Default, expected default, and wealth

Actual default on existing debt reduces aggregate wealth a bit; expected default on existing debt reduces aggregate wealth a bit; but expected default on new debt reduces aggregate wealth a lot. Redistribution of wealth from creditors to debtors may reduce aggregate wealth a lot. Default is a symptom of that problem.

Peter owes Paul $100. What happens to wealth if Peter defaults on his debt? Paul is clearly worse off; his net wealth has fallen $100. That's the easy bit to understand. But Peter is better off; his net wealth has increased by $100. That's the harder bit to understand.

Let's just suppose that some crooked magistrate, acting on a whim, decided to cancel Peter's debt to Paul. Then it's easy to understand that Peter is $100 richer, Paul is $100 poorer. The distribution of wealth has changed but aggregate net wealth is unchanged.

Default (usually) doesn't happen like that. Something must have caused Peter to default, and that something (losing his job, or losing money on investments) made him poorer. That's why it's hard to accept that Peter's wealth rises by $100 when he defaults. So think of it this way: losing his job, or losing his investments, reduced Peter's wealth. Being able to default on his debt offsets some of that loss of wealth. He would be even worse off, $100 worse off, if he lost his job or investments and still had to pay $100 to Paul.

The things that cause default may cause a loss in wealth, but default itself only changes the distribution of wealth, leaving aggregate wealth unchanged. We would get the same loss in aggregate wealth if we ignored debt and default. Default just changes the amounts we owe to ourselves. Macroeconomists can ignore default (unless it's default on international debts, which change the distribution of wealth between us and foreigners).

That isn't right of course, but it is an essential first step.

Default causes transactions costs, which are real and may be big. If you default on a mortgage, the bank will have legal costs, realtor costs, and the house may sit empty for a while. These are all real costs. But they are likely to be some fraction of the loan, for the bank would not spend more than $100 to try to recover $100 (except maybe in some exceptional circumstances to deter others from defaulting).

What about expected default on existing debt? Suppose Peter owes Paul $100, then for some reason the risk of default rises from 0% to 10%. If both are risk-neutral and see the same 10% risk of default, then the value of the debt falls to $90, so Paul's wealth is reduced by $10 and Peter's wealth increases by $10, again with no change in aggregate wealth (though, of course, the thing that caused default risk to increase may have caused wealth to decrease).

Once again, there are the transactions costs of default to consider, only now it's the expected transactions costs. If transactions costs are $20 on a $100 default, then a 10% risk of default causes a $2 reduction in aggregate wealth.

But maybe there's more than just the transactions costs. If Peter knows he will pay the debt, but Paul sees a 10% risk of default, then Peter's liability is worth $100 to Peter, but Paul's asset is only worth $90 to Paul, so aggregate wealth is reduced by $10. But it could equally well go the other way, and increase aggregate wealth, if Paul thinks his asset is safe by Peter thinks he has a risk of default on his liability.

If both are risk-averse, then a random 10% default risk would increase their uncertainty of their wealth, and reduce aggregate wealth. But since default is likely to be highly correlated with other shocks to Peter's wealth, default would make Peter's wealth less uncertain. It could go either way.

But expected default on new debt matters a lot. If Paul expects Peter to default on a debt, Paul will not lend to Peter. Expected default prevents mutually beneficial lending, which reduces aggregate wealth. Paul could increase the interest rate by 10% to cover a 10% risk of default, but the higher interest rate will make it harder for Peter to repay the debt, and so could be self-defeating. If risk of default means that Peter cannot finance a profitable investment, aggregate wealth falls. Even if Peter planned to spend the loan on consumption, both are worse off it Peter wanted to consume now but must wait, and Paul wanted to wait but must consume now.

Debts are promises; promises depend on trust; trust is imperfect; capital markets (markets in loanable funds) are imperfect; moral hazard and adverse selection problems are examples of those imperfections. This means that the distribution of wealth has macroeconomic consequences.

I am not talking about the distribution of wealth between rich people and poor people (though that may matter per se, and for different reasons). I am talking about the distribution of wealth between debtors and creditors.

Some people have investment opportunities; others don't. If knowledge of investment opportunities happened to coincide with the wealth to exploit those opportunities then we wouldn't need capital markets. People would invest their own wealth in their own ventures. But they don't coincide, so we have to overcome capital market imperfections in an attempt to transfer command over resources. We will always fail to do this fully. People with more investment opportunities than wealth will borrow some of the shortfall. People with more wealth than investment opportunities will lend some of the excess. Command over current resources will flow in the right direction, but will not flow enough.

