Skip to content
All library documents

How the Case-Shiller Repeat-Sales Index Methodology Developed

Article Quant Q&A · Author: Gerry
Read the original

Summary

The document examines how the S&P CoreLogic Case-Shiller Home Price Index is constructed and why its official repeat-sales methodology may differ from simplified tutorials. The discussion distinguishes the Bailey–Muth–Nourse approach, which models log price changes with time-period indicators, from later developments that account for the interval between home sales and from Shiller's arithmetic-index approach, which works with sale prices rather than log price differences.

The answer supports the claim that the published S&P methodology is used by citing continuity between an earlier methodology document and a later version, as well as a research paper that identifies the index with Shiller's method. This evidence is described as persuasive but not conclusive, and the exchange does not provide an independent replication. The account is useful for understanding why repeat-sales indices can differ in their regression setup and error assumptions, though it focuses on house-price measurement rather than a trading strategy.

Key ideas

  • The Bailey–Muth–Nourse method uses repeat-sale price changes in a regression framework.
  • Later Case-Shiller work modeled sale-interval effects through a more complex error structure.
  • Shiller's arithmetic-index method uses sale prices rather than log price differences.
  • The answer cites methodology documents and research literature to support the stated S&P approach, but does not offer an independent replication.

Tags

StatisticsEquitiesUS markets
Full text
# Case Shiller repeat sales index methodology


# Case Shiller repeat sales index methodology












I am trying to find a definitive specification of the index construction methodology for the S&P CoreLogic Case-Shiller Home Price Indices produced by S&P Global – also known simply as Case-Shiller indices. So of course I go to the document titled "S&P CoreLogic Case-Shiller Home Price Indices Methodology", and it is dated November 2021, but I know it's not changed substantially since 2016. The section "Repeat Sales Methodology" p19-23 describes in detail how it's done.

However the method as described does not match (for example) what YouTube tutorial videos show (e.g., here) for Case-Shiller, which is basically Bailey Muth & Nourse (1963) using OLS regression on dummy variables. The methods are pretty different – the "official" one regressing prices on prices using dummy Instrumental Variables, and the index as reciprocals of the coefficients.

I am a little baffled because in my limited experience most people believe Case-Shiller uses Bailey 1963 OLS/WLS. The IV method seems somewhat needlessly inefficient as a 'fix' for stochastic regressors, given that the Bailey regression on dummies does not suffer from this problem. The "official" method is also less flexible for my purposes (which are not really relevant to the question).

Is the S&P method really as described? Does anyone know for sure, has replicated it? It's an odd question I know, but I find it hard to believe the spec in the official documentation.

## Answer by Sharad (score 1)

https://quant.stackexchange.com/a/69681

The evidence I've compiled, while not necessarily dispositive, does make a strong case that the S&P method is as described.

First, I have a copy of the S&P methodology document from 2007 and the section devoted to "Repeat Sales Methodology" appears to be identical to the more recent one, down to quoting the same references.

Second, a 2014 paper (Repeat Sales House Price Index Methodology) which compares four repeat sales indices explicitly references the fact that the S&P Repeat Sales HPI is based on Shiller's 1991 paper on arithmetic indices.

Perhaps one source of confusion might be some misconceptions in your understanding of the historical development of repeat-sales HPIs, which is documented in the paper cited above. Briefly, as you write above, Bailey et al (1963) introduced the concept of repeat sales analysis. The next major innovation (1987, 1989) occurred when Case-Shiller argued that the gap times between house sales had an effect on sale price differences. Essentially, they assumed a more complex form for the error term arising in the Bailey-Muth-Nourse regression model. In 1991, Shiller proposed an index that was constructed from sales prices as opposed to log sale price differences, and this is the methodology used to construct the S&P/Case-Shiller HPI. The cited paper also details some of the pros and cons of each of the methods.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.