By David F. Batten

6. 2 easy version features 185 6. three A Closed version method of Interregional Estimation 189 7 in the direction of an built-in process of versions for nationwide and nearby improvement 205 7. 1 creation 205 7. 2 looking for a Framework for Integration 207 7. three nationwide improvement situations 222 7. four The National-Regional Interlace 231 7. five local improvement situations 236 7. 6 Concluding feedback 244 Appendixes 253 A uncomplicated Microstate Descriptions 253 B Incomplete earlier info: an easy instance 257 C Computing Capital Coefficients and Turnpike recommendations: The DYNIO package deal 259 D Minimizing details Losses in uncomplicated Aggregation: try difficulties 274 E Computing Interregional and Intersectoral Flows: 276 References 287 Index 305 vi record OF FIGURES 1. 1 A three-d advisor to Later Chapters 12 2. 1 old improvement of the Entropy suggestion 32 2. 2 chosen functions of data concept to Input-Output research and interplay Modelling forty eight three. 1 The Bose-Einstein Analogy fifty eight five. 1 The Dog-Leg Input-Output desk 159 7. 1 A common Multilevel Social process 219 7. 2 The Hierarchical approach of types 219 7. three selection of creation recommendations 230 7. four The National-Regional Interface 235 7. five A Sequential Compromise process 243 7. 6 The built-in Modelling procedure 246 vii checklist OF TABLES three. 1 Production-Constrained Microstate Descriptions fifty nine three. 2 Production-Constrained Entropy Formulae sixty two three. three Production-Constrained strategies sixty five three. four Doubly-Constrained strategies seventy three four. 1 The Static Input-Output desk eighty five 4.

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19 See Brillouin (1956) and Jaynes (1957). 20 See Jaynes (1957, p 620). 21 In 1968, Jaynes (1968) acknowledged the earlier suggestions of Gibbs (1902). 22 See Kullback (1959). 23 Notably Renyi (1966) and Theil (1967). 24 See Hobson (1969), and Shannon and Weaver (1949). 25 For example, Hobson (1971), Charnes, Raike and Betti nger (1972), March and Batty (1975), Snickars and Weibull (1977), and Webber (1979) have all suggested that Ik [P;QJ be used to define our uncertainty about the state of the system.

As {Pij} is also unknown, however, a solution to this system for {q .. } sti 11 requires some estimates of 1J 56 {Pij}, Theil persisted with this two-stage approach when he formulated a gravity model for interregional commodity flows. 48) "rs and xi ' ~* A*S Xi ,Xi and Xi are known variables in some base year. rs 1 S . 50) =,x.. 51 ) His final solution was to replace the normalized estimate of x~s by x~s , obtained by minimizing the quantity rs rs I = 1: 1: x. 51) as constraints. 45 Wilson recognized the similarities between Theil's gravity model and a similar model proposed by Leontief and strout.

45) I q. = v. 46) I q .. j 1J 1 and i 1J J plus the usual non-negativity conditions. As {Pij} is also unknown, however, a solution to this system for {q .. } sti 11 requires some estimates of 1J 56 {Pij}, Theil persisted with this two-stage approach when he formulated a gravity model for interregional commodity flows. 48) "rs and xi ' ~* A*S Xi ,Xi and Xi are known variables in some base year. rs 1 S . 50) =,x.. 51 ) His final solution was to replace the normalized estimate of x~s by x~s , obtained by minimizing the quantity rs rs I = 1: 1: x.