Understanding the Stability of General Equilibrium as a Requirement for Getting a Union Card as an Economist: Friday Focus
The problem of economists not understanding what the equilibrium positions of their models mean is a serious one. So, in my mind at least, it is worth a Focus. Unfortunately, it is also a problem that is only understandable and of interest to perhaps 1/50 of the readers of this weblog. To deal with this quandary, I am making it the focus on the day after Thanksgiving, when people should be frantically reading turkey-leftover recipes, like:
Diana Rattray: Leftover Turkey Recipes: “Leftover Turkey Pie… Turkey Quiche With Peppers and Green Onions… Turkey Empanadas… Cajun Turkey Jambalaya… Turkey Curry… Creamy Turkey With Artichokes… Turkey Divan Recipe… Hot Turkey Sandwich… Turkey and Mashed Potato Croquettes… Basic Turkey Stock… Turkey Broccoli Quiche… Creamy Turkey Pie With Biscuit Mix Topping… Turkey, Ham, and Swiss Casserole
Turkey Salad With Red Grapes… Turkey Pasta Casserole With Asparagus and Cheddar Cheese… Turkey and Rice Bake… Savory Turkey Cobbler… Curried Turkey Salad with Cranberries… Kentucky-Style Hot Brown Sandwiches… Turkey Supreme… Turkey Pie With Mushrooms… Turkey, Cheese, and Pasta Wheels… Turkey and Stuffing Bake… Turkey Casserole With Havarti Cheese
Turkey Macaroni Casserole… Turkey Rice Casserole With Curry Powder… Turkey a la King… Turkey Bake with Asparagus… Scalloped Turkey or Chicken… Hot Brown Sandwiches… Turkey Rice Bake… Cheddar Turkey and Rice Casserole… Easy Turkey Sandwich Melt… Open-Face Turkey Sandwiches with Cheese Sauce… Slow Cooker Turkey and Rice… Turkey Pot Pie… Turkey Pot Pie with Cornbread Topping… Turkey, Stuffing, and Broccoli Pie… Turkey Tetrazzini… Turkey Noodle Casserole… Turkey Croquettes… Roasted Turkey Broth… Louisville Creamed Turkey… Curried Turkey Salad… Crockpot Corn Pudding With Turkey… Turkey Divan Soup… Family Style Turkey pie… Easy Turkey & Rice Casserole IV… Turkey Enchiladas… Turkey Hash Recipe…”
And we now resume our normal programming:
I think that the solution is to make every economist pass an exam on Franklin Fisher’s “The Stability of General Equilibrium” and Disequilibrium Foundations of Equilibrium Economics. But that is just me. The problem is urgent. For example, it appears to have led Nick Rowe into a situation in which he appears to be in need of having his meds adjusted:
Nick Rowe: Why inflation will not fall off a bottomless cliff:
If Steve had said ‘This model shows that the central bank should not target a rate of inflation south of XYZ, because if it did so the inflation rate would fall over the edge of a bottomless cliff’ I would be OK with it. But instead Steve is saying ‘This model shows why inflation will not in fact go south of XYZ, because there is no equilibrium inflation rate over the edge of a bottomless cliff’. This is not an isolated example…. somewhere went very deeply wrong with the way macroeconomics is done in some places. I do not know why it went wrong like that. This is not about politics or ideology…. This is not about sticky or flexible prices…. And it’s not about who is more intelligent either. Steve probably is. I despair of my ability to explain to Steve why I think his post is so horribly wrong. Why can’t he just see it! It’s obvious to my eyes. It’s staring me straight in the face!… His formal model is… telling us something interesting about the relationship between liquidity premia, time preference, and the location of the ZLB. It’s his interpretation of that model that is so horribly wrong. It is not an explanation of why inflation did not in fact fall more than it did. How come he can’t see it? How come there will be loads of other economists who won’t see it either? This is not just some random mistake…. What the hell has gone wrong with some of the best and brightest in economics? Is it too much math and not enough economics, so they are flying blind, reading the instruments, but have no idea what those instruments mean? Would it help to force them to say it in words? Or if they drew it in supply and demand curves[?]… But we need math too, sometimes, because some things are hard to say clearly in words, or pictures. I despair…
I would say that while it is not about intelligence, it is about being smart. Intelligence is a tool. If you use your intelligence to rationalize being incurious because you already know everything, or use your intelligence to find more sophisticated and convoluted reasons why what you decided was true before you began thinking is still true, you are not being very smart. Smart and stupid are not innate characteristics, but rather products of a willingness to educate oneself, to ask for and seek help from those smarter than oneself, and to mark one’s beliefs to market.