Capital market imperfections mean that an exogenous redistribution of wealth from creditors to debtors will increase aggregate wealth, by completing the job that capital markets leave unfinished, and doing it better. And a redistribution of wealth the other way will reduce aggregate wealth, by making reliance on imperfect capital markets even greater.

Default is not the problem. Default actually alleviates the problem in part, relative to a world where all debts were strictly enforced. But default is a symptom of the problem: a symptom of the loss of wealth by debtors. If there were a redistribution of wealth away from debtors, that would worsen the problem caused by imperfect capital markets. It would also cause increased defaults as a side-effect. That's why we associate increased defaults with reduced investment and worsening macroeconomic performance.

Peter wants to own a house now, but lacks the wealth to buy one. Paul doesn't want to own a house now, but has the wealth to buy one. So Paul lends Peter the money to buy a house. Then the price of houses falls, and Peter defaults on his mortgage. Peter ends up renting Paul's old apartment, and Paul now owns and moves into Peter's house. The default merely transferred $100 from Paul to Peter. The drop in house prices merely transferred wealth from Peter (the "seller") to Paul (the "buyer"). But both are unhappy. Living in the house isn't worth as much to Paul as it was to Peter.

Default creates an externality. By defaulting on his debt, and walking away from his house, Peter is better off. But he gains at Paul's expense. A mutually beneficial trade is no longer being made. It's no longer being made because Paul can't trust Peter to deliver his side of the exchange. Coasians would call this a transactions cost.

Update: In a comment on another post, "reason" said:

"i.e. Nick, yes no real capital has disappeared, but some parts of the economy will be badly wounded and will change their behaviour drastically. It is like saying that theft has no impact on the economy - the ownership of goods has just changed hands."

I think the analogy between default and theft is a very good one (it doesn't mean that people who default on their debts are morally equivalent to thieves). Bicycle thieves use real resources to steal bicycles; bicycle owners use real resources to try to prevent theft; theft can change ownership to people who value the bicycles less; and some people don't own bicycles because they don't want them stolen. Same as investment and default.

Comments

[reason]

Nick,
Thanks for this I will think about it. You haven't quite attacked it the way I would. Think about all the talk of the enormous destruction of the value of assets (because of repricing) going on at the moment. The assets are the same, but the amount of money invested in them has fallen enormously because of deleveraging. Debt is money and destroying debt by defaulting destroys money. And what happens now with the FLOW of funds to the various parties. The defaulter no longer has to pay his creditor, but he also (mostly) loses the flow of services from something that he used to own. And the creditor no longer gets the flow of income he used to get. Any assets he gets in return are greatly devalued. So oddly, even though in total everybody own the same amount of real wealth everybody feels poorer. With the result that everybody will try to save more.

In addition the process of default will almost certainly cause delays in reallocating the assets to effective uses, so there will be a real loss in income.

Now clearly, the extension of credit to bad risks has mispriced certain assets (the Austrians cheer). Although, it is not clear if that is just because of incorrect expectations or an excessive flow of credit (the Austrians boo).

So by doing this analysis without considering the total volume of debt (treating it as unimportant) you have missed something.

[reason]

I'm sure Steve Keen could explain this better - especially the story about non-conservation of money (he has a paper on that on his web site).

http://www.debtdeflation.com/blogs/wp-content/uploads/2007/09/KeenNonConservationMoney.pdf

also

Endogenous money

http://www.debtdeflation.com/blogs/wp-content/uploads/2007/03/KeenKeynesCircuit.pdf

[Nick Rowe]

reason: I had a very brief read of the two Steve Keen papers above. The first one I couldn't follow. He is assuming more familiarity with some post-Keynesian (and physics?) literature than I have (and is also using some words, like "money" in a very different way). The second paper I could follow a bit more easily, but I disagree with it. Again, his concept of "money" is very different from mine (I think of money as a medium of exchange, so there can too be a commodity money, and money and debt are not the same thing), so then he sort of lost me.

Actually, I find your theft analogy much more helpful.

[GA]

I would put this slightly differently: there is an externality if lenders believe that Paul's default is an indication of the default risk of other borrowers. Given the information asymmetries, it is highly probable that lenders will interpret Paul's actual default as correlated with the potential defaults of others (even if they are actually independent).

