Revised Version of the SOVAM

!JOT F3R QUOTATIOY WITEOUT PERVISSIO?:

OF THE AUTHOR

REYISED VERSION

OF THE SOVAM

Vladimir Iakimets Vladimir Lebedev

September 1985 LT-85-66

Working Papers are interim r e p o r t s on work of t h e International Institute f o r Applied Systems Analysis and h a v e r e c e i v e d only lim- ited review. Views o r opinions e x p r e s s e d h e r e i n d o not neces- s a r i l y r e p r e s e n t t h o s e of t h e Institute or of i t s National Member Organizations.

IWTERNATIO?I'AL IYSTITETE FOR APPLIED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

FOREWORD

Understanding t h e n a t u r e and dimensions of t h e world food problem and t h e policies available t o alleviate i t has been t h e f o c a l point of IIASA's Food and Agriculture P r o g r a m (FAP) since i t began in 1977.

National food systems are highly interdependent, and y e t t h e major policy options e x i s t at t h e national level. T h e r e f o r e , t o e x p l o r e t h e s e options, i t i s n e c e s s a r y both t o develop policy models f o r national economies and t o link them together by t r a d e and c a p i t a l t r a n s f e r s . Over t h e y e a r s FAP h a s , with t h e help of a network of collaborating institutions, developed and linked national policy models of twenty countries, which t o g e t h e r account f o r n e a r l y 80 p e r c e n t of important a g r i c u l t u r a l a t t r i b u t e s such as area, production, population, e x p o r t s , imports and s o on. The remaining c o u n t r i e s are r e p r e s e n t e d by 14 somewhat simpler models of groups of countries.

The c o u n t r i e s constituting t h e Council of Yutual Economic Assistance (CMEA) t o g e t h e r are a major influence on t h e world market. An a g g r e g a t e food and a g r i c u l t u r e model of t h e CMEA, in which t h e CXEA i s t r e a t e d as one nation h a s been developed by t h e PAP, as p a r t of t h e IIASA/FAP basic linked system.

In addition, development of detailed models f o r some of t h e major nations constituting t h e CMEA w a s undertaken. The development of t h e Soviet Agricultural Model (SOVAY) w a s s t a r t e d in l a t e 1983 in collaboration with a number of institutions in t h e Soviet Union. These include t h e All- Union R e s e a r c h Institute of Cybernetics in Agriculture, t h e Computer Center of t h e USSR Academy of Sciences, t h e All-Union R e s e a r c h Institute for Systems Studies, and t h e Central Economic Xathematical Institute.

In this p a p e r Vladimir Iakimets and Vladimir Lebedev d e s c r i b e a revised version of t h e SOVAM.

Kirit S. P a r i k h Program Leader Food and Agriculture P r o g r a m

ABSTRACT

This p a p e r contains t h e r e v i s e d d e s c r i p t i o n of t h e P r o d u c t i o n and E x c h a n g e module of t h e programmed v e r s i o n of t h e SOVAM. The s t r u c t u r e of t h i s v e r - sion and information flows in t h e model e r e a l s o explained. The s p e c i f i c s of t h e algorithmic and programming implementation of t h e S O V A M a r e given.

We are v e r y g r a t e f u l t o Cynthia E n z l b e r g e r f o r typing t h i s p a p e r .

-

vii

-

CONTENTS

1. Introduction 1

2. Yain distinctive f e a t u r e s of t h e SOVAM 1

3. S t r u c t u r e a n d information flows of t h e model 4

4. Production module 6

4 . 1 Planning of a g r i c u l t u r a l production and t r a d e 6 4.2 Yodule of t h e adjustment of planned o u t p u t 1 0

5. Exchange module 11

6. Algorithmic a n d programming s p e c i f i c s of t h e SOVAM implementation 1 2

7. Conclusions 1 4

R e f e r e n c e s 1 4

REVISED VERSION OF THE SOVAM

VLadimir Iakimets VLadimir Lebedev

1. Introduction

This p a p e r i s aimed t o give t h e detailed description of t h e revised version of t h e SOVAM, including t h e s t r u c t u r e and information flows of t h e programmed model, formalized description of t h e a g r i c u l t u r a l production module and exchange module.

The background and requirements t o t h e SOVAM were given in Iakimets (1984). The generai s t r u c t u r e of t h i s model and ideas f o r t h e implementation of main modules were outlined in Fedorov and Iakimets (1985). The f i r s t formalized description of t h e SOVAM c a n be found in Iakimets and Kiselev (1985). In t h a t p a p e r attention w a s paid t o t h e economic background f o r t h e model.

However, during t h e implementation of t h e programmed version of t h e SOVAM, t h e improvement and revision of some elements of t h e model became necessary.

During t h e p r o c e s s of simulation experiments with t h e SOVAM in a s t a n d a l o n e mode, t h e revised versions of i t s main modules were p r e p a r e d . Apart from t h e f o r - malized description of t h e revised versions of t h e Production and Exchange modules t h a t will be given in t h i s p a p e r , t h e n e x t p a p e r will contain t h e description of t h e Policy module.

