Average Debt and Representative Agents

The representative agent is sometimes a useful conceptual fiction. What's the income of the average Canadian? How many hours does the average Canadian work? It's not just theoretical macroeconomists who ask those questions. But it is a useless fiction when we ask about debt. Or rather, at best it's useless; at worst it's dangerously misleading.

If we multiply average hours worked by population, we get the total hours worked by all Canadians. If we multiply average income by population, we get total income of all Canadians. But if we multiply average debt by population, we do not get the total debt of all Canadians.

For example, the Vanier Institute of the Family estimates that the average Canadian household debt at $80,000 (in 2005 dollars, in 2007). Multiply by the number of households, and we get a figure around $1 trillion. It sounds as though Canadian households owe $1 trillion to someone. That's what's dangerously misleading. Who can that someone be? It's not foreigners, because Canada's net foreign debt was a mere $21 billion. It's not the Canadian government, because the government itself is a net debtor. It's not Canadian firms, because Canadian firms are net debtors.

The average Canadian household has $80,000 in debt, which it owes to...the average Canadian household. Plus, the average Canadian household is owed large amounts of money by Canadian governments and firms. The average Canadian household has negative net debt.

The representative agent is a conceptual fiction. When it works, it's very useful. We can imagine a hypothetical country where all people are identical and exactly like the average person in the actual country. To get the aggregate, we just multiply the representative agent by the population. It never works exactly of course (OK, maybe if everything is linear it might). But it doesn't work at all in the case of debt.

If everybody were like the average person, they would still work, and still earn income; but they wouldn't have any debt. The reason Paul borrows from Peter is that Paul and Peter are different. Paul wants to spend more than his income; Peter wants to spend less than his income. The average of Paul and Peter would want to spend all his income, no more and no less.

The representative agent has no debt; he has negative debt (he owns the debt of governments and firms). The representative agent cannot default on his debt, because he has none. But of course some people do have debts, and do default, and these defaults do have macroeconomic consequences. The average is useless for thinking about debt and default. How else can we measure the debt burden, so we can compare default risks across countries, and across time?

We need to look at the distribution of debt across individuals. And we need to focus especially on the right tail of the distribution, at those with the highest debt (or highest debt/income or debt/asset ratios). Those are the people most likely to default. It's the right tail we need to look at, not the median, and certainly not the mean, because the mean or representative agent will never have a negative net worth.

We also need to distinguish between gross debt and net debt. An individual with no gross debt cannot default. An individual who owes $100 and is owed $100 can default (if his asset goes bad), but is less likely to default than someone who has $100 gross debt and no offsetting assets.

We need to look at the distribution of net debt across individuals (or net debt/income ratios). And we need to look at the distribution of gross debt across individuals (or leverage ratios of gross debt to net worth).

If looking at the whole distribution is "too much information", then let's just look at the 10% with the highest debt loads, and take their average. It would be much more useful as a predictor of default risk than any overall average. And at the very least, it would eliminate any conceptual confusions from thinking about the debt of the average or representative agent.

Comments

[JKH]

Nick,

Excellent post – very clear summary of the risk measurement issues.

[Nick Rowe]

This post arose from an interesting discussion in the comments section of Stephen's post on house prices. We should now switch that discussion to this post.

Here is a quote from JKH's latest comment, in reply to my comment that average leverage is zero:

"Or perhaps you are making a larger point and including all types of financial assets as the potential offset to gross household debt. The total includes equities, mutual funds, pension reserves, etc. How does one identify, interpret, or think about the ultimate debt or equity financial claims within this entire financial asset category for this sort of discussion? Mutual funds and pension reserves hold both debt and equity, for example. And if the argument is in this larger sense that gross debt by logic must be offset by some financial asset, debt or otherwise, why doesn’t it work the other way around to arrive at net 0 financial assets as part of household worth? (Here I’m getting quite confused.)

I suppose the bottom line is that you can always interpret the mere existence of positive household net worth as an indicator that there is no net “debt” or net “leverage” for households. That makes the point in the crudest way that households aren’t indebted on a net aggregate basis in the sense of being insolvent on an aggregate basis – “they owe it to themselves” sort of thing."

Nick again: We can interpret "debt" in my post above either in the narrow sense (bonds as opposed to stocks), or in the wider sense of all financial claims. In a closed economy (i.e. ignore international borrowing and lending) then any financial asset, however narrowly defined, has both a creditor and a debtor, so the aggregate net debt of that bit of paper is zero. Aggregate up across all financial assets (except irredeemable paper money, but that's another argument), and we get the same result: zero net debt. Aggregate net worth is the physical stuff: land, buildings, machines etc. (plus irredeemable paper money and other Ponzi assets but that's another argument). Divide Aggregate net worth by population, and the representative agent owns a one millionth (or whatever) share in all the physical assets. If we disaggregate by treating firms and governments as separate entities, then the representative household owns one millionth of all firms' stocks and bonds and government bonds, with zero leverage.

