Hedonic Index Numbers for Rents of Office and Shop Premises in Finland

The focus of the study is to join together regression analysis and index numbers to get quality adjusted price change for rents of office and shop premises. First, we apply simple semilogarithmic linear price models, the fixed effects model (FE), and estimate them by the OLS method. We weight these estimated equations from observations into stratums for unweighted and weighted arithmetic and geometric averages such that the basic algebraic properties of the OLS method are satisfied. We show that the aggregation leads to reparameterization of the FE’s (here stratum effects) of the OLS method for the unweighted and weighted arithmetic and the weighted geometric averages. The solution for the unweighted geometric average is trivial and shown in any statistical textbooks. Second, we apply the Oaxaca decomposition (1973) for the aggregated price models (i.e. stratum aggregates) for these four basic averages and divide the actual price change of these averages into two parts: into quality correction and quality adjusted price changes. For these Oaxaca decompositions of different averages, we apply index number theory to estimate price changes for crude aggregation levels. All our analysis, including the basic and excellent index number formulas (see Vartia and Suoperä, 2018), are based on their logarithmic representations. Our focus for the use of the logarithmic representations culminates into the theorem of additive decomposition of the value change by which we can compare the price change estimates based on unit values (i.e. weighted arithmetic averages) and especially Montgomery-Vartia price index. We show explicitly that inadequate control of rented squares leads to serious bias – the actual price change includes not only price changes but also quantity changes, which may dominate causing serious bias for price index numbers. Our test data comes from the KTI Property Information Ltd covering large municipals in Finland. The data do not include certain ID-key for the construction of bilateral price-links and thus a hedonic method is our approach to measure price index for rents of office and shop premises. The weighting into the population level is at the moment impossible because lack of data, we make all inference only for the conditional information set of our data. All statistical and mathematical methods in this study are programmed by the SAS and the user interface for the official production of statistics by the SAS EG