Post on 02-Aug-2020
WHEN TECHNOLOGICAL COEFFICIENTS
CHANGES NEED TO BE ENDOGENOUS
Maurizio Grassini
24st Inforum World Conference
Osnabrueck 29 August 2 September 2016
Import shares in an Inforum Model
When the IO table is available in domestic (or
total) and imported flows, a matrix of import
shares
MM
is available
MM is a component of the multisectoral model.
playing an important role in the price side of the
model
Between real side and price side
After the real side loop, a new IO table is built.
Multiplying element by element this ‘updated’ IO table by MM matrix, the ‘updated’ import flows matrix isobtained.
The row sum of this matrix gives the vector of
imports :
m^
Import (behavioral) equations give the vector of imports:
m
Between real side and price side
In general m ≠ m^
m comes from behavioral equations so that it
must prevails on m^
Problem : how to shape MM so that its row sum
be equal to m?
Interdyme Report #1Douglas Meade - May, 1995
If the model is forced to take more imports than it has demand for a certain industry, then
output for that industry will be calculated as negative in Seidel(). This unreasonable
result, if not corrected in Seidel(), will then cause other parts of the model to react
strangely. For a forecast of imports to be reasonable, then imports must be less than or
equal to domestic demand
Modelling matrix MM
MM matrix does not play any role in solving the
real side of the IO model.
Actually, it is central in the nominal side
The algorithm for MM
Inforum suggests an algorithm to adjust the MM
coefficients
The algorithm provides increases and decreases
of import shares (the elements of matrix MM)
greater for low shares ad lower for great shares
under the constraint mmij <= 1
When this algorithm is unsuitable
If non-zero import shares are all equal to one
and imports estimated are greater than imports
calculated, m > m^,
their differences cannot be ‘allocated’ by
changing MM coefficients
When the growth of imports causes
trouble
Imports vs negative outputs
or
Running a model and run into negative outputs
and the model builder’s dilemma
fixing or modeling?
The Leontief equation for a
two sectors economy
1 – a11 - a12 q1 C1
=
-a21 1 – a22 q2 C2
Reading the equations by rows
(1 – a11 ) q1 - a12 q2 = C1
-a21 q1 + ( 1 – a22 ) q2 = C2
Reading the equations by columns
1 – a11 - a12 C1
q1+ q2 =
-a21 1 – a22 C2
The Hawkins-Simon conditions
revisited
The corollary:
“A necessary and sufficient condition that
the qi satisfying Aq+f=q be all positive for
any set f>0 is that all principal minors of
the matrix A are positive”
The geometrical analogue of the
Leontief equation: the vector basisC1
1 –a11
1 – a22
- a21 C2
- a12
The representation of vector C
when the Hawkins-Simon conditions are satisfied
C1
1 –a11
C
1 – a22
- a21 C2
- a12
But even if vector C is not strictly positive
qi’s satisfying Aq+f=q are still positive C1
1 –a11
C
1 – a22
- a21
C2
- a12
Vector C is not strictly positive but now
qi’s satisfying Aq+f=q are no longer positive
C1
1 –a11
C
1 – a22 C2
- a21
- a12
Changing the vector basis,
qi’s satisfying Aq+f=q are positive again
C1
1 –a11
C
1- a*22 1 – a22 C2
-a*21 - a21
- a12
Changing the vector basis
Changing the coordinates
a*21 > a21 and a*22 > a22
economically significant solutions are obtained
Changing the Base IO Table
RESOURCES USES
output imports total Com 1 Com 2 Com 3 DFD total
Com 1 61 25 86 18 16 18 34 86
Com 2 55 28 83 13 12 10 48 83
Com 3 32 8 40 10 8 7 15 40
RESOURCES USESoutput imports total Com 1 Com 2 Com 3 DFD total
Com 1 61 25 86 18 16 18 34 86
Com 2 55 28 83 13 12 10 48 83
Com 3 32 8 40 10 8 7 15 40
The IO Table to be updated
Imports of Com 3 increase
RESOURCES USES
output imports total Com 1 Com 2 Com 3 DFD total
Com 1 61 25 86 18 16 18 34 86
Com 2 55 28 83 13 12 10 48 83
Com 3 32 8 40 10 8 7 15 40
RESOURCES USESoutput imports total Com 1 Com 2 Com 3 DFD total
Com 1 61 25 86 18 16 18 34 86
Com 2 55 28 83 13 12 10 48 83
Com 3 32 25 57 10 8 7 15 40???
