# A formal framework for hedonic elementary price indices

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## Abstract

Hedonic methods are considered state of the art for handling quality changes when compiling consumer price indices. The present article proposes first a mathematical description of characteristics and of elementary aggregates. In a following step, a hedonic econometric model is formulated and hedonic elementary population indices are defined. We emphasise that population indices are unobservable economic parameters that need to be estimated by suitable sample indices. It is shown that within the framework developed here, many of the hedonic index formulae used in practice are identified as sample versions corresponding to particular hedonic elementary population indices. The article closes with an empirical part on quarterly housing data where the considered hedonic indices are estimated along with their bootstrapped confidence intervals. It is shown that the computed confidence intervals together with the results from theory suggest a particular answer to the price index problem.

## Keywords

Consumer price index Hedonic regression Elementary aggregate Hedonic elementary price index Wild bootstrap Price index problem Elementary index bias## Notes

### Acknowledgements

Parts of this study were developed within the project ‘Specification, axiomatic foundation, and estimation of hedonic price indices’ funded by the Swiss National Science Foundation as well as the Swiss Federal Statistical Office. The authors acknowledge these fundings. Moreover, they express their gratitude to Wüest & Partner for providing the data for the empirical study.

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