Tuesday, October 25, 2011

NGDP targeting and control theory

The economists Scott Sumner, Karl Smith and David Beckworth, among many others, have been pushing for the past two years a branch of macroeconomics sometimes called quasi-monetarism or market-monetarism. The group of people are all bloggers and, unusually, are not so prominent in their fields. Instead, they've grown in prominence since the financial crisis in advocating a policy that the Federal Reserve can undertake to provide stimulus beyond the zero interest rate bound: NGDP targeting.

The simplistic view of this can be looked at from the equation of exchange:
 MV = PQ
Where M is the supply of money, V denotes the velocity of money, P is the price level and Q is the quantity of goods sold. Currently, the Federal Reserve attempts to set expectations of P by influencing M. What Market Monetarists propose is to target the total product PQ, equivalent to nominal GDP; they argue with some good justification that it is both more beneficial to target the nominal GDP growth rate to provide stimulus during a deflationary period where interest rate signals no longer mean anything. As an added bonus, the Fed saying "I want to see 3 percent nominal growth this year and will print money until I see it" is a helluva lot easier to understand than "we would like the chain-type weighted core basket of goods excluding food and fuel to rise between 4-5% this year." The downside, according to market monetarists, is more monetary supply volatility, since inflation responds slower than NGDP.

There are a whole lot of macroeconomic arguments for and against NGDP targeting. Even though I've been reading about them for a while, my own grasp of the concepts are fuzzy at best and to be perfectly truthful, I haven't had the time to think them through on my own. (Even though the financial crisis refocused my attention on macroeconomics, my passion has always been for sci/tech policy, trade economics and development anyhow). The best places to look if you are interested in the concept are Scott Sumner's website, The Money Illusion and Karl Smith's website, Macro and Other Market Musings.

The reason I'm bringing this up is that as people talked about the concept, I began to think more about the implementation - specifically, as it would relate to analog control theory. At its face, it seems as if NGDP targeting has a remarkable similarity to a system with unstable signal input and analog feedback control.

If we construct the macroeconomy as a single-input-single-output (SISO) system in Laplace-transformed space under an NGDP targeting regime, it might look something like this:
Apologies for horrifying MS paint graph. Of course, this assumes that each transfer function for the Federal Reserve (the signal transducer/sensor), the FOMC (the final control element) and the Macroeconomy (the system) is time-invariant and linear in response. While this is obviously not true of the macroeconomy, for the purposes of modeling we can actually assume that the response time of the macroeconomy dominates the system and that the Fed and FOMC act instantaneously relative to the economy as a whole.

If we assume that the equation of exchange holds, then the macroeconomy is, taking NGDP relative to the money supply, (i.e. d(PQ)/d(M)) we can say that it is a first order system with a variant term dependent on the velocity of money, which is the primary input that disrupts the system. Since the macroeconomy also has the most significant response time in the system, it wouldn't be a stretch to then apply a simple first-order dead-time (FODT) model to it.

At that point, we now have a completely tractable and well-studied control theory problem: a series of time-invariant linear controls in a SISO FODT system. So why not think about a simplistic PID-style controller to replace the decision making process of the Federal Open Market Committee?

In fact, I think that it's best to point out that integral and derivative control would probably be incredibly bad for the macroeconomy. Derivative control is subject to dangerous feedback spirals, particularly when the signal is noisy - and lets face it, it doesn't get much more noisy than this. Integral control is also a bad idea, since monetary policy is only one input to the system, and integral controllers tend to be pretty dumb about applying the same medicine even if it doesn't affect the underlying structural problem.

In the end, that simply leaves proportional control, a simple Laplace-space constant multiplier for the signal. What's funny is that P control most closely resembles what the Fed already does. Milton Friedman once famously said that monetary policy could be carried out by a computer. Although he was referring to monetary neutralism, it seems a neat little idea that it might well apply to NGDP targeting as well - although how in hell you'd figure out how to tune that controller's proportional term I have no idea.

And obligatory disclaimer: no, this is not a call for a Ron Paul style abolish the Fed platform, it's merely an idle exposition of engineering applied to economics. I would rather not have another situation where we have to ask J.P. Morgan to bail out the US government, or to ask J.P. Morgan to bail out the banking system.

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