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Multilateral Index Number Systems for International Price Comparisons: Properties, Existence and Uniqueness

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Abstract

Over the past five decades a number of multilateral index number systems have been proposed for spatial and cross-country price comparisons. These multilateral indexes are usually expressed as solutions to systems of linear or nonlinear equations. In this paper, we provide general theorems that can be used to establish necessary and sufficient conditions for the existence and uniqueness of the Geary-Khamis, IDB, Neary and Rao indexes as well as potential new systems including two generalized systems of index numbers. One of our main results is that the necessary and sufficient conditions for existence and uniqueness of solutions can often be stated in terms of graph-theoretic concepts and a verifiable condition based on observed quantities of commodities.

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  • Gholamreza Hajargasht & D.S. Prasada Rao, 2019. "Multilateral Index Number Systems for International Price Comparisons: Properties, Existence and Uniqueness," CEPA Working Papers Series WP032019, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uqcepa:133
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    File URL: https://economics.uq.edu.au/files/12951/WP032019.pdf
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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Fuentes-Albero, Cristina & Melosi, Leonardo, 2013. "Methods for computing marginal data densities from the Gibbs output," Journal of Econometrics, Elsevier, vol. 175(2), pages 132-141.
    3. repec:wly:japmet:v:32:y:2017:i:4:p:802-818 is not listed on IDEAS
    4. Nott, David J. & Li, Jialiang & Fielding, Mark, 2011. "Importance sampling as a variational approximation," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1052-1055, August.
    5. Perrakis, Konstantinos & Ntzoufras, Ioannis & Tsionas, Efthymios G., 2014. "On the use of marginal posteriors in marginal likelihood estimation via importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 54-69.
    6. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
    7. Kociecki, Andrzej & Rubaszek, Michał & Ca' Zorzi, Michele, 2012. "Bayesian analysis of recursive SVAR models with overidentifying restrictions," Working Paper Series 1492, European Central Bank.
    8. World Bank, 2015. "Purchasing Power Parities and Real Expenditures of World Economics : A Comprehensive Report of the 2011 International Comparison Program," World Bank Publications, The World Bank, number 20526, October.
    9. Sims, Christopher A. & Waggoner, Daniel F. & Zha, Tao, 2008. "Methods for inference in large multiple-equation Markov-switching models," Journal of Econometrics, Elsevier, vol. 146(2), pages 255-274, October.
    10. Chan, Joshua C.C. & Grant, Angelia L., 2015. "Pitfalls of estimating the marginal likelihood using the modified harmonic mean," Economics Letters, Elsevier, vol. 131(C), pages 29-33.
    11. Efthymios Tsionas, 2000. "Full Likelihood Inference in Normal-Gamma Stochastic Frontier Models," Journal of Productivity Analysis, Springer, vol. 13(3), pages 183-205, May.
    12. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    13. Joshua C. C. Chan & Eric Eisenstat, 2015. "Marginal Likelihood Estimation with the Cross-Entropy Method," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 256-285, March.
    14. McGrory, C.A. & Titterington, D.M., 2007. "Variational approximations in Bayesian model selection for finite mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5352-5367, July.
    15. Chib, Siddhartha & Greenberg, Edward & Winkelmann, Rainer, 1998. "Posterior simulation and Bayes factors in panel count data models," Journal of Econometrics, Elsevier, vol. 86(1), pages 33-54, June.
    16. Rao, D.S. Prasada & Hajargasht, Gholamreza, 2016. "Stochastic approach to computation of purchasing power parities in the International Comparison Program (ICP)," Journal of Econometrics, Elsevier, vol. 191(2), pages 414-425.
    17. Robert C. Feenstra & Hong Ma & J. Peter Neary & D.S. Prasada Rao, 2013. "Who Shrunk China? Puzzles in the Measurement of Real GDP," Economic Journal, Royal Economic Society, vol. 123(12), pages 1100-1129, December.
    18. J. Peter Neary, 2004. "Rationalizing the Penn World Table: True Multilateral Indices for International Comparisons of Real Income," American Economic Review, American Economic Association, vol. 94(5), pages 1411-1428, December.
    19. repec:bla:revinw:v:45:y:1999:i:2:p:235-249 is not listed on IDEAS
    20. Ardia, David & Baştürk, Nalan & Hoogerheide, Lennart & van Dijk, Herman K., 2012. "A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3398-3414.
    21. Cuthbert, James R, 1999. "Categorisation of Additive Purchasing Power Parities," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 45(2), pages 235-249, June.
    22. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.
    23. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    24. Sims, Christopher A & Zha, Tao, 1998. "Bayesian Methods for Dynamic Multivariate Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 949-968, November.
    25. Hill, Robert J., 2000. "Measuring substitution bias in international comparisons based on additive purchasing power parity methods," European Economic Review, Elsevier, vol. 44(1), pages 145-162, January.
    26. repec:kap:jproda:v:50:y:2018:i:1:d:10.1007_s11123-018-0531-0 is not listed on IDEAS
    27. van den Broeck, Julien & Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1994. "Stochastic frontier models : A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 61(2), pages 273-303, April.
    28. Doris M. Iklé, 1972. "A New Approach to the Index Number Problem," The Quarterly Journal of Economics, Oxford University Press, vol. 86(2), pages 188-211.
    29. Gholamreza Hajargasht & D. S. Prasada Rao, 2010. "Stochastic Approach To Index Numbers For Multilateral Price Comparisons And Their Standard Errors," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 32-58, June.
    30. Gholamreza Hajargasht & William E. Griffiths, 2018. "Estimation and testing of stochastic frontier models using variational Bayes," Journal of Productivity Analysis, Springer, vol. 50(1), pages 1-24, October.
    31. Jim Griffin & Mark Steel, 2007. "Bayesian stochastic frontier analysis using WinBUGS," Journal of Productivity Analysis, Springer, vol. 27(3), pages 163-176, June.
    32. Reza Hajargasht & Robert J. Hill & D. S. Prasada Rao & Sriram Shankar, 2018. "Spatial Chaining in International Comparisons of Prices and Real Incomes," Graz Economics Papers 2018-03, University of Graz, Department of Economics.
    33. Braun, Michael & McAuliffe, Jon, 2010. "Variational Inference for Large-Scale Models of Discrete Choice," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 324-335.
    34. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2008. "Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4608-4624, June.
    35. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    36. Feenstra, Robert C. & Ma, Hong & Rao, D. S. Prasada, 2009. "Consistent Comparisons Of Real Incomes Across Time And Space," Macroeconomic Dynamics, Cambridge University Press, vol. 13(S2), pages 169-193, September.
    37. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    38. Rao, D. S. Prasada, 1976. "Existence and Uniqueness of a System of Consistent Index Numbers," Economic Review, Hitotsubashi University, vol. 27(3), pages 212-218, July.
    39. Beckers, Dominique E. & Hammond, Christopher J., 1987. "A tractable likelihood function for the normal-gamma stochastic frontier model," Economics Letters, Elsevier, vol. 24(1), pages 33-38.
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    Keywords

    purchasing power parities; international prices; nonlinear Perron-Frobenius problem; connected graphs; DAD problem; generalized mean;

    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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