Milton Friedman first proposed his “plucking model” of the economy back in 1964. In doing so, he said that any economy is sort of mean reverting, in that any setback it might experience, a recession or some such, is merely a temporary deviation from the prior established trend. In his own words (NBER, 44th Annual Report):

Consider an elastic string stretched taut between two points on the underside of a rigid horizontal board and glued lightly to the board. Let the string be plucked at a number of points chosen more or less at random with a force that varies at random, and then held down at the lowest point reached…In this analogy, output is viewed as bumping along the ceiling of maximum feasible output except that every now and then it is plucked down by a cyclical contraction.

Taken a step further to the natural interest rate theory, this would mean that booms and their busts must importantly be *symmetrical*. The larger the decline, the more the natural rate changes so as to produce an equal and opposite recovery which over time brings output back to the level where it would’ve been had the temporary intrusion of the business cycle not interrupted.

The business of monetary and fiscal policy is therefore easily established – do everything possible to reduce the seriousness of the contraction before standing back and watching the economy do its thing.

Simple and elegant, every postwar recession in the US had followed this pattern. So much that in 1993, after the conclusion of the 1990-91 recession, Friedman declared it unequivocal. He even wrote another paper updating the theory’s progress, testifying to its purported evidence and power:

Some twenty‐five years ago, I suggested a model of business fluctuations that stresses occasional events producing contractions and subsequent revivals rather than a self‐generating cyclical process. Evidence for the past quarter century, like evidence presented in my earlier paper for a longer period, supports the view that the model is a useful way to interpret business fluctuations and has sufficiently important implications to justify further empirical work for both the United States and other countries.

But then the Great “Recession” which doesn’t seem to have been the usual recession.

Before getting to that, we’re going to detour first into some math and econometrics. Sincere apologies, but this is necessary to understand how Economists (capital “E”) think about these things; therefore, we can better analyze what and why they believe what they believe (or why they might refuse time after time to believe their own lying eyes).

We have to start with something called a *unit root*. This is actually a mathematical/statistics term. Since we’re dealing with Economics, that’s not unusual. Economists spend their days buried under and inside equations rather than detecting and evaluating real processes across the real economy with their minds open. Remember, Treasury and bond yields down the curve to these people represent a series of one-year forwards just so that they can be fitted into this sort of regression-focused econometrics.

The math actually serves to limit imagination.

Technically, an equation that describes, say, a time series can be written out as a series of monomials. Each of these corresponds to a “root”, which, if it equals 1, means it is a “unit root.”

In econometric time series models, these things can be downright toxic – not a very good reason to hate them as Economists seem to. Rather than dismissing the very possibility, perhaps they should be given to more serious thinking about how it might discredit the model.

For variables like employment or even inflation, the presence of a unit root means the future would be completely unpredictable. Defined as a non-stationary process, or difference stationary, there would be no way of modeling the future based on the past because a unit root would lead to an entirely new future that wouldn’t revert predictably to a deterministic path.

Let me show you what I mean. Using the simplest possible model with a single monomial, we’ll assume we are modeling an economy’s *output gap*. The time series equation is as follows:

V is the output gap at time period n, a function of C, the constant which we’ll set at zero (because the output gap is “supposed” to be zero), plus some value for a potential shock then finally adding an error accounting for some minimal potential for randomness (which we’ll conveniently ignore here for the sake of simplicity).

All the equation really says is that when there is no shock the output gap is zero, therefore the economy behaves predictably as defined by its prior trend. But, if a shock is introduced, then the root highlighted in red comes into play. Any value less than 1 and this means the process is* stationary* or *trend* stationary – in that over time it converges to the prior trend (C) with an output gap of zero.

Here’s what it looks like, and you can see that it looks like every postwar recession up until the Great “Recession.”

Even though the recession may not have been anticipated, the optimal output forecast would still be for a zero output gap. Over time, as Friedman’s plucking model, the shock shrinks back down to nothing and the economy gets back on trend. How much time it takes depends upon the root, in this case I’ve arbitrarily set it at 0.5. The closer to 1, the longer it would take for recovery (which implies other factors beyond our overly simplified model).

Stationary processes like these imply that any shock must – by definition – be a *temporary* one. There can be no other set of outcomes.

Watch what happens, though, if we set the root to exactly 1 – introducing this *unit root* into this simple equation. Very, very different set of results:

A unit root here means that the process is non-stationary (or difference stationary) and therefore in terms of this very simple output gap model the shock in time period 6 couldn’t have possibly have been temporary. A value of 1 or greater means a permanent change (aside, in statistical terms this would mean the entire statistical distribution has changed; mean, standard deviation, the whole works) that wouldn’t have been predictable given the limitations of the future presumably looking like the past.

If the non-stationary model introducing a unit root for our output gap looks familiar to you, it’s because it really should be:

Intuitively, however, Economists are generally right to point out how most variables wouldn’t appear to be able to come with one. The unemployment rate, for example, doesn’t just go up and stay high forever – there aren’t any cases in any time period where that might be a realistic possibility. In each and every business cycle, it leaps as due to the recessionary shock and then comes back down.

Policymakers used to believe that it followed a stationary process pulled (mean reverting) toward its potential defined as “full employment” (curious, then, how they no longer want to define full employment given the appearance of what sure seems to be unit roots in more variables than ever imagined).

While the unemployment rate itself obviously doesn’t have a unit root, perhaps the labor force like the output gap does – leaving the unemployment rate which discards this feature unreliable (which the Fed just recently admitted).

