Commentary

3 Oct 2011 by Jim Fickett.

*Jeremy Nalawaik's method of predicting recessions using the concept of a preceding “stall” period has received considerable attention. The methods are quite interesting, and Nalewaik shows that one of his algorithms can give lower overall errors, in predicting economic indicators three to four quarters ahead, than seen in the so-called Blue Chip Consensus forecasts from economists. Much of what has been written about this work, however, comes from authors who are either unable or unwilling to actually read Nalawaik's paper. In particular, recent slow growth in Gross Domestic Income does not, at least in and of itself, support the idea of a coming recession.*

In an earlier post on recession forecasting, I mentioned the paper Forecasting Recessions Using Stall Speeds by Jeremy Nalewaik. This work has received considerable attention in the financial press, but is widely misunderstood. I would like to give an intelligent layman's overview here.

To review, while many people think of the economy as being either in contraction or expansion, Nalewaik proposes that the economy can be in one of three states: expansion, stall, and contraction. A stall period may come in the middle of an expansion or between an expansion and the following contraction. In forecasting, the importance of the stall period is that (1) it can sometimes be identified as it is happening and (2) a contraction is fairly likely to follow.

The paper has two main parts, one about directly measurable features of the data and the other about the construction of models that facilitate forecasting. The practical forecasting problem is considered in some detail. A model is constructed that uses past NBER recession dates, GDI, the yield curve, unemployment, and housing starts; and this model is back-tested using the preliminary data that was actually available preceding historical recessions.

Just looking at the data, with no model-building, one sees that slow growth is much more common in the year preceding a recession than at other times during an expansion.

Consider first the year-over-year change in Gross Domestic Income (recall that GDI is a better indicator of the business cycle than GDP). Here is the YOY change in GDI since 1948, with recessions shaded and a cutoff of 2% growth marked with a horizontal line (click for larger image):

Rates of YOY growth below 2% occur mostly either in or near recessions. With no fancy algorithm building, one can find some interesting empirical probabilities that are of some help for forecasting. So, for example, YOY growth below 2% is followed by a recession within a year approximately 85% of the time. Since GDI growth from Q2 of 2010 to Q2 of 2011 was 1.9%, news articles in the last few months have made much of this particular rule, implying that because GDI (or, in some articles, GDP) growth was low (“below the stall speed”), a recession was therefore very likely. Note however a major caveat – especially in recent years, YOY growth in GDI of less than 2% often happens after the recession, in the middle of an expansion. In particular, in 2003 there was a stall period well after the 2001 recession, and not followed by a new recession for several years.

We may also look at the quarter-to-quarter rate of growth, which is, as expected, more sensitive but also noisier. Here quarterly growth, at an annual rate, of less than 1% is indicative of a stall. Using preliminary data that was actually available to forecasters before historical recessions, we find that 100% of recessions since 1978 showed, in at least one of the four preceding quarters, quarterly growth, annualized, below 1%, and when a quarter showed growth below 1%, a recession followed within a year 54% of the time.

Q2 of 2011 shows the lowest GDI growth in the last year and a half but, though low, quarterly growth, at an annual rate, was 1.3% and does not meet the 1% threshold. Since 100% of recessions since 1978 were preceded by growth less than 1%, growth in Q2 of 1.3% rules out recent GDI readings as predicting recession. Thus the spate of articles about a stall-speed economy prefiguring recession were highly misleading. Nalewaik's data, considering GDI alone, do not, in fact, suggest a coming recession.

This section can be skipped by those not interested in the details of the computation.

Nalewaik considers models for which, within each of three states (expansion, stall, contraction), economic indicators, such as GDI or the unemployment rate, vary continuously around some preferred value, and that preferred value depends on the state. So GDI growth will change a little each quarter, but might, for example, tend towards a value of about 4% in expansions, 1% in stalls, and -1% in recessions. The model also specifies the probability that the economy will transition from any given state to any other state. For example, when the economy is in expansion mode one quarter, it might stay in expansion mode the next quarter with probability 0.75, switch to stall with probability 0.15, or switch to contraction with probability 0.1. Such models are called “hidden Markov”, or “Markov switching”.

Nalewaik hit on the idea of using three states when he developed two-state models (with just contraction and expansion), and found that the low-growth state often ended up including a recession and part of the preceding expansion.

The parameters, such as the favored growth rate during expansions, or the probability of transitioning from contraction to expansion, are stated to be maximum likelihood estimates, meaning that parameters are chosen so that the given data looks as natural as possible (highest probability) in the model. However details are not given. My experience suggests that a technique called the Gibbs sampler might have been used. This is an empirical, iterative process by which one alternates between dividing the quarters of the historical record into the three states using the best parameterization you have so far, and then using that division into three states to improve the parameters. The process can be initialized by using the known NBER recession dates as a starting point.

Multiple applications of the Gibbs sampler usually result in multiple solutions. So in the end you have many different interpretations of the historical record. Averaging over these different interpretations/models, you can get one best estimate of all the parameters, plus a probabilistic guess about the “real” state behind each quarter of historical data. Here is a typical graph showing the latter:

For the most recent recession, to take one example, the probability that we were in the stall state during all of 2006 and 2007 is very high. Then there is a transition period where the stall state becomes less likely and the recession state the more likely interpretation. At the end of the recession the probability that the correct interpretation is “recession” stays high briefly, but then falls to near zero.

A substantial portion of the paper is spent in exploratory data analysis, using different economic indicators, and different initial conditions in the parameter estimation. The general sense coming out of all this is that the data do seem to support a separate stall state, and that stall state occurs primarily before recessions. In many of the trial models, however, the 1990 recession and the 2001 recession do show some sort of soft patch following the recession, which tends to classify with the stall states of previous recessions.

The paper considers many combinations of variable relevant to detecting the business cycle, and settles on

- GDI, quarterly growth at an annual rate
- Unemployment rate, quarterly change
- Housing starts, the quarterly log change, weighted by residential construction as a fraction of GDP
- The yield curve, measured as the 10-year yield minus the 3-month yield

For practical forecasting, a major issue is that most algorithms are developed using historical data that has been greatly revised over time, while actual forecasts must use lower quality early estimates. For the algorithm using the above variables, Nalewaik goes back to the data that was actually available in the first month after any given quarter in order to estimate the state of that quarter. Here are the results:

The model forecasts are quite impressive, with recessions well marked and often preceded by stall periods. However the predictions are not perfect. Note that the stall concept gave no significant advance warning in either of the 1990 or 2001 recessions, and that in 1992 and 2003 there were stall warnings that were not followed by recessions. Still, the real-time identification of stall periods is obviously good enough to be of practical interest.

Besides giving some hint on the state of the most recent quarter, the model can be used to make explicit probabilistic forecasts, since the probabilities of transitioning from one state to another are part of the model. This also can be used to forecast GDI and other economic variables, given their typical values in the predicted states. Nalewaik shows that such forecasts, looking 3 to 4 quarters in the future, are a little better than the Blue-Chip Consensus.

~~DISCUSSION~~