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FIGURE 1 Summary of Computation of Time Varying Multipliers
STEP 1 Initial Social Accounts Equations
Supply Demand ROW Total Column E
Supply 5 10 10 25 5
Demand 10 5 15 10
ROW 10 5 0 15 10
Total 25 15 15 SUM(E1..E3)
STEP 2 Calculate Coefficients Matrix
Supply Demand ROW Column E
Supply 0.20 0.67 0.67 +E1/E$4
Demand 0.40 0.00 0.33 +E2/E$4
ROW 0.40 0.33 0.00 +E3/E$4
Total 1.00 1.00 1.00 SUM(E9..E11)
STEP 3 Introduce Lags and ROW Feedback
Horizon Supply Demand ROW Column E
12 Lag 3 9 6 3
months Cumulative 0.98 0.74 0.86 1-EXP(-$A16/E16)
Feedback 1 1 0.05 1
Net 0.98 0.74 0.04 +E17*E18
STEP 4 Modify Coefficients Matrix =Q(T)A
Supply Demand ROW Column E
Supply 0.20 0.49 0.03 +E9*E$19
Demand 0.393 0.00 0.01 +E10*E$19
ROW 0.39 0.25 0.00 +E11*E$19
Total 0.98 0.74 0.04 SUM(E23..E25)
STEP 5 Construct Modified Leontief Matrix = I-Q(T)A
Supply Demand ROW Column E
Supply 0.80 -0.49 -0.03 -E23+1
Demand -0.39 1.00 -0.01 -E24
ROW -0.39 -0.25 1.00 -E25
STEP 6 Invert Modified Leontief Matrix = M(T)
Supply Demand ROW Column E
Supply 1.69 0.84 0.06 Matrix Inverse
Demand 0.67 1.34 0.04 of
ROW 0.83 0.66 1.03 Step 5
STEP 7 Calculate Multipliers for other Horizons
Months Supply Demand ROW Column E
0 1.00 1.00 1.00 =IF($A$20=$B50,E$42,E50)
3 1.22 1.06 1.01 etc.
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6 1.42 1.16 1.02
12 1.69 1.34 1.03
24 1.89 1.49 1.05
36 1.94 1.54 1.05
48 1.96 1.55 1.05
60 1.96 1.55 1.05
72 1.96 1.55 1.05
84 1.96 1.55 1.05
96 1.96 1.55 1.05
Multiplier Growth
2.50
2.00
1.50 Supply
Multiplier
Demand
ROW
1.00
0.50
0.00
0 3 6 12 24 36 48 60 72 84 96
Months
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SUM(E1..E3)
SUM(E9..E11)
EXP(-$A16/E16)
+E10*E$19
+E11*E$19
SUM(E23..E25)
Matrix Inverse
$20=$B50,E$42,E50)
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FIGURE 1 Summary of Computation of Time Varying Multipliers
STEP 1 Initial Social Accounts
Supply Demand ROW Total
Supply 5 10 10 25
Demand 10 5 15
ROW 10 5 100000 100015
Total 25 15 100015
STEP 2 Calculate Coefficients Matrix
Supply Demand ROW
Supply 0.20 0.67 0.00
Demand 0.40 0.00 0.00
ROW 0.40 0.33 1.00
Total 1.00 1.00 1.00
STEP 3 Introduce Lags and ROW Feedback
Horizon Supply Demand ROW
100 Lag 6 6 6
months Cumulative 1.00 1.00 1.00
Feedback 1 1.0000 1.0000
Net 1.00 1.00 1.00
STEP 4 Modify Coefficients Matrix =Q(T)A Figure 1. Exogenous Demand
Supply Demand ROW
Supply 0.20 0.67 0.00
Demand 0.400 0.00 0.00
ROW 0.40 0.33 1.00
Total 1.00 1.00 1.00
STEP 5 Construct Modified Leontief Matrix = I-Q(T)A
Supply Demand ROW
Supply 0.80 -0.67 0.00
Demand -0.40 1.00 0.00
