1. 1 Chapter 4: Elements for a Conceptual Framework Workshop on Residential Property Price Indices: Statistics Netherlands, The Hague, February 10-11, 2011. Presenter: Erwin Diewert, Department of Economics, University of British Columbia and School of Economics, University of New South Wales.

2. 2 What Makes House Price Indexes Difficult to Construct? (1) The usual matched model methodology for constructing price indexes cannot be applied in the housing context because, basically, there are no matched models! [ Every house is unique; the depreciation and renovations problem]. (2) Not all houses trade every period. (3) Sometimes the purpose of the index is not clear: do we want an index of house sales or of the stock of houses? Do we want an index of all house sales or just new house sales? (4) For some purposes, we want separate indexes for the structures and land components of house prices. It proves to be a very difficult task to construct these component indexes. Problems (1) and (4) are the main problems.

3. 3 RPPIs and the SNA An RPPI is needed in 3 places in the SNA: to measure the stock of residential properties that exist at a particular location in the country at a particular point in time (needed in the national balance sheets); the sales of residential properties that were sold in a particular location in the country over a particular time period (needed in order to form a price series for real estate sales), and the structures part of the sales of new residential properties that were sold in a particular location in the country over a particular time period (needed in order to estimate real investment). In addition, central banks require a RPPI in order to monitor the possibility of asset bubbles.

4. 4 RPPIs and the CPI A RPPI is required for CPI purposes for some approaches to pricing the services of Owner Occupied Housing (OHH). The approaches that require a RPPI are: The money outlays approach; The user cost approach and The acquisitions approach: (a) include the value of land associated with the acquisition of a new house or (b) exclude the value of land. In this second variant of this approach, a deflator for the value of structures and land improvements is required. The only approach to measuring the real services of OOH that does not require a RPPI is the rental equivalence approach.

5. 5 Four Main Classes of Methods Used to Construct a RPPI Stratification Methods : Mean, median and more detailed stratifications; The Repeat Sales Method; Hedonic Regression Methods; (a) Time dummy hedonic models; (b) Hedonic imputation models; (c) The builder’s model. Assessment Based Methods; (a) SPAR (Sales Price Appraisal Ratio) method; (b) GREG method (being developed by de Haan).

6. 6 More on Stratification Methods The selling price of a property depends on: the area of the structure in squared feet or in meters squared; the area of the land that the structure sits on the location of the property; the age of the structure; the type of structure; the materials used in the construction of the dwelling unit; other price determining characteristics such as the number of bedrooms, the number of bathrooms, an external garage, a swimming pool, landscaping etc. The above characteristics can act as stratification variables.

7. 7 More on Stratification Methods (cont) The mean and median use location and type of housing as stratification variables. This is not sufficient; leads to very unreliable indexes (quality is not held constant). In addition to location and type of housing, the most important stratification variables are: (i) the size of the house in m 2 ; (ii) the lot size and (iii) the age of the structure. But if we stratify according to these 3 variables (say 5 age groups, 3 lot size groups and 3 house size groups, we end up with 45 cells and there may not be enough observations in each period to fill up these cells. Thus we run into difficulties using normal index number theory due to a potentially large number of empty cells and hence a lack of matching! But stratification can work!

8. 8 Data Constraints and Alternative Methods Data constraints may force us to use certain methods. If we know nothing except the selling prices of a certain type of housing in location, then mean or median indexes may be all that can be constructed. If we know in addition, the addresses of the houses sold, then we could implement the Repeat Sales method. This will probably be an improvement over the mean or median indexes but sparseness of repeat sales may lead to volatile indexes plus we expect RS indexes to have a small downward bias due to their neglect of depreciation. If we have additional information on the important characteristics of the houses sold, then we can compute Fisher indexes based on unit value prices and quantities in the cells or we can implement the various hedonic methods.