At Marginal Revolution, Tyler Cowen expresses skepticism about the future of agent-based modeling. Since I've been building my skills in this area for the past year and a half, I'll try to respond.

One request was this:

The role and future of intelligent agent modeling in economics.

Call me a stuck up sticky bit but I don't see a bright future for this technique. We already have, and have had, computable general (and partial) equilibrium models for decades. In those models you try to estimate the parameters from empirical data. The models rarely impress me but there are plenty of situations, such as estimating the effects of changes in the tax code, where we don't have anything better. And so those models survive, and will continue to survive.

I must admit that my understanding of computable general equilibrium models is partial at best. I have a general sense that a compelling comparison-and-contrast of the approaches, showing how the approaches differ, where general equilibrium fails, and how agent-based modeling does better, could be written, maybe has been written. I think I could recognize it if I saw it. I've heard something along these lines argued pretty compellingly by Bob Axtell. But I can't write it myself (yet).

Let me note, though, that agent-based models can and do function out of equilibrium; in fact, strict equilibrium is generally unattainable, though "meta-equilibrium," in which there is ongoing micro motion and key variables fluctuate but general patterns can be described, often emerges. This arguably makes them more realistic, of course, since the world is never in strict equilibrium, but meta-equilibrium at best; however, I don't think realism is the strongest ground on which to defend agent-based modeling. Rather, it is worth noting that there are all sorts of holes in standard competitive equilibrium concepts. For example, there is, strictly speaking, no competitive equilibrium when there are U-shaped cost curves. But most economic activities probably do have U-shaped cost curves.

What's the important innovation behind intelligent agent modeling? To introduce lots of arbitrary assumptions about behavior? Greater realism? Complexity? Considerations of computability? Learning?

Unfortunately, "introducing lots of arbitrary assumptions about behavior" frequently occurs in agent-based models. This is not a virtue of the method. What I try to do is (a) stay as close as possible to standard neoclassical assumptions about behavior, and (b) introduce modifications selectively and carefully, such that they both facilitate theorizing and move the models/simulations in the direction of greater realism. To the other four advantages: no, yes, yes, and yes. One can certainly make the case that agent-based models are/can be more realistic, but it seems to me that decades if not generations of mathematical economics has led to a fairly nuanced understanding among mainstream economists of the relationship between models and reality, which agent-based modelers are yet to develop. Some agent-based models have achieved impressive successes in mimicking real-world phenomena, for example the Zipf distribution in city and firm sizes, but that these distributions derive from arbitrary assumptions reduces their persuasive force. Agent-based models do make it possible to create more complexity, however, precisely because mathematical tractability puts embarassingly narrow boundaries on what systems-of-equations style modeling can do. To cite just one crucial example, the neoclassical production function, Y = K^a * L^b, must be rigidly adhered to in many mathematical models because it alone has the requisite mathematical tractability. Considerations of computability are another advantage: many mathematical problems cannot be solved outright, yet solutions can be estimated with an arbitrary degree of proximity to the true solution, and in a computer, very quickly. Learning is another strong point of agent-based modeling, though not one I deal with much. Evolution is a strength of agent-based models; in fact, my own efforts in this area have given me the impression that evolutionary economics is important but almost impossible to do without agent-based techniques.

We already have enough "existence theorems" as to what is possible in models, namely just about everything.

I'm not quite sure what this means. Does he just mean that people have used models to show all sorts of crazy possibilities? If that's a critique of agent-based modeling, it probably has some force applied to some agent-based papers, which draw weird conclusions from nontransparent premises. I agree that that's not very useful. But our understanding of something as basic as why the economy grows is still so limited that one of the world's leading growth scholars, Elhanan Helpman, titled his recent book The Mystery of Growth. And some of the reasons why growth remains mysterious lie at the heart of economic theory, and are related to the stringent and artificial assumptions that must be imposed on many analytical models in order to make them mathematically tractable.

