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Should Exact Index Numbers Have Standard Errors? Theory and Application to Asian Growth

In: Hard-to-Measure Goods and Services: Essays in Honor of Zvi Griliches

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  • Robert C. Feenstra
  • Marshall B. Reinsdorf

Abstract

In this paper we derive the standard error of a price index when both prices and tastes or technology are treated as stochastic. Changing tastes or technology are a reason for the weights in the price index to be treated as stochastic, which can interact with the stochastic prices themselves. We derive results for the constant elasticity of substitution expenditure function (with Sato-Vartia price index), and also the translog function (with Törnqvist price index), which proves to be more general and easier to implement. In our application to Asian growth, we construct standard errors on the total factor productivity (TFP) estimates of Hsieh (2002) for Singapore. We find that TFP growth is insignificantly different from zero in any year, but cumulative TFP over fifteen years is indeed positive.
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Suggested Citation

  • Robert C. Feenstra & Marshall B. Reinsdorf, 2007. "Should Exact Index Numbers Have Standard Errors? Theory and Application to Asian Growth," NBER Chapters, in: Hard-to-Measure Goods and Services: Essays in Honor of Zvi Griliches, pages 483-513, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberch:0887
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    1. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    2. Sato, Kazuo, 1976. "The Ideal Log-Change Index Number," The Review of Economics and Statistics, MIT Press, vol. 58(2), pages 223-228, May.
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    5. Hulten, Charles R., 1986. "Productivity change, capacity utilization, and the sources of efficiency growth," Journal of Econometrics, Elsevier, vol. 33(1-2), pages 31-50.
    6. Diewert, Erwin, 2007. "Index Numbers," Economics working papers diewert-07-01-03-08-17-23, Vancouver School of Economics, revised 31 Jan 2007.
    7. Berndt, Ernst R. & Fuss, Melvyn A., 1986. "Productivity measurement with adjustments for variations in capacity utilization and other forms of temporary equilibrium," Journal of Econometrics, Elsevier, vol. 33(1-2), pages 7-29.
    8. Alwyn Young, 1992. "A Tale of Two Cities: Factor Accumulation and Technical Change in Hong Kong and Singapore," NBER Chapters, in: NBER Macroeconomics Annual 1992, Volume 7, pages 13-64, National Bureau of Economic Research, Inc.
    9. Chang-Tai Hsieh, 2002. "What Explains the Industrial Revolution in East Asia? Evidence From the Factor Markets," American Economic Review, American Economic Association, vol. 92(3), pages 502-526, June.
    10. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    11. Alwyn Young, 1995. "The Tyranny of Numbers: Confronting the Statistical Realities of the East Asian Growth Experience," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 641-680.
    12. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
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    Cited by:

    1. John Fernald & Brent Neiman, 2011. "Growth Accounting with Misallocation: Or, Doing Less with More in Singapore," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(2), pages 29-74, April.
    2. Redding, Stephen J. & Weinstein, David E., 2016. "A unified approach to estimating demand and welfare," LSE Research Online Documents on Economics 67681, London School of Economics and Political Science, LSE Library.
    3. David R Baqaee & Ariel Burstein, 2023. "Welfare and Output With Income Effects and Taste Shocks," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(2), pages 769-834.
    4. Paul Armknecht & Mick Silver, 2014. "Post-Laspeyres: The Case for a New Formula for Compiling Consumer Price Indexes," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(2), pages 225-244, June.
    5. John Fernald & Brent Neiman, 2011. "Growth Accounting with Misallocation: Or, Doing Less with More in Singapore," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(2), pages 29-74, April.
    6. Stephen J Redding & David E Weinstein, 2020. "Measuring Aggregate Price Indices with Taste Shocks: Theory and Evidence for CES Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(1), pages 503-560.
    7. Gabriel Ehrlich & John Haltiwanger & Ron Jarmin & David Johnson & Ed Olivares & Luke Pardue & Matthew D. Shapiro & Laura Yi Zhao, 2023. "Quality Adjustment at Scale: Hedonic vs. Exact Demand-Based Price Indices," Working Papers 23-26, Center for Economic Studies, U.S. Census Bureau.
    8. Greenlees John S. & Williams Elliot, 2010. "Reconsideration of Weighting and Updating Procedures in the US CPI," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 230(6), pages 741-758, December.
    9. Benjamin R. Mandel, 2011. "The dynamics and differentiation of Latin American metal exports," Staff Reports 508, Federal Reserve Bank of New York.
    10. Baldwin, John R. Maynard, Jean-Pierre Tanguay, Marc Wong, Fanny Yan, Beiling, 2005. "Comparaison des niveaux de productivité au Canada et aux États-Unis : étude de certains aspects de la mesure," Série de documents de recherche sur l'analyse économique (AE) 2005028f, Statistics Canada, Direction des études analytiques.
    11. John S. Greenlees & Elliot Williams, 2009. "Reconsideration of Weighting and Updating Procedures in the US CPI," Working Papers 431, U.S. Bureau of Labor Statistics.

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    More about this item

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • O53 - Economic Development, Innovation, Technological Change, and Growth - - Economywide Country Studies - - - Asia including Middle East

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