Statistical Illusions Entry #0443 Classified Declassified

The reason a leading indicator stops leading

It led because of a structure that produced the delay. When the structure changes, the correlation stays in the historical data and leaves the future.

No visual record attached The written record below is complete.
Plate 493 — Eleven right, and the twelfth

Intuition test — answer before you read on

Why does a reliable leading indicator eventually stop predicting?

The series called eleven of the last twelve turns, and it is on every dashboard because of that record. The twelfth is where the relationship ended, and the record is why nobody looked for the reason it had worked.

What everyone sees

A leading indicator is treated as a property of the series — something it is, established by its track record and expected to persist. It is not a property. It is a relationship that held while certain arrangements held, and the track record is silent about which arrangements those were.

What is actually happening

Lucas argued that estimated relationships between economic variables are conditional on the policy regime and behaviour that produced them, so using such a relationship as a basis for action can change the very structure that generated it — which makes historical fit a poor guarantee of future performance. Diebold and Rudebusch scored composite leading indicators against the record and found that their apparent accuracy shrank substantially once real-time data and subsequent revisions were used instead of the final revised series, meaning part of the impressive hit rate was an artefact of hindsight. Together they explain the pattern. The indicator worked inside a structure and was scored with information nobody had at the time.

Why it stays hidden

The decay hides because it is only visible in prospect. Every dashboard shows the historical fit, which remains excellent, and the break appears as a single miss to be explained by unusual circumstances. Meanwhile the sequence of small structural changes that removed the lag is not recorded anywhere as an event.

An indicator leads because of a structure, not because of its history. Fit is measured with data nobody had at the time.

An indicator leads because of a structure, not because of its history. Fit is measured with data nobody had at the time.

The hidden part — entry #0443

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An indicator leads because of a structure, not because of its history. Fit is measured with data nobody had at the time.

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Sources & further reading 2
  1. Lucas — econometric policy evaluation: a critique
  2. Diebold & Rudebusch — scoring the leading indicators

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