# A formal framework for hedonic elementary price indices

- 255 Downloads

## 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.

## References

- Balk, B.M.: Price indexes for elementary aggregates: the sampling approach. J. Off. Stat.
**21**(4), 675–699 (2005)Google Scholar - Beer, M.: Hedonic elementary price indices: axiomatic foundation and estimation techniques. Ph.D. thesis, University of Fribourg Switzerland (2006). http://doc.rero.ch/record/6424
- Beer, M.: Bootstrapping a hedonic price index: experience from used cars data. AStA Adv. Stat. Anal.
**91**(1), 77–92 (2007). doi: 10.1007/s10182-006-0015-9 MathSciNetCrossRefzbMATHGoogle Scholar - Brachinger, H.W.: Statistical theory of hedonic price indices. DQE Working Paper 1, Department of Quantitative Economics, University of Fribourg Switzerland (2002). http://econpapers.repec.org/RePEc:fri:dqewps:wp0001
- Brachinger, H.W., Beer, M.: The econometric foundations of hedonic elementary price indices. DQE Working Paper 12, Department of Quantitative Economics, University of Fribourg Switzerland (2009). http://econpapers.repec.org/RePEc:fri:dqewps:wp0012
- Court, A.T.: Hedonic price indexes with automotive examples. The Dynamics of Automobile Demand, pp. 99–117. General Motors Corporation, New York (1939)Google Scholar
- Curry, B., Morgan, P., Silver, M.: Hedonic regressions: mis-specification and neural networks. Appl. Econ.
**33**(5), 659–671 (2001). doi: 10.1080/00036840122335 CrossRefGoogle Scholar - Davidson, R., Flachaire, E.: The wild bootstrap, tamed at last. Econometric society world congress 2000 contributed papers, Econometric Society (2000)Google Scholar
- Dickie, M., Delorme Jr., C.D., Humphreys, J.M.: Hedonic prices, goods-specific effects and functional form: inferences from cross-section time series data. Appl. Econ.
**29**(2), 239–249 (1997)CrossRefGoogle Scholar - Diewert, W.E., Heravi, S., Silver, M.: Hedonic imputation versus time dummy hedonic indexes. In: Diewert, W.E., Greenlees, J.S., Hulten, C.R. (eds.) Price Index Concepts and Measurement, chap 4, pp. 161–196. University of Chicago Press, Chicago (2009)CrossRefGoogle Scholar
- Dorfman, A.H., Leaver, S., Lent, J.: Some observations on price index estimators. Statistical Policy Working Paper 29, Bureau of Labor Statistics (1999). http://www.bls.gov/ore/pdf/st990080.pdf. Accessed 12 Aug 2016
- Eichhorn, W.: What is an economic index? An attempt of an answer. In: Eichhorn, W., Henn, R., Opitz, O., Shephard, R.W. (eds.) Theory and Applications of Economic Indices, pp. 3–42. Physica-Verlag, Würzburg (1978)CrossRefGoogle Scholar
- Eichhorn, W., Voeller, J.: Theory of the Price Index. Lecture Notes in Economics and Mathematical Systems. Springer, Berlin (1976)Google Scholar
- European Commission, IMF, OECD, United Nations, The World Bank (eds.) System of National Accounts 2008, United Nations, chap 15: Price and Volume Measures (2009). http://unstats.un.org/unsd/nationalaccount/docs/SNA2008.pdf
- Fletcher, M., Gallimore, P., Mangan, J.: Heteroscedasticity in hedonic house price models. J. Prop. Res.
**17**(2), 37–41 (2000)CrossRefGoogle Scholar - Gábor, E., Vermeulen, P.: New evidence on elementary index bias. ECB Working Paper 1754, European Central Bank. (2014). doi: 10.2866/36724
- Goodman, A.C., Thibodeau, T.G.: Age-related heteroskedasticity in hedonic house price equations. J. Hous. Res.
**6**(1), 25–42 (1995)Google Scholar - Griliches, Z.: Hedonic price indexes for automobiles: an econometric analysis of quality change. In: Griliches, Z. (ed.) Price Indexes and Quality Change, pp. 55–87. Harvard University Press, Cambridge (1971)CrossRefGoogle Scholar
- Hill, R.: Hedonic Price Indexes for Housing. OECD Statistics Working Papers 2011/01, OECD Publishing. (2011). doi: 10.1787/5kghzxpt6g6f-en
- Hill, R.J., Melser, D.: Hedonic imputation and the price index problem: an application to housing. Econ. Inq.
**46**(4), 593–609 (2008). doi: 10.1111/j.1465-7295.2007.00110.x CrossRefGoogle Scholar - ILO, IMF, OECD, UNECE, Eurostat, The World Bank (eds.): Consumer price index manual: theory and practice. International Labour Office, Geneva. (2010). http://www.ilo.org/public/english/bureau/stat/guides/cpi/, partially revised version published online, Accessed 12 Aug 2016
- Imai, S., Diewert, E., Shimizu, C.: Consumer price index biases: elementary index biases vs. sampling biases. Paper prepared for the fourteenth group meeting, Ottawa Group on Price Indices. (2015). http://www.stat.go.jp/english/info/meetings/og2015/pdf/t1s1p3_pap.pdf, accessed 12 Aug 2016
- Lancaster, K.J.: A new approach to consumer theory. J. Polit. Econ.
**74**(2), 132–157 (1966)CrossRefGoogle Scholar - Lancaster, K.J.: Consumer Demand: A New Approach. No. 5 in Columbia Studies in Economics. Columbia University Press, New York (1971)Google Scholar
- Long, J.S., Ervin, L.H.: Using heteroscedasticity consistent standard errors in the linear regression model. Am. Stat.
**54**(3), 217–224 (2000)Google Scholar - Milgate, M.: Goods and commodities. In: Eatwell, J., Milgate, M., Newman, P. (eds.) The New Palgrave: A Dictionary of Economics, pp 546–549. The Macmillan Press Limited, London (1987)Google Scholar
- R Core Team: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. (2016). https://www.R-project.org/
- Rosen, S.: Hedonic prices and implicit markets: product differentiation in pure competition. J. Polit. Econ.
**82**(1), 34–55 (1974)CrossRefGoogle Scholar - Silver, M., Heravi, S.: The measurement of quality-adjusted price changes. In: Feenstra, R.C., Shapiro, M.D. (eds.) Scanner Data and Price Indexes. Studies in Income and Wealth, vol. 64, pp. 277–316. The University of Chicago Press, Chicago (2003)CrossRefGoogle Scholar
- Silver, M., Heravi, S.: Why elementary price index number formulas differ: evidence on price dispersion. J. Econom.
**140**(2), 874–883 (2007). doi: 10.1016/j.jeconom.2006.07.017 MathSciNetCrossRefzbMATHGoogle Scholar - Stevenson, S.: New empirical evidence on heteroscedasticity in hedonic housing models. J. Hous. Econ.
**13**(2), 136–153 (2004)MathSciNetCrossRefGoogle Scholar - Triplett, J.E.: Hedonic functions and hedonic indexes. In: Eatwell, J., Milgate, M., Newman, P. (eds.) The New Palgrave: A Dictionary of Economics, pp 630–634. The Macmillan Press Limited, London (1987)Google Scholar
- Triplett, J.E.: Handbook on hedonic indexes and quality adjustments in price indexes: special application to information technology products. Working Paper 2004/9, OECD Directorate for Science, Technology and Industry, Paris. (2004). doi: 10.1787/643587187107