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I guess it's comforting that our decision-makers understand these points, even if journalists sometimes get it wrong.

Something about this post makes me uneasy. Are you arguing that debt/gdp is irrelevant as long as people aren't at risk of bankruptcy? What about the effects of changing spending patterns as people desperately try to avoid bankruptcy? What are the implications for the economy when essentially non-productive industries (most of the financial sector) consume an ever greater share of national income? How does a rise in interest rates influence the numbers?

Debt is like a row of upright dominoes. If John owes Suzy 100$, Suzy owes Bob 100$, Bob owes Mary 100$ then Mary owes John 100$, everyone's debt cancels out, and if the general level of debt is small, the default of one person will not cause anyone else to default in turn. Now multiply those amounts by a million, and if one person defaults, the dominos start to tumble - everyone defaults in succession. When debt/income ratios are too high, the economy becomes vulnerable to a domino debt default credit crisis.

Reminds me of the 1998 ice storm in Quebec. When too much ice would cause one pylon to come crashing down, a domino effect caused the whole line of pylons to come crashing down. The solution, applied by Hydro Quebec when they rebuilt the lines, is that every few pylons is extra-strong so that it can resist a domino-like collapse.

I guess, if we stretch the analogy, this means that a financial system is as strong as its strongest link - which would be the central bank.

I'm not sure where I'm going with this or if I'm even making any sense. I've had a long day.

Stephen: yes, much better than the other way round!

pointbite: aggregate debt/GDP numbers are worse than irrelevant; they are highly misleading. The true aggregate (net) household debt/GDP ratio is negative.

Alex: your point is actually (potentially) a very good one.

I have been saying "Look, we need to disaggregate debt, and look at each household, and see how much each household owes".

And you are saying (or trying to say) "Look, we need to disaggregate further than that Nick, and see how much each household owes to whom".

In other words, I have been thinking of a vector, a list of the debt owed by each of the n households. I ought to be thinking of an nXn matrix, with each cell in the matrix saying how much household i owes to household j.

I'm always happy to criticize the media for oversimplifying things, but do you really think there is a reason why aggregate debt levels aren't a good proxy for the general risks due to high levels of indebtedness? Or, as the report says, "The vulnerability of Canadian households to adverse shocks to wealth and income has risen in recent years as aggregate debt levels have grown relative to income."

It's a pretty good report overall. I hadn't realized that Canadian bank leverage ratios used to be so high (page 46). Interesting that the financial sector was able to reduce its leverage so much during the 1980's while it at the same time debt levels relative to GDP were rising in all areas of the economy - is that just the effect of high bank profits, or were they losing market share to non-banks, or am I missing some other explanation?

Along with pointbite, I'd be more interested in seeing the impact of stress to household balance sheets caused by either deflation or an increase in interest rates than the increase in unemployment.


Suppose there are n households, firms, governments (ignore foreigners). Line them all up in some order, horizontally along the top, and vertically down the side of a matrix. A cell i,j shows how much i owes j. A negative cell means j owes i.

The main diagonal is full of zeros (i owes himself $0). The matrix is a mirror of itself either side of the main diagonal, with pluses replacing minuses, and vice versa.

Aggregate gross debt is the sum of all the positive cells. Aggregate net debt is the sum of all the positive and negative cells (it's zero).

If we want to look at who will default (who has the most debt) we should first add up all the rows (or all the columns) to get the distribution of net debt across individuals. That's what I wanted. But if there are cascading defaults, that won't be enough. If one person defaults on a debt, it may convert another person's + into a 0. We need to look at the whole pattern in the whole matrix.

The cascade pushing someone from + to 0 doesn't happen in a vacuum. He will no longer have the capacity to lend, he will no longer behave like someone with a +, it will devalue the assets of other lenders, it will scare other potential lenders, it will scare other potential borrowers, etc. Thinking about your matrix, if you plotted it in 3d, imagine a scenario with the corners at level X then imagine the corners at level 100X. Is it your argument the difference is irrelevant, so long as the risk of bankruptcy is stable? Spending patterns don't change? Income inequality doesn't change? What about if the picture isn't so symmetrical, what if the majority of people are borrowers and only a few are lenders? What if the lenders have fractional reserves? When the assets are valued in their favor they are a net creditor, when the dominoes fall they instantly become next debtors. Sorry I'm rambling a bit, it's been a long day...

I think there is a problem here that is being missed by looking only at the relatively healthy Canadian economy. Looking at the static picture can miss the dynamics. The problem that had been building up primarilly in the US over the last 20 years has been that this level of debt has been increasing, and increasing in precisely those households that need to be building their net wealth to finance their retirement. So long as asset prices were increasing the vulnerability of that net wealth to a necessary asset price correction was hidden. Attempts at rebalance will reverse this dynamic with dramatic effect on net financial flows. Looking just at short-term financability is missing important aspects.

