Difference between revisions of "Dynamic Input-Output Models"
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== Definition == | == Definition == | ||
| − | '''Dynamic Input-Output Models''' is a category of various possible generalization of the basic [[Input- | + | '''Dynamic Input-Output Models''' is a category of various possible generalization of the basic [[Input-Output Model]] that allow accounting for more sophisticated temporal behavior<ref>Eurostat Manual of Supply, Use and Input-Output Tables, 2008 edition</ref> |
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== Formula == | == Formula == | ||
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* Xt = AXt + Ct + BXt + 1 - BXt | * Xt = AXt + Ct + BXt + 1 - BXt | ||
* (I – A + B) Xt = Ct + BX | * (I – A + B) Xt = Ct + BX | ||
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The production of period t is defined: | The production of period t is defined: | ||
| + | * X = (I – A + B)-1 (C + BX ) | ||
| − | |||
while the production of period t+1 is determined by: | while the production of period t+1 is determined by: | ||
| + | * X =B-1[(I – A + B)X - C ] | ||
| − | |||
Where: | Where: | ||
| − | |||
* Y = final demand | * Y = final demand | ||
* I = unit matrix | * I = unit matrix | ||
| Line 28: | Line 27: | ||
* D = induced investment | * D = induced investment | ||
* T = time index | * 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. | 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. | ||
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== Issues and Challenges == | == Issues and Challenges == | ||
Revision as of 16:06, 28 February 2022
Definition
Dynamic Input-Output Models is a category of various possible generalization of the basic Input-Output 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
