A Discrepancies between intra-

Nordic exports, calculated in iterative step t.and

intra-Nordic exports, calcu- discrepancies are lated in iterative step t-1, unacceptably are calculated.

discrepancies are sufficiently small

The values, calcu- lated in the last iterative step, for intra-Nordic exports, and the correspon- , ding values for im- j ports, are Rtrans- , formed and tabulated.

d e s c r i b e s , i n a s i m p l e way, how t h e v a r i o u s p a r t s of t h e model system a r e r e l a t e d t o each o t h e r .

The t r a d e model i s r e p r e s e n t e d by t h e a r e a between t h e two d o t t e d l i n e s , w h i l e t h e a r e a s o u t s i d e t h e s e l i n e s r e p r e s e n t t h e n a t i o n a l models. The t r a n s f o r m a t i o n s and r e t r a n s f o r m a t i o n s mentioned a r e n e c e s s a r y f o r two r e a s o n s :

-

The commodity c l a s s i f i c a t i o n s of t h e n a t i o n a l models do n o t c o i n c i d e w i t h t h e commodity c l a s s i f i c a t i o n of t h e t r a d e model.

- The c u r r e n c y used i n t h e t r a d e model i s d i f f e r e n t from t h e c u r r e n c i e s u s e d i n t h e n a t i o n a l models.

The i t e r a t i v e p r o c e s s t h a t t a k e s p l a c e w i t h i n t h e t r a d e m o d e l s t a r t s f r o m i m p o r t f i g u r e s c a l c u l a t e d i n t h e n a t i o n a l m o d e l s , t r a n s f o r m e d t o s a t i s f y t h e r e - q u i r e m e n t s of t h e t r a d e model. The f i g u r e s r e s u l t i n g from t h e c a l c u l a t i o n s , i n t h e t r a d e model, of each Nordic c o u n t r y ' s i n t r a - N o r d i c e x p o r t s a r e com- p a r e d t o t h e c o r r e s p o n d i n g e s t i m a t e s u s e d i n t h e n a t i o n a l models, t r a n s f o r m e d t o s a t i s f y t h e r e q u i r e m e n t s of t h e t r a d e model. I f t h e d i s c r e p a n c i e s a r e r e g a r d e d t o be s u f f i c i e n t l y s m a l l , t h e i t e r a t i v e p r o c e s s i s c o n c l u d e d . On t h e o t h e r hand, i f t h e d i s c r e p a n c i e s a r e r e g a r d e d t o be u n a c c e p t a b l y l a r g e , t h e i t e r a t i v e p r o c e s s c o n t i n u e s by r e c a l c u l a t i o n s , i n t h e t r a d e model, of e a c h Nordic c o u n t r y ' s i n t r a - N o r d i c e x p o r t s . The n e c e s s a r y i n p u t s of i m p o r t f i g u r e s i n t h e s e r e c a l c u l a t i o n s a r e e s t i m a t e d by means of impact m a t r i c e s , d e r i v e d from t h e n a t i o n a l models. The i t e r a t i v e p r o c e s s , a s d e s c r i b e d a b o v e , c o n t i n u e s u n t i l t h e d i s c r e p a n c i e s mentioned above a r e r e g a r d e d t o be s u f f i c i e n t l y s m a l l .

3 . 2 . The e q u a t i o n system of t h e t r a d e model

The t r a d e model p r e s e n t e d below i s a s i m p l e q u a n t i t y model a n d s h o u l d be r e g a r d e d a s t h e f i r s t s t e p towards a more e l a b o r a t e t r a d e model.

The b a s i c r e l a t i o n i n t h e t r a d e model i s t h e r e l a t i o n f o r c o u n t r y k ' s 1 ) i n t r a - N o r d i c e x p o r t s :

where

1 ) I n t h i s p a p e r , e x c e p t where i t i s e x p l i c i t l y s t a t e d n o t t o be t h e c a s e , k , 1 = D , F, N , S where D , F, N and S d e n o t e Denmark, F i n l a n d , Norway a n d Sweden, r e s p e c t i v e l y .

