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…......