Declan: "... but do you really think there is a reason why aggregate debt levels aren't a good proxy for the general risks due to high levels of indebtedness?"

I can think of examples where it would be a bad proxy:
1. Suppose the most indebted reduce their debt a little, and the least indebted increase their debt by more, aggregate debt would rise, but the risks of default would be less.
2. More importantly. Suppose one person goes into debt to buy a financial asset from a firm. Now suppose instead that he goes into debt to splurge on a gig feast. His gross debt goes up the same amount in each case, but the second is riskier.

"Interesting that the financial sector was able to reduce its leverage so much during the 1980's while it at the same time debt levels relative to GDP were rising in all areas of the economy - is that just the effect of high bank profits, or were they losing market share to non-banks, or am I missing some other explanation?"

Dunno. My guess is that the banks lost money in the early 1980's, and spent the rest of the 80's restoring their capital back to normal through retained earnings.

pointbite: "What about if the picture isn't so symmetrical, what if the majority of people are borrowers and only a few are lenders? What if the lenders have fractional reserves? When the assets are valued in their favor they are a net creditor, when the dominoes fall they instantly become next debtors." That's exactly the sort of disaggregated data that matters, and that only the debt matrix could reveal.

reason: yep, movies are better, but a good snapshot is at least a good start.

Declan: I forgot this bit:

"Furthermore, microdata from Ipsos Reid indicate that the proportion of vulnerable households (those with a DSR above 40 per cent) remained relatively stable at 2.8 per cent in the second half of 2008, but the share of debt carried by these households decreased markedly to 4.7 per cent, down from 5.9 per cent in the same period a year earlier."

That bit of the report tells me that in this particular case, aggregate gross debt was not a good proxy for what is happening at the highly-indebted tail of the distribution, which is the bit that matters.

"2. More importantly. Suppose one person goes into debt to buy a financial asset from a firm. Now suppose instead that he goes into debt to splurge on a gig feast. His gross debt goes up the same amount in each case, but the second is riskier."

True for the individual, but you also need to know what the firm selling the financial asset does with the money. Systemic risk may still have increased (in fact there is a danger that our "investor" has a false sense of security that our older and wiser rager doesn't.)

Isn't consumption always 'riskier' than investment to the system? If the value of the investment goes to zero, it's as if the owner consumed something with zero utility. Or am I looking at this incorrectly?

reason: agreed. You have to look at everyone.

Andrew. I think that's right. As long as there is some liquidity to the investment (so you can sell it), or it earns (or could earn) some income (to help pay your interest on debt).

^ Then investment is no riskier than consumption, and usually less risky. Consumption always goes to zero, and investment only sometimes.

For something akin to the matrix way of thinking about this, a recent speech out of the Bank of England -- "Rethinking the Financial Network" -- might be worth a read:

http://www.bankofengland.co.uk/publications/speeches/2009/speech386.pdf

"Isn't consumption always 'riskier' than investment to the system? If the value of the investment goes to zero, it's as if the owner consumed something with zero utility. Or am I looking at this incorrectly?"

I won't say you are wrong, but there is inevitably another side to this story. It goes like this. Financing consumption means that somebody is making a decision to buy something he/she finds useful. That consumption will encourage investment and enterprise and skill development that may eventually have a wide application (i.e. may be an expanding industry).

Financing speculative investment means that somebody is making a guess as to what people might be prepared to pay for. It might be a total waste of time and might for instance lead to employees investing in skills that prove useless. Worse it may turn out to damaging to people or the environment. The future is uncertain, unforseen eventualities are commonplace. Never say never.

I'm a little late coming back to this, but just to be clear, I understand that it is *possible* for two cases of similar aggregate debt levels leading to different levels of risk due to indebtedness, I'm just skeptical that in practice there is much *actual* difference that would mean that aggregate debt levels aren't a good proxy for the overall indebtedness risk.

For example, it's possible that two batters are both hitting .330 but only one is good because the other one has just been getting lucky so far, but nevertheless, batting averages are generally used as a standard metric with a limited usefulness seen for investigating other factors such as 'batting average on balls in play' which will differentiate between two players with the same average (if there is a difference).

Declan: OK, I see your point. Even though we can agree that aggregate debt is not the theoretically correct thing to look at, and we can think of examples where aggregate debt might rise, and the risk of default fall (or vice versa), maybe in practice the correlation is good enough that aggregate debt is useful, as a proxy.

Unfortunately, I don't think we have much in the way of either empirical or theoretical analysis to answer this question. Though it could presumably be done, certainly the empirical part.