2) The symbol o means e l e m e n t by element m u l t i p l i c a t i o n of v e c t o r s ( o r m a t r i c e s ) and r e q u i r e s t h a t t h e v e c t o r s ( o r m a t r i c e s ) i n v o l v e d a r e of

t h e same o r d e r : Z = X o Y , where X and Y a r e v e c t o r s (of t h e same o r d e r ) means t h a t Z . = X.

.

Y . f o r a l l i.

1 1 1

xk

= vector1) of intra-Nordic exports of NoRDHAND-commodities2) from country k ; constant (1980-) prices; US$.

rk

⁼ vector of correction parameters for intra-Nordic exports of NORDHAND- commodities from country k ;

Mkl(k+l) ⁼ vector of market shares by (NoRDHAND-) comodity of country k in country 1's imports3).

Akl(k+l) = vector of parameters for exogenous adjustments of the market shares by (NORDHAND-) commodity of country k in country 1's imports;

B' = vector of imports of NORDHAND-commodities to country 1; constant (1980-) prices; US$.

The parameters for exogenous adjustments, the elements of Akl(k+l), are initially given by

and is introduced to be able, in a simple way, to adjust the intra-Nordic market shares. Instead of adjusting the elements of Mk1(k*l) directly, we substitute the initial values of the elements of Ak1(k*l) by alternative values, different from 1 5).

Given the particular role of A (k*l), (1) kl could be expressed in the following way: Country k's intra-Nordic exports of NORDHAND-commodities is equal to the other Nordic countries imports of NORDHAND-commodities from country k , corrected (by means of

rk)

to account for cif-fob factors and other sources of deviations between figures reported by exporting countries and figures reported by importing countries.

Before the iterative process, briefly described in section 3.1, is started, the correction parameters, the elements of rk, are calculated on the basis of actual figures for 1980, for country k's intra-Nordic exports of NORDHAND-commodities and for the other Nordic countries' imports of NORDHAND-commodities:

1 ) The number of commodities classified according to the commodity classi-

fication of the trade model is 36, and in this paper, except where it is explicity stated not to be the case, all vectors are of order (36

.

^1).

2) The term NORDHAND-commodities is used to denote the commodities of the trade model.

3) These market shares are calculated on the basis of actual figures, from OECD1s trade statistics, for 1980.

4) e is a column vector with all elements equal to 1.

5) Analyses of the effects of policy measures affecting the intra-Nordic market shares can thereby be linked to the trade model through Ak1(k*l).

k 1 k

where X (T=O) and B (T=O) a r e i d e n t i c a l t o X and B1, r e s p e c t i v e l y , e x c e p t f o r t h e f a c t t h a t t h e i r e l e m e n t s a r e a c t u a l f i g u r e s f o r 1 9 8 0 ~ ) .

Country k ' s i n t r a - N o r d i c e x p o r t s and c o u n t r y k ' s i m p o r t s a r e c a l c u l a t e d i n an i t e r a t i v e p r o c e s s . I n each i t e r a t i v e s t e p , c o u n t r y k ' s i n t r a - N o r d i c e x p o r t s of NORDHAND-commodities a r e c a l c u l a t e d on t h e b a s i s of f i g u r e s , c a l c u l a t e d i n t h e p r e c e d i n g i t e r a t i v e s t e p , f o r t h e o t h e r Nordic c o u n t r i e s ' i m p o r t s of NORDHAND-commodities. F o r m a l l y , t h i s p r o c e d u r e i s d e s c r i b e d by

where, compared t o ( I ) , t h e s u b s c r i p t s t and t - 1 , d e n o t i n g i t e r a t i v e s t e p s , have been a d d e d .

I n e a c h i t e r a t i v e s t e p , r a t e s of change of c o u n t r y k ' s i n t r a - N o r d i c e x p o r t s of NORDHAND-commodities a r e c a l c u l a t e d :

The i t e r a t i v e p r o c e s s c o n t i n u e s u n t i l t h e f o l l o w i n g c o n d i t i o n i s s a t i s f i e d :

' k where E i s t h e a c c e p t a b i l i t y l i m i t f o r t h e v a l u e s of t h e e l e m e n t s of

I X

_t

I .

