Entropy Theory and RAS are Friends

May 1999 Presented at the 2nd Annual Conference on Global Economic Analysis Recent research in applications of entropy theory to matrix balancing problems in eco-nomics has put powerful new tools in the hands of data base developers, but overshadowed some previous findings. We recall earlier findings that the RAS is an entropy-theoretic model. Investigating the properties of a more recently proposed entropy-theoretic model, we find that in general the RAS remains preferable. We show further that the RAS can be obtained also as a generalised cross-entropy model. Finally, we present examples illus-trating how entropy-theoretic techniques can extend the RAS to handle a wider range of problems.

[1]  Michael Bacharach,et al.  Biproportional matrices & input-output change , 1970 .

[2]  Douglas J. Miller,et al.  Maximum entropy econometrics: robust estimation with limited data , 1996 .

[3]  Andrei N. Kolmogorov,et al.  Logical basis for information theory and probability theory , 1968, IEEE Trans. Inf. Theory.

[4]  Sherman Robinson,et al.  Updating and Estimating a Social Accounting Matrix Using Cross Entropy Methods , 2001 .

[5]  Richard Sinkhorn.  A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices , 1964 .

[6]  Henri Theil,et al.  The Information Approach to the Prediction of Interregional Trade Flows , 1966 .

[7]  W. E. Silver,et al.  Economics and Information Theory , 1967 .

[8]  Michael Bacharach,et al.  Input-Output Relationships 1954-1966 , 1965 .

[9]  P. Preckel.  LEAST SQUARES AND ENTROPY AS PENALTY FUNCTIONS by , 1998 .

[10]  R. P. Byron,et al.  The estimation of large social account matrices , 1978 .

[11]  Jean Benard.  Réseau des échanges internationaux et planification ouverte , 1963 .

[12]  Stavros A. Zenios,et al.  A Comparative Study of Algorithms for Matrix Balancing , 1990, Oper. Res..

[13]  John L. Kelly,et al.  A new interpretation of information rate , 1956, IRE Trans. Inf. Theory.

[14]  L. Bregman.  Proof of the convergence of Sheleikhovskii's method for a problem with transportation constraints , 1967 .

[15]  J. N. Kapur,et al.  Entropy optimization principles with applications , 1992 .

[16]  K. E. Boulding,et al.  The structure of American economy, 1919-1929 : an empirical application of equilibrium analysis , 1942 .

[17]  W. Deming,et al.  On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known , 1940 .