task 4 worksheet
TRANSCRIPT
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Task 4: Constructing an unconstrained multiplier model
2007 SAM for Ghana with 3 sectors
Units: Millions of new Ghanaian Cedis (current prices)aagr aind asrv cagr cind csrv lab cap
aagr 7,070
aind 9,084
asrv 8,842
cagr 606 831 126
cind 599 3,423 1,889
csrv 1,313 880 2,361
lab 4,215 2,254 3,248
cap 336 1,696 1,218
hrur 5,054 1,248
hurb 4,663 2,002
gov 160 1,869 343
s-i
row 575 7,450 415
tot 7,070 9,084 8,842 7,805 18,403 9,599 9,717 3,250
PART 1: Calculating the inverted coefficient matrix
Coefficient matrix (M)
Calculate coefficients by dividing each column through by its column total (see Table 4).
aagr aind asrv cagr cind csrv lab cap
aagr
aind
asrv
cagr
cind
csrv
lab
cap
hrurhurb
gov
s-i
row
tot
Indentity matrix (I)
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Create an identity matrix by placing the value 1 in the diagonal cell entries
aagr aind asrv cagr cind csrv lab cap
aagr
aind
asrv
cagr
cindcsrv
lab
cap
hrur
hurb
gov
s-i
row
Intermediate step (I-M)
Subtract the matrix from the identity matrix
aagr aind asrv cagr cind csrv lab cap
aagr
aind
asrv
cagr
cind
csrv
lab
caphrur
hurb
gov
s-i
row
-0.04
Inverted coefficient matrix (I-M)-1
Invert the above matrix using the Excel "MINVERSE" formula.
aagr aind asrv cagr cind csrv lab cap
aagr
aind
asrv
cagr
cind
csrv
lab
cap
hrur
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hurb
gov
s-i
row
PART 2: The exgenous shock vector
Exogenous demand shock matrix (E)
cagr cind csrv Hint
aagr This matrix shows the size of the exogenous d
aind It is initially set equal to one, which means a 1
asrv You can change the size of the shock to any n
cagr 1.00
cind 1.00 Remember the unit of the shock and hence th
csrv 1.00 (i.e., millions of Ghanaian Cedi at 2007 prices)
lab
cap It is necessary for matrix calculations that all
hrur Note though that we are hiding all zero entrie
hurb
gov
s-i
row
PART 3: The multiplier effects
Multiplier effects Z = (I-M)-1 E
Use the Excel "MMULT" formula to calculate the multiplier effects
cagr cind csrv
aagr Output multipliers
aind
asrv
cagr
cind
csrv
lab GDP or value-added multipliers
caphrur Income multipliers
hurb
gov
s-i 0.25
row
Total multiplier effects by type of multiplier
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Output
GDP Note that income and GDP multipliers should
Income factor taxes in the Ghana SAM (i.e., all value-a
0.61
Q1: Which sector has the largest output multiplier?
A1:
Q2: Which sector has the largest income multiplier?
A2:
Q3: What do you think is the main reason why the multipliers for industry so much lower than f
A3:
Q4: What is the output multiplier effect of a by 35 million cedi increase in agricultural export de
A4:
Q5: Which sector generates the largest income multipler effects for urban households?
A5:
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hrur hurb gov s-i row tot SAM legend
7,070 aagr Activity - a
9,084 aind Activity - in
8,842 asrv Activity - se
2,453 1,773 2,016 7,805 cagr Commodit
2,553 3,238 4,680 2,020 18,403 cind Commodit
705 1,421 1,805 1,115 9,599 csrv Commodit
9,717 lab Factor - lab
3,250 cap Factor - ca
547 409 7,257 hrur Household
840 1,592 9,097 hurb Household
940 739 4,052 gov Governme
1,547 1,725 860 548 4,680 s-i Saving/inve
8,439 row Rest of the
7,257 9,097 4,052 4,680 8,439 tot Column an
hrur hurb gov s-i row Hint
The final three columns in the coe
This means that we must leave th
round-by-round indirect linkage ef
1.00 0.00
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hrur hurb gov s-i row
1.00
hrur hurb gov s-i row Hint
You must use Excel matrix algebra
To do this, do the following four st
1. Highlight the block where you w
2. Then types equals (=) followed
3. Then subtract (-) the coordinate
4. Finally, hold down the control (
Now if you move your cursor over
has "curly" parentheses or bracket
a formula is matrix algebra.
1.00
hrur hurb gov s-i row
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0.42 1.00
emand shock for each commodity.
million cedi increase in demand for each commodity.
mber.
e multiplier is in value terms
.
f the cell entries have a value, even if is zero.
s (see the Tools-Options drop-down menu).
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be the same since there are no
dded is paid to households).
r other sectors?
and?
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riculture
dustry
rvices
- agriculture
- industry
- services
or
ital
- rural
- urban
t
stment
world
row total
ficient matrix are exogenous accounts in our model.
se accounts as zero, since they do not generate
fects. All other columns should sum to one.
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commands for this exercise.
eps when entering the formula:
ant your answer to be (B67:N79).
y the coordinates for the entire identity matrix (B49:N61).
s for the entire coefficient matrix (B30:N42) (leave out the total row)
TRL) and SHIFT keys, and then press enter
the matrix to the left you should see that your formula
s around it (i.e., { and }). This is how Excel shows that