Suppose half the households (the evens) borrow from the other half (the odds) so they can invest in more corporate stocks and bonds. The evens are then leveraged. The odds own fewer corporate stocks and bonds than the evens, but they also hold the household debt (the IOUs from the evens). So we could say the odds have zero leverage, or we could say that they have negative leverage in their corporate investments.

Yep, this is confirming me in my view. Any discussion of debt, or leverage in terms of average or representative agents is just conceptually confusing. Debt is all about distribution, between sectors, and between individuals. You (nearly) always lose information when you aggregate, but in the case of debt you lose all the information.

By making a purely arbitrary assumption ("let's count an IOU when it's a liability in an individual's balance sheet but ignore it when it's an asset") you get an average (or aggregate) number which is non-zero. But it doesn't tell us what we want to know. Averages just aren't useful for thinking about debt.

[Andrew F]

It's funny. It seems many (seemingly intelligent) people were lead astray by forgetting this principle as they analyzed the situation in the US.

[Nick Rowe]

Thanks JKH! (We were posting at the same time)

[Nick Rowe]

Andrew F: yes, there are two sorts of errors we can make when we look at average gross debt, and they go in somewhat different directions:

1. We can be overly worried that Canadians have too much debt, and ought to save more (forgetting the offsetting assets).

2. We can be overly confident that default risk is low, since the average Canadian can easily cover his debts with his assets or income (forgetting that it's the tails who default).

[Ryberg]

Ther is another error being made in this discussion. Debt involves the "time value of money". A borrower promises to repay a loan in the future with future resources. Lower interest rates have the effect of encouraging borrowers to consume more of those future resources. "Too much" debt means too many of the future resources are committed to the past. Aggregate levels do matter and to say that we owe it to ourselves demonstrates a lack of understanding of what debt is. Debt growth is unsustainable because this is like eating your seed corn. For a time, we have financial resources that appear to be as good as economic resources but they are not. To make matters worse, we denominate those economic resources using a financial resource yard stick. The extent of the damage from too much debt for too long is very hard to see, let alone manage.

[David Pearson]

I disagree in part with your analysis. Total U.S. credit as a % of GDP is a misleading measure, according to your thesis, because most of it we Americans owe to ourselves. So what if its much higher than historically?

Debt is a financial claim on either future cash flows or (in the case of secured debt) existing physical assets. Let's leave aside the secured debt for the moment. Higher debt as a % of GDP means more more actors have shifted consumption to the present, and correspondingly more have agreed to forgo present consumption in favor of those future cash flows. The money's been spent by on group: its gone, hopefully into productive assets, but possible into circus tickets, popcorn and cotton candy. Here's the rub: the higher the debt, the more the risk that the cash flows will never materialize, and the more the probability of a large future reduction in consumption as 1) the borrowers reduce spending; and 2) the creditors don't get to increase spending.

So debt is a measure of risk. The higher the debt (average or total), the higher the risk of a drop in a population's standard of living.

Back to secured assets. In their case, the creditors should be able to recover their cash by seizing and selling the assets. The largest piece of the secured lending pie is real estate. What we learned in the U.S. during the Great Depression is that, for political reasons, residential real estate becomes essentially unsecured lending in a severe downturn. That's because states enact foreclosure moratoriums (2/3 of all states did back then). Such moratoriums are under discussion now, as are bankruptcy cram-downs which effectively accomplish the same thing. So, while many people like to take residential mortgages out of the debt equation, it should very much remain "in".

[Nick Rowe]

Thanks Ryberg and David:

I feel another post welling up inside me.... That's what's so good about blogs: you make a post, then people reply with comments, which leads to another post....just like a good conversation.

Your comments are partly similar. What is the relation between aggregate gross debt and investment, future consumption, (and risk)? It's related to my post, but still different enough, and a big enough question, to deserve a post of its own. So I'm going to try to get my head clear on it first, and then post.

David: If I interpret your comment correctly, the part about secured debt is more of an aside, correct? The main thrust of your argument comes through even if we ignore the distinction?

[David Pearson]

Nick,

Yes its a bit of an aside. Its more directed at those who want to look at total credit "ex" mortgage debt, on the basis that you have to net out the assets supporting those mortgages. Supply-side, pro-debt commentators (e.g. David Malpass) tended to argue the run-up in U.S. debt didn't matter because most of it was mortgage debt, which in turn was secured.

