Repeat-sales indices explained

A repeat-sales index measures price change using only properties that have sold more than once. The same address, two dates, two prices. Because the property is identical on both occasions, its size, type, street and garden cancel out, and what is left is the market. It is the cleanest answer to the composition problem because it needs no weights and makes no assumption about which homes are comparable.

How does a repeat-sales index work?

Take every pair of sales of the same property. For each pair, the ratio of the two prices is the market’s movement between those two dates, plus noise: if the second price is half again the first, that pair says the market moved by half over the holding period, give or take everything particular to that home and those two days. Do that for millions of pairs spanning overlapping periods and you can solve for a single series that best explains all of them at once. Bailey, Muth and Nourse set this out in 1963 as a regression of log price ratios on period dummies, and it remains the baseline.

Case and Shiller’s refinement adds weighting, because a pair held for twenty years carries more accumulated idiosyncratic drift than one held for two, and treating them equally overweights the noisy ones. It is the better estimator and it costs an assumption: the weights come from a model of how variance grows with holding period.

What does it fix that a median cannot?

Composition, completely and by construction. A median moves when what sells changes; a repeat-sales index cannot, because the thing being measured is the same thing at both ends of every observation. It is the right instrument for “has this market risen” and it is why the method underpins some of the best-known housing indices.

How does it sit against the other instruments?

Three instruments dominate published housing statistics, and they answer different questions. A median states a level. A mix-adjusted median states a level while holding composition fixed. A repeat-sales index states change, and nothing else. Most disagreements between published figures are two instruments answering two different questions rather than either of them being wrong.

What does the method cost you?

Coverage. Only a minority of any register can be paired. Homes that have sold once, or not at all, contribute nothing, and homes that turn over frequently are over-represented relative to the stock.

Selection. Properties that change hands twice within a window are not a random sample. Frequently traded stock skews towards flats, towards investor ownership and towards particular locations.

Exclusions that have to be made. A pair is only informative if the thing sold is the same thing both times, so new-build first sales, property-type changes and implausibly short holds are normally removed. Every exclusion is a judgement, and a publisher should say what it removed and how much.

Which bias can no repeat-sales index remove?

A repeat-sales index cannot tell a rising market from an extended kitchen. Both are the same address selling for more. Every repeat-sales index in the world therefore carries an upward bias of unknown size, concentrated in exactly the stock most likely to be improved between sales.

There is no fix from within the method: correcting it would need a record of what was done to each property between the two sales, and no transaction register carries one. The honest response is to state it rather than to imply a precision the method does not have, and to remember that a confidence interval on such an index describes sampling uncertainty only. It says nothing about renovation.

When should you reach for a repeat-sales index?

Use a repeat-sales index when the question is about change and you are worried the mix moved: a long horizon, a market with a lot of new supply, or a comparison between areas whose housing differs. Use a median when the question is about level, which an index cannot answer at all.

Best of all, use both and check them against each other. Where a market’s median rate and its repeat-sales index disagree about a decade, that disagreement is itself the finding, and it usually means the mix moved. One market on this network publishes both, with the interval on every point and the renovation caveat attached, and it publishes the series twice: once in cash and once in today’s money, because the two tell different stories over thirty years. The same estimator also needs a minimum number of pairs per period, which is the general problem of how many sales a figure needs applied to a series rather than to a place.