## Monday, September 2, 2013

### The useless power of expectations

Scott Sumner has another post up heavy with expectations. He rhetorically asks for the step in his argument at which a reader disembarks. Well, Step 1 is supply and demand with a shift in the supply curve resulting in a drop in price. I'll buy that one. Step 2 goes too far:
2. Same thing, but assume the company merely announces the big gold discovery, but it is credible. Now gold prices would plunge on the announcement.
How far do they plunge? In Step 1 it was a series of market transactions causing the price to take a random walk with a downward drift of unknown duration. We can't know the final equilibrium price (EMH). If people knew the final equilibrium price (they expected it) the price it would head directly there. But it doesn't.

There are some cases I would not have a problem with the "expectations" argument. If company ABC announces it will buy company XYZ at 10 dollars per share, then the price of XYZ's stock fairly rapidly becomes 9.94 dollars per share. However this is not really a functioning market; it is similar to government price setting on a smaller scale. And the mining company is not even announcing a huge gold discovery at $600 per ounce. It is announcing it will sell some its stock of company XYZ. Where does the price go? Who knows? Now go a step further imagine that people are "wrong" about the economics. The dominant paradigm includes the idea that a huge gold discovery will ruin the economy because it is ripe with moral hazard -- too much money makes people lazy. Widespread deflation will result. This expectation will push down the price of gold even farther than than the equilibrium price due to supply and demand. Now what happens? • The price drifts back to the equilibrium price in the case of no moral hazard. [Did the power of expectations vanish?] • The price stays at a level expected by moral hazard. [Did the law of supply and demand vanish?] These two cases are particularly relevant to the case of Japan. Is the current price level where it is because the BOJ is expected to take back all the base money and thus supply and demand is powerless? Or is the current price level where it is because of supply and demand and thus expectations are powerless? The information transfer model says the latter. Or more precisely, the information transfer model doesn't make the distinction between prices that come to equilibrium because of market forces or expectations. Expectations are part of the market forces (we make no assumptions about the information being transferred from the demand to the supply; it includes "Kevin thinks$5 is too high" and "Kyoko thinks the price will rise to 1800 ¥ given the current trend of exchange rates before falling to 200 ¥") and their effect on equilibrium prices is indistinguishable from the invisible hand. This resolves the tension between the two bullets above. There never was a price expected by moral hazard that differed from the equilibrium price.

1. Maybe there is a good conservation of market information argument: the amount of information created by a market coming to an equilibrium price cannot be destroyed?

Expectations seem to be able to arrive at prices without expending the "energy" in a market process.

2. Maybe this is a better way to state the second paragraph:

How far does the price plunge? In Step 1 (where the gold was produced) there were a series of market transactions causing the price to take a random walk with a downward drift of unknown duration. We can't know the final equilibrium price in the Step 1 case(EMH), so how can we know it in the Step 2 case (where the gold was announced)? If people knew the final equilibrium price (they expected it) the price it would head directly there regardless of whether they produced it or announced it.

3. A more succinct summary of the second half of this post:

Rational expectations assumes the information shock is not the model itself (deviations from perfect foresight are random), therefore you must already have the correct model in order to use rational expectations.