Iliadi, Fotoula and Mariolis, Theodore and Soklis, George and Tsoulfidis, Lefteris (2012): Bienenfeld’s approximation of production prices and eigenvalue distribution: some more evidence from five European economies.

PDF
MPRA_paper_36282.pdf Download (590kB)  Preview 
Abstract
This paper tests Bienenfeld’s polynomial approximation of production prices using data from ten symmetric inputoutput tables of five European economies. The empirical results show that the quadratic formula works extremely well and its accuracy is connected to the actual distribution of the eigenvalues of the matrices of vertically integrated technical coefficients.
Item Type:  MPRA Paper 

Original Title:  Bienenfeld’s approximation of production prices and eigenvalue distribution: some more evidence from five European economies 
Language:  English 
Keywords:  Bienenfeld’s approximation; Damping ratio; Eigenvalue distribution; Empirical evidence; Production prices 
Subjects:  B  History of Economic Thought, Methodology, and Heterodox Approaches > B5  Current Heterodox Approaches > B51  Socialist ; Marxian ; Sraffian D  Microeconomics > D4  Market Structure, Pricing, and Design > D46  Value Theory D  Microeconomics > D5  General Equilibrium and Disequilibrium > D57  InputOutput Tables and Analysis C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67  InputOutput Models E  Macroeconomics and Monetary Economics > E1  General Aggregative Models > E11  Marxian ; Sraffian ; Kaleckian 
Item ID:  36282 
Depositing User:  Theodore Mariolis 
Date Deposited:  30. Jan 2012 07:43 
Last Modified:  12. Feb 2013 13:28 
References:  Bienenfeld, M. (1988) Regularity in price changes as an effect of changes in distribution, Cambridge Journal of Economics, 12 (2), pp. 247255. Bródy, A. (1997) The second eigenvalue of the Leontief matrix, Economic Systems Research, 9 (3), pp. 253258. Burmeister, E. (1968) On a theorem of Sraffa, Economica, 35 (137), pp. 8387. Goldberg, G., Okunev, P., Neumann, M. and Schneider, H. (2000) Distribution of subdominant eigenvalues of random matrices, Methodology and Computing in Applied Probability, 2 (2), pp. 137151. Goldberg, G. and Neumann, M. (2003) Distribution of subdominant eigenvalues of matrices with random rows, Society for Industrial and Applied Mathematics Journal on Matrix Analysis and Applications, 24 (3), pp. 747761. Hartfiel, D. J. and Meyer, C. D. (1998) On the structure of stochastic matrices with a subdominant eigenvalue near 1, Linear Algebra and its Applications, 272 (13), pp. 193203. Keyfitz, N. and Caswell, H. (2005) Applied Mathematical Demography, Third Edition (New York: Springer). Kurz, H. D. and Salvadori, N. (1995) Theory of Production. A LongPeriod Analysis (Cambridge: Cambridge University Press). Maitre, J. F. (1970) Sur la séparation des valeurs propres d’une matrice positive, Revue Française d’Informatique and et de recherche opérationnel, Série Rouge, 4 (3), pp. 118124. Mariolis, T. and Soklis, G. (2010) Additive labour values and prices of production: evidence from the supply and use tables of the French, German and Greek economies, Economic Issues, 15 (2), pp. 87107. Mariolis, T., Soklis, G. and Iliadi, F. (2010) Eigenvalue distribution and Bienenfeld’s quadratic formula (in Greek), Internal Report of the ‘Study Group on Sraffian Economics’, July 2010, Department of Public Administration, Panteion University, Mimeo. Mariolis, T. and Soklis, G. (2011) On constructing numerairefree measures of pricevalue deviation: a note on the SteedmanTomkins distance, Cambridge Journal of Economics, 35 (3), pp. 613618. Mariolis, T. and Tsoulfidis, L. (2009) Decomposing the changes in production prices into ‘capitalintensity’ and ‘price’ effects: theory and evidence from the Chinese economy, Contributions to Political Economy, 28 (1), pp. 122. Mariolis, T. and Tsoulfidis, L. (2010a) Measures of production pricelabour value deviation and income distribution in actual economies: a note, Metroeconomica, 61 (4), pp. 701710 (enlarged version: Measures of production pricelabour value deviation and