Walrasian general equilibrium theory models the economy as a system of demand and supply equations. The quantities of goods traded, and the prices at which they are traded, are the solution to that system of equations.
Who solves those equations? A fictional Walrasian auctioneer, who calls out prices at random, asks people their demands and supplies at those prices, and then adjusts the prices if demands do not equal supplies. That's the Walrasian "tatonnement", or groping by trial and error towards the equilibrium.
The Walrasian auction happens outside of real time. All offers to buy and sell are nullified until the auctioneer has found the equilibrium price vector. Real time does not begin, and trade does not take place, until the Walrasian auctioneer has solved the system of equations.
Arnold Kling rejects the Walrasian auctioneer. He's obviously right. The groping towards equilibrium takes time. Real people are solving those equations. Or trying to, because the equations are changing as fast as they grope towards the solution.
But Arnold is not quite right when he says this:
"In both standard and Austrian economics, the price system is supposed to take care of the process of adjusting to technological change. This is what we would expect if the instant that a technological change took place, the Walrasian auctioneer quickly tested thousands of different price vectors to find one that induces full employment. In the real world, adjustment is a lot messier."
(I will let the Austrians speak for themselves, but my reading of Austrian economics says that they are among the least likely to accept the Walrasian auctioneer.)
Monetarists (and Keynesians) reject the Walrasian auctioneer too. If the Walrasian auctioneer existed, money would be (approximately) neutral. It would have no effect on real variables. A change in monetary policy changes one variable in the whole system of equations. We model-builders can see precisely what effects that has on the solution to our model. All nominal variables change in proportion, and no real variables change at all. We built the model, so it's easy for us to see the solution to the system of equations. We play the role of Walrasian auctioneer. But the real people facing a change in monetary policy in the real world have to grope towards that solution themselves. Nobody tells them the answer. And it takes them time to solve the equations. And if one of them gets the answer wrong, that changes the question all the others must answer.
That's why monetary policy has real effects, in the "short run".
Real people take time to solve the equations. And so trade takes place at disequilibrium prices. There is "false trading". In that respect, there is no difference whatsoever between Arnold Kling and Monetarists (or Keynesians).
Many shocks hit the economy that have nothing to do with money. And adjusting Arnold's Patterns of Sustainable Specialisation and Trade to those shocks is a non-trivial problem, which takes real entrepreneurs (or ordinary people acting in an entrepreneurial capacity) time to resolve. In that respect, there is also no difference between Arnold Kling and Monetarists (or Keynesians).
But when I hear the word "recession" I reach for my monetary disequilibrium. A recession isn't just a decline in the overall volume of trade. In a recession, it becomes much harder to sell things and easier to buy things. We buy things with money, and we sell things for money. I can't even talk about it being harder to buy things and easier to sell things without talking about money. In a recession it's easier to sell money, and harder to buy money. That sure looks like a monetary phenomenon to me.
Now part of the economy is not a monetary exchange economy. The whole household sector, and the Patterns of Sustainable Specialisation and Trade that take place between family members, friends, and neighbours, is not a monetary system. And that non-monetary PSST sector may actually expand during a recession. It takes up part of the slack to compensate for the recession in the monetary economy. The unemployed worker grows and eats his own vegetables, and neigbours fix each other's cars and houses, because they can't spare the cash to "pay" someone to do it. They pay in kind. They resort to barter. Or DIY autarky. The growth in the non-monetary sector makes recessions sure look like a monetary phenomenon to me.
Money exists precisely because there is no one big Walrasian market where all goods can be exchanged against all goods simultaneously. People hold stocks of money and carry it from market to market, exchanging money for goods at each market. We couldn't be Monetarists and Walrasians at the same time.
The clock stops during the Walrasian auction. It doesn't matter how the Walrasian auctioneer solves the system of equations. He has an infinite amount of time to do the job. He doesn't even need to grope in the right direction. He can just keep on guessing at random until he hits on the solution by sheer luck. Do a grid search of the n-dimensional price vector and solve it by brute force. Who cares. But it does matter if real people are solving the equations in real time. Because the economy we see is the economy created by their repeated attempts to solve those equations.
Here's Arnold again:
"I wish I could say more. In subsequent chapters I will say more, proposing some crude models. But doing away with the fiction of a Walrasian auctioneer puts me at a disadvantage."
Welcome to the club, Arnold!
Actually modelling how people solve those equations is hard. We aren't smarter than the people solving the equations. We aren't more knowledgeable than the people solving the equations. If it were easy for us to model how they solve the equations, and what happens while they are solving them, the equations themselves would be easy to solve. And they aren't. It's a bit like Karl Popper on predicting inventions. If we could predict inventions, we could already have invented the inventions we predicted.