2. The main distinctive features of the SOVAM

The s t r u c t u r e of t h e Soviet macroeconomic national a g r i c u l t u r a l policy model (SOVAM) w a s conceived from t h e beginning (Iakimets 1984) in such a way t o r e f l e c t t h e specifics of t h e USSR a g r i c u l t u r a l policy and direction f o r t h e intensification of a g r i c u l t u r a l production taking into account changes in world market induced by interactions of o t h e r national models within t h e BLS.

Realizing t h e complexity of a construction of a n adequate USSR model of such a level of aggregation as t h e BLS models a r e , we have had in mind t h e implementa- tion of a n "open" model. I t means t h a t t h e model under development should b e allowed a step-by-step improvement and detailization of i t s s t r u c t u r e , information flows, objectives and constraints on t h e basis of simulation experiments with i t with t h e BLS.

Due t o t h e specifics of t h e centrally planned economy and peculiarities of t h e Soviet a g r i c u l t u r a l system and Soviet foreign t r a d e , t h e macroeconomic agricul- t u r a l policy model (SOVAM) developed possesses a number of distinctive f e a t u r e s in comparison with t h e o t h e r BLS models with t h e s t a n d a r d s t r u c t u r e . In t h i s section t h e main such f e a t u r e s implemented in t h e formalized and programmed version of t h e SOVAM a r e briefly described.

(1) The policy t o provide t h e country's population with food commodities under stabile moderate p r i c e s always was, is, and will b e , one of t h e most important s t r a t e g i c elements of t h e Soviet national economy. Recent implementation of this policy i s r e f l e c t e d by t h e USSR food program f o r t h e period 1982-1990.

The principal objective of t h i s program i s t o achieve t a r g e t e d consumption of t h e main s t a p l e foods f o r people, reflecting t h e improvement of t h e balance of t h e i r diet mainly due t o a n intensification of t h e internal production. There- f o r e t h e c u r r e n t tendencies in implementation of t h e s e t a r g e t s are used in t h e model explicitly.

(2) Direct influences of fluctuations of world market p r i c e s on domestic consumer and producer p r i c e s a r e absent even f o r climatically unfavourable years.

Therefore policy instruments describing the domestic p r i c e formation system a r e determined by internal aonaitions of agricultural production and distribu- tion of agricultural commodities.

However, in spite of permanently increasing trends of production, volumes of produced outputs, especially c r o p outputs, a r e fluctuated mainly due t o weather impact. I t affects t h e s t r u c t u r e of balances of t h e c r o p s commodities utilization and especially those c r o p s which a r e used f o r livestock feed.

A s a n implication t o alleviate t h e effects of weather fluctuations t h e world market is used f o r import of feed commodities t o support livestock produc- tion. In this sense t h e SOVAM should reflect explicitly relationships between livestock production, fluctuations of domestic feed production induced by weather influences, and agricultural trade. In t h a t sense t h e production of livestock commodities is strongly dependent upon t h e intensification of inter- nal c r o p production through agro-technological improvement and f o r t h e transition period when t h e stabile c r o p s production is achieved, t h e world market will be considered as a source f o r import in cases of shortages of domestic feed outputs. Therefore t h e SOVAM envisages t h r e e levels of agro- technological improvement of internal production with t h e help of corresponding yield functions. The special module f o r planning of agricul- tural output, import, feed and a c r e a g e allocation taking into account world market p r i c e s f o r t h e previous y e a r w a s c r e a t e d in t h e SOVAM f o r these pur- poses.

(3) To r e f l e c t t h e impact of weather fluctuations on c r o p s output a s e p a r a t e module f o r adjustment of planned indicators was introduced within t h e SOVAM.

In this module a p a r t from recalculation of t h e c r o p s output, t h e adjustment of stocks, import volumes and balances f o r c r o p s utilization a r e considered explicitly. This i s once more a distinctive f e a t u r e of t h e model.

( 4 ) The dependence of livestock output on feed supply forced t o introduce t h r e e types of feed balances (in feed units, protein and concentrates utilization). I t effected t h e extension of lists of commodities f o r example, by introducing as one of t h e main commodities green feeds. I t is especially important if t h e available potential f o r increasing its production in t h e Soviet Union is taken into account.

(5) Apart from this commodity, a number of o t h e r (important f o r Soviet agricul- t u r e and agricultural t r a d e ) commodities were included in t h e SOVAM list.

These changes were concerned mainly with disaggregation of such commodities in t h e BLS list as "other food", "other animal" and "non-food" (see Table 1). In compiling t h e SOVAM list of commodities such c r i t e r i a as t h e i r c u r r e n t impor- tance f o r Soviet agriculture, coincidence with t a r g e t e d consumption in t h e food program, possible restructuring of future output as w e l l as significance f o r Soviet agricultural t r a d e were taken into consideration.