HOW TO TACKLE GROWING IMPORT
SHARES OVER TOTAL RESOURCES
AN INSIGHT THROUGH INFORUM
COUNTRY MODELS
Continue… with numerical examples
A GLANCE AT IMPORTS SUBSTITUTION IN THE
ITALIAN ECONOMY
ITALIAN ECONOMY
IMPORTS-OUTPUT RATIOSyears 2000-2011
0,0
5,0
10,0
15,0
20,0
25,0
30,0
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
20
10
20
11
20
12
ELECTR FABR MET NON-MET
PETROLEUM PAPER FOOD
MACHINERY AGR WOOD
0,0
10,0
20,0
30,0
40,0
50,0
60,0
70,0
80,0
90,0
100,0
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
TEXTILES OTHER TRAN EL. EQUIP
BASIC MET CHEM VEHICLES
RUBBER FURNITURE
ITALIAN ECONOMY
COMPUTERS IMPORTS-OUTPUT RATIOyears 2000-2011
0,0
20,0
40,0
60,0
80,0
100,0
120,0
140,0
160,0
180,0
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
WARNING
WHEN IMPORTS DISPLAY A GENERAL POSITIVE
TREND, THE TECHNOLOGY OBSERVED IN THE
BASE YEAR (OR IN THE LAST AVAILABLE YEAR)
MAY NOT BE APPROPRIATE TO GENERATE
PLAUSIBLE FORECAST
(AS SHOWN ABOVE BY MEANS OF GEOMETRICAL
REPRESENTATION)
TACKLING THE PROBLEM
RELYNG UPON MAKESHIFTS
A way to tackle such a problem is to make
import equations ‘silent’.
The present release of the INFORUM French
model offers an example of such makeshifts.
The new INFORUM French model
Two makeshifts for imports
if(t>=imp.LastDat) imp=ebemul(outc,imprat);
.
or
.
if(t>=imp.LastDat) {
provv=outc.sum();
Outsum.set(provv);
imp=ebemul(impfac,(Outsum-outc));
}
Makeshifts compromise in the
INFORUM Italian modelif(t>impshr.LastDat)impshrfunc(rimpsh, imptiml,rp);
if(t>=imp.LastDat) { importfunc(sc1cpa, impshr, outc);
provv=outc.sum();
imp[4] =ratMinCav[t]*(provv-outc[4]);
imp[6] =ratAbbi[t]*(provv-outc[6]);
imp[11]=ratChimici[t]*(provv-outc[11]);
imp[12]=ratFarma[t]*(provv-outc[12]);
imp[15]=ratMetalli[t]*(provv-outc[15]);
imp[17]=ratInforma[t]*(provv-outc[17]);
imp[20]=ratAuto[t]*(provv-outc[20]);
imp[33]=ratTAereo[t]*(provv-outc[33]);
imp[3]=ratPesce[t]*(provv-outc[3]);
imp[31]=ratTerra[t]*(provv-outc[31]);
}
The compromise
• imports of the sector responsible for
generating negative outputs may be linked to
the Total output of the economy
• in such cases sectoral imports are computed
as share of the economy total output
• This makeshift is useful if applied to a short
number of sectors and preferably those where
the researcher’s interest is minor.
