Debt to income levels are high by historical standards in Canada and the US. Here's a recent report (pdf) from TD Economics showing household debt/income ratios at around 150% in both countries. But is that "too high"? And is that evidence that some people, like the Flopsy Bunnies, are very improvident?
I'm going to play with a very simple model, and do some back of the envelope calculations, to try to work out what the average debt to income level would be even if everybody were perfectly provident.
In my toy model, total debt/GDP ratios are driven by lifecycle savings. It is providence that causes high total debt/GDP ratios. Provident people save and lend for their retirement, which creates debt. But the most interesting (to me) result is that forced saving in pension plans has a very large effect on personal debt/income ratios. The greater is forced saving, the smaller is voluntary saving, and the more slowly people pay down their mortgages. It is easy to explain high personal debt/income ratios in this way. You can easily get personal debt/income ratios around 100% just from this cause alone.
Here's the model:
Forget about kids. We don't count kids. Everybody is born at age 20, works for 40 years earning $150 per year, then retires for 20 years, then dies aged 80. So average adult earnings are $100 per year over the 60 year adult lifespan. Nothing ever changes in this economy. Every cohort is exactly the same size, and there is zero growth in income. Every individual is perfectly provident, and saves $50 per year while working, and so is able to consume a constant $100 per year both while working and in retirement. With zero time preference, and zero growth in income or population, the rate of interest is also zero.
Each person's stock of savings starts at zero, grows at $50 per year to a maximum of $2,000 at age 60, then declines at $100 per year until they die with zero. That means the average stock of savings is $1,000 per person. That is 10 times average income per person.
Suppose that all those savings are lent to firms, which therefore own all the real assets in this economy. And suppose the savings are lent in the form of debt, rather than equity. That means the total debt/GDP ratio in this economy would be 1,000%. Is that "too high"? That's what providence requires.
Now suppose that firms' CFO's insist they stick to a standard 60/40 debt/equity ratio. So the average stock of personal savings, $1,000 per person, is held as $600 in corporate debat and $400 in shares. That still gives us a total debt/GDP ratio of 600%. Is that "too high"?
So far, all debt is corporate debt. There is no personal debt. Let's change the model to bring in personal debt.
Suppose it takes 2 years' labour to build a house, so houses cost $300, and the average house price to income ratio is 3. A lot of different things could happen, now we have introduced houses into the model.
At one extreme, we could assume that firms own all the houses, and everybody rents. That has no effect of debt/GDP levels, and there's still no personal debt.
Or we could assume that everybody buys a house at age 26, with no mortgage, and sells it again at age 77, to finance their last 3 years of retirement. So people live in their own house for 51 years and rent for the remaining 9 years of their lives. So individuals own a fraction 51/60 of the housing stock, and firms own the remaining 9/60. That reduces total assets held by firms by (51/60)x$300 = $255. If firms use only debt-finance, and issue no shares, the debt/GDP ratio falls from 1,000% to 745%. If firms use 60/40 debt/equity financing, the debt/GDP ratio falls from 600% to 447%. Personal debt remains at zero.
Now let's bring in mortgages. Suppose nobody rents. They buy a house at age 20, with a 100% mortgage, then get a reverse mortgage sometime during retirement, and die with a 100% mortgage.
If people pay down the mortgage first, rather than saving by lending to firms, the average mortgage debt is very small, even though I have assumed zero-down mortgages initially. The initial mortgage is paid off with 6 years' savings, and the final reverse mortgage is run down over 3 years. So people only have a mortgage for 9 of their 60 years, and the average mortgage is $150 for those 9 years, so the averge level of personal debt is only (9/60)x$150 = $22.50, or 22.5% of income. If we assume people first rent and save for a downpayment, the average personal debt/income ratio would be even lower than 22.5%. What could explain the much higher levels of personal debt we see?