(6) According t o a number of c u r r e n t governmental resolutions decisions con- cerning t h e improvement and intensification of c r o p s and feed production were made. Some of these decisions a r e related t o possible s t r u c t u r a l changes of the agricultural production in t h e USSR. Therefore, instead of t h e BLS-like model we constructed a simulation optimization model, variables of which can b e used f o r searching f o r preferable acceptable combinations of some s t r u c t u r a l changes (acreage s t r u c t u r e , interbalanced volumes of feed and livestock commodities production, etc. ).

Table 1. Commodity L i s t s

SOVAM Units of FAP

measurement

Units of measurement

- -

1. wheat

l o 3

mt 1. wheat

l o 3

mt

2. r i c e , milled

l o 3

^mt 2. r i c e , milled

l o 3

^mt

3. c o a r s e g r a i n

lo3

^mt 3. c o a r s e g r a i n

l o 3

^mt

4. g r e e n feed

l o 3

mt

5. p r o t e i n feed.

l o 3

mt 7. p r o t e i n f e e d

lo3

mt

p r o t e i n equivalent p r o t e i n equivalent 6. vegetable oil

lo3

mt

7 . s u g a r 1 0 3 mt

8. vegetables

l o 3

^mt 8 . o t h e r food mill US $ 1970

9 . potato 1 0 3 mt

10. f r u i t s 1 0 3 mt

-

11. cotton

l o 3

^mt 9. non-food

- -

mill US $ 1 9 7 0 1 2 . bovine & ovine

lo3

mt 4. bovine & ovine

l o 3

m t

carcass weight carcass weight

13. p o r k

l o 3

^{mt 6.} o t h e r animal

l o 3

^mt

carcass weight p r o t e i n equivalent

1 4 . poultry

l o 3

^mt

1 5 . d a i r y

l o 3

m t 5. d a i r y f r e s h milk

equivalent

lo3

mt f r e s h milk equivalent

1 6 . eggs

l o 3

mt 6. o t h e r animal

l o 3

mt

p r o t e i n equivalent p r o t e i n equivalent 1 7 . wool, g r e a s y

lo3

mt 9. non-food mill US $ 1 9 7 0 18. non-agriculture mill US $1970 10. non-agriculture mill US $ 1 9 7 0

(7) Taking into account t h e e x i s t e n c e of t h e s p e c i f i c time relationship between volumes of production of f e e d s and livestock commodities e x p r e s s i n g in t h a t t h e feed produced in c u r r e n t y e a r h a r v e s t i s used with time lag delay f o r livestock production in t h e next y e a r , in t h e model t h e double balancing t h e livestock commodities is stipulated. Namely, t h e balance of t h e livestock com- modities utilization in a y e a r u n d e r simulation is based on d a t a about volumes of t h e production of t h e s e commodities, calculated in t h e previous period and planned values of human consumption and import of i t in c u r r e n t y e a r . The

balance of t h e s e commodities utilization for t h e next y e a r i s calculated taking into account values of desired t a r g e t e d consumption and sought for planned production in y e a r ( t + l ) and planned import in y e a r t.

3. Structure and information flows of the model

This section contains t h e description of t h e s t r u c t u r e a n d information flows of t h e SOVAM c u r r e n t version (Figure 1 ) and its list of commodities compared with t h e BLS list (Table 1 ) . Main distinctive f e a t u r e s of t h e SOVAM described in Section 2 are reflected in i t s s t r u c t u r e and are induced corresponding information f l o w s . Because this p a p e r does not contain t h e formalized description of t h e a g r i c u l t u r a l policy module (it will b e done in t h e n e x t p a p e r ) t h e r e f o r e corresponding informa- tion flows connecting t h i s module with o t h e r modules of t h e SOVAM are given without mathematical notations.

As i t i s shown in Figure 1 th e SOVAM has t h r e e main modules: Policy, Produc- tion and Exchange modules. The Policy module includes t w o submodules: decisions on buageting, production, consumption and foreign t r a d e and t h e submodule of national accounting. The Production module contains t h r e e submodules: module f o r planning of a g r i c u l t u r a l output. module for adjustment of planned output and module of non-agricultural production. The Exchange module includes t h e exchange p r o c e d u r e by itself and t h r e e intermediate blocks for aggregating and splitting imports and p r i c e s of commodities from t h e SOVAM commodity list to t h e BLS one and vice v e r s a . 'The description of mathematical notations given in Figure 1 c a n b e found in t h e n e x t section of this p a p e r .

Let us now give a s h o r t description of t h e main information flows of t h e SOVAM following t h e specific f e a t u r e s of t h e model given in t h e previous section.

