Value Data and the Fisher Index

Read  full  paper  at:http://www.scirp.org/journal/PaperInformation.aspx?PaperID=55732#.VS9-A9KqpBc

ABSTRACT

In this paper we show how to use value data (price times quantity) to construct Fisher price and quantity indexes. In particular, we think of revenue and expenditure data. This model extends the work of Cross and F?re, who showed how to recover relative prices from value data with no explicit price or quantity information. We examine the accuracy of our model over a range of price changes, firm sample sizes, and response variation, in a Monte Carlo experiment in which firms respond to price changes with error. The model outperforms it component indexes with accuracy levels that increase with response variation.

Cite this paper

Cross, R. and Färe, R. (2015) Value Data and the Fisher Index. Theoretical Economics Letters, 5, 262-267. doi:10.4236/tel.2015.52031.

References

[1] Cobb, C.W. and Douglas, P.H. (1928) A Theory of Production. American Economic Review, 18, 139-165.
[2] Farrell, M.J. (1957) The Measurement of Productive Efficiency. Journal of the Royal Statistical Society, Series A, 120, 253-281. http://dx.doi.org/10.2307/2343100
[3] Shephard, R.W. (1953) Cost and Production Functions. Princeton University Press, Princeton.
[4] Bowley, A.L. (1899) Wages, Nominal and Real. In: Palgrave, R.H.I., Ed., Dictionary of Political Economy, Macmillan, London.
[5] Fisher, I. (1921) The Best Form of Index Number. Journal of the American Statistical Association, 17, 533-537. http://dx.doi.org/10.2307/2965310
[6] Fisher, I. (1922) The Making of Index Numbers. Houghton-Mifflin, Boston.
[7] Konüs, A.A. (1939) The Problem of the True Index of the Cost of Living. Econometrica, 7, 10-29. http://dx.doi.org/10.2307/1906997
[8] Diewert, W.E. (1976) Exact and Superlative Index Numbers. Journal of Econometrics, 4, 115-145. http://dx.doi.org/10.1016/0304-4076(76)90009-9
[9] Diewert, W.E. (1992) Fisher Ideal Output, Input, and Productivity Indexes Revisited. Journal of Productivity Analysis, 3, 211-248. http://dx.doi.org/10.1007/BF00158354
[10] Malmquist, S. (1953) Index Numbers and Indifference Surfaces. Trabajos de Estatistica, 4, 209-242. http://dx.doi.org/10.1007/BF03006863
[11] Afriat, S.N. (1967) The Construction of Utility Functions from Expenditure Data. International Economics Review, 8, 67-77. http://dx.doi.org/10.2307/2525382
[12] Afriat, S.N. (1972) Efficiency Estimation of Production Functions. International Economics Review, 13, 568-598. http://dx.doi.org/10.2307/2525845
[13] Cross, R.M. and Fare, R. (2009) Value Data and the Bennet Price and Quantity Indicators. Economics Letters, 102, 19-21. http://dx.doi.org/10.1016/j.econlet.2008.10.003
[14] Balk, B.M. (2008) Price and Quantity Index Numbers. Cambridge University Press, New York. http://dx.doi.org/10.1017/CBO9780511720758
[15] Varian, H.R. (1984) The Nonparametric Approach to Production Analysis. Econometrica, 52, 579-597. http://dx.doi.org/10.2307/1913466
[16] Fare, R. and Primont, D. (1995) Multi-Output Production and Duality: Theory and Applications. Kluwer Academic Publishers, Netherlands. http://dx.doi.org/10.1007/978-94-011-0651-1
[17] Kuosmanen, T., Cherchye, L. and Simplanen, T. (2006) The Law of One Price in Data Envelopment Analysis: Restricting Weight Flexibility across Firms. European Journal of Operational Research, 170, 735-757. http://dx.doi.org/10.1016/j.ejor.2004.07.063
Advertisements

发表评论

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / 更改 )

Twitter picture

You are commenting using your Twitter account. Log Out / 更改 )

Facebook photo

You are commenting using your Facebook account. Log Out / 更改 )

Google+ photo

You are commenting using your Google+ account. Log Out / 更改 )

Connecting to %s