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  • Per Hjertstrand (a1), James L. Swofford (a2) and Gerald A. Whitney (a3)

For previously identified weakly separable blockings of goods and assets, we construct aggregates using four superlative index numbers, the Fisher, Sato-Vartia, Törnqvist, and Walsh, two non-superlative indexes, the Laspeyres and Paasche, and the atheoretical simple summation. We conduct several tests to examine how well each of these aggregates “fit” the data. These tests are how close the aggregates come to solving the revealed preference conditions for weak separability, how often each aggregate gets the direction of change correct, and how well the aggregates mimic the preference ranking from revealed preference tests. We find that, as the number of goods and assets being aggregated increases, the problems with simple summation manifest.

Corresponding author
Address correspondence to: James Swofford, Department of Economics and Finance, University of South Alabama, Mobile, AL 36688, USA; e-mail: Phone: +1 251 460 6705.
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We thank two referees, Bill Barnett, and participants at the Society for Economic Measurement conference in Thessaloniki in July 2016 and the 3rd HenU/Infer Workshop on Applied Macroeconomics in March 2017 in Kaifeng for very helpful comments. Hjertstrand would like to thank the Jan Wallander och Tom Hedelius, Marcus och Marianne Wallenberg, and Johan och Jakob Söderberg foundations for financial support.

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Afriat, S. N. (1967) The construction of utility functions from expenditure data. International Economic Review 8, 6677.
Balk, M. B. (1995) Axiomatic price theory: A survey. International Statistical Review 63, 6393.
Barnett, W. A. (1980) Economic monetary aggregate: An application of index number and aggregation theory. Journal of Econometrics 14, 1148.
Barnett, W. A. and Choi, K.-H. (2008) Operational identification of the complete class of superlative index numbers: An application of Galois theory. Journal of Mathematical Economics 44, 603612.
Caves, D. W., Christensen, L. R. and Diewert, W. E. (1982) The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica 50, 13931414.
Cherchye, L., Demuynck, T., De Rock, B. and Hjertstrand, P. (2015) Revealed preference tests for weak separability: An integer programming approach. Journal of Econometrics 186, 129141.
Chrystal, K. A. and MacDonald, R. (1994) Empirical evidence on the recent behavior and usefulness of simple-sum and weighted measures of the money stock. Federal Reserve Bank of St. Louis Review 76, 73109.
Diewert, W. E. (1976) Exact and superlative index numbers. Journal of Econometrics 4, 115145.
Diewert, W. E. (1978) Superlative index numbers and consistency in aggregation. Econometrica, 46, 883900.
Diewert, W. E. (1993) Overview of volume 1. In: Diewert, W. E. and Nakamura, A. O. (eds.), Essays in Index Number Theory, pp. 131. Amsterdam: Elsevier Science Publishers B.V.
Diewert, W. E. and Parkan, C. (1985) Tests for the consistency of consumer data. Journal of Econometrics 30, 127147.
Elger, T. and Jones, B. E. (2008) Can rejections of weak separability be attributed to random measurement error in the data? Economic Letters 99, 4447.
Fleissig, A. R. and Whitney, G. A. (2003) A new PC-based test for Varian’s weak separability conditions. Journal of Business and Economic Statistics 21, 133144.
Fleissig, A. R. and Whitney, G. A. (2008) A nonparametric test of weak separability and consumer preferences. Journal of Econometrics 147, 275281.
Fisher, I. (1922) The Making of Index Numbers. Boston, MA: Houghton-Mifflin.
Friedman, M. and Schwartz, A. J. (1963) A Monetary History of the United States, 1867–1960. Study by the National Bureau of Economic Research. Princeton: Princeton University Press.
Friedman, M. and Schwartz, A. J. (1970) Monetary Statistics of the United States: Estimates, Sources, Methods. Study by the National Bureau of Economic Research. New York: Columbia University Press.
Hicks, J. R. (1946) Value and Capital, 2nd ed. Oxford: Clarendon Press.
Hjertstrand, P. (2009) A Monte Carlo study of the necessary and sufficient conditions for weak separability. Advances in Econometrics 24, 151182.
Hjertstrand, P., Swofford, J. L. and Whitney, G. (2016) Mixed integer programming revealed preference tests of utility maximization and weak separability of consumption, leisure and money. Journal of Money Credit and Banking 58, 15471561.
ILO (2004) Consumer Price Index Manual: Theory and Practice. Geneva: International Labour Organization. Downloadable at:
IMF (2005) Producer Price Index Manual: Theory and Practice. Washington, D.C.: International Monetary Fund. Downloadable at:
Jones, B. E., Dutkowsky, D. H. and Elger, T. (2005) Sweep programs and optimal monetary aggregation. Journal of Banking & Finance 29, 483508.
Leontief, W. V. (1936) Composite commodities and the problem of index numbers. Econometrica 4, 3559.
Samuelson, P. A. (1983) Foundations of Economic Analysis, Enlarged Edition. Cambridge, MA: Harvard University Press.
Schrijver, A. (1998) Theory of Linear and Integer Programming. Chichester, England: John Wiley & Sons.
Swofford, J. L. and Whitney, G. A. (1994) A revealed preference test for weakly separable utility maximization with incomplete adjustment. Journal of Econometrics 60, 235249.
Varian, H. R. (1983) Nonparametric tests of consumer behavior. Review of Economic Studies 50, 99110.
Vartia, Y. (1976) Ideal log-change index numbers. Scandinavian Journal of Statistics 3, 121126.
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Macroeconomic Dynamics
  • ISSN: 1365-1005
  • EISSN: 1469-8056
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