(1) Based on t h e r e s u l t s of simulation in y e a r (t-1) within t h e Policy module deci- sions on budgeting, production, consumption and foreign t r a d e in a c c o r d a n c e with determined functions and relations are elaborated f o r t h e y e a r under simulation. These include f i r s t of all allocation of total investments between a g r i c u l t u r a l and nonagricultural sectors and decisions concerning t h e public and p r i v a t e consumption and foreign t r a d e . Production decisions are r e l a t e d to rates and s h a r e s of a g r i c u l t u r a l production and to generation of inputs f o r agriculture. Consumption decisions include t a r g e t s for a g r i c u l t u r a l and non- agricultural goods consumption. For example, t h e s e t a r g e t s f o r a g r i c u l t u r a l goods are g e n e r a t e d following t h e USSR Food Program. Trade decisions are r e l a t e d mainly to t h e calculation of planned value of e x p o r t (import) of goods for t h e y e a r under simulation.

(2) On t h e basis of some of t h e above mentioned decisions (consumption t a r g e t s , inputs and s h a r e s of production of various a g r i c u l t u r a l goods, etc.) and based on t h e d a t a of t h e equilibrium world market p r i c e s for t h e previous y e a r and given planned t a r g e t s for livestock outputs within t h e module for planning of agricultural output t h e optimization problem i s solved. The allocation of a c r e a g e and determination of planned volumes of c r o p outputs and t h e i r utili- zation for feed for y e a r t and livestock output f o r y e a r ( t + l ) , as w e l l as determination of planned volumes of import for all agricultural commodities i s sought in t h i s module. Balances of c r o p s utilization for feed and balances for e a c h commodity utilization for t h e y e a r under simulation and balances of pos- sible utilization of livestock commodities in t h e n e x t period ( t + l ) are taken into account during t h i s problem solving.

W

2

POLICY MODULE !

I

C I National accounts

I I

0 b

historical (GDP, domestic ! I

f

export, trends prices policy, rates

i 1

^b

4 import

of development, etc.)

1 I

^b

1 Trade changes

0

r~ decisions

A A

1 I

0 c

I ^I

P - I

z

V)

I

CC 1 1

C 0 CC

ye,

I

C

I ; .

^{v v}

^*

^v

ⁱ

^Ya(t)

1 U ( t )

I - i-+ U ( t )

I

(D Module for planning Non-

- i

^{I f} I

D

1 ~ " ( t - 1 1 1

j

of agricultural output agricultural i

1

a I

fi 1,

production

rn i

I

;;

1

1 I :

I

I

i ^{d, T W S I}

I

-

UP' (t

+

¹ )

I

5 g ^I ₁

^{I i r\ C\ 1}

i YP' (t) zP' (t) wP' ( t )

i

1

I

2

^I

o R(t)

up'

^(t

+

^{1 )}

E

I

01

I

I

v i I

I

U ( t

+

1)

Exchange b

imports

f EXCHANGE MODULE prices

I I

I

PRODUCTIONMODULE i

/

(t - 1) I ! 1 t ' ( t + l )

I World market

(3) Planned outputs and imports f o r c r o p s found in t h e module f o r planning of a g r i c u l t u r a l output are c o r r e c t e d within t h e module of t h e adjustment of planned output, taking into consideration exogenously g e n e r a t e d information on t h e impact of w e a t h e r fluctuation on various c r o p production. A s a r e s u l t new values of c r o p o u t p u t s and t h e i r utilization are found. A s a n implication t h e change of balances f o r utilization of commodities o c c u r through corresponding manipulations of s t o c k s and imports taking into account param- eters and c o n s t r a i n s given in t h e Policy module.

(4) Updated d e s i r e d imports are a g g r e g a t e d t o b e consistent with t h e BLS list of commodities f o r t h e linkage p r o c e d u r e . These a g g r e g a t e d values of imports (desired) are used t h e n for t h e exchange with t h e world m a r k e t within t h e framework of t h e BLS i t e r a t i v e p r o c e d u r e f o r s e a r c h i n g equilibrium p r i c e s . To r e f l e c t t h e impact of t h e world market on t h e s e p r i c e s during t h i s i t e r a t i v e p r o c e d u r e t h e value of t r a d e balance endogenously ( f o r t h e SOVAM as a whole) calculated within t h e Policy module is used in t h e exchange module. If t h e f i r s t estimate of t h i s value t u r n s out t o b e more t h a n t h e e x p e c t e d value of a g r i c u l t u r a l imports t h e n r e c e i v e d savings are transmitted into t h e Policy module and t h e s e are distributed t h e r e in a predetermined p r o p o r t i o n between consumption and investments. Final adjustment of t h e commodity bal- a n c e s is realized after t h e splitting a g g r e g a t e d imports corresponding t o equilibrium p r i c e s .

( 5 ) Results of t h e simulation f o r t h e y e a r t are used as input d a t a f o r t h e n e x t period ( t + l ) . Thus t h e adjustment of livestock output is made and national accounts inciuding GDP calculating based on d a t a on a g r i c u l t u r a l and non- a g r i c u l t u r a l o u t p u t s and domestic p r i c e s , utilization of GDP f o r consumption, investment and foreign t r a d e etc.

