Task 5 Worksheet

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 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 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 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 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

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


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.


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



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1.00

1.00

1.001.00

1.00

1.00

1.00

1.00

1.00


-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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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


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


18/19


19/19

g

er and construction

nsports

s

es

e

uring

water and construction

transports

vices

rvices

Documents

Task 5 Worksheet