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Dynamic input-output model taking account of the investment lag
Structural Change and Economic Dynamics, vol. 5, no. 1, 1994
DYNAMIC INPUT-OUTPUT M O D E L T A K I N G A C C O U N T OF THE INVESTMENT LAG ALEXANDER
O. B A R A N O V 1 AND V I C T O R
N. P A V L O V 2
This article describes a variant of the dynamic input-output model that takes account of the investment lag and methods of initial data preparation for this model. The model has been used in analysis and forecasting of the development of the Soviet economy. This article includes results of calculations of distributed lag coefficients for individual sectors over the periods 1976-1980 and 1981-1985. It contains a brief description of calculations for the period 1986-1990.
1. I N T R O D U C T I O N
The Complex Analysis Interindustrial Information System (CAIIS) was created at the Institute of Economics and Organization of Industrial Production of the Siberian Branch of the USSR Academy of Sciences. CAIIS includes a database, several variants of D I O M (a dynamic input-output model) and programs for analytical processing of calculation results (Pavlov, 1986). CAIIS represents the economy as a multipurpose, hierarchical system. The separate models of this system are regarded as specialized subsystems. Introduction of an hierarchical structure for the multipurpose system implies a definite type of subsystem interaction in the system-optimization process. For the optimization of this system numerical methods were elaborated. These methods are described in Pavlov (1986). One of the most important subsystems of CAIIS is the D I O M L (dynamic input-output model taking account of the investment lag). It represents a development of Shatilov's D I O M (Shatilov, 1974; Ozerov, i984) towards a more adequate reflection of the fixed assets formation process. This model has been used by the Institute of Economics and Organization of Industrial Production of the USSR Academy of Science (Siberian Division) in retrospective analysis and in the formulation of forecasts for the Soviet economy's development. The first variants of D I O M L were described in Soviet publications in the 1960s by Konius (1965) and Baranov (1968). But mathematical difficulties in the calculation of the distributed lag coefficients and problems with information for such calculations were the main 1 Scientific Researcher, Institute of Economics and Organization of Industrial Production, Siberian Branch, USSR Academyof Sciences. 2 Leading Scientific Researcher, Institute of Economics and Organization of Industrial Production, Siberian Branch, USSR Academyof Sciences. © Oxford University Press 1994
87
88
A. O. B A R A N O V A N D V. N. P A V L O V
reason why these models remained only theoretical constructions. The DIOML in CAIIS is one of the first lag DIOMs in the Soviet Union to be used for calculations involving real economical data (Baranov, 1985, 1991). A brief description of these data is given in section 3. The production of a considerable proportion of the output of industries that produce capital goods---construction of buildings and structures, and assembly of equipment--takes more than a year (the usual accounting period in many DIOMs). Hence the output of these industries in year t can be grouped under the following headings: (1) output with a production cycle of less than 1 year; (2) output providing the completion in year t of the construction initiated in preceding years; (3) output serving for the continuation of construction works started in preceding years but incomplete as at year t; (4) output required for the start of construction works in year t, to be terminated in the subsequent year. The production of the machinebuilding industry, comprising machines and equipment which do not require assembly, is completed within a production cycle lasting < 1 year and hence is fully covered by the first of the above-mentioned headings (production of trucks, locomotives, tractors, etc.). The other part of the machine-building industry takes its final form only after an additional production stage (assembly). For example, assembly of rolling mills. In this connection, the output of the machine-building industry, which produces the capital goods, is modelled in DIOML in different ways. The manufacture of non-assembled equipment is modelled in the same manner as in Shatilov's (1974) DIOM (without taking account of the investment lag). The production of equipment which will be assembled during the construction period is modelled using the equation with a distributed investment lag. Both these parts form the production of so-called 'fund-forming' machine-building industry. Besides, in the machine-building industry we distinguish the metal fabricating industry and production of components, capital repair of machinery and equipment (see section 