10yr-3mo Term Spreads and Probit Model Recession Forecasts: Germany, UK, Canada vs. US

For the US, Germany, UK and Canada:

Figure 1: Estimated probability of recession for indicated months based on 10 year-3 month spread lagged 12 months for US (black), Germany (brown), UK (green) and Canada (red). Recession probability from probit model. Source: Federal Reserve via FRED, OECD, NBER, and author’s calculations.

Of course, most of the concern has arisen due to inversion of the 10yr-2yr spread (e.g., Deutsche Bank) As noted in Chinn and Kucko (2015), the 10yr-3mo spread has had more predictive power. However, one can see the divergence in predictions in the US case in Figure 2 below (compared against Germany, UK, and Canada).

Figure 2: Estimated probability of recession for indicated months based on 10 year-3 month Treasury spread lagged 12 months US (blue), for 10 year-2 year spread (brown). Recession probability from probit model. NBER defined recession dates peak-to-trough shaded gray. Source: Federal Reserve via FRED, OECD, NBER, and author’s calculations.

I didn’t have ready access to 2 year government bond yields for the other three countries (snapshot for several G-20 countries as of March, see here), so here are the estimates based on 10 year-3 month spreads. Keep in mind, Chinn and Kucko (2015) find the spread works well for US and Germany in the 1990’s and 2000’s, less well for the other countries examined.

Figure 3: Estimated probability of recession for indicated months based on 10 year-3 month spread lagged 12 months for Germany (blue). 3 month yield is interbank rate. Recession probability from probit model. ECRI defined recession dates shaded gray. Source: OECD via FRED, ECRI, and author’s calculations.

Figure 4: Estimated probability of recession for indicated months based on 10 year-3 month spread lagged 12 months for United Kingdom (blue). 3 month yield is interbank rate. Recession probability from probit model. ECRI defined recession dates shaded gray. Source: OECD via FRED, ECRI, and author’s calculations.

Figure 5: Estimated probability of recession for indicated months based on 10 year-3 month spread lagged 12 months for Canada (blue). 3 month yield is interbank rate. Recession probability from probit model. ECRI defined recession dates shaded gray. Source: OECD via FRED, ECRI, and author’s calculations.

How well do the models fit? One can see that depending on the threshold used, the German  model misses one recent recession (i.e., false negative), and UK model would have given one false positive. And the Canadian model would have signalled the last two recessions with only a very low threshold. The McFadden pseudo-R-squareds are 0.21, 0.33, and 0.37 for Germany, UK, and Canada respectively. The corresponding figure for the US is 0.26, 1960-2022M03 (0.23 for 10yr-2yr, 1976M06-2022M03).

While the current fad is to focus on the 10yr-2yr spread (for the US, see discussion here), Engstrom and Sharpe (March 2022) argue this spread has no incremental predictive power over the near term forward spread (6 month forward 3 month yield minus 3 month yield). Miller (2019) examines many combinations of spreads, and finds for the 1984-2018 period, the highest AUROC (ratio of predicted positives to true positives) at the 12 month horizon is the 10yr-Fed funds and 5yr-Fed funds, followed closely by the10yr-3mo spread.