Jahrbuch für Regionalwissenschaft

, Volume 33, Issue 2, pp 135–150 | Cite as

The ADETON method

An application for the estimation of regional flow matrices
Original Paper
First Online:
Accepted:
  • 129 Downloads

Abstract

A problem encountered in many contexts is the estimation of matrices or tables from aggregate, heterogeneous, incomplete and contradictory information. In this paper the Adeton method is presented which can be used for this estimation task under quite general conditions. The Adeton method was originally developed to estimate flow matrices of regional labour markets in the Multi-Accounting System (MAS). However, it is applicable for many purposes, e.g. to estimate contingency tables or input-output and other flow matrices.

Adeton is based on a Bayesian inference model: Given a prior probability distribution on the set of possible matrices and information about the actual matrix consisting of a set of linear equality and inequality constraints, the complete matrix with highest posterior probability is calculated. The advantage of the Adeton approach is that it is possible to specify soft constraints which are obeyed only up to a certain degree.

It is shown that Adeton is an estimation method of entropy optimization type and in this respect is a generalization of the well known Iterative Proportional Fitting Algorithm (used in log-linear models) or of the equivalent RAS method (used in input-output analysis).

Keywords

Bayesian inference Worker flows Regional labour market 
This is a preview of subscription content, log in to check access.

References

  1. Bernardo JM, Smith AFM (1994) Bayesian theory. Wiley, Chichester CrossRefGoogle Scholar
  2. Blien U, Graef F (1998) Entropy optimizing methods for the estimation of tables. In: Balderjahn I, Mathar R, Schader M (eds) Classification, data analysis, and data highways. Proceedings of the 21st annual conference of the Gesellschaft für Klassifikation. Springer, Berlin, pp 3–15 CrossRefGoogle Scholar
  3. Blien U, Tassinopoulos A (2001) Forecasting regional employment with the ENTROP method. Reg Stud 35(2):113–124 CrossRefGoogle Scholar
  4. Deming WE, Stephan FF (1940) On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Ann Math Stat 11(1):427–444 CrossRefGoogle Scholar
  5. Ehrgott M (2005) Multicriteria optimization. Springer, Berlin, Heidelberg Google Scholar
  6. Flegg AF, Tohmo T (2011) Regional input-output tables and the FLQ formula: a case study of Finland. Reg Stud 47(5):703–721 CrossRefGoogle Scholar
  7. Haas A, Rothe T (2007) Labour market in motion: analysing regional flows in a multi-accounting system. Labour 21(4–5):667–687 CrossRefGoogle Scholar
  8. Hepple LW (1995a) Bayesian techniques in spatial and network econometrics: 1. Model comparison and posterior odds. Environ Plan A 27:447–469 CrossRefGoogle Scholar
  9. Hepple LW (1995b) Bayesian techniques in spatial and network econometrics: 2. Computational methods and algorithms. Environ Plan A 27:615–644 CrossRefGoogle Scholar
  10. Judge GG, Mittelhammer RC (2011) An information theoretic approach to econometrics. Cambridge University, Cambridge CrossRefGoogle Scholar
  11. Kádas SA, Klafszky E (1976) Estimation of the parameters in the gravity model for trip distribution. Reg Sci Urban Econ 6:439–457 CrossRefGoogle Scholar
  12. Kočvara M, Stingl M (2003) PENNON—a code for convex nonlinear and semidefinite programming. Optim Methods Softw 8(3):317–333 CrossRefGoogle Scholar
  13. Kullback S (1968) Information theory and statistics, 2nd edn. Dover, New York Google Scholar
  14. de Mesnard L (1994) Unicity of biproportion. SIAM J Matrix Anal Appl 15(2):490–495 CrossRefGoogle Scholar
  15. de Mesnard L, Miller RE (2006) A note on added information in the RAS procedure: reexamination of some evidence. J Reg Sci 46(3):517–528 CrossRefGoogle Scholar
  16. Niven RK (2006) Combinatorial information theory: I. Philosophical basis of cross-entropy and entropy. arXiv:cond-mat/0512017 v2
  17. Rampa G (2008) Using weighted least squares to deflate input-output tables. Econ Syst Res 20(3):259–276 CrossRefGoogle Scholar
  18. Raymer J, Willekens F (eds) (2007) International migration in Europe: data, models and estimates. Wiley, Chichester Google Scholar
  19. Reinberg A, Hummel M (2006) Zwanzig Jahre Bildungsgesamtrechnung. Beiträge zur Arbeitsmarkt- und Berufsforschung 306, Nürnberg Google Scholar
  20. Robert CP (2007) The Bayesian choice. Springer, New York Google Scholar
  21. Rodrigues J (2011) A Bayesian method to reconcile conflicting input-output data. Paper presented at the 14th annual conference on global economic analysis, Venice, Italy Google Scholar
  22. Roy JR, Hewings GJD (2009) Regional input-output with endogenous internal and external network flows. In: Karlsson C, Cheshire P, Andersson AE, Stough RR (eds) New directions in regional economic development. Springer, Berlin, Heidelberg, pp 161–176 CrossRefGoogle Scholar
  23. Shannon CE, Weaver W (1949) The mathematical theory of communication. University of Illinois Press, Urbana Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.IABNürnbergGermany
  2. 2.Otto-Friedrich-Universität BambergBambergGermany
  3. 3.Friedrich-Alexander-UniversitätErlangen-NürnbergGermany

Personalised recommendations