Where maths ends, computers begin
Machines have finally made their mark on economic theory with their use in agent-based modelling and simulations
Computers have transformed economic analysis. Data can be analysed in ways that would have astonished earlier generations of economists. But computers have made less of an impact on economic theory. The typical economic model describes a small number of decision makers whose thought processes (which may or may not be rational) can be boiled down to solving a fairly simple piece of maths.
Macroeconomics is similar, with each decision maker billed as a “representative agent”. The behaviour of all consumers can be summarised by figuring out what a typical consumer would do. Some objections to this approach are obvious, but it has not been easy to find an alternative. In recent years, though, computers have begun to change that, and make their mark on economic theory at last.
Perhaps the most ambitious use of computers is in agent-based modelling. Rather than letting one agent represent all consumers, you create a computer model with lots of agents. Computers aren’t strictly necessary: the most famous agent-based model, created by the great Thomas Schelling, used coins and a chessboard. But the model was highly stylised, with about 40 agents. Modern computers could in principle model every single person in the economy.
Econo-physicist Doyne Farmer, computer scientist Robert Axtell, macroeconomist Peter Howitt and microeconomist John Geanakoplos have been trying to create such a model. “We’re trying to get a simulation of the economy that’s faithful to the economy,” says Farmer. “Where you see macroeconomics emerging from the microscopic interactions of individuals.”
The early fruits of this project include a model of the housing bubble in Washington DC. The advantage of studying housing is that a good deal of information is publicly available both about the price history of each house, and about the characteristics of the people doing the buying and selling. The agent-based model can thus be carefully calibrated. The conclusion: the bubble wasn’t driven by low interest rates but by increasing loan-to-value ratios – an important finding for central banks looking to prevent future bubbles.
A less flashy use of computers is to run simulations to estimate an individual’s best course of action in an uncertain world. Consider this question: if you opened your mail this morning to discover that someone had sent a cheque for £10,000 – a tax refund, perhaps – how quickly should you spend it? The answer can’t be solved mathematically because so much of it depends on unknowns, such as future income. Yet we need to know how people will behave because the relationship between consumption and different sorts of income is fundamental to understanding how the economy works.
Keynesian ideas suggest people will spend such windfalls quickly. Milton Friedman tackled the question in 1957 and developed the idea of “permanent income”, smoothing out windfalls. But if you use traditional mathematical methods to model Friedman’s ideas, you’ll conclude that individuals will spend only 5 per cent or so of the windfall, while Friedman reckoned it was more like a third.
The difference lies in dealing with the uncertainties of life. The economist Christopher Carroll has found that computer simulations can encompass this uncertainty, and produce very similar answers to Friedman’s educated guess.
This is promising yet awkward for economics. Computer simulations cannot be checked, and unless traditional methods are completely superseded, there is bound to be an awkward gap between where the optimising mathematics ends, and the computer simulations begin. The future of economics may depend on finding ways to bridge that gap.
Also published at ft.com.
4 Comments
Julien Couvreur says:
As with all models, there is an important question: how do you know if it tells you something about reality? Why should you trust its conclusion?
Schelling’s checkerboard is useful in that it provides some intuition as to how segregation could happen even if individuals are not racist. But it does not allow much conclusions beyond that (this is the mechanism at work, or even one of the main factors).
To me, a model becomes trustworthy is it reliably predicts a number of surprising events with a good degree of accuracy. How about you, what bar do you apply to consider a model convincing? Does the model of the housing bubble pass that bar?
7th of October, 2012Richard Mischook says:
As a software engineer who originally started university as an Econ major I’m intrigued by the idea of using software to model agents as described here. But as a software engineer I’m also skeptical of the power of these simulations to teach us anything new. My gut instinct is that the outcomes of these models will be determined by the biases and pre-conceptions of the programmers. I could be wrong of course, as I say it’s more of a hunch on my part than a cogent argument. But the anecdotal evidence from the GFC tells me that computer models are more likely to mislead than to inform.
7th of October, 2012Harald Uhlig says:
This article is not only far behind the curve, it is also besides the point. Non-representative agent models have been used routinely in macro since 15 years or more (witness all the computational multi-period OLG models on pension reforms in the 90′s for example, or the work by Krusell and Smith or by Dirk Krueger or … ). And computers have been used far longer than that. The true art always lies in constructing a meaningful model that is appropriate for the question at hand, and that delivers powerful and interesting insights. You need to understand where the results are coming from: simplicity is therefore often a virtue, not a vice (and that is why representative agent models can still be remarkably useful for a range of questions). That principle also serves as a check on the computer output: do I understand what I just calculated? Just because someone turns on a computer and simulates a million agents does not mean that anything of interest emerges. The first lesson when using a computer is “garbage in, garbage out”. That’s why the best researchers in that field work hard on creating interesting models. I am looking forward to, say, the work that Geanakoplos etc is doing: he is very smart, his work is very insightful and I would be very surprised if the selling point of his work won’t be “I can simulate 40 000 agents on my computer”.
11th of October, 2012Harald Uhlig says:
spelling mistake, the last sentence was meant to read: “I would be very surprised if the selling point of his work will be “I can simulate 40 000 agents on my computer”.”
11th of October, 2012