Is the business cycle a cycle?

Modern "business cycle" models used by mainstream macroeconomists are, for the post part, not actually models of cycles. When we think of a "cycle", most of us think of something like this:



This is a wave, also known as a harmonic function. When things like this happen in nature - like the Earth going around the Sun, or a ball bouncing on a spring, or water undulating up and down - it comes from some sort of restorative force. With a restorative force, being up high is what makes you more likely to come back down, and being low is what makes you more likely to go back up. Just imagine a ball on a spring; when the spring is really stretched out, all the force is pulling the ball in the direction opposite to the stretch. This causes cycles.

It's natural to think of business cycles this way. We see a recession come on the heels of a boom - like the 2008 crash after the 2006-7 boom, or the 2001 crash after the late-90s boom - and we can easily conclude that booms cause busts.

So you might be surprised to learn that very, very few macroeconomists think this! And very, very few macroeconomic models actually have this property.

In modern macro models, business "cycles" are nothing like waves. A boom does not make a bust more likely, nor vice versa. Modern macro models assume that what looks like a "cycle" is actually something called a "trend-stationary stochastic process" (like an AR(1)). This is a system where random disturbances ("shocks") are temporary, because they decay over time. After a shock, the system reverts to the mean (i.e., to the "trend"). This is very different from harmonic motion - a boom need not be followed by a bust - but it can end up looking like waves when you graph it:



See? Kind of looks like waves, but actually is something completely different. The fact that peaks and valleys seem to alternate is not caused by "restorative forces" like a spring, it's just a statistical property of the randomness of the shocks. (Aside for nerds: Yes of course it's possible to write down an AR model with oscillatory behavior, but this isn't what's done in any macro model I've ever seen.)

So in other words, most modern "business cycle" models assume that the "cyclical" appearance of the business cycle is an illusion.

When I first realized this in grad school, I scoffed. But in fact, economists might have good empirical reasons for thinking that what we're looking at is not a wave. Harmonic motion is inherently periodic; it repeats at regular intervals, while the fake cycles of a trend-stationary AR-type process generally do not. You can look at a time-series (such as "detrended" GDP) and look at how periodic it is, by looking at a Fourier Transform or spectral density plot. Real cycles will show up as spikes or bumps on the spectral plot, while most AR-type processes will show up as flat lines or exponential decays - basically, garbage.

And it turns out that when we look at business cycles this way, we can't see a wave. One reason is because our time series are just really short - we've only been measuring things like GDP since WW2, and certainly nothing much longer than a century...and usually at monthly or quarterly frequencies. That's not a lot of data. But the other reason is that the things we call "recessions" don't seem to come at any sort of regular interval. Just take a look (the gray bars are official recessions):



Also, there's the fact that the picture above is just one kind of "detrending" (a Hodrick-Prescott Filter, invented by Ed Prescott of "Real Business Cycle" fame). Other assumptions about the trend will lead to other frequency distributions. Different trend assumptions basically redefine the phenomenon of the business cycle.

(In addition, the "business cycle" might actually be several different types of phenomenon! GDP might go up and down for a number of different reasons (Robert Lucas now believes this). . If some of those reasons are periodic and some aren't, it will make it difficult to extract the signal from the noise, especially if the periodic cycles have very long periods. For example, some people now think that there are "business supercycles" that take much longer than what we usually call the "business cycle", and which are periodic. My advisor, Miles Kimball, is very interested in this idea. But of course, very long cycles make our lack-of-data problem much, much worse.)

But in any case, there was one famous literary economist who claimed that booms lead inevitably to busts. This was Hyman Minsky. Very few macroeconomists followed Minsky's line of thinking, but a few did, and even in the modern day there are some who do. Steve Keen is one of these.

Keen is currently constructing a software tool that allows people to make simple business-cycle models. These are not "microfounded" models of the type normally published in mainstream economics journals (DSGE models). Instead, they model aggregate economic variables directly, using ordinary differential equations. The tool, appropriately, is called "Minksy" (here is a link to the Kickstarter page for Minsky).

True to its name, Minsky pops out business cycles that are true waves. See here for a video of these cycles. Sure enough, booms cause busts and busts cause booms.

But what are the prospects for tools and models of this type to forecast the business cycle? Well, I have to say, as far as I know, the prospects are not good at all, for reasons listed above. The actual business cycle does not look periodic (except possibly at many-decade-long frequencies), so "cycles" of the type produced by the Minsky tool - or at least, of the type shown in the videos - seem highly unlikely to have predictive power in the real world (and predictive power is precisely what modern macro most sorely lacks!).

But even so, I personally am very fond of the idea that booms cause busts - that the business "cycle" is not just a statistical illusion. My gut tells me that this is really going on. But business cycles don't look periodic! They don't look like waves. So maybe there is another type of "restorative force" acting on the economy, causing some kind of non-periodic cyclical motion?

There are mathematical models that have this property. In particular, I'm thinking of Hidden Semi-Markov Models, or HSMMs. In an HSMM, there are two "states" of the economy - a good state, and a bad state. Transitions between these states are abrupt and sudden, rather than smooth as in a harmonic wave. Also, these transitions happen randomly, unlike the predictable periodic motion of waves. But still, booms cause busts! Because in an HSMM, the likelihood of a transition increases as the time since the last transition increases. In other words, the longer your economy stays in a "boom" state, the bigger the chances that you're about to suddenly experience a crash and a transition to a "bust" state.

HSMM's capture some of my own intuition about business cycles. The idea of two different "regimes" definitely fits with the notion of the "balance sheet recession", in which people's behavior toward debt shifts quickly between "borrowing mode" and "saving mode", and the likelihood of shifting into "saving mode" is higher when you've accumulated more debt from being in "borrowing mode" for longer. It also fits loosely with the idea that the regimes could be linked to financial markets, since financial market models often have "bull" and "bear" regimes; usually these are modeled by a Hidden Markov Model, which is a bit different, but an HSMM is not too far removed from that.

Anyway, I'd be interested to see people pursue Minsky's alternative concept of business cycles by trying out models like that. Here, for anyone interested, is a good summary of the technical particulars of Hidden Semi-Markov Models.


Update: A commenter asks whether an HSMM could really "explain" business cycles. Good question! Well, it depends on what "explain" means. If you want to describe business cycles in terms of more general classes of economic phenomena, then you'll need to microfound the model in some way (of course, if business cycles turn out to be emergent, then this will not be possible to do). If business cycles can be microfounded, that will almost certainly improve forecasts, too. And if you want to offer policy advice, e.g. on how government could act to damp out business cycles, you'll need some assumption of structural-ness. so my suggestions in this post just apply to people who want to forecast (i.e. predict) business cycles based on observations of aggregates.

Update 2: Commented ivansml finds a paper that tried the HSMM approach in 1994! The paper was published in the Journal of Business and Economic Statistics (a publication of the American Statistical Association).