We can make some sort of broad general statements. New PSST's will be more likely to appear in areas that are the most profitable. Prices will be more likely to rise in markets of excess demand. Expectations of what other people will be doing will tend to matter. Quantities traded in a market will be the lesser of demand and supply in that market. If people are constrained in their purchases or sales because of disequilbrium in one market that will generally affect their demands and supplies in other markets. We can even write those broad general statements in equations.
But who solves those new equations?
My hopes of actually modelling this whole process formally aren't that great.
There is a point at which all models must stop.
Worthwhile Canadian Initiative 
Oh, and one more comment (!)
” It does show that agents who have beliefs we know cannot be jointly correct will do stupid things.”
The problem is that any time there is even the slightest disagreement about subjective probabilities — e.g. You believe that there is a 49% chance of rain and I believe that there is a 51% chance of rain, then the beliefs cannot be jointly correct.
So in that case, it is just a statement that “agents will always do stupid things if they trade in arrow-debreu markets”.
I.e. it’s one thing to argue, as per EMH, that the optimists cancel out with the pessimists, so that the mean expectation of all agents, weighted by their wealth, is more or less correct.
But here, the mean is irrelevant, it is the variance that creates inefficiencies, and arguing that there is zero variance in subjective probability estimates is a much stricter assumption than arguing that the mean is basically right.
Who on earth would create a system that required zero variance in beliefs among a heterogenous population as a pre-requisite for efficiency?
And given that you have this problem, why do people keep focusing on incompleteness of markets as the source of trouble? It could well be that we already have too much trading going on, and that more markets would make things worse. In the 70s and early 80s there was literature about this point, but it seems to have been forgotten, and everyone just moved on to the securities version and worried about incomplete markets, when you have this glaring sore thumb of variance of beliefs staring you in the face. Just as an observer, it seems to me that variance in beliefs is a large motivator for people making trades, rather than just variances in their risk tolerance. I would say that variance in utility is secondary to variance in probability estimates, in terms of why people make trades.
Anyways, sorry if I hijacked the thread. I think this stuff is really fascinating.
RSJ:
1. In your 3 period example (0,1,2, with uncertainty over periods 1 and 2): You can define states like {rain in periods 1 and 2), and they can do all the trades they want in period 0. Intuitively, in period 0 they can place a bet on rain in period 2, conditional on rain in period 1. I.e. the bet is off if there’s no rain in period 1. There’s no need to re-open trade.
2. What the ex-post sub-optimality means is this: after the outcome of the bet is revealed, the winner will have consumed too little in the first period, and the loser will have consumed too much. Again, this is just the same as a Robinson Crusoe case, where he bets against Nature with a storeable/investable good. If he wins the bet against Nature, ex post he consumed too little in the first period. If he loses the bet against Nature, ex post he consumed too much in the first period.
The only difference between the 2 person bet and the bet against Nature is that when two risk-averse people bet, you know that at least one of them has the wrong probabilities.
3. Ex post, there exists a dominating allocation if A wins the bet. There exists a different dominating allocation if B wins the bet. But the central planner cannot go back in time to impose that allocation after finding out who wins the bet. And since the central planner doesn’t know ex ante who will win the bet, he can’t impose a dominating allocation before-hand. He doesn’t know which of the two dominating allocations will make both agents better off ex post.
4. True, the central planner can ban gambling. But then he can only evaluate the results of that ban ex ante. And which probabilities should the central planner use? For example, if A knows the “true” probabilities, and B doesn’t, then banning gambling makes A worse off ex ante.
5. If rational agents see that another agent is willing to take the other side of a bet, they will stop and think: “Hmmm he must have different beliefs than me; I wonder if I should change my beliefs?”.
IIRC, there are theorems which imply that agents with common priors and common knowledge of heterogeneous beliefs will not trade, or will adjust their beliefs until they agree. See Milgrom, Stokey (1982). “Information, trade and common knowledge” and Aumann (1976). “Agreeing to Disagree”. The resulting literature is quite large.
anon: Yep. That’s the literature I was alluding to in my point 5 above. It’s important. But RSJ and I are ignoring (setting aside) that literature. We assume people stick to their prior beliefs.
RSJ: BTW:
1. This comment thread is dead anyway, so there’s no worry about going off-topic at this point. So keep arguing if you want.
2. I think that I, you, and anyone else reading, will have learned a lot more from us arguing through these examples than reading the original Starr paper.
3. I still think the simplest example for us to argue through is a simple coin toss 2-period example with risk-averse agents. Your example had state-dependent utility (you like ice tea more when it’s sunny), but I don’t think that’s at all essential, and it just complicates the story.
