Elements of information theory are applied to the problem of estimating interregional flow coefficients in a national system of regions. The inclusion of constraints relating to the capacity of the transportation system justifies the adoption of Jaynes' principle of maximum uncertainty, in place of iterative proportional fitting procedures developed for multidimensional contingency table analysis. The inclusion of a priori information is also discussed.
Get full access to this article
View all access options for this article.
References
1.
Bacharach, M.1970. Biproportional matrices and input-output change. London: Cambridge University Press.
2.
Batten, D. F.1982. Spatial analysis of interacting economies. Boston: Martinus Nijhoff.
3.
Batten, D. F.
and Lesse, P. F. 1979. Information theoretical methods in regional science. Proceedings, 7th Australian conference on urban and regional planning information systems4.7-4.12.
Batty, M.1978. Speculations on an information theoretic approach to spatial representation. In Spatial representation and spatial interaction, ed. I. Masser and P. Brown. Leiden/Boston: Martinus Nijhoff.
6.
Batty, M.
and March, L.1976. The method of residues in urban modelling. Environment and PlanningA 8: 189-214.
7.
Bigsten, A. 1978. Regional inequality and development. Ph.D. dissertation, University of Gothenburg.
8.
Black, W. R.1972. Interregional commodity flows: some experiments with the gravity model. Journal of Regional Science12: 107-118.
9.
Burridge, P.1980. Interregional linkages between national and regional input-output models: a comment. Warwick: University of Warwick, Centre for Industrial Economic and Business Research, Mimeographed.
10.
Carnot, S.1824. Reflexions sur la puissance matrice du feu et sur les machines propres a developer cette puissance. Paris.
11.
Czamanski, S.
and Malizia, E.1969. Applicability and limitations in the use of national input-output tables for regional studies. Papers, Regional Science Association23: 65-77.
12.
Eriksson, J.1980. A note on solution of large sparse maximum entropy problems with linear equality constraints. Mathematical Programming18: 146-154.
13.
Eriksson, J. 1981. Algorithms for entropy and mathematical programming. Linkoping Studies in Science and Technology. Dissertation No. 63, Department of Mathematics, Linkbping University.
14.
Fienberg, S. E.1977. The analysis of cross-classified categorical data. Cambridge, Mass.: MIT Press.
15.
Gordon, I. F.1976. Gravity demand functions, accessibility and regional trade. Regional Studies10: 24-37.
16.
Hobson, A.
and Cheng, B. K.1973. A comparison of the Shannon and Kullback information measures. Journal of Statistical Physics7: 301-310.
17.
Isard, W.1951. Interregional and regional input-output analysis: a model of a space economy. Review of Economics and Statistics33: 318-328.
18.
Jaynes, E. T.1957. Information theory and statistical mechanics. Physics Review106: 620-630.
19.
Jensen, R. C.
, Mandeville, T. and Karunaratne, N. D.1979. Regional economic planning. London: Croom Helm.
20.
Kuliback, S.1959. Information theory and statistics. New York: John Wiley and Sons.
21.
Leontief, W.1951. The structure of the American economy, 1919-1939. New York: Oxford University Press.
22.
Leontief, W.
and Strout, A.1963. Multiregional input-output analysis. In Structural interdependence and economic development, ed. T. Barna. London: St. Martin's Press.
23.
Macgill, S. M.1977. Theoretical properties of biproportional matrix adjustments. Environment and PlanningA 9: 687-701.
24.
Macgill, S. M.
and Wilson, A. G.1979. Equivalences and similarities between some alternative urban and regional models. Sistemi Urbani1: 940.
25.
March, L.
and Batty, M.1975. Generalized measures of information, Bayes' likelihood ratio and Jaynes' formalism. Environment and PlanningB 2: 99-105.
26.
Miernyk, W. H.1968. Long range forecasting with a regional input-output model. Western Economic Journal6: 165-176.
27.
Miernyk, W. H.1972. Regional and interregional input-output models: a reappraisal. In Spatial, Regional and Population Economics, eds. M. Perlman, B. Chinitz and C. J. Leven. New York: Gordon and Breach.
28.
Miernyk, W. H.1976. Comments on recent developments in regional input-output analysis. International Regional Science Review1: 47-55.
29.
Moore, F. T.
and Petersen, J. W.1955. Regional analysis: an interindustry model of Utah. Review of Economics and Statistics37: 368-381.
30.
Morrison, W. I.
and Smith, P.1974. Nonsurvey input-output techniques at the small area level: an evaluation. Journal of Regional Science14: 1-14.
31.
Richardson, H. W.1972. Input-output and regional economics. London: Weidenfeld and Nicolson.
32.
Riefler, R. F.1973. Interregional input-output: a state of the arts survey. In Studies in economic planning over space and time, eds. G. G. Judge and T. Takayama. Amsterdam: North Holland.
33.
Schaffer, W. A.1976. On the use of input-output models for regional planning. Leiden: Martinus Nijhoff.
34.
Schaffer, W. A.
and Chu, K.1969. Nonsurvey techniques for constructing regional inter-industry models. Papers, Regional Science Association23: 83-101.
35.
Shannon, C. E.1948. A mathematical theory of communication. Bell System Technical Journal27: 379-423 and 623-656.
36.
Snickars, F.1979. Construction of interregional input-output tables by efficient information adding. In Spatial statistical analysis, eds. C. Bartels and R. Ketellaper. Leiden: Martinus Nijhoff.
37.
Snickars, F.
and Weibull, J.1977. A minimum information principle: theory and practice. Regional Science and Urban Economics7: 137-168.
38.
Stone, R.
and Brown, A.1965. Behavioral and technical change in economic models. In Problems in economic development, ed. E. A. G. Robinson. New York: Macmillan.
39.
Tiebout, C. M.1957. Regional and interregional input-output models: an appraisal. Southern Economic Journal24: 140-147.
40.
Webber, M. J.1979. Information theory and urban spatial structure. London: Croom Helm.
41.
Williams, H. C. W. L.
and Wilson, A. G.1980. Some comments on the theoretical and analytical structure of urban and regional models. Papers, Regional Science Association45.