In this case, I believe the smarter-than-oneself people who should be asked for help are named Andreu Mas-Colell and Franklin Fisher, from whom I was fortunate enough to learn about “stability of general equilibrium” back when I was in graduate school:
Franklin Fisher: Disequilibrium Foundations of Equilibrium Economics:
Analysis generally proceeds by finding positions of rational expectations equilibrium if the exist. At all other point, agents in the model will have arbitrage opportunities…. The possibility of such arbitrage (plus the assumption that agents are smart enough to take advantage of it) is enough to show that points that are not rational expectations equilibria cannot be points at which the system remains…. Yet this, by itself, is not enough to justify analyzing… as though such equilibria were all that mattered…. The fact that arbitrage will drive the system away from points that are not rational expectations equilibria does not mean that arbitrage will force the system to converge to points that are rational expectations equilibria, the latter proposition is one of stability and it requires a separate proof, Without such a proof–and, indeed, without a proof that such convergence is relatively rapid–there is no foundation for the practice of analyzing only the equilibrium points…
The way I always used to understand it was thus: The economy starts out-of-equilibrium–there are arbitrage opportunities. The ability to detect and trade so as to profit from arbitrage opportunities, however, is not infinite but limited and distributed throughout the economy in some pattern. As people see and act on arbitrage opportunities, they trade, and their trades shift prices and quantities and push the economy closer to an equilibrium in which there are no arbitrage opportunities. The belief that one studies equilibria only is underpinned by a belief that this process of arbitrage-and-convergence is rapid relative to other time scales. The use of the correspondence principle–that the effects of shocks are best modeled as an instantaneous jump from one equilibrium corresponding to the pre-shock environment to another one corresponding to the post-shock environment–requires similar underpinning.
Economics develops. All of a sudden an “equilibrium” is no longer a one-dimensional vector of production, consumption, and trading plans at a single point in time and the price vector that underpins them. All of a sudden an “equilibrium” is a three-index tensor: for each element of the vector, for each possible state of the world, for every moment a set of production, consumption, and trading plans and the prices that underpin them that are consistent with the absence of any arbitrage opportunities, including those generated by agents’ not knowing the true probability distributions exactly. With this new definition of “equilibrium” there is no historical time in which disequilibrium dynamics can play themselves out. And there is no logical process of signals via which people could–if the preferred rational expectations equilibrium was not in fact common knowledge–discover that their collective plans were not self-consistent, and revise them.
Thus everything was “equilibrium”. There was no logical space left anywhere in the model for even the crudest of crude tatonnement. And so for at least half the macroeconomics wing, the idea that there was a subdiscipline called “stability of general equilibrium” and that it was very important simply vanished from their conceptual universe.
Hence we get situations in which very intelligent economists of note and reputation do not act very smart at all, and thus in which Nick Rowe–who does remember and does understand–is on the verge of a nervous breakdown. Thank God he has access to the Canadian health-care system:
Nick Rowe: The usefulness of AS-AD, an example:
Here is a model I saw recently. Except I am the one who has used the AS-AD framework to illustrate that model. The AD curve is drawn under the assumption that the central bank holds the nominal interest rate fixed. According to that model:
- If wages are sticky (so we are on the SRAS) a decrease in AD (the leftward shift from the red to the pink AD curve) will cause a fall in output and employment. OK.
- But if wages are perfectly flexible (so we are on the LRAS) the same decrease in AD will cause an increase in inflation.
The author notes that this result is “counterintuitive”, and says that more research is needed into the question of wage-determination. Anyone familiar with the AS-AD framework would immediately see the problem and start asking questions about the stability of the equilibrium under flexible wages, and would recognise that you usually get counterintuitive comparative statics results if the equilibrium is unstable….
Here we go again. God this is depressing. This is why we must continue to teach AS-AD and make sure that nobody gets out of an economics PhD program without seeing it and understanding it. Otherwise they might end up running US monetary policy, and pulling the levers the wrong way.
1390 words…
UPDATE: Noah Smith has a critique–Not Quite Noahpinion: Does QE cause deflation?–which I think is wrong:
DeLong and Krugman have gone too far. They are arguing from their preferred model…. Williamson is simply using a different model than the standard model, and DeLong and Krugman have not yet examined that model carefully…
Look: Williamson claims that his own model says:
- The real interest rate on bonds is (a) the rate of time preference, plus (b) the derivative of the marginal utility of consumption, minus (c) the liquidity premium on bonds K.
- Set the derivative of the marginal utility of consumption to zero…
- From (1) and (2), the real interest rate on bonds is (a) the rate of time preference, minus (c) the liquidity premium on bonds K.
- Assume we are at the zero lower bound…
- At the zero lower bound, the liquidity premium on bonds K must be equal to the liquidity premium on cash L.
- The real interest rate on bonds is then (a) the rate of time preference, minus (d) the liquidity premium K=L.
- So if you lower (d) the liquidity premium L=K, you will raise the real interest rate on bonds, and so raise the rate of deflation.
- Expanded QE policies lower the liquidity premium L=K.
- Hence expanded QE policies increase the rate of deflation, Q.E.D.
And because Williamson has not paid enough attention to Frank Fisher and company, he is simply wrong in his own model.
In his model, at the ZLB with stable consumption, a reduction in the liquidity premium L=K produces:
- first, an immediate upward climb in the price level as people who no longer value cash and bonds so highly dump it for currently-produced goods and services;
- second, increasing expectations of higher deflation as people regard the now-elevated price level; and,
- third, a new steady-state equilibrium with people comfortable holding the stock of bonds even though the liquidity premium K is less because of the higher expected rate of deflation.
Williamson’s isn’t a model in which expanded QE produces faster deflation. It’s a model in which expanded QE bumps the price level up, and after that price-level bump-up is completed people then expect deflation and a return to normal…