This has interesting implications for why society may see an increased cost of default (in general) as advantageous to society - it may reduce the cost of borrowing overall. Of course, we don't want the cost of default to be too high - i.e. we want to limit the cost of default to the amount of the borrowing, or to the cost of all of the person's assets (bankruptcy), so that borrowers will weigh their expected benefits from borrowing (productivity or expected utility) against their expected loss (including expected cost of default times probability of default).

This doesn't seem to include leverage, however: where the borrower can increase the expected gains against the potential losses (and here we are in to Kahnemann territory about the shape of aversion to risk curves).

[GA]

Should have added: the externality (increased perception of default) does reduce wealth, I think.

[Nick Rowe]

GA: I think you have just added a second externality of default.

Suppose the mortgage is $100, the house is worth $90 to Peter, and $70 to Paul. Clearly it is efficient for Peter to live in (own) the house. But Peter looks at his self-interest and defaults, losing a $90 asset and losing a $100 liability, for a net gain of $10. Paul loses a $100 asset and gains a $70 asset, for a net loss of $30. Social losses are $20, but Peter's private gains are $10. Private incentives do not line up with social efficiency because Peter imposes an external cost on Paul.

That's the first externality. If Peter's default changes expectations about future defaults of future potential borrowers, which harms both future lenders and borrowers by reducing future loans, that's a second externality. That reduces wealth too.

[Declan]

Nick – this is a good post, you’ve done a good job covering off many of the ramifications of one type of negative sum lending (I prefer the game theory 'positive-sum' / 'negative sum transaction' jargon to the macroeconomic 'increase/decrease aggregate wealth' jargon) in the simplified case where there are no banks.

If you want a challenge, I suggest trying to write the same sort of summary for another sort of negative sum lending, the type known as predatory lending (or loan sharking).

I thought it might be interesting to extend your example to the world of fractional reserve banking (that is the world we live in, after all :)

You wrote, "Peter wants to own a house now, but lacks the wealth to buy one. Paul doesn't want to own a house now, but has the wealth to buy one. So Paul lends Peter the money to buy a house. Then the price of houses falls, and Peter defaults on his mortgage. Peter ends up renting Paul's old apartment, and Paul now owns and moves into Peter's house."

Now, let’s translate it to the modern world of banking:

Peter wants to own a house now, but lacks the wealth to buy one. Paul doesn’t want to own a house now, but has the wealth to buy one. Paul puts his money in the bank. The bank then lends Paul’s money out 25 times to 25 homeowners of which Peter is one. Peter then defaults, wiping out the capital that supported not only Paul’s deposit, but the deposits of 24 other people as well. The bank, out of capital, fails. Matthew Cuthbert has a heart attack and dies, leading to much sorrow for Anne of Green Gables. It turns out that the bank was counterparty to tens or hundreds of billions of dollars in credit default swaps and that the money to pay off the claims on these swaps simply doesn’t exist, threatening the collapse of all the counterparties and a complete meltdown of the global financial system. Governments spend trillions of dollars sustaining the whole leveraged house of cards, promising the tax dollars of Peter, Paul and their children and grandchildren in support of this endeavour.

There, that sounds about right.

Back to the topic at hand, historically default was considered to actually *be* theft and people were routinely enslaved or thrown in jail due to defaulting on debts. Eventually, we developed the more subtle mechanism of bankruptcy which punished both the borrower (who would have trouble borrowing again in the future and would have to give up most of their assets) and the lender (who wouldn't get their money back), allowing the borrower to start over with a (mostly) clean slate and providing the lender with an incentive not to enter into loan contracts likely to lead to default.

Where to best draw the line between debtor and creditor rights is still a matter of some debate with for example, a mix of jurisdictions that consider mortgage loans non-recourse, allowing people to walk away with relative impunity (the American approach, for the most part) and jurisdictions that have 'recourse' mortgages meaning the bank can keep chasing you if you walk away from your mortgage (the Canadian approach, outside of Alberta).

Reason – Agree with your first comment, leverage is an important factor here. I read the second paper you linked to from Steve Keen and I read it quickly so I probably missed / misunderstood what we was saying (and as Nick noted he seemed to be using a different definition of money than I am used to which made it a little hard to follow at times), but when he moved from the model on page 10 where the bank sucked up all the money to the model on page 14 where after a certain point in time the bank no longer made any profits, it seemed as though he was suggesting that the bank’s purchases of goods must offset any spread on interest they earn, and that a bank would not (could not?) simply pocket the spread on the interest rather than using it to buy goods. Seems like cheating to me, but again, perhaps I misunderstood. It was interesting anyways, so thanks for the link.

