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A Note on the Stochastic Approach to Index Numbers

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Abstract

In a recent article, Clements and Izan (1987) used the stochastic approach to index-number theory to estimate the rate of inflation and its standard error. Selvanathan (1988) extended their approach to the prices of groups of goods and to prices within groups. In this note, I apply the within-group results to the U.K. alcohol data. Simulation results show that the estimates are unbiased, but the asymptotic standard errors understate the true sampling variability of the estimates. To overcome this problem, I applied the bootstrap technique to obtain alternate standard errors.

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  • Selvanathan, E A, 1989. "A Note on the Stochastic Approach to Index Numbers," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 471-474, October.
    • Handle: RePEc:bes:jnlbes:v:7:y:1989:i:4:p:471-74
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    Cited by:

    1. Gholamreza Hajargasht & D. S. Prasada Rao, 2010. "Stochastic Approach To Index Numbers For Multilateral Price Comparisons And Their Standard Errors," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 32-58, June.
    2. C. Crompton, 1996. "A Reconsideration of the New Stochastic Approach to Index Numbers," Economics Discussion / Working Papers 96-24, The University of Western Australia, Department of Economics.
    3. José‐María Montero & Tiziana Laureti & Román Mínguez & Gema Fernández‐Avilés, 2020. "A Stochastic Model with Penalized Coefficients for Spatial Price Comparisons: An Application to Regional Price Indexes in Italy," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(3), pages 512-533, September.
    4. Christopher J. O'Donnell & Alicia N. Rambaldi & Howard E. Doran, 2001. "Estimating economic relationships subject to firm- and time-varying equality and inequality constraints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 709-726.
    5. O'Donnell, Christopher J., 2000. "Estimating The Characteristics Of Homogeneous Functionsusing Flexible Functional Forms," 2000 Conference (44th), January 23-25, 2000, Sydney, Australia 123713, Australian Agricultural and Resource Economics Society.
    6. E. A. Selvanathan, 2003. "Extending the stochastic approach to index numbers: a comment on Crompton," Applied Economics Letters, Taylor & Francis Journals, vol. 10(4), pages 213-215.
    7. Ogwang, Tomson, 1995. "The stochastic approach to price index numbers: An expository note," Economics Letters, Elsevier, vol. 49(4), pages 373-379, October.
    8. Paul Crompton, 2000. "Extending the stochastic approach to index numbers," Applied Economics Letters, Taylor & Francis Journals, vol. 7(6), pages 367-371.
    9. Ilaria Benedetti & Tiziana Laureti & Luigi Palumbo & Brandon M. Rose, 2022. "Computation of High-Frequency Sub-National Spatial Consumer Price Indexes Using Web Scraping Techniques," Economies, MDPI, vol. 10(4), pages 1-20, April.
    10. Rao, D.S. Prasada & Doran, Howard E. & Selvanathan, E.A., 2003. "Estimation of General and Commodity-Specific Inflation Rates Using Linear Time-Varying Constraints," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 35(Supplemen), pages 1-8.
    11. Selvanathan, E. A. & Selvanathan, S., 2004. "Modelling the commodity prices in the OECD countries: a stochastic approach," Economic Modelling, Elsevier, vol. 21(2), pages 233-247, March.
    12. Iqbal, Javed & Hanif, Muhammad Nadim, 2010. "Measuring Standard Error of Inflation in Pakistan: A Stochastic Approach," MPRA Paper 35422, University Library of Munich, Germany.
    13. Zahid, Asghar & Frahat, Tahira, 2010. "Measuring inflation through stochastic approach to index numbers," MPRA Paper 21513, University Library of Munich, Germany.
    14. Tomson Ogwang, 2022. "The regression approach to the measurement and decomposition of the multidimensional Watts poverty index," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(4), pages 951-973, December.

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