Market Signals Entry #0414 Classified Declassified

The reason a refund rate is published only when low

Voluntary disclosure is not a sample of the facts. Where hiding a number is allowed, every published number is one that its owner preferred to publish.

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Plate 274 — The figures that stayed unpublished

Intuition test — answer before you read on

Why does the average published return rate sit below the true average for a category?

Some sellers state a return rate on the product page. Most do not. The temptation is to treat the published figures as a window onto the category, but they are a window onto a decision: each firm compared its own number with what buyers already assume and spoke only if speaking helped.

What everyone sees

A disclosed statistic is read as a sign of transparency and an undisclosed one as ordinary reticence. That reading treats disclosure as a cultural habit that varies by firm. It is closer to an ongoing calculation, taken separately by each seller, against a moving baseline of what silence is presumed to mean.

What is actually happening

Grossman and Milgrom set out the unravelling result. If disclosure is costless and buyers know sellers can disclose, the seller with the best figure publishes to separate itself, which lowers the expected figure attributed to the remaining silent group, which gives the best of them a reason to publish in turn. Iterated, silence becomes an admission. Real markets stop part way, because disclosure has costs, figures are not comparable across firms, and buyers do not fully reason through the chain. What survives is a censored sample: the visible numbers are drawn from the favourable tail and the average of published rates sits below the average of actual rates.

Why it stays hidden

The censoring is invisible because the missing values leave no trace on the page. A buyer comparing four listings sees the numbers that exist and cannot see the distribution they were selected from. The comparison feels like reading data when it is reading the outcome of four separate decisions about whether data would help.

Where silence is permitted, published figures are a sample of preferences, not a sample of the market.

Where silence is permitted, published figures are a sample of preferences, not a sample of the market.

The hidden part — entry #0414

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Where silence is permitted, published figures are a sample of preferences, not a sample of the market.

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Sources & further reading 2
  1. Grossman — the informational role of warranties and private disclosure
  2. Milgrom & Roberts — relying on the information of interested parties

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