Difference between revisions of "Dynamic Input-Output Models"
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| + | == Definition == | ||
| + | '''Dynamic Input-Output Models''' is a category of various possible generalization of the basic [[Input-Ouput Model]] that allow accounting for more sophisticated temporal behavior<ref>Eurostat Manual of Supply, Use and Input-Output Tables, 2008 edition</ref> | ||
| + | |||
| + | |||
| + | == Formula == | ||
| + | The typical equations of the dynamic input-output model: | ||
| + | * X = AX + C + Dt | ||
| + | * D = BX - BXt t+1 t | ||
| + | * Xt = AXt + Ct + BXt + 1 - BXt | ||
| + | * (I – A + B) Xt = Ct + BX | ||
| + | |||
| + | The production of period t is defined: | ||
| + | |||
| + | * X = (I – A + B)-1 (C + BX ) | ||
| + | |||
| + | while the production of period t+1 is determined by: | ||
| + | |||
| + | * X =B-1[(I – A + B)X - C ] | ||
| + | |||
| + | Where: | ||
| + | |||
| + | * Y = final demand | ||
| + | * I = unit matrix | ||
| + | * A = input coefficients for intermediates | ||
| + | * (I-A)-1 = matrix of cumulative input coefficients (inverse) | ||
| + | * B = input coefficients for capital | ||
| + | * C = exogenous final demand (consumption) | ||
| + | * D = induced investment | ||
| + | * T = time index | ||
| + | |||
| + | This is a system of linear difference equations, since the values of the variables are related to different periods of time. Consumption is expected to grow at the annual rate (1+m)t. | ||
| + | |||
| + | |||
| + | == Issues and Challenges == | ||
| + | Practical problems relate to the matrix B of capital coefficients. | ||
| + | |||
| + | == References == | ||
| + | <references/> | ||
| + | |||
| + | [[Category:EEIO]] | ||
| + | |||
| + | {{#set:Has Formula = HAS_FORMULA}} | ||
| + | |||
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Revision as of 16:05, 28 February 2022
Definition
Dynamic Input-Output Models is a category of various possible generalization of the basic Input-Ouput Model that allow accounting for more sophisticated temporal behavior[1]
Formula
The typical equations of the dynamic input-output model:
- X = AX + C + Dt
- D = BX - BXt t+1 t
- Xt = AXt + Ct + BXt + 1 - BXt
- (I – A + B) Xt = Ct + BX
The production of period t is defined:
- X = (I – A + B)-1 (C + BX )
while the production of period t+1 is determined by:
- X =B-1[(I – A + B)X - C ]
Where:
- Y = final demand
- I = unit matrix
- A = input coefficients for intermediates
- (I-A)-1 = matrix of cumulative input coefficients (inverse)
- B = input coefficients for capital
- C = exogenous final demand (consumption)
- D = induced investment
- T = time index
This is a system of linear difference equations, since the values of the variables are related to different periods of time. Consumption is expected to grow at the annual rate (1+m)t.
Issues and Challenges
Practical problems relate to the matrix B of capital coefficients.
References
- ↑ Eurostat Manual of Supply, Use and Input-Output Tables, 2008 edition
