Repeat sales house price indices: comparative properties under alternative data generation processes

ABSTRACT

Accurate analysis of housing markets requires the use of an appropriate house price index. We compare the properties of two common repeat sales house price indices [Bailey, Muth and Nourse (BMN) and Case-nd Shiller (CS)] with those of Gao and Wang’s unbalanced panel (UP) approach. Using data across three differing housing markets within New Zealand, the three indices produce similar measures of house price movements. When evaluated using separate training and testing sub-samples of the data, none of the three measures is unambiguously superior to the others. When we test properties using simulated data with alternative data generation processes, a clear result emerges: The CS method is clearly superior when relative house prices follow an actual or near random walk; otherwise the UP method is (slightly) superior. Thus researchers should consider the time series properties of their data when choosing a method of house price index construction.

KEYWORDS:

• Repeat sales
• house price index
• Case Shiller
• unbalanced panel

Acknowledgements

We thank the Foundation for Research, Science and Technology (FRST grant MOTU-0601) and the Kelliher Charitable Trust for funding assistance, plus Steve Stillman, Dave Maré, Andrew Coleman, Andre Gao and two referees and the editors of this issue for suggestions. We also thank Wei Zhang and Alex Olssen for assistance. The authors, however, are solely responsible for the views expressed.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Grimes and Young (2010) show that they are also track the related SPAR index developed by Bourassa, Hoesli, and Sun (2006).

2 This condition is similarly assumed in all subsequent expressions in the paper.

3 The Case-Shiller method (that underlies the S&P/Case-Shiller Home Price Indices) forms the basis for the housing futures and options contracts on the Chicago Mercantile Exchange.

4 Dreiman and Pennington-Cross (2004) develop the CS approach further by allowing for asymmetric effects between houses that appreciate above and below the mean rate of appreciation, and allow also for different variances according to the price bracket of the houses.

5 Hwang and Quigley report a likelihood ratio test that rejects the hypothesis of a random walk in (relative) house prices.

6 This proviso is important since one source of non-stationarity in relative house prices may be due to permanent changes to a house, such as addition of a new bathroom.

7 Gao and Wang test both a fixed effects and a random effects specification, rejecting the latter in favour of the former. We follow their approach in our estimates using this method.

8 The UP approach has been used, inter alia, by Grimes and Young (2013) and by Timar, Grimes, and Fabling (2018).

9 It is unlikely that ε_it actually follows a random walk since that would imply that an individual house price could rise or fall indefinitely relative to its regional index. However some degree of persistence is likely. Note that non-stationarity may take forms other than a random walk, such as a one-off permanent change to the value of a property.

10 Auckland Region (which mainly comprises the Auckland urban area) had a population of 1,318,700 in 2006. All population figures are based on the 2006 census night population count (source Statistics New Zealand); 2006 populations are reported as that census is closest to the mid-point of our sample.

11 The UP and BMN methods also produced similar index movements to each other in Gao and Wang's study, based on a smaller sample size of 5000 houses in Maryland.

12 This reflects the choices made by Jiang et al. (2015) in testing their new hedonic house price estimation approach. They assigned all final sales of the houses sold three or more times to the testing set together with 4% of second transactions for houses sold twice, plus 24% of transactions for houses sold once. As ours is a repeat sales study, we do not include houses sold only once so we adjusted upwards the proportion of houses sold twice (from 4% to 5% of those properties) for the testing set.

13 Thus house i has 100 generated series for each of β = 0, β = 0.8, β = 0.9, and β = 1, for each given σ².

Additional information

Funding

This work was supported by Kelliher Charitable Trust; Foundation for Research, Science and Technology [grant number MOTU-0601].