kAs l o n g a s t h e i t e r a t i v e p r o c e s s c o n t i n u e s , new v a l u e s f o r t h e e l e m e n t s of X a r e c a l c u l a t e d a s d e s c r i b e d by ( 4 ) . Through t h ~ r e l a t i o n s i n t h e n a t i o n a l models, t h e new v a l u e s f o r t h e e l e m e n t s of X g e n e r a t e new v a l u e s

f o r t h e e l e m e n t s of B ~ . T h i s f a c t i s a c c o u n t e d f o r by means of t h e f o l l o w - i n g r e l a t i o n :

k .

where t h e s u b s c r i p t s t and t - I d e n o t e i t e r a t i v e s t e p s . V 1 s t h e impact m a t r i x ( c f r . s e c t i o n 3 . 1 ) d e r i v e d from t h e n a t i o n a l model of c o u n t r y k .

1) The symbol I N V a t t a c h e d t o a v e z t o r ( o r a m a t r i x ) means t h a t each element of t h e v e c t o r ( o r t h e m a t r i x ) i s s u b s t i t u t e d by i t s i n v e r s e : Y = INV X , where X i s a v e c t o r , means t h a t Y i = l / X i f o r a l l i.

2) These f i g u r e s a r e f i g u r e s from OECD's t r a d e s t a t i s t i c s .

3 ) The symbol a t t a c h e d t o a v e c t o r means a d i a g o n a l m a t r i x w i t h t h e e l e - ments of t h e v e c t o r a l o n g t h e main d i a g o n a l . The symbols t and t - 1 d e n o t e i t e r a t i v e s t e p s .

4 ) The symbol

I I

a t t a c h e d t o a v e c t o r means t h a t e a c h element of t h e v e c t o r i s s u b s t i t u t e d by i t s n u m e r i c a l v a l u e .

The j ' th element of the i'th row of

vk

I), represents the percentage impact on country k's imports of NORDHAND-commodity i of a one percentage increase in country k's intra-Nordic exports of NORDHAND-commodity j . In this con- text it should be noted that the use of impact matrices is a simplification compared to ordinary calculations in the national models, and that the main reason for using impact matrices is to make the model system easier manage- able.

The iterative process, formally described above, is started by setting

where

Xo k = vector of intra-Nordic exports of NORDHAND-comodities from country k, transformed from estimates used in the national model of country k; constant (1980-) prices; US$.

BE

⁼ vector of imports of NORDHAND-commodities to country k , transformed from figures calculated in the national model of country k; constant

(1 980-) prices; US$.

The values of country k's intra-Nordic exports of NORDHAND-commodities (the values of the elements of ~ k ) , calculated in the last iterative step, and the corresponding values of country k's imports of NORDHAND-commodities (the values of the elements of Bk) are the outputs of the trade model.

3.3. Construction of impact matrices used in the trade model

The construction of the impact matrices used in the trade model neces- sarily involves (cfr. the definition of

vk

in section 3.2) th problems of transformation and retransformation mentioned in section 3.1 27

.

The links between the commodity classification of the national model of country k and the commodity classification of the trade model are given by two value transformation matrices, TAk and Tm. The typical element of T , t. Ak

.,

represents exports of those micro-commodities3) that simultaneously belongij to commodity i of the national model of country k and NORDHAND-

1) The matrix

vk

is of order (36

-

^36).

2) It should be noted, hovever, that the fact that the currency used in the trade model is different from the currencies used in the national models represents no problem in the construction of the impact matrices used in the trade model, since the elements of these matrices represent the percentage impacts on imports of percentage increases in intra-Nordic exports

.

3) The term "micro-commodities1' is used to denote the one-, two- and three- digit SITC-commodities of which the NORDHAND-commodities are aggregates.

4) The value transformation matrices are constructed on the basis of actual figures for 1980, expressed in the national currency of the country in quest ion.

commodity j . The value transformation matrices are formally (and implicitly) defined by (9)-(12) :

where

= exports, from country k , of those components of the commodities of the national model of country k that are classifiable in terms of

~ ~ ~ ~ - c o m o d i t i s s ~ ) ; actual figures for 1980; national currency of ccuntry k; vector of order (nk

-

¹

^12).

where

Ak = vector of exports of NORDHAND-commodities from country k ; actual figures for 1980; national currency of country k.

where

= imports, to country k , of those components of the commodities of the national model of country k that are classifiable in terms of SITC- commodities; actual figures for 1980; national currency of country k ; vector of order (nC

.

