Tuesday, August 19, 2014

The Agent-Based Method

It's nice to see some attention being paid to agent-based computational models on economics blogs, but Chris House has managed to misrepresent the methodology so completely that his post is likely to do more harm than good. 

In comparing the agent-based method to the more standard dynamic stochastic general equilibrium (DSGE) approach, House begins as follows:
Probably the most important distinguishing feature is that, in an ABM, the interactions are governed by rules of behavior that the modeler simply encodes directly into the system individuals who populate the environment.
So far so good, although I would not have used the qualifier "simply", since encoded rules can be highly complex. For instance, an ABM that seeks to describe the trading process in an asset market may have multiple participant types (liquidity, information, and high-frequency traders for instance) and some of these may be using extremely sophisticated strategies.

How does this approach compare with DSGE models? House argues that the key difference lies in assumptions about rationality and self-interest:
People who write down DSGE models don’t do that. Instead, they make assumptions on what people want. They also place assumptions on the constraints people face. Based on the combination of goals and constraints, the behavior is derived. The reason that economists set up their theories this way – by making assumptions about goals and then drawing conclusions about behavior – is that they are following in the central tradition of all of economics, namely that allocations and decisions and choices are guided by self-interest. This goes all the way back to Adam Smith and it’s the organizing philosophy of all economics. Decisions and actions in such an environment are all made with an eye towards achieving some goal or some objective. For consumers this is typically utility maximization – a purely subjective assessment of well-being.  For firms, the objective is typically profit maximization. This is exactly where rationality enters into economics. Rationality means that the “agents” that inhabit an economic system make choices based on their own preferences.
This, to say the least, is grossly misleading. The rules encoded in an ABM could easily specify what individuals want and then proceed from there. For instance, we could start from the premise that our high-frequency traders want to maximize profits. They can only do this by submitting orders of various types, the consequences of which will depend on the orders placed by others. Each agent can have a highly sophisticated strategy that maps historical data, including the current order book, into new orders. The strategy can be sensitive to beliefs about the stream of income that will be derived from ownership of the asset over a given horizon, and may also be sensitive to beliefs about the strategies in use by others. Agents can be as sophisticated and forward-looking in their pursuit of self-interest in an ABM as you care to make them; they can even be set up to make choices based on solutions to dynamic programming problems, provided that these are based on private beliefs about the future that change endogenously over time. 

What you cannot have in an ABM is the assumption that, from the outset, individual plans are mutually consistent. That is, you cannot simply assume that the economy is tracing out an equilibrium path. The agent-based approach is at heart a model of disequilibrium dynamics, in which the mutual consistency of plans, if it arises at all, has to do so endogenously through a clearly specified adjustment process. This is the key difference between the ABM and DSGE approaches, and it's right there in the acronym of the latter.

A typical (though not universal) feature of agent-based models is an evolutionary process, that allows successful strategies to proliferate over time at the expense of less successful ones. Since success itself is frequency dependent---the payoffs to a strategy depend on the prevailing distribution of strategies in the population---we have strong feedback between behavior and environment. Returning to the example of trading, an arbitrage-based strategy may be highly profitable when rare but much less so when prevalent. This rich feedback between environment and behavior, with the distribution of strategies determining the environment faced by each, and the payoffs to each strategy determining changes in their composition, is a fundamental feature of agent-based models. In failing to understand this, House makes claims that are close to being the opposite of the truth: 
Ironically, eliminating rational behavior also eliminates an important source of feedback – namely the feedback from the environment to behavior.  This type of two-way feedback is prevalent in economics and it’s why equilibria of economic models are often the solutions to fixed-point mappings. Agents make choices based on the features of the economy.  The features of the economy in turn depend on the choices of the agents. This gives us a circularity which needs to be resolved in standard models. This circularity is cut in the ABMs however since the choice functions do not depend on the environment. This is somewhat ironic since many of the critics of economics stress such feedback loops as important mechanisms.
It is absolutely true that dynamics in agent-based models do not require the computation of fixed points, but this is a strength rather than a weakness, and has nothing to do with the absence of feedback effects. These effects arise dynamically in calendar time, not through some mystical process by which coordination is instantaneously achieved and continuously maintained. 

It's worth thinking about how the learning literature in macroeconomics, dating back to Marcet and Sargent and substantially advanced by Evans and Honkapohja fits into this schema. Such learning models drop the assumption that beliefs continuously satisfy mutual consistency, and therefore take a small step towards the ABM approach. But it really is a small step, since a great deal of coordination continues to be assumed. For instance, in the canonical learning model, there is a parameter about which learning occurs, and the system is self-referential in that beliefs about the parameter determine its realized value. This allows for the possibility that individuals may hold incorrect beliefs, but limits quite severely---and more importantly, exogenously---the structure of such errors. This is done for understandable reasons of tractability, and allows for analytical solutions and convergence results to be obtained. But there is way too much coordination in beliefs across individuals assumed for this to be considered part of the ABM family.

The title of House's post asks (in response to an earlier piece by Mark Buchanan) whether agent-based models really are the future of the discipline. I have argued previously that they are enormously promising, but face one major methodological obstacle that needs to be overcome. This is the problem of quality control: unlike papers in empirical fields (where causal identification is paramount) or in theory (where robustness is key) there is no set of criteria, widely agreed upon, that can allow a referee to determine whether a given set of simulation results provides a deep and generalizable insight into the workings of the economy. One of the most celebrated agent-based models in economics---the Schelling segregation model---is also among the very earliest. Effective and acclaimed recent exemplars are in short supply, though there is certainly research effort at the highest levels pointed in this direction. The claim that such models can displace the equilibrium approach entirely is much too grandiose, but they should be able to find ample space alongside more orthodox approaches in time. 


The example of interacting trading strategies in this post wasn't pulled out of thin air; market ecology has been a recurrent theme on this blog. In ongoing work with Yeon-Koo Che and Jinwoo Kim, I am exploring the interaction of trading strategies in asset markets, with the goal of addressing some questions about the impact on volatility and welfare of high-frequency trading. We have found the agent-based approach very useful in thinking about these questions, and I'll present some preliminary results at a session on the methodology at the Rethinking Economics conference in New York next month. The event is free and open to the public but seating is limited and registration required.


Update: Chris House responds, leaping from the assertion that agent-based models disregard rationality and self-interest to the diametrically opposed claim that DSGEs are a special case of agent-based models. Noah Smith concurs, but seems to misunderstand not just the agent-based method but also the rational expectations hypothesis. Leigh Tesfatsion's two comments on Chris' posts are spot on, and it's worth spending a bit of time on her agent-based computational economics page. There you will find the following definition (italics added):
Agent-based computational economics (ACE) is the computational modeling of economic processes (including whole economies) as open-ended dynamic systems of interacting agents... ACE modeling is analogous to a culture-dish laboratory experiment for a virtual world. Starting from an initial world state, specified by the modeler, the virtual world should be capable of evolving over time driven solely by the interactions of the agents that reside within the world. No resort to externally imposed sky-hooks enforcing global coordination, such as market clearing and rational expectations constraints, should be needed to drive or support the dynamics of this world.
As I said in a response to Noah, the claim that DSGE's are a special case of agent-based models is not just wrong, it makes the case for pluralism harder to make. But the good news is that there seems to be a lot of interest in the approach among graduate students. I introduced the basic idea at the end of a graduate math methods course for first year PhD students at Columbia a couple of years ago, and it was really nice to see a few of them show up to the agent-based modeling session at the recent Rethinking Economics conference. I suspect that before long, knowledge of this (along with more orthodox methods) will be an asset in the job market.