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EXACT AND SUPERLATIVE PRICE AND QUANTITY INDICATORS

Published online by Cambridge University Press:  15 September 2009

W. Erwin Diewert  and
Hideyuki Mizobuchi
W. Erwin Diewert*
Affiliation:
University of British Columbia
Hideyuki Mizobuchi
Affiliation:
University of British Columbia
*
Address correspondence to: W. Erwin Diewert, Department of Economics, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada; e-mail: diewert@econ.ubc.ca.
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Abstract

The traditional economic approach to index number theory is based on a ratio of cost functions. Diewert defined superlative price and quantity indices as observable indices that were exact for a ratio of unit cost functions or for a ratio of linearly homogeneous utility functions. The present paper looks for counterparts to his results in the difference context, for both flexible homothetic and flexible nonhomothetic preferences. The Bennet indicators of price and quantity change turn out to be superlative for the nonhomothetic case. The underlying preferences are of the translation-homothetic form discussed by Balk, Chambers, Dickenson, Färe, and Grosskopf.

Keywords

Equivalent and Compensating VariationsExact and Superlative IndicesBennet Indicators

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Type
Articles
Information
Macroeconomic Dynamics , Volume 13 , Supplement S2: Measurement with Theory , September 2009 , pp. 335 - 380
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Afriat, S.N. (1972) The theory of international comparisons of real income and prices. In Daly, D. J. (ed.), International Comparisons of Prices and Outputs, pp. 13–69. Chicago: University of Chicago Press.Google Scholar
Allen, R.G.D. (1949) The economic theory of index numbers. Economica 16, 197–203.CrossRefGoogle Scholar
Balk, B.M. (1989) Changing consumer preferences and the cost of living index: Theory and nonparametric expressions. Journal of Economics 50 (2), 157–169.CrossRefGoogle Scholar
Balk, B.M. (1995) Axiomatic price index theory: A survey. International Statistical Review 63, 69–93.CrossRefGoogle Scholar
Balk, B.M. (2007) Measuring Productivity Change without Neoclassical Assumptions: A Conceptual Analysis. Paper presented at the Sixth Annual Ottawa Productivity Workshop, Bank of Canada, May 14–15, 2007.Google Scholar
Balk, B.M., Färe, R., and Grosskopf, S. (2004) The theory of economic price and quantity indicators. Economic Theory 23, 149–164.CrossRefGoogle Scholar
Bennet, T.L. (1920) The theory of measurement of changes in cost of living. Journal of the Royal Statistics Society 83, 455–462.CrossRefGoogle Scholar
Blackorby, C., Boyce, R., and Russell, R.R. (1978) Estimation of demand systems generated by the Gorman polar form: A generalization of the S-branch utility tree. Econometrica 46, 345–363.CrossRefGoogle Scholar
Blackorby, C. and Diewert, W.E. (1979) Expenditure functions, local duality and second order approximations. Econometrica 47, 579–601.CrossRefGoogle Scholar
Chambers, R.G. (2001) Consumers' surplus as an exact and superlative cardinal welfare indicator. International Economic Review 41, 105–119.CrossRefGoogle Scholar
Chambers, R.G. and Färe, R. (1998) Translation homotheticity. Economic Theory 11, 629–641.CrossRefGoogle Scholar
Dickinson, J.G. (1980) Parallel preference structures in labour supply and commodity demand: An adaptation of the Gorman polar form. Econometrica 48, 1711–1725.CrossRefGoogle Scholar
Diewert, W.E. (1974) Applications of duality theory. In Intriligator, M.D. and Kendrick, D.A. (eds.), Frontiers of Quantitative Economics, vol. II, pp. 106–171. Amsterdam: North-Holland. Available at http://www.econ.ubc.ca/diewert/theory.pdf. Accessed 19 June 2009.Google Scholar
Diewert, W.E. (1976) Exact and superlative index numbers. Journal of Econometrics 4, 114–145.CrossRefGoogle Scholar
Diewert, W.E. (1992a) Exact and superlative welfare change indicators. Economic Inquiry 30, 565–582.CrossRefGoogle Scholar
Diewert, W.E. (1992b) Fisher ideal output, input and productivity indexes revisited. Journal of Productivity Analysis 3, 211–248.CrossRefGoogle Scholar
Diewert, W.E. (1993) Duality approaches to microeconomic theory. In Diewert, W.E. and Nakamura, A.O. (eds.), Essays in Index Number Theory, vol. 1, pp. 105–175. Amsterdam: North-Holland.Google Scholar
Diewert, W.E. (2002) The quadratic approximation lemma and decompositions of superlative indexes. Journal of Economic and Social Measurement 28, 63–88.CrossRefGoogle Scholar
Diewert, W.E. (2005) Index number theory using differences instead of ratios. American Journal of Economics and Sociology 64 (1), 311–360.CrossRefGoogle Scholar
Diewert, W.E. and Lawrence, D. (2006) Measuring the Contributions of Productivity and Terms of Trade to Australia's Economic Welfare. Report by Meyrick and Associates to the Productivity Commission, Canberra, Australia.Google Scholar