But if there does exist micro data, like the Ipsos Reed survey data the Bank is using, and if that survey is updated regularly (I'm less sure about that), then it would be better to use that data directly rather than aggregate debt, even if it did turn out that aggregate debt were a fairly good empricial proxy for the real thing.

Yep. If aggregate debt were zero, then the risk of anyone defaulting is also obviously zero. And if we double each and every individual's debt, then the risk of default would rise too. So there has to be some proxy relation between risk of default and aggregate debt.

But there is one other reason I find aggregate debt so misleading. When people hear that aggregate debt is too high, they think that everyone must save more. But that isn't true at all (especially if there is no net foreign debt, as in Canada). What it means instead is that some people (net debtors) must save more, and other people (net creditors) must save less.

Your point about fundamental differences is well taken but two counter points need to be made. Aggregate data exposes systemic risk as a whole. Just because not everybody is dangerously exposed to debt does not mean that the default of the even small percentage that goes into default cannot expose the financial system to severe losses. As well, just because Bob owes me $100 and I owe the Fred $100, it is misleading albeit true to day my net debt is zero. Whether or not Bob defaults, I'm still liable to Fred. This is why the failure of Bear Stern set off a chain of CDS exposure in the financial system.

In other words, aggregate debt is still a valid measure of risk in the system.

tony: I agree with your point that just because my net debt is zero doesn't mean I have no default risk. But trying to distill that risk into one number -- aggregate debt -- is not the solution. We need to look at the whole matrix of debt, to see if there is a risk of cascading defaults.

I stopped reading after the third paragraph. Saying that foreigners owe us money and we owe them money, so we cancel out?!?!?!?! OK ill owe you a million dollars and you owe me a hundred, and we will just call it even. Sound reasonable? Didn't think so. Just because we all owe each other money doesn't mean we all owe each other the same amount of money.

The government does owe money, but only to people the borrowed from. If I own 50 grand in Canada savings bonds then the government owes me 50 grand (plus interest). But if I hold no bonds and no stocks and no GICs or any other type of money savings, then no one owes me money. If I have 10 grand in the bank and a 400K mortgage, then I owe a whole bunch of money. Even if the house is worth a million bucks, I still owe the bank 400 grand.

I didn't give the rest of the story a chance because the beginning made so little sense that is sparked me into writing this.

davers: Take the time to understand what Nick is saying. At first I made the mistake you are making. I find it easier to think about the world as a whole to simplify the problem. For every debtor their is a creditor somewhere, so by definition net debt for the world is zero (at least until we have inter-planetary trade). So how can the world have a debt problem? Well, it's the type of debt and the distribution of debt that matters. Some configurations are fragile and prone to cascading collapse that wreck the economy, other configurations are stable. But it's the configuration that matters. The net is always 0 and tells us nothing. The same line of thinking applies more or less to countries, with a few added complexities.

davers: I'm not sure how you misread what I said: "We owe foreigners money, and foreigners owe us money, and the two amounts roughly cancel out, so forget foreigners." The key point is "..the two amounts roughly cancel out...". In other words, we owe them about the same amount of money that they owe us. Canada's net foreign debt (from the latest data) is roughly zero.

And what Patrick said about the rest. The whole point of my post was that these aggregate numbers don't tell us what we need to know. Some people ARE in debt; others aren't in debt and are OWED money. We have to look at individual households to see what's going on. That's what I was trying to say. And I DID say just that, again and again, right from the first paragraph!

...tangential to the discussion. Keynes came out with a consumption function, trying to measure how much an increase in income increases consumption. This was attempted amneded with "Life Cycle Hypothesis", which guessed that individuals try to temper consumption to save for retirement, though we really aren't that rational. Anyway, I don't see it in the wiki but more personal debt is equivalent to strengthening "Life Cycle Hypothesis" behaviour.
I view less fat and bloated consumption as a chance to reorient the economy happier and healthier, but the framework is already there to explain why people and banks pay off debts and save with stimulus cash rather than spend. Though rather than bail out fast food (and derivatives) to retrieve demand, I think government should be subsidizing personal trainers (small businesses) and stuff.

Patrick,

I dont know if I agree with you that the net debt of the world is zero. Wealth can be created or destroyed. The US is printing money like crazy right now, with nothing to really back it up. They are just creating more money that has value because they say it has value. What does this do to the net debt of the world?

Nick,

Obviously there are people in debt, and people with wealth. No matter how bad the average is, you will always be able to find a shining example of someone who is doing really well. On the other hand there will be someone out there who is way worse than the average to compensate for the guy doing really well. It just seemed like you tried to do a bunch of written gymnastics to get from "average household in debt 140% of income" to "average household owed 140% of income". All I know is I have no debt and dont plan on going into debt until I buy a home in a few years and get a mortgage.

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