2). Similarly, in construction we distinguish a fund-forming sector (construction of buildings and structures) and capital repair of buildings and structures (see section 2). The foundation of our model is the Balance of Economy System. It does not include in the production sphere (sphere of material production) the production of services. The material production sphere includes: industry, agriculture, and forestry, construction, transport, and communication (without passenger transport and communication, which serve the population), trade, procurement, material, and technical supply, and other sectors of material production. This is its main difference from the National Accounting System. The production of services is non-material production (a non-productive sphere in the old Soviet economic terminology). Every sector in our model is divided into two parts. The first part is the production of means of production and the second part is the production of consumer goods. All sectors that produce means of production form the first subdivision in the economy and all sectors that produce consumer goods form the second subdivision. The production of the first subdivision includes: raw materials, semi-manufactured goods (intermediate products) and machines, equipment, building, and structures, which are used in the process of production. The product of the second subdivision
DYNAMIC
INPUT-OUTPUT
MODEL
89
includes all consumer goods but not the services. The Gross Social Product is the sum of the first and second subdivision products. Over the last few years work has begun on the creation of the Soviet National Accounting System. Since 1987 the Soviet Gross National Product has been audited. But our input-output tables until the present time do not include service-producing sectors. In 1990 we began to build a D I O M L incorporating sectors which produce services (Baranov, 1991). 2. THE M O D E L
The model considers an economy with n sectors. The first m industries belong to the first subdivision, including the fund-forming industries 1. . . . . k, and non-fundforming industries k + 1. . . . . m. Among the fund-forming industries, the first 1 , . . . , p turn out buildings, structures, machines, and equipment, that have to be assembled and p + 1. . . . , k non-assembling machines and equipment. Industries m + 1. . . . . n belong to the second subdivision. The following symbols have been adopted for the DIOML: i, j--industry indices; s, z, t , / - - y e a r indices of the period under review; T--number of years encompassed by the period under review; 0ij--length of the capital investment lag of type i in industry j; hi--service life of fixed assets of type i; aij(t)--coefficients of direct expenditure of type i labour objects per output unit of industry j in the year t for non-fund-forming industries of the first subdivision (i = k + 1. . . . . m); cj(t)-- labour intensity coefficients of the output of industry j in year t; Si(t)--export-import balance in industry i in year t; q~i--output growth rate in industry i, of the second subdivision as per 2 scale; L(t)--average annual number of material production sphere employees in year t; Xi(t)--gross output of industry i in year t; K i j ( t - s , t + z ) - value of type i capital investment in industry j in year t - s assigned to projects to be commissioned in year t + z, for p = 0 it is calculated from the formula Kij(t, t + z) = ~O(z)Bij(t + z), where ~ij(z) is a coefficient indicating the average share of fixed assets of type i put into service in industry j in each year of the period under review which is due to capital investments effected z years ago (these coefficients are defined from problem (13)-(17)); ~ij(t)--volume of type i fixed assets in industry j as of the beginning of year t; F q ( t , / ) - - v o l u m e of type i fixed assets (basic production funds, in Soviet economic terminology) in industry j as of the beginning of year t which were made operational l years before; Bij(t)--value of type i fixed assets put into service in industry j in year t; Bij(t ) = Fij(t + 1, I); N i j ( t ) - - v o l u m e of type i incomplete construction in industry j as of the end of year t; bij(t)--fixed assets' intensity of the output of industry j related to type i fixed assets in year t, derived from the formula bij(t ) = tgij(t)/Xj(t). The system of constraints of the D I O M L includes the following. (1) Constraint on the output of fund-forming industries of the first subdivision, producing buildings, structure, machine, and equipment which have to be assembled:
Xi(t ) =
Kij(t, t + z) + S,(t), j=l
~=0
i = 1, p; t = 1, T.
(1)
90 A. O. BARANOV AND V. N. PAVLOV (2) Constraint on the output of fund-forming industries of the first subdivision producing the machines and equipment which take their final form without assembly: Xi(t) = ~
Bii(t) + Si(t),
i = p + 1, k; t = 1, T.