The CGE models already have the problem of oversensitivity to the initial assumptions; in part they work because we use our intuition to calibrate the parameters and to throw out implausible results. We're going to have to do the same with the intelligent agent models and the fact that those models "sound more real" is not actually a significant benefit.

Cowen's talking at a high level here, and I'm not sure I completely understand him, not because he's writing clumsily but because a lot is packed into these sentences. I think I agree with him. I'm not sure that it's inevitable that agent-based models will suffer from "oversensitivity to initial assumptions," however. In particular, I think some of the models I'm working on are/will be robust to a lot of variation in initial assumptions. Moreover, the initial assumptions that do the real work will be very closely related to familiar neoclassical assumptions: agents, firms, utility functions, production functions, etc. The difference is that the agent-based approach will allow me to get past a lot of mathematical-tractability roadblocks that stopped theorists who didn't have the benefit of using agent-based techniques.

What can be done will be done and so people will build intelligent models for at least the next twenty years. But it's hard for me to see them changing anyone's mind about any major outstanding issue in economics. What comes out will be a function of what goes in. In contrast, regressions and simple models have in many cases changed people's minds.

We'll see. Again, I think the stuff I'm working on has very fundamental implications for the definition of capital, the theory of technological change, the relationship between capital accumulation and economic growth, the role of Austrian-style roundaboutness, and maybe a lot of other issues, such as business cycles, money, economic geography, the role of information in market economies, etc. I think I'll write a book, people will read it, and they will think about all these things differently. It will not be a result of what goes into the models. I think my starting places are sensible and/or standard. Rather, I think I will (a) be able to demonstrate stuff that people have only been able to intuit, and (b) encounter some provocative surprises.

Sometimes a theory model tells you there are many many equilibria, as in much of game theory. I believe that result is to be taken seriously and we should conclude that many different things can happen in that situation. I am suspicious of trying to solve for the correct or most likely equilibrium by introducing many more specific assumptions.

The fact that I'm not sure why these remarks-- quite worthwhile in themselves-- should appear in a post about agent-based modeling is revealing of something. Does Tyler think agent-based modelers introduce arbitrary assumptions to narrow multiple-equilibria results to single-equilibrium results-- and if so, that they do so more often than, say, neoclassical theorists? That's not my impression, but Tyler is a well-read guy, and if he thinks so, it probably happens. To make a different point, though, I think we do observe a lot of equilibrium in the world-- equilibrium that restores itself if disrupted, and therefore does not seem to be "multiple." For example, the number of jobs in the United States closely tracks the number of workers. Keynes seems to have thought that full employment was just one possible equilibrium state of the economy, no more natural than others, and that there was no mechanism to ensure full employment. Putting to one side the cogent theoretical critiques of this view by Friedman, Lucas, etc., it doesn't seem to be borne out historically: the US is basically always pretty close to full employment. There isn't some 25%-unemployment equilibrium, with the US jumping back and forth. Since single-equilibrium seems, in many cases at least, to be the way the world works, we are justified in trying to explain it theoretically.

In my possibly overdogmatic view, economics is most useful when its models are relatively simple and intuitive. We've run out of new models which are simple and intuitive. So the theory game is over.

This is too big a claim for me to argue with here. I'll just state without justification that I diametrically disagree. More and more I find myself amazed by how large a part of the world's economic phenomena lacks really compelling theoretical explanation. Of course I haven't read anything close to all the economic theory there is, and it would be a bit difficult to justify the rough process by which I've extrapolated from the theory I have read to guess the explanatory effectiveness of the theory I haven't read. But my intuition, for what is worth, is that, contra "the theory game is over," the theory game has hardly begun.

Addendum: Bob Murphy asks:

It may be apocryphal for all I know, but I once read that the editor of the journal to whom Einstein sent his paper on special relativity put it down and realized that physics would never be the same (or something like that).

Is something like that even possible in economics? What would it be like? Say, the Lucas critique times 10?

The answer is no, in my view this is not possible, for reasons given above.

At the risk of bravado, I think a book something like that is possible in economics, that it is greatly needed, and that I'm going to write it in the next two or three years.

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