Quantitative Models for Predicting Recessions Based on Yield Curve Spreads

The Probit Model: A Primer

The relationship between the yield curve and recessions is not just a qualitative observation; it can be quantified. The most common tool for this is the probit model, a type of regression analysis used to model a binary outcome (in this case, recession or no recession). The model takes a set of input variables, including the yield curve spread, and produces a probability of the outcome occurring. The output of a probit model is a probability score between 0 and 1, which can be interpreted as the probability of a recession occurring within a given time horizon (e.g., the next 12 months).

Building a Recession Probability Model

A simple probit model for recession forecasting can be built using just one input variable: the spread between the 10-year Treasury yield and the 3-month Treasury yield. This spread has been shown to be one of the most reliable predictors of recessions. The model is estimated using historical data on the yield spread and NBER-defined recession dates. The output of the model is a formula that can be used to calculate the probability of a recession given the current level of the yield spread. For example, the model might show that a yield spread of -50 basis points corresponds to a 60% probability of a recession in the next 12 months.

Interpreting the Model's Output

The output of a probit model should be interpreted with caution. It is a probability, not a certainty. A high recession probability does not guarantee that a recession will occur, and a low probability does not guarantee that it won't. The model's output should be used as one input among many in a trader's decision-making process. It is also important to be aware of the model's limitations. Probit models are based on historical data and may not be as effective in predicting recessions in a changing economic environment. For example, the unprecedented level of central bank intervention in recent years may have altered the historical relationship between the yield curve and the economy.

Enhancing the Model

The simple probit model can be enhanced by adding other economic variables. For example, a more complex model might include variables such as the unemployment rate, inflation, and stock market performance. The inclusion of these variables can improve the model's accuracy and provide a more nuanced view of recession risk. However, there is a trade-off between model complexity and interpretability. A more complex model may be more accurate, but it may also be more difficult to understand and interpret. For most traders, a simple and transparent model based on the yield curve spread is a good starting point.