Is There a Functional Relation between the Median Index and the Repeat-Sales Index?

Abstract

There exist basically two kinds of real estate indexes, the panel (or flow) indexes and the repeat-sales index (RSI). Inside the first family, the simpler example is the median index which is defined at a given date as the arithmetic average of all the observed transaction prices per square meter. One of the drawbacks with such a calculation lies in its ignorance of the quality variations. Hence the observed transactions prices won't be a simple consequence of the real estate market changes since it will also incorporate the capital gains or losses stemming from the quality modifications. The hedonic indexes, which are also panel indexes, had been developed to manage this problem. The fundamental idea is to separate the quality effect from the intrinsic real estate variations. These two techniques (median and hedonic) are completely focused on a specific date t and the estimation is made directly on the transactions prices observed at this moment, whatever be the past or the future. The second approach is based on the repeat-sales technique. The sample is made of goods whose purchase prices and resale prices are known and consequently the dataset is much more limited than the one used for the hedonic index. This kind of sample allows calculating the return rates realised during the holding periods and the estimation is made directly on these rates, no longer on prices. Econometrically speaking, this method is simpler and doesn't necessitate the very accurate and heavy information required by the hedonic regressions to catch the quality changes. The temporal structure is different of the panel indexes because the RSI value at t is a function of the purchase prices (before t) and the resale prices (after t).

The work presented here isn't empirical in the sense that it doesn't produce the values of an index from a sample associated to a given urban area. The aim rather consists in going back over the formulation of a repeat-sales index (RSI) and to deepen it in order to study the possibility of a functional relation between a repeat-sales index and a panel index. The solution of this initial problem requires heavy theoretical developments, but as we will see all along this dissertation, these efforts of abstraction will be greatly rewarded. For example we'll get as a by-product, a data analysis methodology more detailed than the single index values and allowing a better exploitation of the information embedded in the dataset. It gathers in a unified framework several concepts (instantaneous and mean rates, length of the holding periods, quantity of information provided by a trade, levels of liquidity for the buy-side and for the sell-side), whose evolutions can be observed jointly.

Keywords: repeat-sales index, median index, information measure