Do Real Commodity Prices Trend Down? Prebisch–Singer, 1960–2025, and Why the Usual t-Statistic Overstates the Evidence Tenfold

The Prebisch-Singer hypothesis says that the prices of primary commodities fall over time relative to manufactures. I test it on the World Bank's real commodity price indices (nominal indices deflated by the manufactures unit value index, MUV), annual 1960 to 2025, released 2 September 2026. A least-squares trend on log prices gives the familiar result: agriculture falls at 0.421% a year (t = minus 3.26), food at 0.411%, beverages at 0.718% and raw materials at 0.255%, all significant by the usual standard errors. Unit-root tests do not reject a random walk for any index, and stationarity tests reject trend-stationarity for eight of ten (one of them marginally). I derive the exact variance of the least-squares trend when prices follow a random walk, show that it tends to 1.2 sigma squared over n, and prove that the naive t-statistic is inflated by a factor of about the square root of 1.5n, which is 9.95 for 66 years. A simulation confirms the factor (9.84) and shows that a nominal 5% test rejects a true zero trend in 84% of samples. The efficient estimator under a random walk, the mean of annual log changes, gives agriculture minus 0.195% a year with a t-statistic of minus 0.17. Non-energy prices fell at 1.48% a year from 1960 to 1990 and rose at 1.35% a year from 1990 to 2025, neither distinguishable from zero. Over 66 years, the data do not establish a secular decline.