To econometricians, this sort of thing should have been impossible. Even now, many perhaps most remain convinced there can be no unit roots in any of their models. Yet, evidence. Evidence. EVIDENCE.

For what? *Non-transitory* economic shocks. Meaning permanent. That’s really what we are talking about in both worlds – the real and the statistical. A unit root again implies the possibility of *permanent* shocks (which could be good as well as bad) when it has been totally taken for granted that any shock would only ever be temporary.

Why?

Remember how statistics work: the math is limited to the past in order to project the future. A permanent shock violates this assumption because, by definition, it introduces some factor which must *not* have existed in the past; or, alternatively, in the *chosen set of factors* from which to begin modeling from that past. For econometricians, this is abhorrent.

Over here in the real world, hey, this is a dynamic place which is always changing in ways people in the past could never have conceived. And if you aren’t paying full attention to everything important about the past, then double bad on you.

For one thing, there’s this focus on the post-war era. That’s just not long enough to have developed a substantial, significant data set conclusively defining temporary versus permanent shocks. Up until 2007, there hadn’t been permanent shocks observed, at least not since the Great Depression.

But, if we’re arbitrarily confining our data set to just the postwar period, there has to be some legitimate reason for doing so – otherwise it’s dangerous cherry picking. The most common reason is limitations about the data itself; detailed or hard figures didn’t exist before Economists made concerted efforts to create them following WWII.

One of the most informative papers on the subject of unit roots in economic data modeling I’ve come across is this one published in October 1989 (I like both its work as well as the beautiful and appropriate simplicity of its abstract). The two authors’ conclusions, despite 42 pages of work, modeling, equations, and commentary is equally simple.

There’s just not enough data to know for sure whether root units appear, should appear, or whether even we might care that they can or could. But Economists have made hard assumptions anyway.

Not surprisingly, the literature on persistence has become intertwined with recent controversies over the empirical plausibility of two important classes of statistical univariate time series models: trend stationary and difference stationary models. Ultimately, proponents of the view that shocks to real GNP are persistent must build their case on the empirical plausibility of the hypothesis real GNP is difference rather than trend stationary or, in other words, that real GNP has a unit root.

And while the authors believe that possibility very small, they just can’t say with any degree of certainty (here’s the killer):

…it seems clear that economists ought to be extremely skeptical of any argument that purports to support one view or the other. Simply put, it’s hard to believe that

a mere 40 years of data contain any evidence on the only experiment that is relevant. [emphasis added]

We are finally verging on the “good luck” territory espoused by several Economists in trying to explain the “good times” which might have coincided with the lack of a unit root in the econometric equations.

In other words, the “good luck” theories actually pertained to the curious but, for Economics, unexplained lack of monetary shocks as had been quite common in the *prewar* era – and the depressions rather than recessions which had typically accompanied them. Thus, in one very, very important sense, *confining the data set to just the postwar experience* these statistical models all assume that *such monetary interruptions can only have been a thing of the past*.

Well, August 2007 more than put that idea to rest – in the real world.

But, *what if* the lack of a unit root – meaning shocks can only be temporary interruptions – had instead wrongly assumed this function of “good luck” in the money system? Put another way, couldn’t we better explain this by viewing the world from the eurodollar perspective? I (obviously) think so.

During the exclusive postwar era, when shocks were temporary (no unit roots), the global monetary system which econometrics paid no mind about was expanding vigorously precluding the kind of monetary interruption like those in the prewar period. To many, this was “good luck” while in the models it wasn’t featured at all.

The eurodollar era from roughly the mid-fifties to August 2007, this same postwar period, it was *an unrecognized island of monetary stability* (or, at worst “too much” money, as during the Great Inflation, never “too little” until the era’s end) which neither data nor interpretation paid any attention to. Shocks were assumed to be temporary because they had been temporary, but assumed by the math to be so only in ignoring this other major factor taking place outside of every mainstream view.

That island of stability, good luck, ran out and – a ha! – *now* it looks like a unit root or maybe several have showed up in the numbers, a lot of numbers, and all across the world, at exactly the same time bad luck, the unseen, unappreciated end of monetary stability, appears to have taken over.

But, and this is the point, if you still cling to the belief that post-war data is the only data which matters, defining for you the entire realm of possibilities (which the 1989 paper told you to be wary about), and that permanent shocks, like unit roots, are impossible because it foils econometrics by leaving the future so unpredictable (to the models), then the specious argument which follows is entirely one of econometrics than real economy.

And that, my friends, is how we end up with an unending series of absurd, idiotic never-ending QE’s that never work leaving for the whole global economy such obvious lack of recovery that to all these dangerously flawed models just can’t be possible.

The shock, the *monetary* shock, sure seems to have been *permanent* after all rather than impossible as determined by a data set, and imaginations, all too narrow. All the evidence says so (only starting with the interest rate fallacy). For Economists and econometrics, they have no eurodollar to explain *everything*; none now, and none during the pre-2007 postwar data mining.

The eurodollar system does exist, however, and has for more than half a century whether it ever made it into a model or not. The models don’t confer reality on the real world, they are overly simplified views of it in order to make predictions about the future. The fact that it’s been ignored only begins to explain these mathematical (as well as market) conundrums, why the models never work. Insert Stan Fischer apology here.

The increasingly established unit root of the *missing* monetary monomial.

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