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7/30/2019 Task 5 Worksheet
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Task 5: Interpreting results from a constrained multiplier model
2007 SAM for Ghana with 7 sectors
Units: Millions of new Ghanaian Cedis (current prices)aagr amin aman aelw acon apubs aprv cagr
aagr 7,070
amin
aman
aelw
acon
apubs
aprv
cagr 606 831 126
cmin 13 56
cman 574 413 1,303 1,059 1,418 53 307
celw 26 114 374 91 25 6 80
ccon 1,249 53 677 76 706 135 782
cpubs
cprvs 64 73 95 643
lab 4,215 251 823 1,179 1,089 1,285 874
cap 336 505 436 755 271 394 552
hrur
hurb
gov 160
s-irow 575
tot 7,070 1,410 4,458 3,217 3,605 1,873 3,363 7,805
PART 1: Calculating the adjusted inverted coefficient matrix
Coefficient matrix (M)
Each cell entry is divided by its column total
aagr amin aman aelw acon apubs aprv cagr
aagr 0.91amin
aman
aelw
acon
apubs
aprv
cagr 0.09 0.19 0.04
cmin 0.00 0.02
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cman 0.08 0.29 0.29 0.33 0.39 0.03 0.09
celw 0.00 0.08 0.08 0.03 0.01 0.00 0.02
ccon 0.18 0.04 0.15 0.02 0.20 0.07 0.23
cpubs
cprvs 0.01 0.05 0.03 0.19
lab 0.60 0.18 0.18 0.37 0.30 0.69 0.26
cap 0.05 0.36 0.10 0.23 0.08 0.21 0.16hrur
hurb
gov 0.02
s-i
row 0.07
tot 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Adjusted coefficient matrix (M*)
If sector is constrained then use remove link to domestic production and shift demand change to exoge
aagr amin aman aelw acon apubs aprv cagr
aagr 0.91
amin
aman
aelw
acon
apubs
aprv
cagr 0.09 0.19 0.04
cmin 0.00 0.02
cman 0.08 0.29 0.29 0.33 0.39 0.03 0.09celw 0.00 0.08 0.08 0.03 0.01 0.00 0.02
ccon 0.18 0.04 0.15 0.02 0.20 0.07 0.23
cpubs
cprvs 0.01 0.05 0.03 0.19
lab 0.60 0.18 0.18 0.37 0.30 0.69 0.26
cap 0.05 0.36 0.10 0.23 0.08 0.21 0.16
hrur
hurb
gov 0.02
s-i
row 0.07
Identity matrix (I)
aagr amin aman aelw acon apubs aprv cagr
aagr 1.00
amin 1.00
aman 1.00
aelw 1.00
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acon 1.00
apubs 1.00
aprv 1.00
cagr 1.00
cmin
cman
celwccon
cpubs
cprvs
lab
cap
hrur
hurb
gov
s-i
row
Intermediate step (I-M*)
Subtract the adjusted coefficient matrix from the identity matrix
aagr amin aman aelw acon apubs aprv cagr
aagr 1.00 -0.91
amin 1.00
aman 1.00
aelw 1.00
acon 1.00
apubs 1.00aprv 1.00
cagr -0.09 -0.19 -0.04 1.00
cmin 0.00 -0.02
cman -0.08 -0.29 -0.29 -0.33 -0.39 -0.03 -0.09
celw 0.00 -0.08 -0.08 -0.03 -0.01 0.00 -0.02
ccon -0.18 -0.04 -0.15 -0.02 -0.20 -0.07 -0.23
cpubs
cprvs -0.01 -0.05 -0.03 -0.19
lab -0.60 -0.18 -0.18 -0.37 -0.30 -0.69 -0.26
cap -0.05 -0.36 -0.10 -0.23 -0.08 -0.21 -0.16
hrur
hurb
gov -0.02
s-i
row -0.07
Inverted adjusted coefficient matrix (I-M*)-1
Invert the above matrix using the Excel "MINVERSE" formula.
