## The Fed has raised interest rates multiple times this year, leading to considerable discussion about the possibility of an inverted yield curve

An inverted yield curve occurs when the shorter end of the curve is yielding more than the longer end and is normally seen as a leading indicator for a recession. The below chart shows the 10-Year Treasury Yield (the long end of the curve) minus the 3-Month T-Bill Yield (the short end of the curve) over time.

This spread is normally positive but has inverted before each of the last three recessions. This pattern lends credibility to the relationship between an inverted curve and an economic downturn.

To quantify this phenomenon, Jonathan Wright, at the time a Fed Economist, created regression models to estimate the probability of a recession in the next four quarters, using the spread between the 10-Year and the 3-Month as the predictive variable [1]. Using the structure found in his paper, we created a logit regression model [2], also with the aim of estimating the probability of a recession in the next four quarters. Our first model (in the chart below) estimates the probability using the spread between the 10-Year Treasury and the 3-Month T-Bill as the only explanatory variable.

This model has been a relatively reliable predictor of past U.S. recessions; there have been spikes in probability without a recession but there has not been a recession without a spike in probability. The model is currently stating a 15.4% chance of a downturn in the next four quarters. This model is similar in outcome to the recession probability model published by the New York Fed (below), which is currently stating a 13.6% chance of a recession.

However, one of Wright’s conclusions is that these types of models can be improved upon by including the level of the federal funds rate as an explanatory variable alongside the spread between the 10-Year Treasury and 3-Month T-Bill. Recreating our logit model while controlling for the average federal funds rate in each quarter produces the following chart.

This model states only a 0.35% chance of a recession in the next four quarters, lower than the models that do not control for the federal funds rate. Wright concludes that this model is a statistically better fit than models that omit the federal funds rate.

Although models that include the federal funds rate may be a statistically stronger fit, one thing to consider is that the federal funds rate before each of the last few recessions has been falling. In other words, the economy has been increasingly intolerant to higher federal funds rates. Therefore, while one is statistically superior, it might be useful to take both model types into consideration.

## Based on this type of yield curve analysis, regardless of model type, it is unlikely that there will be a recession in the next four quarters.

*Sources & Citations:*

[1] Wright, Jonathan H. “The Yield Curve and Predicting Recessions.” Finance and Economics Discussion Series. 2006.

[2] A regression model adapted to accommodate a binary outcome. In this case “0” means no recession and “1” means recession.