I t should b e noted t h a t modules f o r p r e p a r a t i o n of input, intermediated and output files are not shown in Figure 1.

4. Production module

4.1. Planning of agricultural production and trade Let us denote:

i

= -

l , n , is index of c r o p commodities, n,

=

11 , i

= -

l , n l is index of livestock commodities, nl

=

6 ,

k

= 1,K

is index of t h e agrotechnology used for c r o p production, K

=

3.

The t o t a l number-of t h e a g r i c u l t u r a l commodities in t h e SOVAM is n

=

n,

+

nl

=

1 7

Let u s specify v a r i a b l e s of t h e module u n d e r consideration:

xik(t)s t h e a c r e a g e of i-th c r o p cultivated u n d e r k-th agrotechnology in y e a r

-

t , i

=

l , n , , k

=

l , K ;

u f l ( t + l ) i s planned output of i-th livestock commodity in y e a r ( t + l ) , i

= -

l , n l ; zfl(t) is planned import ( e x p o r t ) of i-th commodity in y e a r t , i

= -

1 , n ;

wrl(t) is planned utilization of i-th c r o p commodity f o r feed in y e a r t , i

= -

l , n ,

.

Let us specify a l s o t h e following intermediate variables:

-

y r l ( t ) is planned output of i-th c r o p commodity in y e a r t , i

=

l , n , ,

d r l ( t ) is planned human consumption of i-th c r o p commodity in y e a r t , i

= -

1 , n ,

c;rl(t) a r e normative losses of i-th c r o p in y e a r t , i

= l,n,

^;

kpl(t) i s normative utilizaton of i-th c r o p f o r s e e d s in y e a r t, i

= --

l , n c ; xi(t) a r e losses of i-th livestock commodity in y e a r t , i

=

l , n l

-

;

vt(t) is an intermediate utilization of i-th livestock commodity in y e a r t, i

= -

l , n l x f l ( t + l ) a r e e x p e c t e d losses of i-th livestock commodity in y e a r ( t + l ) , i

= -

l , n l ; v f l ( t + l ) i s an expected intermediate utilizaton of i-th livestock commodity in y e a r

-

( t + l ) , i

=

l , n l ;

P a r a m e t e r s given f o r t h e planning module include:

at i s normative e x p e n d i t u r e s of feed units f o r t h e production of one unit of i-th

-

livestock commodity, i

=

l , n l ;

bi i s normative e x p e n d i t u r e s of p r o t e i n s f o r t h e production of one unit of i-th

-

livestock commodity, i

=

l , n l ;

ci i s normative e x p e n d i t u r e s of c o n c e n t r a t e s f o r t h e production of one unit of i-th

-

livestock commodity, i

=

l , n l ;

qi is content of f e e d units in one unit of i-th feed, i

=

- l , n c ;

6t

i s content of protein in one unit of i-th feed, i

=

l . n c ;

gi is coefficient of normative expenditures of i-th c o n c e n t r a t e , i

=

- l , n c ; oi is allowed change of t h e a c r e a g e f o r i-th c r o p , i

= -

l , n c ;

hfik is normative increment of f e r t i l i z e r application f o r i-th c r o p cultivated under

- -

k-th agrotechnology, i

=

l , n c , k

=

1 , K ;

-

c;i is coefficient of normative losses of i-th c r o p , i

=

l , n c ,

1-11

i s coefficient of normative utilization of i-th c r o p f o r s e e d s , i

=

l , n c ,

xi

i s coefficient of normative losses of i-th livestock commodity, i

= -

l , n c ;

vi i s coefficient of normative intermediate consumption of i-th livestock commo-

-

dity, i

=

l , n l ;

T ~is p a r a m e t e r f o r determination of s h a r e s of + ~ m e a t production, i

=

1 2 , 13;

are right-hand c o n s t r a i n t s f o r m e a t production, i

=

1 2 , 13;

vi+l

i s p a r a m e t e r determining t h e s t r u c t u r e of meat import, i

=

1 2 , 13;

vf

i s amount of f e e d units given f o r a g r i c u l t u r e outside,

vp

i s amount of p r o t e i n given f o r a g r i c u l t u r e outside, A is maximum available t o t a l a c r e a g e ,

yl, y2 a r e correspondingly s h a r e s of wheat and r i c e outputs used f o r feed.

Let us define exogenously calculated (in relation t o t h e module under con-

sideration) p a r a m e t e r s in y e a r t :

-

di*(t) i s t a r g e t of human consumption of i-th commodity i

=

l , n ;

AF(t) is increment of t o t a l amount of f e r t i l i z e r s delivered t o a g r i c u l t u r e ( r e l a t i v e t o basic y e a r ) ;

n f ( t ) i s t h e output of f e e d units from p a s t u r e s ; n p ( t ) is t h e output of p r o t e i n from p a s t u r e s ;

Yik(t) is t r e n d yield of i-th c r o p cultivated under k-th agrotechnology (i

= -

l , n c , k

= 1,K

) calculated f o r example as follows:

Yik(t)

=

yoi

+

ali

.

t

+ a z i .

