part of the increase in the incomes of two-parent families with children comes from increased female labour force participation, part comes from a change in who is married and who has kids, and part comes from changes in the earnings of parents, all else being equal.

[Jim Sentance]

I usually get annoyed that people don't adjust even for household size in doing these, but this is much better.

Just to point out clearly, those seniors making out like bandits here are not yet baby-boomers.

[Phil Koop]

"t's actually quite hard to figure out how much of the change in median household incomes over time is due to Simpson's Paradox-type composition effects"

Judea Pearl likes to distinguish between "Simpson's reversal", which is the indisputable arithmetic fact that, say, 2/3 + 5/9 is not equal to 7/12, and "Simpson's surprise", which is the mistaken causal interpretation of this fact (that's the paradox part.)

"Do econometricians talk about Simpson's Paradox a lot?"

I wouldn't know, not being an econometrician. But Simpson's paradox often arises when measuring correlations in one guise or another. For example, a regression fit to an aggregation of data can reverse sign when fitted separately to each disaggregated element. A classic example of this comes from economics (it was on the Wikipedia page last time I looked): demand is positively correlated with price in a certain dataset. But when demand and price are plotted separately against time, they are negatively correlated in each period. Time was the confounding variable.

"Honestly, I don't remember encountering the term before."

And yet I think the phenomenon has come up before in one of your posts ... didn't you blog about the Berkeley admissions discrimination case? (Or am I confabulating?)

[Nick Rowe]

Phil: I think it came up in one of my old posts. But I may be confabulating too. I had forgotten it, until it came up again here.

Aha! The search box helps. It has come up 4 times before!

[Nick Rowe]

Ooops, make that 3 times before. Jessica Simpson doesn't count.

[Chris J]

Is the right thing to do is total income / ( adults in labour force + adults who want to be in labour force )?

[Ron Waller]

The main factor driving down median household income from 1980 to 1995 was the Bank of Canada's monetary policy. If one looks at the top graph "Median household (real) income 202-0203" the drops in median income correspond to inflation-fighting monetary policy.

There were two main monetary shocks. First the Volcker Shock which caused the 1982 recession. The bank rate reached a high of 21% in 1981. This broke the back of inflation which peaked at 13% in 1981. From 1984 to 1989 inflation was around 4%. During this shock family median income fell from $52,300 to $45,600 (1980-1983; 13% drop.)

The second shock began in 1989. Interest rates reached a high of 14% during 1990. This manufactured the 1991 recession. The goal of the Bank of Canada at this time was to establish a 2% inflation target. Median income fell from $49,700 to $40,300 (1989-1993; 19% drop.)

There was a mini-shock in 1995. The bank rate dropped below 4% in 1994. Rates peaked at 8.5% in 1995. Incomes dropped from $41,100 to $40,300 (1995-1996.)

During this 'great moderation' (1989-1995,) Canada's interest rates were higher than the US Fed's. This would suggest the BoC overshot its inflation target. From 1996 to 2002, therefore, the BoC had to lower the bank rate below the Fed's. This caused the dollar to drop from 74 cents to a low of 63 cents by 2002. During this period, the Canadian inflation rate remained below US rate (despite the 14% drop in the dollar.)

During this boost from the Bank of Canada, which created an export boom, median income rose from $40,300 to $45,400 (1996-2001; 13% gain.)

The next boost appears to have come from an external factor: namely the war in Iraq. This caused a steep rise in the price of oil which accompanied a steep rise in the Canadian and Australian dollars (the graphs are very similar.) The CAD rose 60% in value from 2003 to 2008 (63 cents to around parity,) where it remained until 2013.

Median income during this time increased from $45,300 peaking at $49,300 (2003-2008; 9% gain.)

It should be noted that Canada had robust GDP growth from 1997-2000. But lackluster growth from 2003-2008 (before the meltdown.) So it wasn't a booming economy responsible for the second boost in income.

According to StatCan real family median income rose 4.5% from 1985 to 2007. According to the OECD, it rose 0.8% during this time (calculated in 2007 US $ PPP) — one of the lowest growth rates.

GDP per capita rose 44% (1985-2007.)

[Ron Waller]

REAL INCOME GROWTH: 1982-2011 (max range for CANSIM 204-0002)

* GPD per capita (TED 2014; 2013 US $ PPP)

43,589 / 27,113 = 1.6077 => 61% increase

* Median family income (2011 constant dollars; CANSIM 202-0203; All family units):

47,700 / 47,800 = 0.9979 => 0% increase

* Top income with capital gains (median income for group; current dollars to 2002 constant dollars; CANSIM 204-0002 -> CANSIM 326-0021 All-items CPI):

Top 1%

(321,700/1.199) / (93,600/0.549) = 1.5737 => 57% increase

Top 0.1%

(1,209,400/1.199) / (262,400/0.549) = 2.1104 => 111% increase

Top 0.01%

(5,018,900/1.199) / (845,900/0.549) = 2.7167 => 172% increase

[Frances Woolley]

Ron: "According to StatCan real family median income rose 4.5% from 1985 to 2007. According to the OECD, it rose 0.8% during this time (calculated in 2007 US $ PPP) — one of the lowest growth rates."

One difference is that the OECD considers "equivalized" household median income, that is, it adjusts for household size/the economies of scale that can be achieved from living together, and then estimates the median. Statistics Canada, as far as I can tell, doesn't do that "equivalizing" calculation. Though to the extent that households are getting smaller, I would have thought that equivalized incomes would be rising by more than unadjusted income.