income distribution in actual economies: theory and empirical evidence, Discussion Paper No. 02/2010, Discussion Paper Series, University of Macedonia, Department of Economics. http://econlab.uom.gr/~econwp/pdf/dp0210.pdf ). Mariolis, T. and Tsoulfidis, L. (2010b) Eigenvalue distribution and the production priceprofit rate relationship in linear singleproduct systems: theory and empirical evidence, Discussion Paper No. 16/2010, Discussion Paper Series, University of Macedonia, Department of Economics. http://econlab.uom.gr/~econwp/pdf/dp162010.pdf Mariolis, T. and Tsoulfidis, L. (2011) Eigenvalue distribution and the production priceprofit rate relationship: theory and empirical evidence, Evolutionary and Institutional Economics Review, 8 (1), pp. 87122. Ochoa, E. (1989) Value, prices and wageprofit curves in the US economy, Cambridge Journal of Economics, 13 (3), pp. 413429. Ostrowski, A. M. (1963) On positive matrices, Mathematische Annalen, 150 (3), pp. 276284. Pasinetti, L. (1973) The notion of vertical integration in economic analysis, Metroeconomica, 25 (1), pp. 129. Pasinetti, L. (1977) Lectures on the Theory of Production (New York: Columbia University Press). Petrović, P. (1991) Shape of a wageprofit curve, some methodology and empirical evidence, Metroeconomica, 42 (2), pp. 93112. Schefold, B. (2008a) C.E.S. production functions in the light of the Cambridge critique, Journal of Macroeconomics, 30 (2), pp. 783797. Schefold, B. (2008b) Families of strongly curved and of nearly linear wage curves: a contribution to the debate about the surrogate production function, Bulletin of Political Economy, 2 (1), pp. 124. Schefold, B. (2008c) Approximate surrogate production functions, Institut für Volkswirtschaftslehre, Johann Wolfgang GoetheUniversität, Mimeo. Seneta, R. E. (2006) Nonnegative Matrices and Markov Chains, Revised Printing, Springer Series in Statistics (New York: Springer). Shaikh, A. M. (1998) The empirical strength of the labour theory of value, in: R. Bellofiore (Ed.) (1998) Marxian Economics: A Reappraisal, vol. 2, pp. 225251 (New York: St. Martin’s Press). Shaikh, A. (2010) The empirical linearity of Sraffa’s critical outputcapital ratios, New School for Social Research, Mimeo (Forthcoming in a Festschrift Volume in Honor of Heinz Kurz). http://homepage.newschool.edu/~AShaikh/Shaikh%20Kurz%20fest%20linear%20std%20prices.pdf Soklis, G. (2009) Alternative value bases and prices: evidence from the inputoutput tables of the Swedish economy, Journal of Applied InputOutput Analysis, 15 (1), pp. 2139. Soklis, G. (2011) Shape of wageprofit curves in joint production systems: evidence from the supply and use tables of the Finnish economy, Metroeconomica, 62 (4), pp. 548560 (enlarged version: Wageprofit curves of the Finnish economy: evidence from the supply and use tables, MPRA Paper No. 30183, http://mpra.ub.unimuenchen.de/30183/). Sraffa, P. (1960) Production of Commodities by Means of Commodities. Prelude to a Critique of Economic Theory (Cambridge: Cambridge University Press). Steedman, I. (1999) Vertical integration and ‘reduction to dated quantities of labour’, in: G. Mongiovi and F. Petri (Eds) (1999) Value Distribution and Capital. Essays in Honour of Pierangelo Garegnani, pp. 314318 (London and New York: Routledge). Steedman, I. and Tomkins, J. (1998) On measuring the deviation of prices from values, Cambridge Journal of Economics, 22 (3), pp. 379385. Steenge, A. E. and Thissen, M. J. P. M. (2005) A new matrix theorem: interpretation in terms of internal trade structure and implications for dynamic systems, Journal of Economics, 84 (1), pp. 7194. Sun, G. Z. (2008) The first two eigenvalues of large random matrices and Brody’s hypothesis on the stability of large inputoutput systems, Economic Systems Research, 20 (4), pp. 429432. Tsoulfidis, L. and Mariolis, T. (2007) Labour values, prices of production and the effects of income distribution: evidence from the Greek economy, Economic Systems Research, 19 (4), pp. 425437. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/36282 