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aagr amin aman aelw acon apubs aprv cagr
aagr 1.48 0.35 0.50 0.35 0.31 0.44 0.40 1.34
amin 0.00 1.00 0.01 0.02 0.00 0.00 0.00 0.00
aman 0.27 0.30 1.31 0.31 0.33 0.25 0.27 0.24
aelw 0.07 0.15 0.15 1.10 0.07 0.08 0.10 0.07
acon 0.41 0.24 0.38 0.21 1.39 0.29 0.50 0.37
apubs 0.01 0.00 0.00 0.00 0.00 1.01 0.00 0.01aprv 0.18 0.20 0.13 0.14 0.15 0.19 1.36 0.16
cagr 0.53 0.38 0.55 0.39 0.34 0.49 0.44 1.48
cmin 0.00 0.00 0.01 0.02 0.00 0.00 0.00 0.00
cman 0.83 0.93 0.96 0.95 1.01 0.78 0.84 0.75
celw 0.07 0.15 0.15 0.10 0.07 0.08 0.10 0.07
ccon 0.44 0.26 0.41 0.22 0.43 0.31 0.54 0.40
cpubs 0.01 0.00 0.00 0.00 0.00 0.01 0.00 0.01
cprvs 0.20 0.22 0.15 0.16 0.17 0.21 0.40 0.18
lab 1.14 0.62 0.75 0.77 0.73 1.16 0.83 1.03
cap 0.18 0.49 0.24 0.35 0.19 0.33 0.33 0.16
hrur 0.66 0.51 0.48 0.54 0.45 0.73 0.56 0.60
hurb 0.65 0.60 0.51 0.59 0.47 0.76 0.60 0.59
gov 0.23 0.22 0.23 0.22 0.23 0.22 0.23 0.23
s-i 0.26 0.22 0.20 0.23 0.19 0.30 0.23 0.24
row 0.51 0.56 0.58 0.56 0.59 0.48 0.53 0.54
B-matrix
aagr amin aman aelw acon apubs aprv cagr
aagr
aminaman
aelw
acon
apubs
aprv
cagr 1.00
cmin
cman
celw
ccon
cpubs
cprvs
lab
cap
hrur
hurb
gov
s-i
row
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PART 2: The exgenous shock vector
Exogenous demand shock matrix (E)
cagr cmin cman celw ccon cpubs cprvs
aagramin
aman
aelw
acon
apubs
aprv
cagr 1.00
cmin 1.00
cman 1.00
celw 1.00
ccon 1.00
cpubs 1.00
cprvs 1.00
lab
cap
hrur
hurb
gov
s-i
row
PART 3: The multiplier effects
Multiplier effects Z = (I-M*)-1 B E
Calculated using constrained multiplier formula (see Equation 5.6)
cagr cmin cman celw ccon cpubs cprvs
aagr 1.34 0.35 0.16 0.35 0.28 0.44 0.35 Output mul
amin 0.00 1.00 0.00 0.02 0.00 0.00 0.00
aman 0.24 0.30 0.43 0.30 0.30 0.25 0.24
aelw 0.07 0.15 0.05 1.08 0.06 0.08 0.08acon 0.37 0.24 0.12 0.21 1.29 0.29 0.44
apubs 0.01 0.00 0.00 0.00 0.00 1.01 0.00
aprv 0.16 0.20 0.04 0.14 0.14 0.19 1.19
cagr 1.48 0.38 0.18 0.38 0.31 0.49 0.39
cmin 0.00 1.00 0.00 0.02 0.00 0.00 0.00
cman 0.75 0.93 1.31 0.94 0.93 0.78 0.74
celw 0.07 0.15 0.05 1.10 0.07 0.08 0.09
ccon 0.40 0.26 0.13 0.22 1.39 0.31 0.48
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cpubs 0.01 0.00 0.00 0.00 0.00 1.01 0.00
cprvs 0.18 0.22 0.05 0.16 0.16 0.21 1.36
lab 1.03 0.62 0.24 0.77 0.68 1.16 0.73 GDP or val
cap 0.16 0.49 0.08 0.35 0.18 0.33 0.29
hrur 0.60 0.51 0.16 0.53 0.42 0.73 0.49 Income mu
hurb 0.59 0.60 0.16 0.58 0.43 0.76 0.53
gov 0.23 0.22 0.21 0.22 0.28 0.22 0.22s-i 0.24 0.22 0.06 0.22 0.17 0.30 0.21
row 0.54 0.56 0.73 0.56 0.54 0.48 0.58
Total multiplier effects by type of multiplier
Output 2.19 2.24 0.80 2.11 2.08 2.25 2.32
GDP 1.19 1.11 0.32 1.11 0.85 1.49 1.02 Note that i
Income 1.19 1.11 0.32 1.11 0.85 1.49 1.02 factor taxe
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cmin cman celw ccon cpubs cprvs lab cap hrur
1,410
4,458
3,217
3,605
1,873
3,363
2,453
2,395
158
73
33
599
5,054 1,248
4,663 2,002
1,844 25 298 45
1,5477,440 9 415
1,410 13,742 3,251 3,904 1,873 3,822 9,717 3,250 7,257
cmin cman celw ccon cpubs cprvs lab cap hrur
1.00
0.32
0.99
0.92
1.00
0.88
0.34
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0.33
0.02
0.01
0.00
0.08
0.52 0.38
0.48 0.62
0.13 0.01 0.08 0.01
0.21
0.54 0.00 0.11
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
nous component.
