Accounting for variety

Winkler, Julian (2022): Accounting for variety.

Abstract

I introduce a general method to account for the distribution of underlying components (variety) of an aggregate quantity, using the notion of entropy. This accounting decomposition enables a number of insightful applications for index numbers in economics. The cross-entropy of GDP with respect to a benchmark captures the change in its distribution, and thus how well this benchmark matches data for price and volume indices across time. This 'error' changes demonstrably over time. Accounting of variety also lends itself to an decomposition of labour productivity growth by a technology component (how many more `average' goods are produced per unit of labor?), an allocation component (does the distribution of labor inputs converge to the distribution of outputs?), and cost disease (does the distribution of expenditures diverge from the distribution of outputs?).

• Item Type: MPRA Paper
• Language: English
• Keywords: National accounting, beyond GDP, entropy, misallocation
• Subjects: E - Macroeconomics and Monetary Economics > E0 - General > E01 - Measurement and Data on National Income and Product Accounts and Wealth ; Environmental Accounts; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O47 - Empirical Studies of Economic Growth ; Aggregate Productivity ; Cross-Country Output Convergence

References

Aghion, P., Bergeaud, A., Boppart, T., Klenow, P. J. & Li, H. (2019), ‘Missing growth from creative destruction’, American Economic Review 109(8), 2795–2822.

Aghion, P. & Howitt, P. (1992), ‘A model of growth through creative destruction’, Econometrica 60(2), 323–351.

Baqaee, D. & Burstein, A. (2021), Welfare and output with income effects and taste shocks, Working Paper 28754, National Bureau of Economic Research.

Bresnahan, T. F. & Gordon, R. J., eds (1997), The Economics of New Goods, University of Chicago Press.

Cover, T. M. & Thomas, J. A. (2005), Entropy, Relative Entropy, and Mutual Information, John Wiley & Sons, Ltd, chapter 2, pp. 13–55.

Diewert, W. (1976), ‘Exact and superlative index numbers’, Journal of Econometrics 4(2), 115 – 145.

Eichhorn, W. (1978), Systems of Functional Equations in the Theory of the Price Index, Addison-Wesley Publishing Company, chapter 8, pp. 151–172.

Fisher, I. (1922), The Making of Index Numbers, Houghton-Mifflin.

Goldin, I., Koutroumpis, P., Lafond, F. & Winkler, J. (2021), ‘Why is productivity slowing down?’, Working Paper .

Gordon, R. J. (2009), Apparel prices 1914-93 and the hulten/bruegel paradox, in W. E. Diewert, J. S. Greenlees & C. R. Hulten, eds, ‘Price Index Concepts and Measurement’, University of Chicago Press, pp. 85–128.

Hulten, C. R. (1997), Comment on “do real-output and real-wage measures capture reality? The history of lighting suggests not”, in Bresnahan & Gordon (1997), pp. 66–70.

Nordhaus, W. D. (1997), Do real-output and real-wage measures capture reality? The history of lighting suggests not, in Bresnahan & Gordon (1997), pp. 27–70.

Redding, S. J. & Weinstein, D. E. (2019), ‘Measuring Aggregate Price Indices with Taste Shocks: Theory and Evidence for CES Preferences’, The Quarterly Journal of Economics 135(1), 503–560.

Sato, K. (1976), ‘The ideal log-change index number’, The Review of Economics and Statistics 58(2), 223–228.

Shannon, C. E. (1948), ‘A Mathematical Theory of Communication’, The Bell System Technical Journal 27, 379 – 423.

Tang, J. & Wang, W. (2004), ‘Sources of aggregate labour productivity growth in canada and the United States’, The Canadian Journal of Economics / Revue canadienne d’Economique 37(2), 421–444.

Törnqvist, L. (1936), ‘The bank of finland’s consumption price index’, Bank of Finland Monthly Bulletin 10, 1–8.

Vartia, Y. O. (1976), ‘Ideal log-change index numbers’, Scandinavian Journal of Statistics 3(3), 121–126.