Mark Thoma over at Economist View has an interesting post on output gaps in recoveries. It is well worth reading. His point, briefly, is that potential output has a cyclical component that increases or decreases along with demand. When there is a shock to aggregate demand, firms lay off workers, reducing aggregate supply. By the same token, if firms hire previously unemployed workers in response to an increase in aggregate demand, aggregate supply increases.

All this matters: there is a debate in the U.S. on whether fiscal policy should be used to accelerate the return to full employment (potential output) and whether the Federal Reserve should begin to unwind its current aggressive monetary policy stance, embodied in the commitment to keep interest rates steady for the foreseeable future. If the economy is already at or near capacity, fiscal stimulus would not raise employment but would raise public debt. Conversely, a premature tightening of monetary policy, when output remains well below potential, could lead to relapse into recession and increase the risk of deflation. As noted, the issue is important.

Professor Thoma’s post also got me thinking about Peter Diamond’s matching model of aggregate demand in the “island economy” (Islands in the Sun and European Stagnation)used by Robert Lucas to study asset pricing. Instead of a “representative agent,” however, Diamond assumed an island populated by many individuals each of whom can pick the fruit from their trees, but is forbidden by taboo from eating their own fruit. To consume, the islanders have to find another individual with whom to trade. (Like the Lucas model, this is obviously an abstraction. But, remember, the purpose of a model is not replicate reality, but to isolate a particular feature of the economy to better understand it.)

Because it is costly to climb the coconut tree, an individual’s decision to climb a tree to collect the fruit is a function of his/her expectation of finding a match – there is little sense climbing the tree if you are not going to find someone with whom to trade. Of course, if the individual doesn’t climb the tree, he won’t find a match (because he doesn’t have anything to trade!) so the expectation is self-fulfilling. But the interesting thing here is that there isn’t a unique equilibrium that determines the level of activity (output); instead, there are multiple possible equilibria associated with a high level of activity and a low level of activity. This aspect of the model corresponds nicely to the notion that a recession can be attributed to a Keynesian coordination failure.

Moreover, there is a positive externality associated with one individual’s decision to climb and trade. The more individuals that opt to engage in the market by collecting the fruit and searching for a match, the greater the likelihood that other individuals will find a match.

Similarly, consider the case of positive externalities in aggregate supply. What if climbing the trees on the island economy increases the harvest – perhaps because climbing helps in the pollination process or, say, clears away dead bark that is susceptible to infection. In any event, production has a positive externality on the fecundity of the fruit trees. If the island is initially stuck in the low level of output equilibrium, this effect reinforces the argument for some policy to move the island economy to the high level.

Let’s leave the island economy and consider an economy stuck in a low-output equilibrium; think of a firm that would like to increase production to meet demand for its good. Increasing production would require additional workers that are currently unemployed and raise aggregate supply. The problem is that output requires some input (say a delivery service) that is uneconomical at the firm's level of demand. But, without the input, the firm can't produce – nor is it economic for the firm to internalize the delivery service. The economy remains in the low-level output equilibrium, with the demand for the firm's output unsatisfied.

Now assume that there is an aggregate demand shock (say a fiscal expansion) that raises the demand for all goods. It is now economic for the input (delivery service) to be provided and the firm therefore hires additional labour to expand production. Other firms acting likewise help to move the economy out of the low-level output equilibrium.

Of course, while such positive external effects are possible when there are ample unemployed resources, they would disappear as employment rises and rising wages offset the positive external effect. But at that point the economy has returned to full employment.

What might the policy implication be? I’m not sure, but in the current situation in which the U.S. finds itself, it may be that policy should err on the side of expansion. That could be the intent of the Fed’s commitment to keep interest constant over the foreseeable future.

There isn’t a unique equilibrium that determines the level of activity (output); instead, there are multiple possible equilibria associated with a high level of activity and a low level of activity.
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