(Shutterstock/Maria Skaldina)
(Shutterstock/Maria Skaldina)

At this point in the year, many Canadians longingly daydream of escaping the winter blues by taking a vacation on an island in the sun. The sun, the surf, the palms swaying in the breeze…

These thoughts distracted me this week whilst I was reading the results of the second round of the ECB’s Long-Term Refinancing Operation and news of the continuing challenges faced by the euro zone. And they reminded me of an influential theoretical paper on asset pricing written almost 35 years ago by Robert Lucas (“Asset Prices in an Exchange Economy,” Econometrica, 46, 1978:1429–1445).

Lucas conceived an artificial economy (say, a tropical island) populated with many identical individuals, each with an ownership claim on a fruit tree. The trees are inexhaustible and bear the same perishable fruit each period that cannot be stored. Now, you might think that if the trees all yielded the same quantity of fruit on the same schedule there would be very little to model. Each individual would consume the fruit from his or her tree and there would be no exchange, no market; no need to value the asset. You would be right. But that was not the point of the exercise.

Lucas wanted to model the price of the tree (the asset) as a function of the fruit it yields (or the stream of dividends) and the extent to which the owner-cum-consumer values future versus present consumption. However, modelling an economy – even an artificial economy – made up of a large number of different individuals each with a different tree (or, say, with different abilities and levels of wealth) is an incredibly difficult task. An assumption or two (such as identical agents) allows a complex problem to be reduced to a far simpler exercise of solving the 'representative agent' problem. Unfortunately, that assumption – made for mathematical tractability – eliminates much of the interesting economics of the real world, which focuses on the consequences of heterogeneous individuals that have access to different information.

As Paul Krugman might say of the Lucas paper, though it may be beauty, it is not truth. Nevertheless, it is an elegant paper that employs fairly advanced mathematical methods to solve for an asset pricing equation for the fruit tree. The counter-intuitive answer is that the price of the tree does not necessarily depend on the expected harvest of fruit. This is because the owner is also the consumer; an increase in future production therefore means higher future consumption and lower future marginal utility of consumption. The higher future production of the tree is counterbalanced by lower marginal utility in the asset pricing equation.

“Okay,” you say, “what does any of this have to do with global stagnation?” Good question.

To answer it, extend the Lucas tree model to allow for other islands, each with a different type of fruit tree and inhabited by individuals with different rates of time preference – some are impatient consumers; others are prepared to postpone consumption. We now have the possibility of trade across islands, as individuals on the different islands trade for the different types of fruit (assume that they all want variety in their diets). Moreover, as long as the claims on fruit trees are transferable and enforceable between islands, we have the possibility of trade over time, or borrowing and lending.

Under these assumptions, impatient consumers, who want to consume more today, will borrow against the future fruit of their tree; more patient consumers will accumulate claims on the trees of these impatient consumers. As long as an individual tree owner limits his or her borrowing to a level that is less than the stream of all future fruit produced by his or her tree, all is well. (Of course, this is a gross simplification that ignores the discounting of future harvests; it is made solely in the interests of simplicity.) The impatient will repay their debts from the fruit of their trees in future periods.

If the amount borrowed exceeds the future fecundity of the trees, however, someone is certain to be disappointed. The tree owner loses title to the stream of dividends, which is transferred to the lender. While that may provide some sense satisfaction to the lender, it does not make up for the fact he or she will not recover all that was “lent.” Inter-temporal trade (borrowing and lending) could collapse.

Forward-looking patient consumers (ok, savers) will anticipate this problem and demand some collateral (a claim on some other 'safe' asset) before lending. The objective of collateral is to align incentives so that borrowers don’t take on too much debt ex ante, and to protect lenders against losses, ex post, should borrowers violate their borrowing limits given by the stream of future harvests from their trees.

