Advertisement

Swiss Journal of Economics and Statistics

, Volume 144, Issue 2, pp 117–151 | Cite as

Improving Models of Income Dynamics Using Cross-Section-Information

  • Robert Aebi
  • Klaus Neusser
  • Peter Steiner
Open Access
Article

Summary

Based on a relative entropy approach, this paper proposes a method to estimate or update transition matrices using just cross-sectional observations at two points in time. The method is then applied to explain the development of the US income distribution. Starting from three hypothesized transition matrices and a transition matrix estimated from the PSID data, we show how these matrices must be adjusted in the light of the cross-sectional information. Finally, we explore the consequences of these updated transition matrices for the future development of the US income distribution.

Keywords

income distribution income dynamics relative entropy 

JEL-Classification

D31 C51 

References

  1. Adelman, Irma, Samuel Morley, Christoph Schenzler, and Matthew Warning (1994), “Estimating Income Mobility from Census Data”, Journal of Policy Modeling, 16, pp. 187–213.CrossRefGoogle Scholar
  2. Aebi, Robert and Masao Nagasawa (1992), “Large Deviations and the propagation of Chaos for Schrödinger Processes”, Probability Theory and Related Fields, 94, pp. 53–68.CrossRefGoogle Scholar
  3. Aebi, Robert (1996), “Schrödinger’s Time-Reversal of Natural Laws”, The Mathematical Intelligencer, 18, pp. 62–67.CrossRefGoogle Scholar
  4. Aebi, Robert (1997), “Contingency Tables with Prescribed Marginals”, Statistical Papers, 38, pp. 219–229.CrossRefGoogle Scholar
  5. Aebi, Robert, Klaus Neusser, and Peter Steiner (1999), “Evaluating Theories of Income Dynamics: A Probabilistic Approach”, Discussion Paper 99-05, University of Berne.Google Scholar
  6. Aebi, Robert, Klaus Neusser, and Peter Steiner (2006), “A Large Deviation Approach to the Measurement of Mobility”, Swiss Journal of Economics and Statistics, 142 (2), pp. 195–222.Google Scholar
  7. Bartholomew, David J. (1982), Stochastic Models of Social Processes (3rd ed.), Chichester.Google Scholar
  8. Boyarsky, Abraham, and Pawel Góra (1997), Laws of Chaos, Boston.Google Scholar
  9. Burkhauser, Richard V., Amy Crews Cutts, Mary C. Daly, and Stephen P. Jenkins (1999), “Testing the Significance of Income Distribution Changes over the 1980s Business Cycle: A Cross-National Comparison”, Journal of Applied Econometrics, 14, pp. 253–272.CrossRefGoogle Scholar
  10. Champernowne, David G. (1953), “A Model of Income Distribution”, Economic Journal, 63, pp. 318–351.CrossRefGoogle Scholar
  11. Csiszár, Imre. (1975), “I-Divergence Geometry of Probability Distributions and Minimization Problems”, The Annals of Probability, 3, pp. 146–158.CrossRefGoogle Scholar
  12. Deming, W. Edwards and Frederick F. Stephan (1940), “On a Least Squares Adjustment of a Sampled Frequency Table when the Expected Marginal Totals are Known”, Annals of Mathematical Statistics, 11, pp. 427–444.CrossRefGoogle Scholar
  13. Ellis, Richard S. (1985), Entropy, Large Deviations, and Statistical Mechanics, New York.Google Scholar
  14. Golan, Amos, George G. Judge, and Douglas Miller (1996), Maximum Entropy Econometrics, Chichester.Google Scholar
  15. Haberman, Shelby J. (1984), “Adjustment by Minimum Discriminant Information”, Annals of Statistics, 12, pp. 971–988.CrossRefGoogle Scholar
  16. Ireland, C. Terrence, and Solomon Kullback (1968), “Contingency Tables with Given Marginals”, Biometrika, 55, pp. 179–188.CrossRefGoogle Scholar
  17. Kalbfleisch, John D., and Jerald F. Lawless (1984), “Least-Squares Estimation of Transition Probabilities from Aggregate Data”, Canadian Journal of Statistics, 12, pp. 169–182.CrossRefGoogle Scholar
  18. Kullback, Solomon (1959), Information Theory and Statistics, New York.Google Scholar
  19. Lanford, Oscar E. (1973), “Entropy and Equilibrium States in Classical Statistical Mechanics”, Lecture Notes in Physics, 20, pp. 1–113.CrossRefGoogle Scholar
  20. Lee, Tsoung-Chao, George G. Judge, and Arnold Zellner (1970), Estimating the Parameters of the Markov Model from Aggregate Time Series Data, Amsterdam.Google Scholar
  21. Prais, Sig J. (1955), “Measuring Social Mobility”, Journal of the Royal Statistical Society, 188, pp. 56–66.CrossRefGoogle Scholar
  22. Schrödinger, Erwin (1931), “Über die Umkehrung der Naturgesetze”, Sitzungsberichte der Preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, pp. 144–153.Google Scholar
  23. Silverman, Bernard W. (1986), Density Estimation for Statistics and Data Analysis, London.Google Scholar
  24. Sinkhorn, Richard (1964), “A Relationship between Arbitrary Positive Matrices and Doubly Stochastic Matrices”, The Annals of Mathematical Statistics, 35, pp. 876–879.CrossRefGoogle Scholar
  25. Sinkhorn, Richard (1967), “Diagonal Equivalence to Matrices with Prescribed Row and Column Sums”, The American Mathematical Monthly, 74, pp. 402–405.CrossRefGoogle Scholar
  26. Smith, John H. (1947), “Estimation of Linear Functions of Cell Proportions”, Annals of Mathematical Statistics, 13, pp. 166–178.Google Scholar
  27. Steiner, Peter (2004), Anwendungen von Konzepten grosser Abweichungen auf Fragestellungen der Einkommensdynamik, Berlin.Google Scholar
  28. Tauchen, George (1986), “Finite State Markov-Chain Approximations to Univariate and Vector Autoregressions”, Economics Letters, 20, pp. 177–181.CrossRefGoogle Scholar
  29. White, Halbert (1994), Estimation, Inference and Specification Analysis, Cambridge.Google Scholar

Copyright information

© Swiss Journal of Economics and Statistics 2008

Authors and Affiliations

  • Robert Aebi
    • 1
  • Klaus Neusser
    • 2
  • Peter Steiner
    • 2
    • 3
  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis PasteurStrasbourg CedexFrance
  2. 2.Department of EconomicsUniversity of BernBernSwitzerland
  3. 3.State Secretariat for Economic Affairs, SECOBernSwitzerland

Personalised recommendations