[GA]

Nick: I generally wouldn't refer to an impact on a party to the transaction as an externality (be the default expected or otherwise). It seems in your reply the direct parties are affected; how is this an externality?

My point is, is there a way to understand the losses other than a transfer of wealth (between the parties to the transaction)?

And it seems to me that there is a relatively simple explanation that corresponds to reality: perceived risk of default being based on observed defaults from "similar classes" of borrowers (where that classification will likely be erroneous to some degree, and quite probably consistently erroneous and skewed/biased). Or, perhaps risk of default for everyone is seen to be higher on every default, and the relationship is highly non-linear.

[reason]

I don't think you have to agree with Steve Keens definition of money to see the point that a default on a loan from a bank might reduce the money supply (this happens whether you assume as Steve Keen does that money created in a loan is permanent money - which can be relent after repayment, or only money until the debt is repaid - in which case the relending recreates the money).

[Nick Rowe]

Declan: Thanks! But after reading the really good comments here, I'm almost tempted to re-write it from scratch. Not so much changing the gist of what I said, but adding things, and making it all clearer and more logical.

I think your extension to fractional reserve banking is correct (I will return to this below). But let's be clear on one thing: when you say "fractional reserves" I think you are talking about (or should be talking about) *capital* reserves (i.e. the bank's leverage ratio), not currency reserves. (Or do they both matter? My head's not clear this morning.)

I was also trying to get my head clear on the ethics of default vs theft. One's a sin of ommission; the other's a sin of commission. That matters in some ethical systems, but it's not obvious why it should matter to a utilitarian/consequentialist (which is the ethical perspective normally most in tune with economists' perspective). If one argues that people can't help but default sometimes, another could reply that maybe people can't help but steal (rather than starve) sometimes too. Dunno. It is interesting what you say about them having been seen as morally equivalent in the past. There were interesting arguments in the comments section of the Calculated Risk blog a few months back. Some argued it was ethically quite OK to walk away from a negative equity mortgage (and non-recourse); in effect saying that this was part of the rules of the game, and that a mortgage was merely a put option on the house (did I get the finance-theory right?). Others said you had a moral obligation to repay the mortgage, even though it was legally unenforceable. Dunno. But the very ambiguity in the moral rules/conventions is important by itself.

GA: Fair point. There are the first and second parties to a transaction (the buyer and seller). I think the original definition of an externality was an uncompensated cost or benefit on a third party, who was not part of the original transaction, which matches how you use the word. I tend to stretch that original definition, and use it to refer to all uncompensated costs or benefits. A monopolist who raises the price above the competitive equilibrium imposes an external cost on the buyers. When I play my music too loud I impose an external cost on my neighbour. But I don't think I'm alone in stretching the usage of the word this way. When Peter defaults, he imposes an uncompensated cost on Paul. It's at least *like* an externality. So we get an inefficient allocation of resources (who lives in the house). And this is quite apart from the true externalities (via expectations of future defaults) on future borrowers and lenders you (correctly) identify.

reason: OK, I get it now. It's much clearer as you explain it. And I agree that it doesn't depend on Steve Keen's particular definition of money. Now my head is clearer. If we assume BOTH fractional currency reserves, AND fractional capital reserves (see my reply to Declan above), then default can cause bank failure or at least contraction (capital reserve ratio matters here), and bank failure or contraction will cause a reduction in the (M1, M2, anything above M0) money supply (currency reserve ratio matters here). Got it!

Damn! I really should re-write this post from scratch, to bring all this in. (But I probably won't.)

[Declan]

Nick, just to clarify, I was referring to capital reserves. Since Canada has no specific fractional reserve requirement any more, I think this is the only kind of reserve that matters.

So, for example, under Basel I, the (capital) reserve requirement for a residential mortgage was 4%, allowing leverage of 25:1 (1/.04 = 25), hence my example with 25 houses financed from one deposit.

Under the current Basel II capital rules, the capital requirement will vary from bank to bank, but will be in the same order of magnitude as it was for Basel I in most cases.

[reason]

P.S.
The reason that Steve Keen makes these rather unconventional definitions (following Keynes) is that he is trying to debunk the "you need a growing money supply in order to repay debt with interest" meme by arguing that that is confusing the stock of money with a flow of payments.

[Nick Rowe]

reason: Aha! That makes sense. I wish him good luck in debunking that weird meme.