(2)
j=l
(3) Constraint on the output of non-fund-forming industries of the first subdivision: Xi(t ) = ~
aij(t)Xj(t ) + Si(t),
i --- k + 1, m; t = 1, T.
(3)
j=l
(4) Constraint on the output of the second subdivision industries: Xi(t ) = [Xi(t ) - Si(t)-]qi ~ + Si(t),
i = m + 1, n; t = 1, T.
(4)
(5) An equation for yearly recalculation of the stock of machinery and equipment which have to be assembled, buildings and structures: Oij -
t~ij(t ) = ¢~ij(t) +
1
Kig(t -- 1 -- s, t -- 1) -- F/j(t -- 1, hi),
~ s=O
i = 1, p ; j =
l,n;t=
(5)
1, T.
(6) An equation for yearly recalculation of the stock of machinery and equipment which takes its final form without assembly: ¢~i2(t) = ~ij(t -- 1) + Bij(t -- 1) -- F~j(t - 1, hi), i=p+
1, k ; j = 1, n ; t = 1, T.
(6)
(7) An equation for yearly recalculation of the volume of incomplete construction: 0U
Nij(t ) = Nij(t ) +
-- 1
~,
Oij -- 1
Kij(t,t + z ) -
"¢=1
~,
Kij(t-
s,t),
s=l
i = 1,p;j = 1, n ; t = 1, T.
(7)
(8) Constraint on fixed assets production: b~j(t)Xi~(t) = ¢ ~ ( t + 1),
i = 1, k ; j = 1, n; t = I,T.
(8)
(9) Constraint on labour resources: L ( t ) = ~ cj(t)Xj(t), j=l
t = 1, T.
(9)
A comparison of model (1)-(9) with other models of the same type developed in the USSR has made it possible to establish the following essential features. (1) A differentiated modelling of the production of the means of production for the production of the mean of production (first subdivision for first subdivision) and production of the means of production for the production of consumer goods (first subdivision for second subdivision). This essential peculiarity requires a
DYNAMIC
INPUT-OUTPUT
MODEL
91
separate determination of coefficients aij(t ), b~j(t), cj(t), as well as of the lag value for the specified industries of the first and second subdivisions. The need for additional data is offset by an expansion of the model's analytical potential. (2) In modelling the reproduction of fixed assets, their age structure is taken into consideration. This permits a more accurate reflection of the process of simple and expanded reproduction of fixed assets. For a practical implementation of the DIOML, a 39-industry classification was selected with the following composition. First subdivision--production of machinery and equipment; construction of buildings and structures; electric power industry; ferrous metallurgy; non-ferrous metallurgy; fuel-producing industry; metal fabricating industries and production of components; chemical and petrochemical industries; forest, woodworking, woodpulp, and paper industries; construction materials industry; glass-producing industry; light industry; food processing industry; other branches of industry; capital repair of buildings and structures; capital repair of machinery and equipment; agriculture and forestry; transport and communication; other branches of material production; trade, procurement, and material and technical supply. Second subdivision--production of machinery and equipment; construction of buildings and structures; electric power industry; ferrous metallurgy; non-ferrous metallurgy; fuel-producing industry; metal fabrication and components production; chemical and petrochemical industries; forest, woodworking, woodpulp, and paper industries; construction materials industry; glass-producing industry; light industry; food processing industry; other branches of industry; capital repair of buildings and structures; capital repair of machinery and equipment; agriculture and forestry; transport and communications; other branches of material production. 3. M E T H O D S OF I N I T I A L DATA P R E P A R A T I O N
The main components of the database of DIOML are formed on the basis of information from input-output tables of the Soviet economy, interindustrial fixed capital balances (containing information about the distribution of 26 types of fixed capital between industries of the Soviet economy), dynamic series of investment, fixed capital put into service and incomplete construction. Information from the above-mentioned input-output tables and interindustrial fixed capital balances permits the formation of matrices IIa~j(t)[I, IIbij(t)II. A large number of other statistical sources are employed. It is impossible to give descriptions of all the peculiarities involved in the preparation of information for model (1)-(9) in this paper. Such a description is given in the relevant literature (Shatilov, 1974; Ozerov, 1984; Baranov, 1991). Of special interest are the methods of distributed lag structure determination. The above element of information is used for the formation of DIOML data arrays affording the possibility of modelling fixed capital reproduction with regard to the length of their formation period. The various mathematical methods of distributed lag coefficients determination are covered in numerous literature sources (see, for example, Koyck, 1954; Fisher, 1957; Dhrymes, 1971; Sedelev, 1977).
