## Saturday, April 2, 2011

### More on Farmer/Kocherlakota

This is an update on this post and Roger Farmer's reply. I was't really satisfied with all of Roger's explanation, so I went back to his model, simplified it, worked it out, and wrote this.

Basically, I think this statement from a commenter, which Roger endorses, is nonsense:
Think of it this way. With a centralized labor market, the real wage is pinned down by the intersection of labor demand and supply. With search, the labor market need not clear: the labor supply FOC is missing, and we need to add something else to close the model. One thing to add is an explicit bargaining model that effectively pins down the wage. An alternative is to say that output is demand-determined, and that the wage is the marginal product of labor at the demand determined level of output. Then firms are on their labor demand curve, but workers are not on their labor supply curve (but the beauty of search - unemployed workers will take a job at any positive wage).
Roger's model is internally consistent and coherent. In equilibrium everyone is optimizing. There is no notion of output being "demand determined" or some people being on demand curves while others are off supply curves. That language did not help me. It just made me confused. Roger may think it helps him, but I think not.

Roger's model is very nice, as it can capture the essence of Keynes (new or old) in a very simple and clean way. It is a bit of a chicken model though.

1. This seems a very reasonable chicken model. There is an externality: households do not internalize the effect of their search decision on other households' matching probability. The first best could be achieved if the government announced that it would implement a tax on wage income equal to:

1 - z * (1 - delta) / w

where w is the market-clearing wage. Then the only REE will be the optimal one.

2. Steve, give us an example of a non-chicken model.

3. Didn't he mean the model in which the level of aggregate activity is pinned down by an exogenous expected return to capital (not RE/model-consistent)?

4. First anonymous,

Excellent. I didn't think of the tax. That's the simplest solution. I'm not sure we want to call this an externality though, even though a seemingly-Pigouvian tax works. I wouldn't say that I create an externality for someone else when I buy more peanuts. Maybe this is another one of my pet peeves. The word "externality" tends to pop up in the coordination failure literature.

David,

I think I have one written down that I can show you. Credit can get screwed up because there are some bad borrowers - call them jerks - who are jerks because people treat them that way. With limited commitment, I don't want to give a loan to someone who will not receive loans in the future. That person has nothing to lose and will default. Now introduce safe government debt. It mitigates the problem as it alters incentives, and it is non-Ricardian. The government has no informational advantage or superior ability to collect on its debts.

last anonymous,

The capital pricing is a red herring in Farmer's model. You can take that out, like I did, and it does not matter.

5. Fewer comments than you normally get. So let me just add that I really like this post, so you don't misinterpret the lack of comments. I'm still thinking through your model. Hope to have something substantive to say about it later.

6. A more substantive comment:

In your model, the worker is also a customer. He gets paid in kind, and consumes what he has produced.

Matching the right worker to the right job is a non-trivial problem.

Matching the right output good to the right customer is also a non-trivial problem.

Trying to solve both those matching problems in one exchange is an almost impossible problem. You need a workers that has the skills needed for the job, plus that same worker has to have the right preferences to want to consume what he has produced. You need a double coincidence of matches.

Monetary exchange lets us separate these two matching problems, so we convert one almost impossible matching problems into two easier matching problems.

But monetary exchange introduces a third element into the matching function. There's U, V, and also M/P. If M/P is too low, it makes separating the two matching problems harder.

A recession is where each of the two matching problems is solvable, but we can't solve both at the same time. Workers and employers can find each other. Customers and producers can find each other. But it's almost impossible for an employer to find a worker who is also a customer.

7. A revised version of your model:

Each agent works on his own farm, but cannot eat the food he has produced. Food must be eaten at the point of production. He divides his time between: producing food; waiting at the farm gate for a customer; shopping at other farms. When a shopper finds a farmer waiting at the gate he exchanges all his money for food at price P and eats the food.

The matching function will be something like:

Food sold = U.V.(M/P)

8. My preferred monetary vehicle is a Lagos-Wright construct these days. You can do that here. Do the random matching in two stages - labor market matching, then matching to sell the goods produced, where you need monetary exchange. The valued money is then the "bubble" that Kocherlakota is talking about, and you get some interaction between what is going on with the monetary exchange and the coordination problem in the labor market. You will like this, Nick, as it can produce the quasi-monetarist (or new monetarist) liquidity shortages that you are interested in.

9. Steve: ah well, you have now inspired me to build my own search model, with money, FWIW!

10. Steve,

When you have the time, could you please expound upon Hall´s new paper,

http://www.princeton.edu/economics/seminar-schedule-by-prog/macros11/pdfs/FPFU032411.pdf

Krugman wrote a short post on it, but I didn´t come to the same conclusions he did after reading the paper. Thanks very much.

Hamed

11. Hamed,

Thanks. I'll have a look when I get a chance.

Steve

12. Professor Williamson,

Have you seen this book (just go down a little bit when you have opened up the website)?:

What do you think of it?

Let me anyway state that yours is reckoned by everybody as a terrific book! I just love it!!

13. Gillman's book looks interesting. I didn't know about it. I was talking about textbooks the other day with Michele Boldrin. It's a bit of a funny business. In some sense anyone, like me, writing a textbook, is going to borrow ideas from many places. I didn't invent the real business cycle model, a Woodford sticky price model, or a two-period Fisherian model of interest rate deermination, but I put all those things in the book and try to distill it in a way an undergraduate (hopefully) can understand. Then there is a copyright page in my book, so someone is not allowed to copy word-for-word what I wrote and call it their book, and they cannot photocopy my book and resell it. Why not?

14. Well, you can fix that. Just make the next version of your book freely available just like Michele and David Levine did with their "Intellectual Monopoly" book.

Added consumer surplus will greatly exceed the fraction of monopoly rents that you capture after the publisher's cut.

15. It's not a Pareto improvement though, and my kids need an education.