ROW -0.40 -0.33 0.00
STEP 6 Invert Modified Leontief Matrix = M(T)
Supply Demand ROW
Supply 4326.44 4325.82 4324.57
Demand 2595.49 2596.24 2594.74
ROW ######## ######## ########
1000000
Horizon Multiplier Impact 100000
0.0001 1.0 10.0 -15.0
6 1.3 15.8 -24.8 10000
Multi[liers
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Multi[liers
12 1.6 20.5 -32.6
24 1.8 24.3 -38.8 1000
48 2.6 25.0 -40.0
100
60 7.4 25.0 -40.0
120 121226.5 25.0 -40.0
10
1000 ######## 25.0 -64.0
10000 ######## 25.0 -64.0
1
100000 ######## 25.0 -64.0
1000000 ######## 25.0 -64.0
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Figure 1. Exogenous Demand equals Exports in a Closed Economy
Base Year Output Levels
Supply Demand ROW
25 15 100015
Horizon = 100 months
Feedback = 1.0000000
Exogenous Demand
Supply Demand ROW Total
10 5 -15 0
Impacts
Supply Demand ROW Total
Supply 43264 21629 -64868 24.99
Demand 25955 12981 -38921 14.99
ROW 173008580 86504289 -259512909 -39.98
Net Impact 0.00
Divergent Multipliers and Convergent Impacts
1000000 50.0
45.0
Multiplier
100000
40.0
Impact 35.0
10000
30.0
Impacts
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30.0
Impacts
1000 25.0
20.0
100
15.0
10.0
10
5.0
1 0.0
0 6 12 24 48 60 120
Horizon (months)
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FIGURE 1 Summary of Computation of Time Varying Multipliers
STEP 1 Initial Social Accounts
Supply Demand ROW Total
Supply 5 10 10 25
Demand 10 0 5 15
ROW 10 5 0 15
Total 25 15 15
STEP 2 Calculate Coefficients Matrix
Supply Demand ROW
Supply 0.20 0.67 0.67
Demand 0.40 0.00 0.33
ROW 0.40 0.33 0.00
Total 1.00 1.00 1.00
STEP 3 Introduce Lags and ROW Feedback STEP 3 Introduce Lags and ROW Feedba
Horizon Supply Demand ROW Horizon
12 Lag 3 9 6 1000 Lag
Cumulative 0.98 0.74 0.86 Cumulative
Feedback 1 1 0.05 Feedback
Net 0.98 0.74 0.04 Net
STEP 4 Modify Coefficients Matrix =Q(T)A STEP 4 Modify Coefficients Matrix =Q(T)A
Supply Demand ROW
Supply 0.20 0.49 0.03 Supply
Demand 0.393 0.00 0.01 Demand
ROW 0.39 0.25 0.00 ROW
Total 0.98 0.74 0.04 Total
STEP 5 Construct Modified Leontief Matrix = I-Q(T)A STEP 5 Construct Modified Leontief Matr
Supply Demand ROW
Supply 0.80 -0.49 -0.03 Supply
Demand -0.39 1.00 -0.01 Demand
ROW -0.39 -0.25 1.00 ROW
STEP 6 Invert Modified Leontief Matrix = M(T) STEP 6 Invert Modified Leontief Matrix =
Supply Demand ROW
Supply 1.69 0.84 0.06 Supply
Demand 0.67 1.34 0.04 Demand
ROW 0.83 0.66 1.03 ROW
STEP 7 Calculate Multipliers for other Horizons
Months Supply Demand ROW Approximation
0 1.00 1.00 1.00 1.00
12 1.69 1.34 1.03 1.69
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24 1.89 1.49 1.05 1.88