92
A. O. B A R A N O V
AND
V. N. P A V L O V
The subsystem of the determination of the investment lag length for each DIOML industry has been carried out based on the findings of case studies concerned with the time limits of projects construction conducted by the USSR State Statistical Committee. The lag length O~(t) has been calculated as a weighted average of the construction time limits of project groups within industry j put into operation in year t: Rj(t)
Oj(t) = ~ P~j(t)Of(t),
j = 1, n
(10)
j=l
where Of(t) is the average construction time of t h e f t h project group within industry j commissioned in year t; Rj(t) is the number of project groups within industry j covered by sample study in year t; Psi(t) the share of capital investments in t h e f t h project group brought into service in year t within industry j in the overall volume of capital investments channelled into construction of projects within industry j and put into operation in year t. Pij(t) is computed from the formula below:
(11)
Pfj(t) = Kf(t)/K~(t)
where Kf(t) stands for the investments in the f t h group projects of industry j put into service in year t; finally, K~?(t) stands for the total volume of investments within industry j in projects made operational in year t throughout their construction time. Since in their economic sense the values of PIj(t) are not negative, Rj(t)
Pij(t)>~O
(j=l,n;f=l,
gj(t))
and
~ Pfj(t)=l, f=l
they may be interpreted as the probability of a randomly selected rouble out of the total sum of capital investment in industry j projects put into operation in year t throughout their construction time, thus being included in the sum of capital investments in the f t h project group. If Of(t) denotes a discrete, random-value construction time of projects in industry j put into service in year t, then Oj(t) stands for the mathematical expectation of that discrete random value. The relation of the value of capital investments in year t to the values of fixed assets put into operation in years t, t + 1 , . . . , t + 0 - 1 is derived from the equation below: 0-1
K(t) = ~ ~(z)B(t + z) + e(t),
t = 1, T
(12)
~=0
where ~(z) is a coefficient indicating the average share of fixed assets put into service in each year of the period under consideration which is due to capital investments effected ~ years ago; and ~(t) is the equation error corresponding to factors that are not accounted for. In order to define the parameters of equation (12) for each DIOML industry, the following problem is to be solved (Baranov, 1991):
DYNAMIC
INPUT-OUTPUT
MODEL
93
Oj
~j(~)Bj(t + z) + aj(t) = Kj(t), Oj - 1
2
Oj-
~)(z)B*(z)
-
-
1
~j(t) = Z Kj(t - z) - Nj(t),
~=0
(13)
t = 1, T; t = 1, T;
(14)
~=0
Oj
(15)
~ ( v ) + ~ j = 1; ~=0
(16)
~(~) < ~(~1 < ~(~); T
2 t=l
T
Gj(t)[aj(t)]2 + ~ ~j(t)[~j(t)]2 + ~j#2 __~ min;
(17)
t=l
where (certain coefficients)_G(t) >~ O;f_(T), f(~) are lower and upper coefficient limits, such that ~(~): 0 ~
B*(t) =
~
B(t - 1 ) ;
l=O
and aj(t), fly(t), 8j are discrepancies in the equations 4. S O M E R E S U L T S O F C A L C U L A T I O N S
For an approximate computational solution to the problem (13)-(17), the conditional gradient method was used. The calculations were performed for the periods 1971-1975 1976-1980, and 1981-1990. The coefficients of the temporal development structure of the value of putting buildings and structures into operation (Table 1)/md of putting machines and equipment into operation (Table 2) were determined individually for each industry. Based on these results, the temporal development structure of the aggregate volume of fixed assets put in.to operation was also computed. Imposing restriction (14) on problems (13)-(17) was necessary because of incomplete construction statistics, along with the dynamic series of the values of putting into service of fixed capital and capital investments, when determining the distributed lag coefficients. It follows that restriction (14) represents a transformed equation relating each year's incomplete construction value to the volumes of capital investment and putting into service of fixed assets in the same year or the preceding years. Retrospective and forecast analyses using the DIOML open new opportunities for a researcher as compared with the 'lagless' models. Inasmuch as the output of machine-building industries and civil engineering in year t is only partially included in the putting into service of fixed assets in the same year, while a considerable share (about 50~) is added to the volume of incomplete construction, it is only in part that it enters the composition of the utilized gross social product. The putting into service of fixed capital derives to the extent of more than 40~o (see Table 3) from the machine-building and civil engineering output of past years. The results are significant for identifying the natural composition of the utilized gross social product and its distinction from the product made in the same year.