^&,(t)

+

agi hfik,

where yoi i s initial value of yield, ali , azi , a3i a r e statistically estimated parame- ters, and AK,(t) i s exogenously (for t h e module u n d e r consideration) calculated increment of c a p i t a l s t o c k s in a g r i c u l t u r e ,

p y ( t ) is world m a r k e t p r i c e * f o r i-th commodity, i

= -

l , n ,

O

i s policy p a r a m e t e r t o r e f l e c t t a r g e t s in t r a d e of livestock commodities.

Aggregating and splitting t h e world market p r i c e s from t h e SOVAM list t o t h e BLS list of commodities and inversely is implemented as follows:

p r ( t )

=

jjiw(t), i = n

~ ; ( t )

=

$'(t), p r ( t )

=

0.27 E r ( t ) , pT(t)

=

0.118 P r ( t ) , p r ( t )

=

0.175 E r ( t ) , p r ( t )

=

0.069 p t ( t ) , P G ( ~ )

=

0.18 p r ( t > , p E ( t )

=

0.18 p r ( t ) , P G ( ~ )

= -

~qw(t), p z ( t )

=

0.098 p r ( t ) , p G ( t )

=

0.123 E c ( t ) , P G ( ~ )

=

P F ( t ) #

~ g ( t >

=

0.11 E:(t), p;b(t)

=

0.934 p r ( t ) .

H e r e &(t) i s worid m a r k e t p r i c e of i-th commodity f o r t h e BLS list. And finally w e specify t h e following p a r a m e t e r s of t h e moduie which a r e endogenously calculated:

--

xi(t-1) i s a c r e a g e of i-th c r o p , i

=

l , n c ui(t) i s output of livestock commodity, i

=

1,n:

--

The problem is t o find values of

- - -- -- -

xik(t), i

=

l , n c , k

=

l , ~ , w r l ( t ) , i

=

l , n c , u f l ( t

+

I ) , i

=

l , n l , z f l ( t ) , i

=

1 , n t o minimize

s u b j e c t to:

A. Crop Production

y f l ( t )

= z-

^{yik(t) * xik(t) a i}

⁼

^{l , n c}

--

c r o p output;

k = l . K

c o n s t r a i n t s f o r changes of i-th c r o p a c r e a g e ;

C -

^Z-xik(t)

^a

^A t o t a l a c r e a g e ; i=:,n, k = l , K

* Endogenous u s i n g these prices will be described in the paper about linked version of the

SOVAhr,.

~ ~ ~ ( t - 1 ) ^B i

= --

l , n c

condition f o r non decreasing a c r e a g e of i-th c r o p under k-th agrotechnology in next y e a r ;

x-

b f i k . x i k ( t ) a A F ( t ) f e r t i l i z e r application:

i = l , n c k=-

B. Balances of feed utilization

c_

^a,

^.

u f l ( t + l )

-

n f ( t + l )

- af

^s

C -

^qi

^-

^{wfl(t) ,} feed units balance;

i=l,nl i = l , n c

2-

^bi

^.

~ p l ( t + l )

-

n p ( t + i )

-

^{Qp s}

c - ei ^.

~ p l ( t ) , protein feeds balance;

i = l , n i i = l , n c

C

^{c, upl(t+l)}

^{a C}

^{gi a wfl(t) ,G}

⁼

^{t1,2,3j E}

-

^{l , n c} balance of concentrates;

i = l , n l i€G

wf'l(t)

= ri .

~ ! l ( t ) , i

=

11.2

I

^f

--

l , n c utilization of wheat and r i c e f o r feed.

C. S t r u c t u r e of t h e meat output

u f l ( t + l ) 2

UP ^-

^{T~ +I}

^.

u f i l ( t + l ) i

=

12,13.

D.

Baiances of t h e utiLization of commodities:

f o r c r o p s

d f l ( t )

=

y,P1(t)

+

z,P1(t)

-

wfl(t)

-

op1(t)

-

CLpl(t) ,

-

l , n c ofl(t)

=

oi

.

yF1(t) , l , n c

-

f o r livestock commodities ( c u r r e n t y e a r )

f o r livestock commodities (next y e a r )

E. S t r u c t u r e of t h e meat t r a d e z f l ( t ) r q i + l

-

zPfl(t) ⁱ

=

12,13 F. Human consumption of commodities d f l ( t ) r d,*(t) i

= -

2,n

4.2. Modl;le of the adjustment of planned output

This module i s used f o r t h e adjustment of planned values of output and import for some of t h e commodities under t h e impact of weather fluctuations, generated with t h e help of scenarios, constructed on t h e basis of analysis of historical data.

For t h e s e purposes changes of stocks of commodities are implemented taking into account t h e value of a g r a i n equivalent (Q (t)) of t h e difference between planned and "actual" output.