[Declan]

I don't have much to add to David's excellent comment (although you don't need foreclosure moratoriums to make real estate loans into a source of losses, all you need is a big enough price drop to wipe out the equity) but just one more point. You write:

"The average Canadian household has $80,000 in debt, which it owes to...the average Canadian household."

This isn't true of course. People don't borrow from each other, they borrow from banks. And the bank is not a passive intermediary, allowing me to lend you my money indirectly, it actually creates (most of) the money that is borrowed. While your post is mostly valid, it reads like you imagine we live in a world with 100% reserve requirements for banks. If you're going to write a post about gross debt and risk, you'll need to consider the role played by bank leverage.

[JKH]

Declan,

We do owe it to ourselves. Household assets include bank liabilities owed to households. Household liabilities include bank assets that represent financial claims on households. When summing up the financial position of households, you include the perspective of households and eliminate the perspective of banks in order to avoid double counting in the analysis.

The fact that banks create the money that is borrowed merely reinforces Nick’s point. The borrower, when his own bank account is initially credited with funds, temporarily owes it to himself at the micro level. When he uses that money for its intended purpose, and disburses it to some other actor in the system, it will show up as a financial asset (direct or indirect) of some other household. Then we still owe to ourselves at the macro level.

I’m not sure I get your point about reserve requirements, but I see nothing in Nick’s post that reflects what you suggest.

Bank leverage is just another term for bank liabilities, which include the money that banks create, as per paragraph above.

[Nick Rowe]

I agree with JKH above.

If banks had 100% (currency) reserve requirements, banks would effectively be warehouses for the safekeeping of currency. They would reduce the risk of theft, and make it easier to make payments at a distance, and have a record of those payments, but we could ignore them as financial intermediaries.

[Ryberg]

A good argument can be made that we do not owe it to ourselves. The Federal Reserve reported the following:

Domestic nonfinancial debt owed $32,938 billion
Rest of World Borrowing $ 1,962
Financial Sector Borrowing $16,904
Total Borrowing $51,796

Domestic nonfinancial credit held $ 6,154 billion
Rest of World lending $ 7,853
Financial Sector Lending $37,789
Total Lending $51,796

We owe it to the banks and the financial sector. What's more, the financial institutions owe themselves half of what we owe. That's all funny money in my book because it financial liabilities backed by financial assets. Banks create money out of thin air when they create loans. Loans to the nonfinancial sector may stimulate the economy but loans to the financial sector just stimulate finance. This is what has made our Ponzi economy possible.

[JKH]

The argument that we owe it to ourselves is not meant to suggest there aren’t financial intermediaries.

The point is that that at the macro level the size of the debt owed by households is equal to the size of the debt they own.

Obviously financial intermediaries are involved. That’s why the form of the debt owed (e.g. mortgages) is different than the form of the debt owned (e.g. savings accounts).

[Declan]

"The borrower, when his own bank account is initially credited with funds, temporarily owes it to himself at the micro level."

Right, because the bank would never be so rude as to demand interest payments! :) The point I was trying to make, and failed apparently, was that the role of bank as intermediary *matters*. Higher gross debt levels across society (regardless of their distribution) suggest that a) the banks are extracting a higher percentage of the wealth of society via their rate spread - leading more people to not be able to repay their debts and b) banks are more highly leveraged, making them more vulnerable to collapse if people can't pay their debts. It's not really a good combination. The fact that accounting entries balance isn't particularly relevant and would be true even if we quintupled our total gross debt levels. I mentioned 100% reserve requirements because under that scenario, you could, as Nick says, ignore the risks I outlined above.

As an aside, I'm not sure why you would equate leverage with liabilities. Leverage relates to Assets / Capital, not Assets - Capital. In other words, naturally a large bank has more liabilities than a small one, but that does not mean they have higher leverage.

Anyway, don't take it from me, take it from the head of the biggest bank in the world:
http://www.reuters.com/article/rbssFinancialServicesAndRealEstateNews/idUSL1014625020080610

Having said all that, I agree with 95% of what Nick wrote in the post, I just wanted to highlight some of the risks posed by magnitude of debt (due to fractional reserve banking) in addition to distribution of debt.

[JKH]

“The point I was trying to make”:

I didn’t realize that’s the point you were making, but its clearer now and I don’t disagree with it.

I’m reasonably familiar with what leverage is. I was referring to it in a general sense as a function of debt, without attempting to define it – also not clear.

(e.g. D/E + 1).

[Declan]

Yes, I figured you knew what leverage was, I just wanted to clarify in case you were making some point that I was missing.