# Estimating Recession Risk Probabilities With A Probit Model

Whenever I update The Capital Spectator Economic Trend Index (CS-ETI), as I did last week, someone usually asks how to interpret the data. In particular, how should we translate CS-ETI’s raw numbers into probabilities for estimating recession risk? One solution is looking at the data through the filter of what’s known as a probit model.

For those who don’t know, a probit model is a form of regression analysis that transforms predictions into a range of probabilities between 0% and 100%. I’ll spare everyone the details of calculation here other than to say that a probit regression is moderately easy to compute in Excel, R, and other software.1 Now it’s on to the task at hand: translating CS-ETI into something more intuitive.

But first a bit of perspective by letting the raw numbers suggest a rule of thumb. History implies that we should think of recession risk as threatening when CS-ETI falls under the 60% mark, which means that less than 60% of the underlying indicators are trending positive (for the definition of “trending” for each indicator, see the data table in this post). A reading under 50% is an even stronger warning and effectively the point of no return. The lone exception since the early 1970s was in late-1989/early 1990, although it can be argued that the brief rebound after dipping under 50% without a downturn was associated with the bounce of optimism that accompanied the end of the Cold War during that period. In any case, the recession was only delayed for a few months rather than averted. The August reading, by the way, was around 76%. Although that’s still well above 60%, it’s been falling lately.

The question is whether there’s an alternative to the heuristic analysis above that provides more specificity and quantitative discipline for evaluating CS-ETI’s signals? Yes, and a probit model shows us the way. Consider the next chart, which transforms the data in the chart above into monthly probabilities of whether a recession is underway in any given month. In other words, CS-ETI is the independent variable and the probit model is using it to predict the state of the dependent variable—the presence, or not, of recession on a month-by-month basis.

It’s all quite straightforward in the sense that we can use NBER’s historical data that labels each month as recessionary, or not. Next, we use the probit model to interpret that history via CS-ETI for estimating where we stand currently. Each month in history is referenced as either a 0 (no recession) or 1 (recession). With some basic econometric modeling, we can regress CS-ETI (or any other set of economic or financial indicators) against that binary history of the business cyle and compute the probabilities of recession risk using the latest data.

As you can see in the second chart above, the fit is rather tight. The current estimate (based on the latest published numbers through August) tells us that the probability of a downturn was quite low—around 1%.

All the usual caveats apply, of course, and so we shouldn’t rely on this measure alone (or any one model) to evaluate the business cycle. That said, I’ve looked at the vintage data (to the extent that I can find it) for the 17 variables used to calculate CS-ETI and the probit model results are similar—close enough to expect that the real-time updates should provide a relatively timely warning when recession risk is on the march.

Still, there’s no substitute for looking at the business cycle from multiple angles, using a range of data and models. Another approach is “nowcasting” the next quarter’s GDP for developing some intuition about the economy’s near-term future, as shown here. Plugging in CS-ETI into a probit model is another view, but there’s no assurance that it’ll always be flawless. Recognizing that limitation, this analysis confirms the message in the raw CS-ETI data, namely: August wasn’t the start of a new recession.

September’s profile, of course, is open for debate. True, an early clue via the ISM Manufacturing Index offers a bit of optimism, but it’s still early. Some analysts have already concluded that the economy is in recession, or that the risk is so high that September’s fate has been sealed. They may be right, but their warnings are still suspect based on the numbers available so far. September’s profile is still mostly a mystery, but not for long.

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^ 1. Any good econometric textbook will outline the mechanics. For example, see pp. 254-257 in the 3rd edition of Robert Pindyck and Daniel Rubinfeld’s Econometric Models and Economic Forecasts.

This post was originally published at The Capital Spectator and is reproduced here with permission.