Introduction to statistical background The hedonic method Introduction to statistical background 26th May of 2015

Hedonic price index in housing Brief historical Hedonic price index in housing context Price characteristics methods Estimation of a price Estimation of a change of price Estimation of a change of price with time-dummies The hedonic method: introduction to statistical background 26th May of 2015

Brief historical The hedonic method dates back at least to Waugh (1928). Other early contributors include Court (1939) and Stone (1954). It is only after Griliches (1961, 1971) that hedonic methods started to receive serious attention. The conceptual basis of the approach was laid down by Lancaster (1966) and Rosen (1974). The hedonic method: introduction to statistical background 26th May of 2015

Brief historical When a price depend simultaneously of several characteristics, Lancaster explained in “A new approach to consumer theory” that the only way to estimate the impact of each characteristics on the price was to resolve a model. A hedonic model regresses the price of a product on a vector of characteristics. The hedonic equation is a reduced form equation that is determined by the interaction of supply and demand. The hedonic method: introduction to statistical background 26th May of 2015

Brief historical The hedonic method is used for two main purposes: to qualify adjust the observed prices (left hand side of the hedonic equation) so as to allow the construction of a quality-adjusted price index. to estimate the willing to pay for, or marginal cost of producing, the characteristics (right hand side of the hedonic equation), or even of the underlying demand or supply functions of these characteristics and corresponding consumer or producer surplus. The hedonic method: introduction to statistical background 26th May of 2015

Hedonic price index in housing context Housing is an extreme case of a differentiated product in the sense that every house is different. Also, unlike computers or cars, on of the most important characteristics of a house is its localisation. We can distinguish between physical and location attributes: Physical attributes: number of bedroom, land area Location attributes: the distance to amenities such as shopping centre, park, school, transport. And some of hedonic regressions for housing suffered from omitted variables (physical or location). The hedonic method: introduction to statistical background 26th May of 2015

Hedonic price index in housing context Hedonic methods are used for three main purposes in a housing context: To construct quality-adjusted house price indexes, To provide automated valuation of properties (or general appraisals), To explain variation in house price or to determine the impact on house prices of certain characteristics such as environmental bads such as pollution, local taxes and public school provision and crime. The first hedonic house price index was produced by US Census in 1968. The hedonic method: introduction to statistical background 26th May of 2015

Characteristics prices methods In this approach to compiling a hedonic price index, separate regressions are run for all time period and the index is constructed by making use of the predicted prices based on the regression coefficients. With this method, the implicit characteristics prices can vary over time. Usually, the sample is stratified in order to analyze each part of the sample with specific characteristics. In the model, the coefficient of the variable can be analyze as the partial derivation of the function relatively to this variable. In this document, we don’t use stratification in order to simplify the explanation. But in the French producer price index for construction we have three strata. The hedonic method: introduction to statistical background 26th May of 2015

Estimation of a price with characteristics prices methods First of all, we suppose that: Sample data are available on prices and relevant characteristics of houses sold in the base period 0 and each comparison period t. The linear hedonic model holds true and is estimated on the data of period 0 and period t separately. This yields regression coefficients (k=1,…, N) and for s=0,t The predicted prices for each individual property are and It is possible to compute predicted period 0 and period t prices for standardized property with fixed characteristics z*k. the resulting price relative is The hedonic method: introduction to statistical background 26th May of 2015

Estimation of a price with characteristics prices methods This expression is a quality-adjustment price index because the characteristics are kept fixed. But different values of z*k will give different index numbers. You can select a sample average characteristics of the base period and the sample averages of comparisons period t (t=1, ..,T) Or The hedonic method: introduction to statistical background 26th May of 2015

Estimation of a price with characteristics prices methods The characteristics prices method can also applied in combination with log-linear model. Running separate regressions of this model on the sample data for periods o and t yields predicted prices (after exponentiation) And The hedonic method: introduction to statistical background 26th May of 2015

Each estimation is independent from the previous one. Estimation of a price with characteristics prices methods using time-dummies In order not to revise indices previous periods each time we add a trimester, the regression is performed on slippery time windows (6 quarters). Therefore, the estimate made a trimester of the year does not review the previous quarter. Each estimation is independent from the previous one. The hedonic method: introduction to statistical background 26th May of 2015

Estimation of a price with characteristics prices methods using time-dummies To protect the quality of the model of a “effect size ” from a large building we used dwellings means in the grouped individual and in collective dwellings. The average housing costs are the total price of the building divided by the number of dwellings The average housing area to the total area of ​​the building divided by the number of dwellings The hedonic method: introduction to statistical background 26th May of 2015

Estimation of a price with characteristics prices methods using time-dummies The logarithm of the price of a building is a function of the logarithm of its space area, physical characteristics Location characteristics The time-dummy A with noise The hedonic method: introduction to statistical background 26th May of 2015

Estimation of a price with characteristics prices methods using time-dummies Elementary price indices Each model is used to calculate a price index evolution of construction grade (pure individual, grouped individually and collectively) quarterly constant quality from the exponential of difference between the coefficient of the last quarter and the coefficient of the previous quarter. It then calculates an index with a reference 1 in Q1 year Y0 quarterly measure the evolution of prices of building category i (pure individual, grouped individual and collective dwellings) and writes: The hedonic method: introduction to statistical background 26th May of 2015

Output price index for construction Thank you for your attention! Insee 18 bd Adolphe-Pinard 75675 Paris Cedex 14 www.insee.fr Informations statistiques : www.insee.fr / Contacter l’Insee 09 72 72 4000 (coût d’un appel local) du lundi au vendredi de 9h00 à 17h00 Contact M. Gérard Vittek Tél. : 01 41 17 51 15 email : gerard.vittek@insee.fr