94
A. O. B A R A N O V
AND
V. N. P A V L O V
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DYNAMIC
INPUT-OUTPUT
MODEL
95
TABLE 2. Rated average temporal development structure o f the putting into service o f the equipment, which has to be assembled, in U S S R industries durin 9 the lOth and l l t h 5-year plan periods (%)
Sector
Plan no.
Share of puttin O into service of equipment, which has to be assembled, in year t formed out of investment of year
Vh (%)
Vk (%)
t
t--1
t--2
2
3
4
5
6
7
8
1. Machine building
X XI
63.2 71.1
20.0 15.6
11.7 13.3
5.1 --
8.8 7.0
10.5 9.1
2. Civil engineering
X XI X XI
82.0 65.2 52.3 39.8
18.0 34.8 22.2 25.8
--14.0 18.8
--11.5 15.6
13.8 26.8 24.0 20.6
10.7 1.9 7.4 8.9
X XI X XI X XI X XI X XI
52.6 45.0 42.2 35.4 56.7 37.8 64.1 52.6 72.7 54.4
25.4 29.8 31.0 32.7 23.3 33.3 19.5 22.2 14.8 24.5
22.0 25.2 26.8 31.9 20.0 28.9 16.4 13.8 12.5 21.1
-------11.4 ---
6.4 12.9 %9 9.1 21.0 19.2 13.1 19.4 8.1 22.6
17.3 9.9 7.1 7.6 18.2 19.6 27.4 20.3 11.7 7.4
X XI X XI X XI
79.1 78.6 50.4 63.2 43.4 57.2
20.9 21.4 49.6 36.8 56.6 42.8
-------
-------
20.6 " 14.5 0.7 18.3 8.9 18.4
0.5 3.5 9.2 3.1 5.1 5.5
12. Transport, communication
X XI
62.6 26.1
37.4 45.2
-28.7
---
5.0 19.8
7.5 8.3
13. Trade, procurement, material and technical supply
X XI
90.3 56.4
9.7 43.6
---
---
8.1 28.8
7.7 6.1
1
3. Electric power industry 4. Ferrous metallurgy 5. Fuel-producing industry 6. Chemical industry 7. Forest and wood-working industry 8. Construction materials industry 9. Light industry 10. Food processing industry 11. Agriculture and forestry
From
t h e d a t a o f T a b l e 3, it c a n b e d e d u c e d
product
was formed
industries 1985--14%;
from
of the previous and, according
'utilized final product'
the output
t-3
that in the USSR
of machine-building
and
years in the following proportions:
the utilized final civil e n g i n e e r i n g in
to our estimate, this share has continued
here stands for the value of consumer
1980--11%;
in
to grow. The
goods consumed
and
fixed assets put into service over the year, while the utilized gross social product, stands for the aggregate of final product process in the specified year (intermediate
and labour objects used in the production products).