36 1.94 1.54 1.05 1.94
48 1.96 1.55 1.05 1.96
60 1.96 1.55 1.05 1.96
72 1.96 1.55 1.05 1.96
84 1.96 1.55 1.05 1.96
96 1.96 1.55 1.05 1.96
108 1.96 1.55 1.05 1.96
120 1.96 1.55 1.05 1.96
1.008 1.005192 1.000604
0 1
1
1
12 1.69 0.84 0.06
0.67 1.34 0.04
0.83 0.66 1.03
1000 1.96 1.34 0.09
0.80 1.55 0.05
1.05 1.05 1.05
Avlag 9.64 12.08 10.18
6.56 12.54 9.01
7.79 12.17 11.95
Increment
DELAY 60 0.00 0.02 0.00 0.00 0.01
0.00 0.01 0.00 0.00 0.00
0.00 0.01 0.00 0.00 0.01
Direct
EVENT TIME Supply Demand ROW
0
12
24 -2
36
48
60
72
84 1
96
108
120
Impact after Delay 5
Supply Demand ROW
0 0.0 0.0 0.0
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12 0.0 0.0 0.0
24 0.0 0.0 0.0
36 0.0 0.0 0.0
48 0.0 0.0 0.0
60 0.0 0.0 0.0
72 0.0 0.0 0.0
84 0.0 0.0 0.0
96 0.0 0.0 0.0
108 0.0 0.0 0.0
120 0.0 0.0 0.0
1.5
Supply Demand ROW
1 0.0 0.0 0.0
0.5
1 0.0 0.0 0.0
1 0.0 0.0 0.0
1 0.0 0.0 0.0
-0.5
1 0.0 0.0 0.0
1 0.0 0.0 0.0 -
2 0.0 0.0 0.0
-1.5
3 0.0 0.0 0.0
4 0.0 0.0 0.0 -
5 0.0 0.0 0.0
6 0.0 0.0 0.0
1 Total
Supply Demand ROW
0 0.0 0.0 0.0
12 0.0 0.0 0.0
24 -2.0 0.0 0.0
36 -1.4 -1.3 -1.7
48 -0.4 -0.2 -0.4
60 -0.1 0.0 -0.1
72 0.0 0.0 0.0
84 -0.8 0.9 -0.3
96 0.8 0.3 0.7
108 0.3 0.1 0.2
120 0.1 0.1 0.1
-3.490 -0.163 -1.416
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Introduce Lags and ROW Feedback
Supply Demand ROW
3.00 9.00 6.00
1.00 1.00 1.00
1.00 1.00 0.05
1.00 1.00 0.05
Modify Coefficients Matrix =Q(T)A
Supply Demand ROW
0.20 0.67 0.03
0.40 0.00 0.02
0.40 0.33 0.00
1.00 1.00 0.05
Construct Modified Leontief Matrix = I-Q(T)A
Supply Demand ROW
0.80 -0.67 -0.03
-0.40 1.00 -0.02
-0.40 -0.33 1.00
Invert Modified Leontief Matrix = M(T)
Supply Demand ROW
1.96 1.34 0.09 9.6 12.1 10.2
0.80 1.55 0.05 6.6 12.5 9.0
1.05 1.05 1.05 7.8 12.2 11.9
Multiplier Growth
2.50
2.00
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2.00
1.50
Multiplier
1.00
0.50
0.00
0 12 24 36 48 60 72
Months
Total
0.00 1.96 1.33 0.09
0.00 0.80 1.55 0.05
0.00 1.05 1.05 1.05
0.0 0.0 0.0
0.0 0.0 0.0
-3.9 -1.6 -2.1
0.0 0.0 0.0
0.0 0.0 0.0
0.0 0.0 0.0
0.0 0.0 0.0
1.3 1.5 1.0
0.0 0.0 0.0
0.0 0.0 0.0
-2.6 -0.1 -1.1
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2
1.5
1
0.5 Supply
0 Demand
ROW
-0.5
-1
-1.5
-2
5.0 5.0
4.0 4.0
3.0 3.0
2.0 2.0
1.0 Supply 1.0
0.0 Demand 0.0
-1.0 ROW -1.0
-2.0 -2.0
-3.0 -3.0
-4.0 -4.0
-5.0 -5.0
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Multiplier Growth
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Supply
Demand
ROW
72 84 96 108 120
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Supply
Demand
ROW
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