How to avoid makeshifts
A model builder’ proposal
Seidel2 implementation
sum = f[i];
for(j = first; j <= last; j++) sum += A[i][j]*q[j];
sumNet = sum - f[i];
sum -= A[i][i]*q[i]; // Take off the diagonal element of sum
sum = sum/(1.- A[i][i]);
// if (i == 31 && iter == 0) {
if (sum < 0.0) {
ratio =(q[i]-f[i])/sumNet;
for(j = first; j <= last; j++) A[i][j] *=ratio;
sum = q[i];
}
Three Scenarios
• Scenario A – Land transport services imports are modelled as a ratio of the economy Total output.
• Scenario B - Total resources import shares equations are used to compute sectoral imports.
• Scenario C - Land transport services intermediate consumptions (technical coefficients) are adjustedjust when its output becomes negative.
Import shares observed and
forecasted in Scenarios B and C
Pr�ducts �f agricu�turePr�ducts �f agricu�turei�p�rt shares �bserved a�d f�recasted
1�00
0�50
0�00
2000 2005 2010 2015 2020 2025 2030
�i�i�g a�d quarryi�g�i�i�g a�d quarryi�gi�p�rt shares �bserved a�d f�recasted
1�00
0�50
0�00
2000 2005 2010 2015 2020 2025 2030
Pr�ducts �f f�restryPr�ducts �f f�restryi�p�rt shares �bserved a�d f�recasted
1�00
0�50
0�00
2000 2005 2010 2015 2020 2025 2030
�a�d tra�sp�rt services�a�d tra�sp�rt servicesi�p�rt shares �bserved a�d f�recasted
1�00
0�50
0�00
2000 2005 2010 2015 2020 2025 2030
�a�d tra�sp�rt services�a�d tra�sp�rt services�utput
120000
40000
!40000
2010 2015 2020 2025 2030
SCE%ARI)*A SCE%ARI)*B SCE%ARI)*C
Supp�rt services f�r tra�sp�rtati��Supp�rt services f�r tra�sp�rtati���utput
85000
62500
40000
2010 2015 2020 2025 2030
Base�i�e I�p�rtsFu�cti�� TecC�ef*ad0ust�e�t
C�1e a�d refi�ed petr��eu� pr�ductsC�1e a�d refi�ed petr��eu� pr�ducts�utput
80000
60000
40000
2010 2015 2020 2025 2030
Base�i�e I�p�rtsFu�cti�� TecC�ef*ad0ust�e�t
Che�ica�s a�d che�ica� pr�ductsChe�ica�s a�d che�ica� pr�ducts�utput
90000
60000
30000
2010 2015 2020 2025 2030
Base�i�e I�p�rtsFu�cti�� TecC�ef*ad0ust�e�t
P�sta� a�d c�urier servicesP�sta� a�d c�urier services�utput
8000
5000
2000
2010 2015 2020 2025 2030
Base�i�e I�p�rtsFu�cti�� TecC�ef*ad0ust�e�t
A Scenario number 4
An experiment Adjusting the A matrix
every year
Seidel2 implementation
sum = f[i];
for(j = first; j <= last; j++) sum += A[i][j]*q[j];
sumNet = sum - f[i];
sum -= A[i][i]*q[i]; // Take off the diagonal element of sum
sum = sum/(1.- A[i][i]);
// if (i == 31 && iter == 0) {
if (sum < 0.0) {
ratio =(q[i]-f[i])/sumNet;
for(j = first; j <= last; j++) A[i][j] *=ratio;
sum = q[i];
}
Impact of the Vector bases on output
C1
1 –a11
C
1- a*22 1 – a22
C -a*21 - a21
C2
- a12
When a vector basis
cannot produce positive outputs
C1
1 –a11
C1
-a21 1 – a22
- a12
Tech�ica� c�efficie�t A31�31Tech�ica� c�efficie�t A31�31�a�d tra�sp�rt services
1�00
0�50
0�00
2010 2015 2020 2025 2030
BASE STEP FREE C)%
S � � e T e c h � i c a � c � e f f i c i e � t sS � � e T e c h � i c a � c � e f f i c i e � t s�a� d t ra �sp �r t s er vic es
0�30
0�15
0�00
2010 2015 2020 2025 2030
aa bb cc dd
Continue…......