Simplest example is a 2 period coin toss, with risk averse agents, and everything symmetric. If A wins the toss, the dominating allocation has A consume more in period 1, less in period 2, and B doing the opposite. And vice versa if B wins.
Nick,
“True, the central planner can ban gambling. But then he can only evaluate the results of that ban ex ante. And which probabilities should the central planner use? ”
In a pure exchange economy, if everyone starts out with the same endowment, and if the social planner just invents some probabilities and then allocates commodities based on solving that maximization problem, the resulting allocation of endowments will have the following properties:
1. It will be ex-post efficient in all states
2. It will be independent of which probabilities were assigned by the social planner
3. It will reduce to the market allocation in that case when everyone agrees on the state probabilities, regardless of whether the market participants share the same set of probabilities as the social planner.
4. It will deliver a greater total utility in all states, than would be delivered if everyone started out with the same endowment and engaged in voluntary trade (with equality holding when everyone’s beliefs are identical).
Now you are right, it will not ex-post pareto dominate the market outcome when there is disagreement, but that market outcome is ex-post pareto-inefficient, whereas the planner’s outcome is ex-post pareto efficient, and the planner’s outcome has higher social welfare (e.g. total utility). Key to this result is that when endowments are identical, then the probability of a state occurring, if universally believed, has nothing to do with the final allocation of that state-commodity.
The probability estimate of a state occurring always influences price of the state commodity, and so it influences the budget constraint. But if everyone has the same endowment, then everyone has the same budget constraint, and solving the competitive equilibrium problem amounts to solving the FOC
p(i,s)MRS(i,s) = MRS(j,s)p(j,s)
where p(i,s) is the probability that agent i believes that state S will occur. and MRS(i,s) is the marginal rate of substitution from giving up 1 unit of the present good for 1 unit of the good that will be obtained in state s. Notice that if the beliefs are shared, then the probabilities cancel out, and play no role in setting the final allocation of goods.
Therefore the social planner does not need to “know” the probabilities.
Any set of probabilities, if shared, will yield the same allocation — the allocation will be set by MRS.
Now, suppose everyone does not start out with the same endowment — which is crucial for 1-4 to hold. In that case, first do a transfer to equalize the endowments and then proceed as above.
In terms of whether the utility of consuming the state-commodity should depend on the state — of course it should!
This is because unlike your example, the agents are not placing bets against nature, they are placing bets against each other.
Your model — placing bets against someone outside the model — is a production model in which you decide to plant one kind of seed if you think it will rain or not. It will give you the wrong intuition.
That is why you keep thinking it is important that agents know the “true” probability. But when agents have the same initial endowment and are placing bets against each other, then the true probability is not important. All that is important is whether one agent enjoys the state commodity more than another. Assuming everyone starts out with the same endowment, the fact that probabilities are assigned to states is just an illusion that allows people to confuse each other and get into trouble. The usefulness of the model is that utility differs across states.
And this is how you can achieve idiosyncratic insurance. Suppose the states were “it rains on A” and “it does not rain on A”. Or equivalently, suppose B didn’t care if he was drinking iced tea in the rain.
Then even though A cannot prevent it raining on him, he can sell some of that state-commodity to B in exchange for more present consumption, or more consumption should it be sunny.
B will be happy to enjoy iced tea if it is raining on A, so that state commodity is more valuable to B than it is to A, and therefore there are gains from trade available. Trade will occur up until those gains are exhausted, and B will end up with “interest” or additional expected consumption of iced tea due to the fact that he is better able to bear the risk of it raining on A.
But again, the equilibrium allocation will not be determined by the probability of it raining on A, but by the relative difference in preference for that state-commodity. The price of the commodity will be affected by the likelihood of the state, in that the value of the rain-on-A commodity goes up and the value of the sun-on-A commodity falls. But the resulting allocation will not change as the probabilities change, if everyone starts out with the same initial endowment.
But what the agents cannot do is mitigate the effects of systemic risk. If it rains on both B and A, and if both B and A have the same preference for tea when it rains, then by trading, they cannot improve their situation, and again, this is also independent of the probability of rain occurring.
On the other hand, when you are betting against nature, and not against each other, then you are not trying to obtain gains from trade, you are trying to increase your overall endowment by making wise production decisions. That’s a completely different issue, and it has its own intuition which does not apply here.
Similarly, if you are trying to endogenize the probabilities (or the utility functions), then that’s another separate issue. Of course, everything is endogenous, including both beliefs and preferences, and of course maximizing your endowment by making wise investment decisions is important. But those considerations are exogenous to this pure exchange model in which state-commidities, preferences, and beliefs are given, and we are just searching for the optimal allocation of consumption across time.