This study combines heterogeneously behaving cross-sectional regressions and hedonic quality adjusting in traditional index number framework. The approach provides a transparent mathematical representation of quality correction and quality adjustment of price changes in elementary aggregates. We propose an alternative to the standard Griliches-type time-dummy hedonic approach, which in the sense of index number theory is more interpretable and mathematically transparent between actual average price changes, quality correction and quality adjustment. In the first stage, the problem of heterogeneously behaving cross-sectional models is handled using the principle of hierarchical, ‘nested’, price models. The price models are formulated by combining the proper partition of observations (categorization of observations) and the proper classification of observations into the most homogeneously behaving subgroups (heterogeneous between subgroups) using standard statistical inference. These are achieved using the FE-models (fixed effects) familiar to economists. In the second stage, the estimated price models are aggregated from observation level into the level of partition (i.e., into stratums), where the so-called Oaxaca decompositions are computed. This decomposition, although not unambiguous, consistently divides the actual price change into quality corrections and quality adjusted price change for each stratum. We show what is the ideal selection of decompositions based on the algebraic properties of the OLS method. In the third stage, the stratum level decompositions are aggregated into higher levels similarly as in a traditional index number calculation where ‘a weighted-by-economic-importance’- variable takes a central role. We use several basic and excellent index number formulas. The study ends in empirical application of used cars in Finland.
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