Actual output of c r o p s under weather fluctuations (Y;(t)) is determined as fol- lows:

y;(t>

=

t i ( t )

.

yf'l(t) , i

=

Ln,.

-

Grain equivalent of deviations in feed supply from planned value i s defined as fol- lows:

where

w;(t)

=

max tw'J1(t)

-

^y'J1(t)

+

Y;(t), O j i s a c t u a l utilization potato f o r feed, Stocks of corresponding commodities are used f o r elimination of consequences of weather shocks:

hSl(t)

=

maxI(1

-

yl) (Yt(t)

-

yfl(t)), -Sl(t)j changes of wheat stocks.

hS3(t)

=

max IQ(t),

-

S3(t) j changes of coarse grain s t o c k s where

S i ( t + l )

=

Si(t)

+

hSi(t), i

=

1,3 are s t o c k s of wheat and coarse grain Corresponding adjustment of t h e import of commodities i s made:

z t ( t )

=

zfl(t)

+

( 1

-

^{r l )}

.

(yfl(t) -Yt(t))

+

ASl@) f o r w h e a t z;(t)

=

z j l ( t ) - Q ( t )

+

hS3(t) f o r coarse grain

z$(t)

=

z t l ( t )

+

max IyJ1(t)

-

Y;(t)

-

wJ1(t),O j f o r potato z;(t)

=

max Iz/"(t)

+

(1

-

oi)(Yf"(t)

-

Y;(t)),oj. i

=

6,7,8,10 for vegetable oil, s u g a r , vegetables and fruits.

+(wJ1(t)

-

wt(t))

.

(fig

- o3 ^-

^{q9/q3) , 01 for} protein feed

zia(t)

=

zfl(t), i

=

2,11,17 for r i c e , cotton and all livestock commodities.

5. Exchange module

F i r s t of all t h e aggregation of imports f o r a g r i c u l t u r a l commodities calculated in t h e adjustment module t o t h e imports of t h e BLS list of commodities i s implemented as follows:

-

~ f ( t )

=

z?(t) i

=

1,3 Zi(t)

=

z&(t)

Z,d(t>

=

z&(t)

~ , d ( t )

=

0.098 zT3(t)

+

0.123 ^' ~ ? ~ ( t )

+

0.11 ^' ZT6(t) Z,d(t)

=

zga(t)

~ , d ( t )

=

C.27

.

z t ( t )

+

0.118

.

z;(t)

+

0.175 z i ( t )

+

0.069

-

^z$(t)

+

0.18

.

z&(t)

-

^d

z 9 ( t )

=

0.18 z&(t)

+

0.934

.

zf7(t)

H e r e z f ( t ) i s d e s i r a b l e import of i-th commodity of t h e BLS list. What is concerned t o t h e non-agricultural commodity, i t i s determined h e r e as follows (linked version of t h e SOVAM will contain endogenous calculation of it):

where R(t) now i s exogenously given.* R(t) i s h a r d c u r r e n c y available f o r import of a g r i c u l t u r a l commodities in y e a r t. "Actual" imports in r e s p o n s e t o world m a r k e t equilibrium p r i c e s 6 y ( t ) ) are calculated as follows:

A s a matter of f a c t t h i s formula i s t h e solution of t h e following optimization prob- lem:

h t ( i i ( t )

-

ZP(t))' ⁺ min

-

i =1,10 Z l

s u b j e c t to:

where hi are specifically defined weights.

Within t h i s module t h e calculation of t h e a c t u a l output f o r livestock commodities f o r t h e n e x t p e r i o d ( t + l ) i s a l s o made.

Endogenous c a l c u l a t i o n o f R ( t ) will be d e s c r i b e d i n t h e n e x t paper d e v o t e d t o p o l i c y module.

6. Algorithmic and programming specifics of the SOVAM implementation.

The work on computer implementation of t h e SOVAK f o r t h e BLS was performed as a two-phase activity. In a few words t h e f i r s t phase might be defined as "vali- dating t h e model". The term "validating" should b e t r e a t e d h e r e in a v e r y broad sense. Extremely high level of aggregation of t h e model (imposed by i t s assign- ment) provides a wide spectrum of opportunities f o r varying t h e s t r u c t u r e of i t s relations and f o r defining numerical values of i t s p a r a m e t e r s . Our purpose w a s t o choose t h e version of t h e model's s t r u c t u r e and t h e values of model's p a r a m e t e r s which would provide sufficient fitness of t h e r e s u l t s of simulation of p a s t t o histor- ical d a t a and a l s o would provide c r e d i b l e f o r e c a s t s f o r t h e f u t u r e . A t t h e same time, when varying t h e model's s t r u c t u r e we had not t o go out of t h e set of n a t u r - ally i n t e r p r e t a b l e r e l a t i o n s , and choosing t h e values of those p a r a m e t e r s which have c l e a r physical meaning w e had not t o g e t a p a r t from t h e i r s t a t i s t i c a l esti- mates. The r e s t r i c t i o n s s t a t e d were considered as n e c e s s a r y conditions f o r t h e model's adequacy.

