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Do central banks use some form of engineering-style PID control systems/feedback loops to implement monetary policy?

I'm an electrical engineering student taking microeconomics/macroeconomics and a lot of it, at least in terms of government policy to control inflation and interest rates, seems applicable to control systems engineering. However, I can't find a great deal of hard literature about it.

Just as a for instance, one could use PID control to set an output, say inflation rate, to follow a specific course or remain steady given certain inputs, say GDP or interest rates or productivity, and given external disturbances, say Brexit. And even if the controller can't prevent catastrophes altogether, it can dampen the response so that sudden and jerky crashes are smoothed out.

Why or why not does economic policy use established control theory? If it does, what applications can this be seen?

Thanks in advance!

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Economists have been exploring control theory applications to macro economics for decades. For example, here is a 40 year-old research paper written in 1976 on the topic.

top of page 2 (also numbered 171)

In the past decade, a number of engineers and economists have asked the question: "If modern control theory can improve the guidance of airplanes and spacecraft, can it also help in the control of inflation and unemployment?"

Non-linear adaptive human behavior, uncertainty and governmental decentralization of control (i.e., democracy) are the main reasons I believe control theory has not become a more common tool for policy makers. Economics is simply not an exact science. Whereas engineering is more so. So control theory is more useful in the engineering discipline.

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  • $\begingroup$ Makes sense, sounds like a good research subject though. Thanks! $\endgroup$ – Charles Clayton Oct 23 '16 at 19:39
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For a PID system to work, you need to be (at least approximately) correct about the relationship between the variables you are trying to manage. Unfortunately the relationships between macroeconomic variables as predicted by mainstream economics has such a poor correspondence with reality, that any PID system based on these theories is doomed to fail.

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Economists use optimal control both in microeconomics and in macroeconomics. Your question is about economic policy in particular, but policy decisions can be guided both by micro and macro models.

Macroeconomics

Central banks do use both simple feedback loops (think Taylor rule) and optimal control analysis to guide decisions. There is this Federal Reserve note from 2014 with introductory information and some references. It describes FRB/US model, which helps find the optimal path for the federal funds rate to minimize a given loss function.

Microeconomics

Microeconomic models can also guide policy decisions, for example, there is an active literature on oligopoly from optimal control theory perspective, which historically focused on advertising (e.g. this survey from 1977). These can be used to predict behavior of agents on micro level and motivate policy decisions as well.

Microeconomics even contains a nice extension of optimal control to a setting with multiple decision-makers called differential game theory, which I will attempt to loosely describe as non-cooperative optimal control.

These models are further from policy making, but more of "exact science" type. Searching this stackexchange for "optimal control" brings up some relevant results too.

Drawbacks

Speaking of Taylor rule, John Taylor and John Williams in this 2010 paper argue against complex rules in favor of simpler ones. They mention the more obvious problems of measurement error and unobservables, which we have to make assumptions about: expectations, learning etc. However, they also state that simpler rules have advantage of working in a wider set of settings in practice:

"One potential shortcoming of the optimal control approach is that it ignores uncertainty about the specification of the model. Although in principle one can incorporate various types of uncertainty to the analysis of optimal policy, in practice computational feasibility limits what can be done. As a result, existing optimal control policy analysis is typically done using a single reference model, which is assumed to be true." (page 29)

The paper has other references and history of the topic.

In the same note by Federal reserve there is also a warning:

"These models are by necessity an abstraction of a much more complex economic reality, and hence the actual strategies followed by the Federal Reserve and other central banks necessarily retain an important judgmental component."

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A small addendum. Lars Peter Hansen and Thomas J. Sargent wrote the book "Robustness", which is an attempt to apply robust control to economics. They treated robust control from a game theoretical perspective.

In general, ecomics uses optimal control theory, which was the state of the art in the 1960s. The state of the art in the 1990s control theory (when I last worked in the field) was robust control, which fairly explicitly rejected the optimal control methodology.

Robust control introduced the notion of model error. (The game theoretic approach used by Hansen and Sargent attempts to emulate uncertainty via game theory, but the equivalence between model uncertainty and the game theoretic approach breaks down for nonlinear systems.) Without taking into account the reality that our models are incorrect, optimal control strategies tended to fail. A test pilot was killed by a defective optimal controller, and certification boards barred such controllers from aircraft. This killed optimal control as a strategy for control design.

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