What might this collateral be? Well, assume that all the individual harvesters on an island agree to pool a small fraction of the fruit from their trees each period and issue claims on this pool. For the sake of argument, call this claim a sovereign bond. The bond allows for inter-temporal trade on the island – an individual can give up more of his or her fruit today to acquire claims on more fruit later. Moreover, because it doesn’t represent the claim on one, possibly irresponsible, borrower, but on the harvest of an entire island, the bond can be used as collateral to support borrowing and lending across islands.

But what would happen if the amount of bonds, or claims on the future pooled stream of an island’s fruit trees, exceeds the productivity of the trees or the willingness of the various harvesters to contribute to the pool? We are then back in the situation in which lending collapses. And if inter-temporal trade falls into stagnation, spatial trade between islands could decline as well.

I worry that this might be the situation that threatens Europe and, if unchecked, the global economy. Put simply: the debt problems that afflict some members on the periphery of the euro zone have undermined the collateral on which other lending is supported. With those foundations collapsing, banks are loath to lend; with credit markets seizing up, economic activity is slowing and Europe is sliding into recession.

The policy response from the core of the euro zone has been to implore members on the periphery to do more fiscal adjustment and to exhort them to do structural reforms. Let’s consider each of these policy proposals in turn using our tree model.

Calls for more fiscal adjustment are equivalent to the tree owners foregoing more their own consumption in order to meet their external obligations. That would be both economically and morally justified if borrowers could pay – in the sense that their trees are capable of producing enough fruit to meet debt payments and satisfy their own consumption. If, as we are assuming, the external claims on the tree exceed its fruit-bearing capacity, however, it really isn’t feasible. Moreover, before we even get to that point, there is a limit to how much indebted tree owners are willing to transfer to their creditors. Once that point is reached, the tree owner will seek protection from the external creditor.

This underscores the key importance of enforceability of claims between islands. A century or more ago, claims between 'islands' were enforced by gunships in the harbour and marines occupying the customs house – err, sorry collecting the 'fruit.' That is no longer the case. As a result, there is a risk attached to sovereign lending; when sovereigns default, the creditors typically negotiate to write-down the value of their claims. Greece provides a timely example.

Exhortations for more structural reforms, meanwhile, are equivalent to asking the tree owners to work harder to increase yields by, say, weeding around their trees. Fair enough. But tree owners have no incentive to expend that effort if the results go to creditors on other islands. In this case, the debt overhang is sufficiently high that the incentives are distorted and behaviour becomes pathological: the German hyperinflation of the early 1920s was largely a self-inflicted wound intended to punish France and Belgium for having occupied the Ruhr to extract reparation payments.

Of course, the situation in members on the periphery of the euro zone is slightly more complicated than our artificial islands economy. But there are worrying signs – too much debt, protests against calls for more austerity and growing concerns about national sovereignty.

All this is bad enough. But, wait, it could get worse – much worse. The structure of the European Financial Stability Facility (EFSF) holds members jointly and severally responsible for the debts of the facility. As a result, should some members default on their obligations and, in effect, defect from the cooperative outcome of supporting the EFSF, the obligations of the remaining members increase. Were the process to continue, at some point, one country (for the sake of argument, Germany) could inherit responsibility for all obligations. Even before this calamitous outcome, however, credit markets would begin worrying as the perceived credit-worthiness of the governments backing the EFSF is downgraded. In this scenario, the debt of even the strongest euro zone sovereign may lose it value as collateral supporting other lending.

Such an outcome would, indeed, be a recipe for a crisis. With a shortage of collateral for the system, Europe could stagnate and 'pathological' policies, which Keynes described as beggar-thy-neighbour policies destructive of national and international prosperity, could once again be the rule and not the exception.

In those circumstances, an island in the sun – far removed from the concerns of asset pricing and collateral shortages in Europe – would be even more enticing to this Canadian suffering cabin fever.

I worry that this might be the situation that threatens Europe and, if unchecked, the global economy. Put simply: the debt problems that afflict some members on the periphery of the euro zone have undermined the collateral on which other lending is suppor
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