Let's bring in compulsory pensions. Suppose the government is afraid that some people might be improvident and won't save enough for their retirement, and so forces them to save. (OK, it's not in the model, but give me a break, because I want to keep the arithmetic simple, even at the expense of a minor inconsistency).
The interaction of compulsory pensions and mortgages will have a very big impact on personal debt levels.
Take an extreme case. Suppose the government makes it compulsory to save the full $50 per year in a company pension plan (which is that same amount a provident person would save voluntarily anyhow). And suppose people insist on living in their own homes, rather than renting, and finance the purchase of their home with a 100% mortgage, which is never paid down at all until the house is sold at death. Personal debt is now $300 per person, or 300% of income.
Let's relax the assumption about compulsory pension plans. Suppose the law requires only $40 per year be saved in the company pension plan, so there is $10 per year extra voluntary saving to pay down the mortgage. It now takes 30 years to pay off the $300 mortgage. So for 10 years, between ages 50 and 60, each person is debt-free. At age 60 they retire and get a reverse-mortgage and withdraw $15 per year for 20 years to supplement their pension. So a fraction (50/60) of the population holds a mortgage, with an average value of $150, meaning personal debt is (50/60)x$150 = $125 per person, or 125% of income.
Let's drop the assumption of 100% mortgage-financing. If a house purchase requires a 33.3% downpayment, of $100, people will rent for 10 years, while saving up the downpayment. And for the last ($100/$15) = 6.66 years of their lives they will rent again, because they will no longer have enough equity in their homes to support a larger reverse mortgage. So a fraction (16.66/60) of the population will rent, and the remainder will own a house, and a fraction (10/60) will own a house with no mortgage. So a fraction ((60-16.66-10)/60) will have a mortgage, with an average value of $100. So the average personal debt will be ((60-16.66-10)/60)x$100 = $55.56, or 55.56% of income.
Some of the above results are obvious.
If you allow 100% mortgages, you will get a bigger perrsonal debt/income ratio than if you don't. If firms use 100% debt finance you will get a bigger total debt ratio than if they don't.
But some results are not so obvious.
Even if there is no financial intermediation, so households lend directly to firms. And even if firms use 60/40 debt/equity financing, the savings preferences of fully provident households would imply a total debt/GDP ratio of 600%.
And the non-obvious result that interests me most is how sensitive the results are to compulsory savings. Small increases in the amount that people are required to save in pension plans will cause large increases in average levels of personal debt/income ratios. In this simple model, it is not improvidence that causes high levels of debt. (In fact, improvidence by itself never causes debt; it is only improvident borrowers plus provident lenders that can create debt, because it takes two to tango -- a borrower and a lender.) Compulsory saving in pension plans reduces voluntary saving outside pension plans, precisely because people are provident in this model. So compulsory saving means people pay down their mortgages more slowly; both because they have less income left to pay down their mortgages, and because they have less need to save by paying down their mortgages.
It's a simple model. If you have a calculator, you can play with the assumptions yourself, and get a wide variety of estimates for debt/income ratios. And you can easily get higher personal debt/income ratios. Suppose house prices are 4 times annual income, rather than the 3 times income I have assumed here. Or add in student debt. Or add in investment in other consumer durables, like cars and furniture. Even if people are saving all they need to maintain the same level of consumption after they retire, any direct investment by the young will be debt-financed. All their savings are tied up in their pension plans.
Of course, none of this says that some people aren't very improvident. And none of this says that there aren't more improvident people than there were in the past. But "high" and rising personal debt levels might also be caused by forced savings, and the use of RSPs and TFSAs. You save in the company pension plan, your CPP, your RSP, and your TSFA, instead of by paying down your mortgage. We can't tell just by looking at average debt/income ratios. You need to break down the aggregate figures, and look carefully at the micro data, and at assets as well as liabilities. And to its credit, TD Economics tried to do just that.
(Hoping I didn't screw up the arithmetic somewhere. Just in case you have never heard it before...There are three types of economist: those who can count; and those who can't.)