How the coupling is measured, and what was wrong before
Prices. Real USGS series (Data Series 140, constant 1998 dollars) for both companion and host. The previous version used the atlas’s trade unit values for the companion side — the same proxy the volatility retest found tracks real price volatility at r=0.13. Coal and natural gas have no USGS series (DS-140 is nonfuel), so those two hosts come from the World Bank Pink Sheet, deflated onto the same 1998 basis using the deflator implied by USGS’s own nominal/real pair.
The control, done properly. Everything in commodities co-moves, so a raw correlation is mostly the macro cycle. The old page handled this by computing corr(companion, host) − corr(companion, base index) and calling the pair host-specific if the gap beat 0.1. That is not a control. Subtracting two correlations is not residualisation, has no sampling theory, and the 0.1 was arbitrary. The correct statistic is the partial correlation: regress the base-metals cycle out of both series, then correlate what is left. That is what this page now does.
The channel, corrected. Joint production says the host drags the companion out of the ground whether anyone wants it or not: host output up → companion supply up → companion price down. That is a claim about the host’s output, not its price — and host price is dominated by the same demand cycle that lifts every metal at once, so a price-price correlation cannot identify it. We therefore also run the regression the theory implies, on host production.
Limits: ~20 annual points per pair, so only large effects are visible. Palladium is dropped: USGS publishes one aggregate platinum-group price, so palladium against platinum would be a series against itself — the old page’s palladium result came from trade unit values and we would rather drop the pair than fake it. Non-atlas by-products are included and flagged: they are the literature’s own test cases and this sample is thin. Input: USGS DS-140 × Pink Sheet → host_coupling.json.
Coupling, before and after a real control
Grey bar = the raw correlation with the best-matching host — what the old page reported. Coloured bar = the partial correlation, after the common commodity cycle is regressed out of both series. The gap between them is the macro cycle, which the old method credited to the host.
Every pair, with honest intervals
| Companion | best host | raw r | partial r | 95% CI | p | verdict |
|---|
★ = one of the atlas’s own 32 materials; the rest are classic by-products included because the sample is thin and they are the pairs the literature itself tests.
The test the theory actually implies
If a companion is dragged out of the ground by its host, then when the host produces more, the companion’s price should fall. That is the joint-production channel, and it is a statement about tonnes, not dollars. So: regress each companion’s annual price change on its host’s annual output change, controlling for the commodity cycle. The theory predicts a negative coefficient.
| Companion | host output | β host output | p | β cycle | p |
|---|
What this does and does not overturn
The episodes are real. Gallium and germanium did spike when China restricted exports in 2023. Cobalt did crash while Indonesian nickel flooded the market. Those are documented events, not statistical artifacts, and nothing here touches them.
The general law is not supported. “Companion prices systematically track their host’s cycle” is a much stronger claim than “in these episodes, host and policy shocks dominated” — and it is the strong version this page was built to test. It fails: with a valid control the coupling is indistinguishable from zero everywhere but bismuth, and the channel the theory names shows nothing at all. So the price test’s “the host decides the direction” is narrowed to the episodic claim its evidence supports.
Why it might still be true and invisible. Honestly stated: host output moves a few percent a year while companion prices swing thirty to fifty. A structural multi-year surge — Indonesia’s nickel build-out — is not a year-on-year wiggle, and an annual log-return test is poorly shaped to catch it. Absence of evidence here is not proof of absence. But the claim was ours to prove, and we have not.
Why not a VAR, or GARCH, or a spillover index? Because they cannot be run honestly on this data. The literature’s frontier for main/by-product linkage — Toda–Yamamoto causality, cointegration, TVP-VAR, multiscale nonlinear Granger — needs monthly or daily series with hundreds of observations. The minor metals have no open high-frequency prices at all; USGS is annual, and twenty points will not support a VAR. Fitting one anyway would produce output, not evidence. The binding constraint here is data, not method, and we would rather say so than dress twenty points in a technique that implies we have two thousand.