# Revised findings

## Research question

Do inflation regimes alter the relationship between commodity returns and commodity-producer equity returns?

## Data audit

The retained prepared dataset contained 104 monthly rows from April 2017 to December 2025. 14 rows recorded Brent, gold and copper returns of exactly zero even though the producer-equity ETFs moved. Those rows were generated by forward-filling missing futures prices before calculating returns in the original workflow and are excluded. After constructing one-month-lagged inflation and the monthly change in the 10-year Treasury yield, the primary model uses **89 observations**.

## Primary specification

The high-inflation indicator equals one when the **previous month's** headline CPI inflation rate is at least **3.0%**. A full-sample interaction model allows each commodity beta to change in the high-inflation regime. Energy and mining equity models include Brent, gold and copper returns simultaneously, the high-inflation indicator, the three interaction terms and the monthly change in the US 10-year Treasury yield. Reported p-values use Newey-West/HAC standard errors with 3 lags.

## Results

- **Brent and energy equities:** the estimated beta is -0.030 in lower-inflation months and 0.493 in high-inflation months. The difference is 0.523 with a HAC p-value of 0.016. The regime difference is statistically distinguishable at the 5% level.
- **Gold and mining equities:** the estimated beta increases from 0.298 to 0.516, but the difference has a HAC p-value of 0.680. The revised analysis does **not** support the original claim that the gold sensitivity changes reliably across regimes.
- **Copper and mining equities:** the estimated beta increases from 0.428 to 0.757, but the difference has a HAC p-value of 0.355. Copper remains positively associated with mining-equity returns, but the regime difference is imprecise at the primary threshold.

## Interpretation

The narrow defensible conclusion is that the transmission of Brent returns into energy-equity returns was materially stronger when inflation was already elevated. The evidence is not strong enough to claim comparable regime shifts for gold or copper. These are associations, not causal estimates, and the sample remains modest.

## Robustness

The file `outputs/threshold_robustness.csv` reports the same interaction specification using the sample-median lagged headline-CPI threshold (2.68%) and round-number thresholds of 3.0%, 3.5% and 4.0%. The Brent interaction remains positive and statistically significant across all four thresholds. Copper's interaction becomes significant only at the higher thresholds, so that result is threshold-sensitive and should not be treated as a stable finding.