When we planned t h e work on computer implementation of t h e model, we definitely understood t h a t i t s s t a r t i n g version (reasonably d i f f e r e n t from t h e version described above) would b e modified many times and t h a t n e c e s s a r y improvements might only b e defined through multiple numerical experiments with t h e model. The effectiveness of experiments of t h a t kind strongly depends on t h e quality of t h e software involved into t h e experiments. Of p a r t i c u l a r importance a r e robustness of t h e programs which r e a l i z e t h e principal computations and conveniences sup- plied by t h e programs used f o r processing of input d a t a and displaying t h e r e s u l t s of runs. With t h i s r e s p e c t we organized t h e f i r s t p h a s e of o u r work on t h e basis of t h r e e g e n e r a l p u r p o s e software units: The MINOS optimizing package, t h e c r o s s - compiler GEMINI, and t h e t a b l e g e n e r a t o r FORTAB (the second and t h i r d were designed by V. Lebedev). The MINOS package w a s used as r o b u s t tool f o r solving l i n e a r program in t h e planning module, t h e GEMINI made i t possible t o r e d u c e t o a minimum t h e reprograming e f f o r t s r e l a t e d t o variations in t h e model's s t r u c t u r e , and FORTAB provided f e a t u r e s f o r simplifying t h e work on displaying t h e r e s u l t s of experiments in a visually convenient form.

The c h a r t of information flows during test experiments with t h e model i s shown in Figure 2. The programs which a r e executed one time f o r e a c h s t e p t of simula- tion r u n and t h e d a t a files c r e a t e d during t h e r u n are s u r r o u n d e d by a dashed line.

The program f o r generating MPS

-

input f o r MINOS in a c c o r d a n c e with formula of t h e planning module a n d t h e program t h a t implements t h e module of adjustment of planned output with preliminary decoding of MPS

-

^{output are} c r e a t e d by GEMINI.

The second, p h a s e of t h e work on implementation of t h e SOVAM f o r t h e BLS h a s r e q u i r e d much more programming e f f o r t s t h a n t h e f i r s t one. I t i s r e l a t e d t o t h e specific of implementation of t h e BLS. Due t o t h i s specific i t i s undesirable t o involve into computations with t h e system any l a r g e r g e n e r a l purpose packages like t h e MINOS. For t h i s r e a s o n i t w a s decided t o apply f o r l i n e a r program in t h e planning module t h e i t e r a t i v e algorithm based on q u a d r a t i c penalty functions. A s CPU time needed f o r execution of simulating programs in t h e BLS i s t h e c r i t i c a l f a c t o r , r a t h e r sophisticated implementation of t h e algorithm w a s n e c e s s a r y . In p a r t i c u l a r , such a n implementation r e q u i r e d t h a t t h e input d a t a of t h e LP problem would b e transformed into t h e format somewhat similar t o MPS format. Having at hand GEMINI system which i s assigned just t o simplify p r e p a r i n g of t h e programs f o r generating MPS files, i t w a s n a t u r a l t o use t h a t system somehow f o r organizing t h e abovementioned transformation in automatic manner. Apparently t h a t implied multiple modifications in GEMINI and t h e s e modifications were performed. A s a r e s u l t t h e tool w a s c r e a t e d which permits t o g e n e r a t e t h e d i f f e r e n t versions of t h e main module of Soviet a g r i c u l t u r a l model f o r t h e BLS automatically: one should

Figure 2: Software Structure f o r t h e S O V A M

only d e s c r i b e t h e planning module and t h e module of adjustment of planned output a t G E X I N I input language.

7 . Conclusions

By v i r t u e of s p e c i f i c s of t h e c e n t r a l l y planned economy t h e s t r u c t u r e and t h e principal modules of t h e SOVAM f o r t h e BLS were c r e a t e d completely differently in comparison t o o t h e r national a g r i c u l t u r a l policy models with s t a n d a r d s t r u c t u r e . To implement s u c h a so-called country-specific model i t w a s n e c e s s a r y t o envisage not only economic a p p r o p r i a t e description of t h e SOVAM but a l s o t o organize specific software f o r validating and improving it. The formalized d e s c r i p t i o n of t h e two main modules: P r o d u c t i o n and Exchange modules are given in t h i s p a p e r as well as t h e software units used f o r computer implementation of t h e model and i t s interaction a r e explained in t h e p a p e r .

REFERENCES

Iakimets, V. (1984). Background and requirements f o r t h e SOVAM: Soviet Agricul- t u r a l Model. IIASA, Laxenburg, WP-84-97.

Fedorov, V. and V . Iakimets (1985). Outline of t h e SOVAM. WP-85-57, IIASA, Laxen- b u r g .

Iakimets, V. and V. Kiselev (1985). F i r s t version of t h e SOVAM. WP-85-60, IIASA, Laxenburg.