Peter Cooper — Disequilibrium Dynamics of Output and Demand

Theoretical studies of output and growth often focus on the behavior of equilibrium output. The usefulness of this approach depends on there being a tendency for actual output to converge on equilibrium output. With such a tendency present, studying the behavior of equilibrium output will tell us something about the behavior of actual output. It is therefore of interest to spell out the process by which an economy in disequilibrium is thought to tend toward equilibrium.

A first step is to consider the disequilibrium behavior of an economy that, for simplicity, is taken to be stationary (non-growing) when in equilibrium. This approach is adopted in the present post. The exercise is really preparation for considering a continually growing economy – a task that is left for a possible future post.…

The material in this post is somewhat technical but hopefully not difficult. Even so, the post is long (about 4000 words) and, for readers not already familiar with similar material, possibly a stretch to read all in one go. I considered separating the post into numerous shorter ones but felt that the loss of continuity would require too much repetition in setting up the discussion each time.

The post is divided into sections that provide natural stopping points for readers who wish to take breaks. The section titles are:

1. Macroeconomic Equilibrium
2. Disequilibrium Behavior
3. Adjustment Process
4. Adjustment in Simple Algebra
5. Convergence as a Power Series: λ = 1
6. Convergence as a Power Series: λ < 1
7. Adjustment of Growth Rates

heteconomist

Disequilibrium Dynamics of Output and Demand
Peter Cooper

Noah Smith — DSGE vs. Weather Forecasting

Why would "disequilibrium dynamics" be important? I can think of several reasons.

Reason 1: The equilibrium may shift at about the same speed that convergence happens. If the economy is trying to hit a moving target, chaos will result. See this paper by Andrew Lo for a semi-technical explanation of why this true. (In math-speak, this happens when the rate of convergence, k, may be of the same order as the parameters governing the time-scale of the shock process.)

Reason 2: The equilibrium may not be stable. See this blog post by Jonathan Schlefer (whosebook I just ordered off of Amazon):In 1960 Herbert Scarf of Yale showed that [even the most ideal kind of] economy can cycle unstably. The picture steadily darkened. Seminal papers in the 1970s, one authored by [General Equilibrium inventor] Debreu, eliminated "any last forlorn hope," as the MIT theorist Franklin Fisher says, of proving that markets would move an economy toward equilibrium. Frank Hahn, a prominent Cambridge University theorist, sums up the matter: "We have no good reason to suppose that there are forces which lead the economy to equilibrium."In other words, the smooth convergence equation that Lucas wrote down may simply not be true.

Reason 3 (the biggie): There may be multiple equilibria. You rarely see famous and influential DSGE papers with multiple equilibria, and when you do see them, there are usually only two equilibria. But I know of absolutely no reason why the real economy should have a unique equilibrium. And I know of absolutely no reason why the number of equilibrium in the economy should be small! But there seems to be a huge publication bias in favor of smaller number of equilibria (Roger Farmer's efforts notwithstanding). This annoys me.

Read the whole thing at Noahpinion

DSGE vs. Weather Forecasting

by Noah Smith
(ht Mark Thoma)