^1).

where

M~ = vector of imports of NORDHAND-commodities to country k; actual figures for 1980; national currency of country k.

From the definitions of the matrices T Ak and T* it follows that they are both of order (nk

.

^36).

The impact matrix is defined by:

where

xk

⁼ vector of intra-Nordic exports of NORDHAND-commodities from country k; actual figures for 1980; national currency of country k.

and where

wk

is a matrix3), the typical element of which, wij, representing k

1) In this context it should be noted that the commodities of the national models also contain components that are not classifiable in terms of SITC-commodities.

2) nk is the number of commodities of the national model of country k.

3) The matrix

wk

is of order (36

-

^36).

the percentage impact on country k's imports of NORDHAND-comodity i of ^a one percentage increase in country k's exports of NORDHAND-commodity j .

(13) implies that each element of V k is proportional to the corresponding element of wk, with the share of intra-Nordic exports in total exports as the proportionality factor.

In the follo in it is shown how the matrix

wK

is constructed:

i. Thematrix Z ^k

-

'

^11, the typical element of which, rij: representing the l?ercentage increase in country k's exports of commodity 1 of the national model of country k that correspond to a one percentage increase in country k's exports of NORDHAND-commodity j, is constructed. The following relation applies:

where

= exports, from country k, of the commodities of the national model of country k; actual figures for 1980; national currency of country k;

vector of order (nk

.

^1).

ii. The columns of Z k are used as inputs in impact calculations in the - national model of country k. The output from these calculations is a matrix

uk

2 ) , the typical element of which, u,.! representing the percentage impact on country k's imports of commodity i og the national model of country k of a one percentage increase in country k's exports of NORDHAND-comodity j . iii. The matrix W k

,

defined above, is constructed. The following relation

-

applies :

The impact matrix, to be used in the trade model, for country k, results from inserting (15) into (13):

3.4. Transforming estimates used in, and outputs from, the national models and retransforming outputs from the trade model

The procedure of transforming estimates used in, and outputs from, the national model of country k to satisfy the requirements of the trade model requires two shares&ansformation matrices, TSAk and TS*. The typical element of TSAk, tij

,

represents the share in total exports of commodity j of the national model of country k accqynted for by exports of those micro- commodities that simultaneously belong to commodity j of the national model of country k and NORDHAND-commodity i. The typical element of TSMk, t S m represents the share in total imports of commodity j of the national model of country k accounted for by imports of those micro-commodities that simultaneously belong to commodity j of the national model of country k and NORDHAND-commodity i. The share transformation matrices are formally de- fined by (17) and (18):

1) The matrix

zk

is of order (nk

.

^36).

k .

2) The matrix U 1s of order (nk

.

^36).

3) The share transformation matrices are constructed on the basis of actual figures for 1980, expressed in the national currency of the country in question.

From the definitions of the matrices TSAk and TSa it follows that they are both of order (36 nk).

As mentioned in section 3.1, the currency used in the trade model5) is different from the currencies used in the national models. Taking account of this fact, the following relation for transforming estimates, used in the national model of country k , of country k's intra-Nordic exports, applies6):

where

ck = units of US$ per unit of the national currency of country k ; figures for the year under consideration.

=k

\o = estimates, used in the national model of country k , of country k's intra-Nordic exports of those components of the commodities of the national model of country k that are classifiable in terms of SITC- commodities; national currency of country k; vector of order (nk

.

^1).

Analogously, the following relation for transforming figures for country k's imports, calculated in the national model of country k , applies:

where

-

^k

The matrix T and the vector are defined in section 3.3.

Ak..

If the mat* h s a t i s f i e d the conditions for invertibility of matrices, INV AN = A;

-I.

However, as will be returned to below, the

-1.

contains some elements that are equal to 0 and, consequently the matrix is not defined.

The matrix T and the vector are defined in section 3.3.

a,.

If the matrix had satisfied the conditions for invertibility of

-. 4

^{I .} However, as will be returned to below, the matrices, INV l$ = MN

vector

%

contains some elements that are equal to 0 and consequently,

A

the matrix

$ -'

is not defined.

