Lag curves

Where the curves peak

If one measure really moved ahead of the other, peaks would sit somewhere in the middle of the range. Instead the bars make a U shape. 580 curves peak at exactly ±10 years. That is the edge of the search, where the curve is still moving when the search runs out. Only 244 peak at zero, and 1644 are spread across all the other gaps combined. A peak at the edge says the measures change slowly. It says nothing about which comes first.

What picking a gap would gain

1122 pairs have a same-year link below 0.1 either way. Of those, 616reach 0.1 at some gap. Picking the best of many similar tries always makes results look stronger than they are. So a site that reported the best gap could turn more than a third of its own “no link” pairs into findings, while every single page still looked careful. This project exists to expose that kind of mistake. So all the curves are shown, and none are ranked. See lag selection and the methodology.

All 2468 curves

The solid dot is the same-year link (lag 0). The hollow dot is the peak. The dashed upright line is zero. Each small chart is scaled to its own highest point, so compare shapes, not heights. Click one to make it bigger. “Lag shopping” means picking whichever gap gives the strongest link. Sorting by “gain from lag shopping” puts first the pairs that a site ranking by gap would push. Their curves show most clearly that the gain comes from slow drift, not timing.

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Worked out over 1990–2025. A lag of k matches each country’s X in one year with its Y k years later. Only countries with data in both years are kept. Then each country is compared only with itself, and each year only with the same year elsewhere. Even a sharp peak in the middle would not show which way things run. Two measures that both follow a third factor at different speeds give exactly that shape.