[Frances Woolley]

Ron - the Stats Can #s are in Canadian dollars; the OECD numbers are in PPP $US. That would cause a big difference in the two trends over time.

[Bob Smith]

Way to complete miss the point of Frances' post there Ron.

[Stephen Gordon]

Really great post. I seem to recall that Tammy Schirle put together some graphs tracking incomes of specific cohorts, but now I can't find them.

[Frances Woolley]

Stephen - thanks so much, also thanks for the tweet (which I would have retweeted, but it seemed too much like blatant self-promotion).

[Too Much Fed]

"It's easy just to focus on a single number, and track that number over time. But to really understand what's going on, one needs to take a cohort approach - think of the population as a whole collection of people of different ages, and think about what is happening to each one of those cohorts as they age over time. Yet this is an order of magnitude more difficult than tracking a single number over time, because it involves thinking in three dimensions, not two."

Can the same concept be applied to average hourly wages, price inflation, and NGDP?

Is there any evidence of the middle class being "hollowed out"?

[Majromax]

> Can the same concept be applied to average hourly wages

Not really, since "average hourly wages" explicitly doesn't control for sectoral shifts or productivity gains through experience.

> price inflation

Yes, that's the entire point behind hedonic adjustments to price indices.

> NGDP

It would make a difference if the composition of a nation changes greatly. For example, the NGDP of the British Empire would certainly show some odd trends. If you're looking at such long time-scales, then normalizing to NGDP per capita would make a great deal of sense.

> Is there any evidence of the middle class being "hollowed out"?

Define middle class, and define "hollowed out"? For reasonable definitions of each, the answer could be trivially yes/no or impossible to say with any certainty.

[Senator-Elect]

Valuable post, Professor Woolley. It hints at the dangers of simplistic statistical analysis. We’re going to be getting all kinds of misleading statistics as the age of Big Data rolls along. Hopefully people with power know how to dig deeper.

This should also be a warning to all the quantitative methods people who look down their noses at qualitative work. Not only can both be equally misleading, but one without the other can lead to wholesale misunderstandings. Sometimes researchers should just ask people what they think or what their lives are like.

One other point: What is the effect of more women entering the workforce starting in the 1970s on the interpretation of these data? Shouldn't the incomes of married couples and two-parent families with children have increased more than they did?

[Frances Woolley]

Senator-Elect: "What is the effect of more women entering the workforce starting in the 1970s on the interpretation of these data? "

Without the increase in female labour force participation, the trend in the incomes of two-parent families with children and non-elderly married couples would look a lot more like the trend in incomes of unattached men. So basically the increase in female labour force participation (and female rates relative to male wages) is what's driving a good chunk of that increase in incomes of married couples/two parent families.

[Ron Waller]

"Ron - the Stats Can #s are in Canadian dollars; the OECD numbers are in PPP $US. That would cause a big difference in the two trends over time."

I threw in the OECD median income study just to provide an international comparison.

Interestingly enough, if one compares real GDP growth from 1985 to 2007, the numbers in constant CAD and constant USD PPP are pretty close:

2007 / 1985

TED 2014 EKS GDP 2013 US $ PPP (both in millions)

1,431,779 / 783,701 = 1.8269

CANSIM 384-0038 GDP at market prices, 2007 constant prices

1,565,900 / 858,990 = 1.823

[Jim Sentance]

One thing your breakdown doesn't adjust for is the likely reality that the two parent families with children (and probably to a lesser extent the single parent families) likely get smaller as you go through this time period.

I'm not entirely certain I'd agree that the single male profile is indicative of what would have happened if women had not upped their labour force participation since the 70's. Both in terms of overall labour market supply effects and internal household division of time and effort terms I think the track would have been higher.

[Frances Woolley]

Jim "I'm not entirely certain I'd agree that the single male profile is indicative of what would have happened if women had not upped their labour force participation since the 70's."

I thought the way I put it i.e. "would look a lot more like..." was vague enough to allow for the possibility that the two profiles could be significantly different! A man with a job is a more attractive marriage market prospect than a man without, so I would figure that selection into/out of marriage is pushing the single male profile down and the married profile up.

[Eric Cai - The Chemical Statistician]

Thanks for this good post, Frances. I took 5 statistics classes at Simon Fraser University and then earned a Master's degree in statistics at the University of Toronto. At no point did I ever learn Simpson's paradox in any of my classes. (I learned about it over lunch with a fellow statistician at SFU.) Thus, I am not surprised that economists don't learn about it in their econometrics classes, even though it is still very disappointing.

This is a great shame, because Simpson's paradox actually arises quite often in practical situations, with sometimes very sad or misleading implications.

Larry Wasserman wrote a nice blog post about Simpson's paradox. Among statistics students, he is well known for the books "All of Statistics" and "All of Non-Parametric Statistics". Among statistics researchers, he is well known as a theorist in statistics and machine learning at Carnegie Mellon and a winner of the COPSS prize in statistics (one of the biggest prizes in academic statistics in the world). He graduated from the University of Toronto's Ph.D program in statistics.

[Frances Woolley]

Eric - thanks for the comment and the links

[Jim Sentance]

I'm suggesting more than simply some sorting.

[Frances Woolley]

Jim - I know, and I'm suggesting sorting is the more important story.