cmin cman celw ccon cpubs cprvs lab cap hrur
1.00
0.32
0.99
0.92
1.00
0.88
0.34
0.330.02
0.01
0.00
0.08
0.52 0.38
0.48 0.62
0.13 0.01 0.08 0.01
0.21
0.54 0.00 0.11
cmin cman celw ccon cpubs cprvs lab cap hrur
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1.00
1.00
1.001.00
1.00
1.00
1.00
1.00
1.00
cmin cman celw ccon cpubs cprvs lab cap hrur
-1.00
-0.32
-0.99
-0.92
-1.00-0.88
-0.34
1.00
1.00 -0.33
1.00 -0.02
1.00 -0.01
1.00 0.00
1.00 -0.08
1.00
1.00
-0.52 -0.38 1.00
-0.48 -0.62
-0.13 -0.01 -0.08 -0.01
-0.21
-0.54 0.00 -0.11
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cmin cman celw ccon cpubs cprvs lab cap hrur
0.35 0.16 0.35 0.28 0.44 0.35 0.47 0.45 0.55
1.00 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00
0.30 0.43 0.30 0.30 0.25 0.24 0.24 0.24 0.25
0.15 0.05 1.08 0.06 0.08 0.08 0.07 0.08 0.07
0.24 0.12 0.21 1.29 0.29 0.44 0.21 0.21 0.22
0.00 0.00 0.00 0.00 1.01 0.00 0.01 0.01 0.010.20 0.04 0.14 0.14 0.19 1.19 0.19 0.20 0.17
0.38 0.18 0.38 0.31 0.49 0.39 0.52 0.49 0.61
1.00 0.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00
0.93 1.31 0.94 0.93 0.78 0.74 0.75 0.74 0.78
0.15 0.05 1.10 0.07 0.08 0.09 0.08 0.08 0.07
0.26 0.13 0.22 1.39 0.31 0.48 0.23 0.23 0.24
0.00 0.00 0.00 0.00 1.01 0.00 0.01 0.01 0.01
0.22 0.05 0.16 0.16 0.21 1.36 0.22 0.23 0.20
0.62 0.24 0.77 0.68 1.16 0.73 1.47 0.46 0.52
0.49 0.08 0.35 0.18 0.33 0.29 0.11 1.11 0.11
0.51 0.16 0.53 0.42 0.73 0.49 0.81 0.67 1.31
0.60 0.16 0.58 0.43 0.76 0.53 0.78 0.91 0.32
0.22 0.21 0.22 0.28 0.22 0.22 0.21 0.22 0.17
0.22 0.06 0.22 0.17 0.30 0.21 0.32 0.31 0.34
0.56 0.73 0.56 0.54 0.48 0.58 0.47 0.46 0.49
cmin cman celw ccon cpubs cprvs lab cap hrur
1.00
1.00
1.00
1.00
1.00
1.00
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This matrix shows the size of the exogenous demand shock for each commodity.It is initially set equal to one, which means a 1 million cedi increase in demand for each commodity.
You can change the size of the shock to any number.
Remember the unit of the shock and hence the multiplier is in value terms
(i.e., millions of Ghanaian Cedi at 2007 prices).
It is necessary for matrix calculations that all of the cell entries have a value, even if is zero.
Note though that we are hiding all zero entries (see the Tools-Options drop-down menu).
PART 4: Deciding on exogenous demand co
Exogenous demand components
Enter a one if the component of demand is exogenous in
gov s-i row
ltipliers 1 1 1
This extended setup allows you to choose exogenous de
1: component is treated as exogenous.0: component is treated as endogenous.
Constrained supply sector
Enter a one if the sector is supply constrained (zero other
cagr cmin cman celw ccon
This extended setup allows you to choose supply constrai
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1: sector is supply constrained
0: sector is not supply constrained
e-added multipliers
ltipliers
come and GDP multipliers should be the same since there are no
in the Ghana SAM (i.e., all value-added is paid to households).
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hurb gov s-i row tot SAM legend
7,070 aagr Activity - agriculture
1,410 amin Activity - mining
4,458 aman Activity - manufacturin
3,217 aelco Activity - electicity, wa
3,605 atrad Activity - trade and tra
1,873 apubs Activity - public service
3,363 aprvs Activity - private servic
1,773 2,016 7,805 cagr Commodity - agricultu
1,341 1,410 cmin Commodity - mining
2,915 2,626 679 13,742 cman Commodity - manufact
323 2,054 3,251 celco Commodity - electicity,
152 3,904 ctrad Commodity - trade an
35 1,805 1,873 cpubs Commodity - public se
1,234 1,115 3,822 cprvs Commodity - private s
9,717 lab Factor - labor
3,250 cap Factor - capital
547 409 7,257 hrur Households - rural
840 1,592 9,097 hurb Households - urban
940 739 4,052 gov Government
1,725 860 548 4,680 s-i Saving/investment8,439 row Rest of the world
9,097 4,052 4,680 8,439 total Column and row total
hurb gov s-i row
0.19
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0.32
0.04
0.02
0.00
0.14
0.10
0.19
1.00
hurb gov s-i row
0.19
0.320.04
0.02
0.00
0.14
0.10
0.19
hurb gov s-i row
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1.00
1.00
1.00
1.00
hurb gov s-i row
-0.19
-0.32
-0.04
-0.02
0.00
-0.14
1.00
-0.10 1.00
-0.19 1.00
1.00
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hurb gov s-i row
0.38
0.00
0.23
0.08
0.20
0.010.21
0.42
0.00
0.72
0.08
0.22
0.01
0.24
0.42
0.11
0.26
1.27
0.26 1.00
0.30 1.00
0.45 1.00
hurb gov s-i row
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ponents and constrained sectors
the model (zero otherwise).
and components.
wise).
cpubs cprvs
ned sectors
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g
er and construction
nsports
s
es
e
uring
water and construction
transports
vices
rvices
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