The currency in the trade model is US$.

(19), and also (21), applies under the assumption that the internal composition (in terms of micro-commodities) of country k's exports (classifiable in terms of SITC-commodities) of each commodity of the national model of country k is unaffected by destinational factors.

The vector :X is defined in section 3.2.

The vector :B is defined in section 3.2.

go

⁼ figures, calculated in the national model of country k , for country

This means that the vectors :A and :M contain elements that are equal to 0. This further means that (cfr. (9) and (11)) the matrices TAk and T*

contain rows in which all elements are equal to 0 and, correspondingly that (cfr. (17) and (18)) the matrices TSAk and TS* contain columns in which all elements are equal to 0. In the following, the matrices that are identical _- to TSAk and TSm, respectively, except for the fact that the columns in which

5) It should be noted that this deletion have to be done in such a way that the resulting matrix, *A which is of order (nk*

.

nk*), satisfy

T ~ ~ k '

the conditions for invertibility of matrices.

model) of country k's imports, the following relation applies:

where TSm is identical to T : ~ *A except for the fact that 36

-

nk* have been deleted2) and where B k A is equal to B exEept for the fact that

,.+(fin) (fin)

the corresponding 36

-

nK'. elements have been deleted.

3.5. S u m a r v of the technical descriution

The technical description of the model system is, in the following, briefly summarized in the form of a flow-chart by means of which the inter- relations between the various parts of the model system, should become parti- cularly apparent. This flow-chart, which is presented 3yelow, is a more precise version of the figure presented in section 3.1

.

1) If the vector - k *

%(fin)' defined by (22) and being of order (nk* I), is extended to include the nk

-

nk* zero elements that correspond to the nk

-

nk* columns of T that was deleted in order to arrive at the

*

^SMk

matrix T -k

we arrive at the vector M which is the vector B k

SMk' fin) (fin)

transformed to satisfy the requirements of the national model of country k.

2) It should be noted that this deletion have to be done in such a way that the resulting

matrix,^*^

which is of order (nk*

-

nk*), satisfy the

SMk

'

conditions for invertibility of matrices.

3) For more precise definitions of the symbols defined in the flow-chart, cfr. sections 3.2 - 3.4.

N a t i o n a l model c a l c u l a t i o n s o f imports

- - -

I

^and ~ ~ ~ f i n , are c a l c u l a t e d

)

by

I

pectively.

4 . AREAS OF APPLlCATION FOR AND FURTHER DEVELOPMENT OF THE NORDHAND MODEL SYSTEM

In section 3, a technical description of the NORDHAND model system was provided. In this section some types of problems for which the model system is supposed to be applied and some of the lines along which the model system is supposed to be further developed are briefly described.

Some of the supposed areas of application for the NORDHAND model system are the following ones:

a) Making a prognosis f the future development of imports and of intra-Nordic exportsPJ under the assumption of constant intra- Nordic market shares, and under reasonable assumptions about the economic policies pursued in the Nordic countries and about the development of the world economy.

b) Making prognoses for the future development of imports and of intra- Nordic exports .2)

-

under alternative assumptions about the development of the intra- Nordic market shares.

-

under the assumption of an expansive economic policy pursued unilaterally in one of the Nordic countries.

-

under the assumption of coordinated expansive economic policies in the Nordic countries.

c) Analyzing the effects on imports and on intra-Nordic exports of

1) Through the relations in the national models it is then possible to make a prognosis, consistent with the prognosis for the future development of imports and of intra-Nordic exports, for the future development of other variables.

2) Through the relations in the national models it is then possible to make prognoses, consistent with the prognoses for the future development of imports and of intra-Nordic exports, for the future development of other variables.

various policy measures used in one or more of the Nordic countries.

The technical descript~on provided by section 3 is a technical descrip- tion of a first version of the NORDHAND model system. Some of the lines along which this first version is supposed to be further developed are the following ones:

a) Making the model system more comprehensive in the sense of including non-Nordic countries.

b ) Making the national models more similar with respect to model

structure.

c) Making the trade model more elaborate by incorporating price relations.

Im Dokument Proceedings of the Fourth IIASA Task Force Meeting on Input-Output Modeling (Seite 158-171)