Paying down debt

Warren Meyer at Coyote makes a familiar argument against the stimulus:
At the end of the day, businesses and individuals have a felt need to deleverage.  That is going to cause a recession, end of story.  The Congress’s and Obama Administration’s obsession with short-circuiting this sensible desire to reduce debt is not only counter-productive, it is offensive.  Banks are sensibly trying to strengthen their balance sheets, but the government wants to stop them. Individuals are trying to cut back on spending, reduce debt, and save more.  Again, the government wants to stop them, by going to debt and spending for them if consumers won’t do it on their own.
This sounds intuitively sensible, but is it correct? As often is the case, a simple model sheds some light on the argument (retrospective note: the model is simple, but the analysis turned out longer than expected. I still think it's worth reading).

Imagine a very small economy with just two people in it. A is a baker and B is a builder.

A can produce enough bread each year to feed two people - 730 loaves - provided he has a shop to bake in. B can construct the equivalent of a two-room house every year.

In year 1, B builds a bakery for A. Since A starts without any resources, he can't pay B for it - so B builds it on credit. To avoid any confusion with monetary instruments (because he's sympathetic to the overworked economist whose model he lives in), A agrees to pay the debt back in bread. The price is 730 loaves of bread (two years worth of personal consumption).

A agrees to pay this off over ten years, at 73 loaves of bread per annum. Of course B needs 365 loaves to live, so he agrees to buy a further 282 loaves each year in exchange for building services. A therefore gets a small extra room added to his house in the first year; B also builds another (bigger) room on his own house. In the second year, A decides to expand his bakery so B builds another room on there instead of adding to A's house. In the third year, A can produce more bread and we can introduce to the model C, a cobbler, who will make some shoes in return for bread. A's income has increased and therefore his ability to service the debt is more secure, reducing B's risk.

Now let's backtrack to year 1: imagine an economic crisis occurs; A and B are worried that a recession may reduce the total output of the economy; they are therefore concerned that A's debt may be too high to service, and decide to pay off the debt more quickly. A is capable of producing 730 loaves in a year - enough to pay off the whole debt in a year - but presumably he doesn't want to starve. So he agrees to repay in two years.

His entire excess production - the 365 loaves that he doesn't eat himself - go to paying off B's debt. And, instead of getting some building services in return, he gets nothing - at least, no goods and services. On the other hand, his debt is being paid off so he does gain a financial asset.

B, instead of adding a room to his own house and a room to A's, is unemployed half the time.He can't build anything for A, because A has nothing to buy it with - his entire disposable income is going to pay off debt. Sure, B can add two rooms to his own house each year instead of one, but that generates much less than double the utility of the first room because of diminishing marginal returns. Whether he decides to stay idle or build the extra room, the population as a whole is less well-off than under the original scenario.

So after two years, B ends up with four extra rooms on his house - or two rooms plus some leisure time - and A with none. And A has not been able to expand his bakery, so production of bread remains at 730 per year and nobody gets any shoes (C might have some extra pairs left over, but how many can you wear at once? In any case he has starved to death in the meantime, since A and B have eaten all the bread). The recession has happened, making A and B's prediction correct and their decision to repay the debt fully justified in its own terms.

Now, at least the debt has been paid off. This means that A's production is now entirely his to distribute, instead of 10% of it going to B. In year 3, A can pay B 365 loaves for building services instead of 282, which lets him buy a bigger and better room. But he's two years behind, so he now has just 1.2 rooms instead of three. Still behind, and still without expanded bread production.

Admittedly this model does not handle certain complexities - notably interest, the startup capital of B, and the feeding of A and B while B is building the bakery in year zero. And it's a very simplistic model, requiring the debt to be paid off artificially fast. But I don't believe any of these complexities are germane to the model.

So - am I saying that a reduction in debt is always destructive of efficiency or welfare? I'm not sure. But debt is a tool for smoothing consumption - over time, and between multiple individuals - both of which by their nature are welfare-increasing. It is natural that debt increases over time as the economic capacity of the economy increases. And it seems like a reduction in gross debt is likely to lead to a reduction in the utility - and thus the market value - of economic output.

Indeed, the problem arises from the existence of multiple equilibria. In the original equilibrium, it was rational for A and B to create the debt and pay it off over ten years. That was the decision they made at the time to maximise their utility.

It's in the second, "crisis" equilibrium that they decide to pay off the debt more quickly, reducing their utility. Behaviour in both cases is rational.

Therefore, if state intervention can move the economy from the second equilibrium to the first, economic welfare is increased. There is no inherent "correct" level of debt, just a level that's appropriate to the specific equilibrium that the economy has found.

And this is what justifies a credit policy - that is, government intervention to prevent the unwinding of debts. If the debts were entered into rationally in a growing economy, and growth can be resumed, then the debts become rational again.

Caveat: I accept that if the debts were not rational - if they were too big to service in the first place - then the above argument does not hold. But I think we can adjust the model to examine that scenario too.

Let's say that the price of building the bakery were 2190 loaves instead of 730, and that the repayments were based on an assumption of substantially increased bread production. A still decides to have the extra room in his house in year 1, delaying the productive investment until year 2. In the meantime, it turns out that the bread productivity projection was wrong, and the repayments are going to be impossible to achieve if A maintains his planned level of shoe consumption.

Does this still call for paying the debt down more quickly? I suggest not. If A tries to pay off the debt all at once he will end up paralysing the economy for six years instead of two, and still won't get the bakery expanded. The way to maximise welfare in this scenario appears to be for A to invest as planned, to extend the repayment term of the loan and reduce B's present shoe consumption below what he planned; or for A to reduce his planned shoe consumption and maintain the term of the loan. This is a matter of allocating property rights (and, with an eye on future incentives, we might allocate them in proportion to who screwed up the investment projections) but makes no difference to total economic output.

There is an unavoidable loss of welfare in comparison to the original business plan, but that welfare was never really available. So our job is to maximise actual welfare, which is still achieved by allowing consumption to be smoothed across time and people, and still making the investment if it is profitable to do so (this is where we may need to reintroduce interest rates to the model).

Perhaps, when the investment turns out less productive than expected, the optimal amount of debt in the economy does reduce. But I suspect the dislocations from reducing gross debt are, in nearly all circumstances, greater than the cost of allowing the debt to remain steady until economic growth catches up with it. This posting is already too long - that analysis will have to wait.


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