Bonds: Probit Models Predict Probability Of Recession

There was much ado over Greenspan's recent comments that there is a 33% chance the U.S. economy will enter into a recession later this year. The Fed seemed to be caught off guard by these comments, and Bernanke testified before Congress that The Fed was still concerned about inflation and the economy is in good shape. Why would Greenspan make such remarks?

We believe it is highly likely that Greenspan's forecast is based on probit models designed by The Fed. For those of you who aren't familiar with a probit model, we will look at the following definitions of probit. Wikipedia's definition is: "In statistics, a probit model is a popular specification of a generalized linear model, using the probit link function. Probit models were introduced by Chester Ittner Bliss. Because the response is a series of binomial results, the likelihood is often assumed to follow the binomial distribution." About Economics defines probit as: "An econometric model in which the dependent variable yi can be only one or zero, and the continuous independent variable xi are estimated in:

Pr(yi=1)=F(xi'b)

Here b is a parameter to be estimated, and F is the normal cdf. The logit model is the same but with a different cdf for F."

For those who still don't know what a probit model is, let's just say it is an econometric forecasting model. Probit models have been used by The Fed to forecast recessions. These models are based on the slope of the yield curve and have been very reliable in forecasting periods of economic weakness. When the 90 day T-Bill yields more than the 10 Year treasury bond, the model views this as a negative development for the economy. The chart below shows the history of the 10 Yr vs. the 90 Day T-Bill for the last 20 years.


Jonathan Wright from the Federal Reserve Board's Division of Monetary Affairs developed a probit model that measures the spread between the 3 month T-Bill yield and the 10 Year Treasury yield. It also looks at the general level of Fed Funds. He has written a working paper entitled "The Yield Curve and Predicting Recessions" which compares 4 different versions of the model. He concludes that measuring the spread between the 3 month T-Bill and the 10 Year Treasury as well as including the level of Fed Funds is the best of the 4 approaches for predicting recessions. The results of the model are shown below. The number at the right is the probability of a recession and the red areas show periods of economic weakness. As you can see, this model has had a very close correlation when predicting periods of economic weakness in the past without giving false signals.


Griffin Kubik, a securities firm in Chicago, replicated this model. The model is currently saying there is a better than 50% chance of a recession in the next 4 Quarters. We have seen other models projecting as high as a 95% chance of recession. Some of these other models are based on the spread between the 1 Year T-Bill and the 10 Year, without factoring in the general level of interest rates. Wright enhanced these earlier models by including Fed Funds as a proxy for interest rates. It seems likely that Greenspan is using some variation of one of these types of probit models. Perhaps he has enhanced Wright's model with some other variable. Although each of these models project different probabilities for a recession, they all agree that the longer The Fed keeps the yield curve inverted, the greater the probability our economy will enter a recession by the end of the year. The chart below shows the current estimation of the probability of a recession using Wright's model. Remember the probability was only at 20% when the chart above was created.