Editing Input–output model (section)

=== Introducing transportation ===

Transportation is implicit in the notion of inter-industry flows. It is explicitly recognized when transportation is identified as an industry – how much is purchased from transportation in order to produce. But this is not very satisfactory because transportation requirements differ, depending on industry locations and capacity constraints on regional production. Also, the receiver of goods generally pays freight cost, and often transportation data are lost because transportation costs are treated as part of the cost of the goods.

[[Walter Isard]] and his student, [[Leon Moses]], were quick to see the spatial economy and transportation implications of input–output, and began work in this area in the 1950s developing a concept of interregional input–output. Take a one region versus the world case. We wish to know something about inter-regional commodity flows, so introduce a column into the table headed "exports" and we introduce an "import" row.

{| border="1" cellpadding="5" cellspacing="0" align="center"
|+'''Table: Adding Export And Import Transactions'''
|Economic Activities
| 1
| 2
| ...
| ...	
| Z
| Exports
| Domestic Final Demand
| Total Outputs
|-
|1
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|							
|-
|2
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|								
|-
|...	
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|							
|-
|...
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|-
|Z
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|-								
|Imports	
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|							
|}

A more satisfactory way to proceed would be to tie regions together at the industry level. That is, we could identify both intra-region inter-industry transactions and inter-region inter-industry transactions. The problem here is that the table grows quickly.

Input–output is conceptually simple. Its extension to a model of equilibrium in the national economy has been done successfully using high-quality data. One who wishes to work with input–output systems must deal with [[industry classification]], data estimation, and inverting very large, often ill-conditioned matrices. The quality of the data and matrices of the input-output model can be improved by modelling activities with digital twins and solving the problem of optimizing management decisions.<ref>{{cite journal |title=Leontev Input-Output Balance Model as a Dynamic System Control Problem |first=S. N. |last=Masaev |year=2021 |journal= Herald of the Bauman Moscow State Technical University. Series Instrument Engineering |volume=2 |issue=135 |pages=66–82 |doi=10.18698/0236-3933-2021-2-66-82 |s2cid=237889078 }}</ref> Moreover, changes in relative prices are not readily handled by this modelling approach alone. Input–output accounts are part and parcel to a more flexible form of modelling, [[computable general equilibrium]] models{{Efn|However, CGE models rely on economic production functions, such as CES functions, and are not suited to representing actual technologies in detail, whereas in IO there is no limit in resolution. Furthermore, the use of CES functions results in using a number of separability assumptions which can have strong implications on the assumed technology.<ref>Shinichiro Nakamura and Yasushi Kondo, Waste Input-Output Analysis: Concepts and Application to Industrial Ecology, Springer, 2009, Section 4.1</ref> }}.

Two additional difficulties are of interest in transportation work. There is the question of substituting one input for another, and there is the question about the stability of coefficients as production increases or decreases. These are intertwined questions. They have to do with the nature of regional production functions.