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Everything Is Under Control

Can control theory save the economy from going down the tubes?

Brian Hayes

Second Guessing

Viewing economics through the lens of control theory amounts to treating the economy as a machine. The machine may be an unwieldy one—something like a heavily laden supertanker, slow to start and stop, difficult to steer—but it still obeys deterministic laws of motion. In particular, a machine never tries to second-guess or outwit the controller. But a human society is not a machine.

In 1976 Robert E. Lucas, Jr., of the University of Chicago presented a caustic critique of mathematical modeling as a tool for setting economic policy. Models, he said, predict the effect of policy changes without acknowledging that rational agents will alter their behavior under the new policies in ways that invalidate the assumptions on which the models were built. For example, if everyone knows (or can infer) the rule by which the Federal Reserve sets interest rates, borrowers and lenders will anticipate any changes in rates, adjusting their behavior in ways that tend to neutralize the effect of the policy change. It’s as if the supertanker, with a mind of its own, could change the shape of the rudder in order to resist commands from the helm.

The Lucas critique attacks not just control theory and mathematical modeling but any reasoned strategy for managing an economy. The most extreme form of the thesis holds that if a policy can be predicted, it will be undermined and rendered ineffective. Thus the attempt to regulate the economy becomes a futile spiral in which people adjust to new policies, the policies are adjusted to account for those adjustments, and so on.

Within the context of control theory, however, the kind of circularity cited by Lucas is not anything out of the ordinary. In any system with closed-loop feedback control—animate or inanimate—the controller affects the state of the plant, which in turn affects the state of the controller, which affects the plant, and so on. The circularity is an essential part of the design and does not lead to undefined behavior or an endless round of readjustments. Assuming that stability criteria are satisfied, the combined system of controller and plant converges on some definite and predictable equilibrium state.

Model of the U.S. economy created by Ray C. FairClick to Enlarge ImageAnother branch of mathematics reaches a similar conclusion from somewhat different premises. In game theory, a contest like the one between a regulator and a population of economic agents generally has a fixed point (called a Nash equilibrium), where neither party can gain by making further changes in strategy. This idea has developed into a theory of “policy games,” which strive to identify those economic models that remain controllable even when the players don’t wish to be controlled.

From a more pragmatic point of view, it’s not clear that real-world economic agents are as strongly motivated to “game the system” as Lucas supposed. Ray C. Fair of Yale University, using a model of the U.S. economy based on decades of empirical data, tested variations of the model in which agents could look ahead and base their behavior on predictions of future regulatory policies. The results suggest that such activity is not common in the real economy. Another series of studies by Glenn D. Rudebusch of the Federal Reserve Bank of San Francisco reached a similar conclusion.

Whatever the merits of the Lucas critique, it had the collateral effect of dampening enthusiasm for applications of control theory in macroeconomics. Research in the area did not end entirely, but the undertaking lost momentum, and control theory has never again been fully in the mainstream of economic thought. Nor has it become a common tool of those who put policy into practice.

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