Diewert, W.E. and Morrison, C.J. (1986) Adjusting output and productivity indexes for changes in the terms of trade. Economic Journal 96, 659–679.CrossRefGoogle Scholar
Diewert, W.E. and Wales, T.J. (1987) Flexible functional forms and global curvature conditions. Econometrica 55, 43–68.CrossRefGoogle Scholar
Diewert, W.E. and Wales, T.J. (1988a) A normalized quadratic semiflexible functional form. Journal of Econometrics 37, 327–42.CrossRefGoogle Scholar
Diewert, W.E. and Wales, T.J. (1988b) Normalized quadratic systems of consumer demand functions. Journal of Business and Economic Statistics 6, 303–12.Google Scholar
Fenchel, W. (1953) Convex Cones, Sets and Functions. Lecture Notes at Princeton University, Department of Mathematics, Princeton, NJ.Google Scholar
Fisher, I. (1922) The Making of Index Numbers. Houghton-Mifflin, Boston.Google Scholar
Fox, K.J. (2006) A method for transitive and additive multilateral comparisons: A transitive Bennet indicator. Journal of Economics 87, 73–87.CrossRefGoogle Scholar
Henderson, A. (1941) Consumer's surplus and the compensating variation. Review of Economic Studies 8, 117–121.CrossRefGoogle Scholar
Hicks, J.R. (1939) Value and Capital. Oxford. UK: Clarendon Press.Google Scholar
Hicks, J.R. (1942) Consumers' surplus and index numbers. Review of Economic Studies 9, 126–137.CrossRefGoogle Scholar
Hicks, J.R. (1943) The four consumer's surpluses. Review of Economic Studies 11, 31–41.CrossRefGoogle Scholar
Hicks, J.R. (1945–1946) The generalized theory of consumers' surplus. Review of Economic Studies 13, 68–74.CrossRefGoogle Scholar
Hicks, J.R. (1946) Value and Capital, 2nd ed.Oxford, UK: Clarendon Press.Google Scholar
Kohli, U. (1990) Growth accounting in the open economy: Parametric and nonparametric estimates. Journal of Economic and Social Measurement 16, 125–136.CrossRefGoogle Scholar
Kohli, U. (1991) Technology, Duality and Foreign Trade: The GNP Function Approach to Modeling Imports and Exports. Ann Arbor: University of Michigan Press.Google Scholar
Konüs, A.A. (1939) The problem of the true index of the cost of living. Econometrica 7, 10–29.CrossRefGoogle Scholar
Konüs, A.A. and Byushgens, S.S. (1926) K probleme pokupatelnoi cili deneg. Voprosi Konyunkturi 2, 151–172.Google Scholar
Lau, L.J. and Tamura, S. (1972) Economies of scale, technical progress and the nonhomothetic generalized Leontief production function: An application to the Japanese petrochemical processing industry. Journal of Political Economy 80, 1167–1187.CrossRefGoogle Scholar
Malmquist, S. (1953) Index numbers and indifference surfaces. Trabajos de Estatistica 4, 209–242.CrossRefGoogle Scholar
Morrison, C. and Diewert, W.E. (1990) Productivity growth and changes in the terms of trade in Japan and the United States. In Hulten, C.R. (ed.). Productivity Growth in Japan and the United States, pp. 201–227. Chicago: University of Chicago Press.Google Scholar
Pollak, R.A. (1983) The theory of the cost-of-living index. In Diewert, W.E. and Montmarquette, C. (eds.). Price Level Measurement, pp. 87–161. Ottawa: Statistics Canada. Reprinted 1989 in R.A. Pollak, The Theory of the Cost-of-Living Index, pp. 3–52. Oxford, UK: Oxford University Press.Google Scholar
Rockafellar, R.T. (1970) Convex Analysis. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Samuelson, P.A. (1947) Foundations of Economic Analysis. Cambridge, MA: Harvard University Press.Google Scholar
Samuelson, P.A. (1953) Prices of factors and goods in general equilibrium. Review of Economic Studies 21, 1–20.CrossRefGoogle Scholar
Samuelson, P.A. (1974) Complementarity—An essay on the 40th anniversary of the Hicks–Allen revolution in demand theory. Journal of Economic Literature 12, 1255–1289.Google Scholar
Samuelson, P.A. and Swamy, S. (1974) Invariant economic index numbers and canonical duality: Survey and synthesis. American Economic Review 64, 566–593.Google Scholar
Shephard, R.W. (1953) Cost and Production Functions. Princeton, NJ: Princeton University Press.Google Scholar
Shephard, R.W. (1970) Theory of Cost and Production Functions. Princeton, NJ: Princeton University Press.Google Scholar
Theil, H. (1967) Economics and Information Theory. Amsterdam: North-Holland.Google Scholar
Törnqvist, L. (1936) The Bank of Finland's consumption price index. Bank of Finland Monthly Bulletin 10, 1–8.Google Scholar
Törnqvist, L. and Törnqvist, E. (1937) Vilket är förhållandet mellan finska markens och svenska kronans köpkraft? Ekonomiska Samfundets Tidskrift 39, 1–39. Reprinted 1981 in Collected Scientific Papers of Leo Törnqvist, pp. 121–160. Helsinki: The Research Institute of the Finnish Economy.Google Scholar
Weitzman, M.L. (1988) Consumer's surplus as an exact approximation when prices are appropriately deflated. Quarterly Journal of Economics 102, 543–553.CrossRefGoogle Scholar