ChatGPT query:
Test the hypothesis that a recession usually occurs 6 to 18 months after the first rate cut from the Federal Reserve after a period of extended tightening. If true provide a model to predict the timing of the recession after the rate cut in September 2024 speciifically and predict when the recession will start. Provide a chain of though for the process.
ChatGPT said:
Thought for 8 seconds
Here’s how I’d go about testing that “6–18-month lag” hypothesis and then use it to forecast the likely recession start after the Fed’s September 2024 rate cut:
1. Define the analysis framework - Identify “extended-tightening” episodes
We need periods in which the Fed funds rate rose cumulatively over at least 12 months.
- Locate the first rate cut after each such tightening.
- Record the NBER recession start date for the recession that followed.
- Compute the lag (in months) from first cut ? recession start.
- Test the hypothesis by checking whether the observed lags fall mostly in the 6–18-month window.
- If supported, fit a simple statistical model (e.g. normal distribution) to those lags.
- Apply the model to the September 2024 cut and forecast the most likely recession start date (with a prediction interval).
2. Historical data and lag calculation
Tightening periodFirst cutRecession startLag (months)|
| Oct ’86 – Dec ’89 | Aug ’89 | Jul ’90 | 11 | | Aug ’69 – Aug ’69 | Aug ’69 | Dec ’69 | 4 | | Jan ’01 – Jan ’01 | Jan ’01 | Mar ’01 | 2 | | Jun ’04 – Jun ’06 | Sep ’07 | Dec ’07 | 3 | | Nov ’73 – Nov ’74 | Nov ’74 | Nov ’73 | –12 (prior) |
- Sources: FOMC historical rate changes; NBER recession chronology.
We see lags in our “extended-tightening” samples of 11, 4, 2, 3 months (and one mismatch in 1973 due to unusual timing), none in the 6–18 month band except the 11-month case.
3. Hypothesis test - Null hypothesis (H0): The lag ~ Uniform(6,18).
- Observed lags: {11, 4, 2, 3}.
- Only 1 of 4 observed falls in [6,18].
A simple binomial check (success = lag in [6,18]) gives
P(1 or fewer successes in n=4|p=1)=?k=01(4k)?pk(1-p)4-k,P(\text{1 or fewer successes in }n=4\mid p=1) = \sum_{k=0}^1 \binom4k\,p^k(1-p)^{4-k},P(1 or fewer successes in n=4|p=1)=k=0?1?(k4?)pk(1-p)4-k, which is extremely unlikely if every cycle truly yields a 6–18-month lag.
Conclusion: The “6–18 month” rule does not hold robustly across post-tightening cycles.
4. A more realistic lag model Because the simple uniform hypothesis fails, we turn instead to the empirical distribution of observed lags:
- Sample lags: 2, 3, 4, 11
- Mean µ = (2+3+4+11)/4 = 5 months
- Std dev s ˜ 3.7 months
We model the lag as
L ?~ ?Normal(µ=5, s=4)(truncated at zero).L \;\sim\; \mathrm{Normal}(\mu=5,\ \sigma=4)\quad\text{(truncated at zero)}.L~Normal(µ=5, s=4)(truncated at zero). From that, a 90 percent prediction interval for the lag is roughly
5±1.645×4 ?˜ ?[–1.6, ?11.6] ?? ?[0, ?12] months.5\pm 1.645\times4 \;\approx\; [–1.6,\;11.6] \;\to\; [0,\;12] \text{ months.}5±1.645×4˜[–1.6,11.6]?[0,12] months. 5. Forecasting from the Sept 2024 cut - First cut date: assumed September 18, 2024 (following FOMC announcement).
- Apply lag distribution:
- Mean forecast: 5 months ? February 18, 2025.
- 90 % interval: 0 to 12 months ? anywhere from Sept 2024 to Sept 2025, with most probability through spring 2025.
?? Best-guess: A recession would most likely begin in February–March 2025, with plausible risks as early as late 2024 or as late as mid-2025.
6. Chain of thought summary - Clarify “extended tightening” to filter out trivial rate cycles.
- Compile past episodes (‘86–’89, ’69, ’01, ’04–’06).
- Extract first cut and recession dates from FOMC and NBER.
- Compute lags and observe their distribution.
- Reject the 6–18 month uniform hypothesis—lags cluster much shorter.
- Fit empirical normal-approximation model (µ˜5 m, s˜4 m).
- Apply to Sept 2024 ? forecast recession start ˜Feb–Mar 2025 (90 % between Sept 2024–Sept 2025).
Caveats and next steps - Sample is very small (n=4), so estimates are noisy.
- You could refine by broadening “tightening” criteria or including mid-century cycles for more data.
- Incorporate macro controls (yield-curve inversions, financial stress indices) to improve timing accuracy.
But with what we have, a recession is most likely in late
winter/early spring 2025 following the September 2024 rate cut.
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Johnny: Obvious that did not happen so the timing is less predicable than can be modelled using a normal distribution. The time window seem to be variable, thought root causes and factors in the last email seem to be important factors. That is why I am running a trailing stop approach to take me out as opposed to trying to time it exactly. |
