ChatGPT:
Test the hypothesis that recessions usually start 6 to 18 months after the fist rate cut by the Federal reserve after a period of extended tightening of interest rates. If true provide a timing model to predict the next recession after the September 2024 rate cut. Provide a train of though to the process.
ChatGPT said:
Thought for 24 seconds
Here’s how we can test and model the “6–18-month lag” hypothesis:
1. Identify Fed “first cuts” after tightening
Several well-documented episodes of extended Fed tightening ended, and the Fed then began cutting rates (“first cut”). A convenient summary identifies seven such “loosening cycles” since 1980: October 1984, June 1989, July 1995, September 1998, January 2001, September 2007, and July 2019 treasurefi.com.
2. Match to NBER recession onsets
Of those seven cycles, four were followed by NBER-dated recessions:
3. Compute historical lags
Lags (in months): {13, 2, 3, 7}
- Mean ˜ (13 + 7 + 3 + 2) / 4 = 6.25 months
- Median = (3 + 7)/2 = 5 months
- Standard deviation ˜ 4.3 months
Only two of the four (1989 and 2019) fall within 6–18 months, so the hypothesis holds in 50% of these cases.
4. Fit a simple predictive model
A normal approximation based on these four observations:
Lag~N(µ=6.25, s=4.3)\text{Lag} \sim \mathcal{N}(\mu=6.25,\ \sigma=4.3)Lag~N(µ=6.25, s=4.3) Truncated at zero, this yields:
- Point estimate ˜ 6.3 months
- 68% confidence interval ˜ [2, 10.6] months
- 95% interval ˜ [0, 14.9] months
5. Apply to the September 2024 first cut
Assuming the Fed’s next “first cut” comes in September 2024, our model implies:
- Most likely recession start: ~6 months later ? March 2025
- Reasonable window (68%): between ~November 2024 and July 2025
- Full range (95%): up through March 2026, though with rapidly diminishing probability beyond mid-2025
Conclusion:
Historically the 6–18 month rule only held half the time; actual lags have ranged from 2 to 13 months with an average near 6 months. Accordingly, if September 2024 marks the first Fed cut, our timing model points to around March 2025 for a recession onset (±4 months), rather than as late as September 2025 or beyond.
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