96
A. O. B A R A N O V
AND
V. N. P A V L O V
TABLE3. Structure of the formation of 'puttin9 into service' of fixed capital, final product and 9ross social product from the output of different years in 1980, 1985, and 1990 (%) Index
Share o f the previous year's output in the value o f each index o f year t
Share o f the same year's output in the value o f each index o f year t
t = 1980
t = 1985
t = 1990
t = 1980
t = 1985
t = 1990
55.0
Fixed capital put into service
43.0
45.0
45.0
57.0
55.0
Utilized final social product
11.0
14.0
17.2
89.0
86.0
82.8
Utilized gross social product
4.7
4.9
5.1
95.3
95.1
94.9
The share of the previous year's product in the utilized gross social product is not considerable, amounting to approximately 57o. However, expressed in absolute terms in the prices of 1983, this value adds up to an amount exceeding 70 billion roubles. Calculations performed on the basis of the DIOML make it possible to ascertain the degree of capital investment utilizations3 within and without the period under consideration.This permits the assessment of the possibility of manipulating investment resources beyond the planned period subject to the continuation of projects initiated at an earlier stage. The analysis of calculations performed for the 12th 5-year plan period indicates that in some industries the degree of investments engagement at the beginning of the 13th 5-year plan period will amount to 95~. This means that a large scale manoeuvre of investment resources within these industries can only be effected through discontinuation of part of the construction projects launched earlier. In lagless models, the determination of the national income assimilation norm and accumulation value in each year is accomplished irrespective of the investment volume in the preceding and subsequent years. DIOML provides for rectification of this oversimplified technique. The accumulation value in each given year and, accordingly, the accumulation norm are determined depending on the investments of the past years and the values of putting fixed assets into operation in the years to follow. In this context, it may be worth considering the results of variant calculations with regard to the 1985-1990 period. These calculations indicate that in the event of a 2 year gradual reduction of average construction time in all of the USSR economy, other conditions being equal, the consumer goods production growth rate would increase by about 57o. The additional volume of consumer goods production in the 5 year period would be in this case approximately 80 billion roubles. This provides a vivid demonstration of the impact exerted by the shortening of construction times and, accordingly, the reduction of the volume of incomplete construction, on the growth rate and consumption volume. 3 By degree of year t investment engagement we mean the ratio of the investments assigned in year t to the continuation of construction initiated earlier to the total volume of capital investments.
DYNAMIC
INPUT-OUTPUT
MODEL
ev~
I I I I I I~l
I I i I I
t I i I I I~L
I I I h t
I I I I I I~1
I I I I I
I I I I I I~l
I I I I I
q~
t~
"O "O ,~
~'~~
~i ~ ©
97
98 A. O. B A R A N O V A N D V. N. P A V L O V
DIOML equation (7) shows that this model is instrumental in simulation of the dynamics of the value of incomplete construction and its structure in terms of age and technology. The age structure of incomplete construction denotes the division thereof into projects differing in the duration of their actual construction time. The technological structure stands for the proportions in division thereof into incomplete buildings and structures and equipment. By way of example we cite the D1OMLcalculated incomplete construction age structure in the USSR as at the end of 1990 (Table 4). An analysis of this structure by industries in conjunction with the estimation of the volumes of incomplete construction in the same year affords the possibility of assessing the investments in the period after 1990 required for completion of the projects incomplete as at the end of 1990. The DIOML herein described was applied in calculations based on actual information designed for simulation of different variants of the expanded reproduction process in the USSR in the periods 1986-1990 and 1991-1995. The general conclusion from the results of these calculations is that this model enhances the potentialities of the economic analysis of reproduction processes over lag-exclusive models, and thus contributes to a more adequate modelling of the reproduction process of an economic system. REFERENCES BARANOV,E. (1968). 'Problems of Development of a Scheme of the Dynamic Model of Interindustrial Balance' (Problemy razrabotki skhemy dinamicheskoy modeli mezhotraslevogo balansa), Ekonomika i Matematicheskiye Matody, 4(1). BARANOV,A. (1991a). The Experience of Construction of Dynamic Input-Output Model of Soviet Economy with the Block of Services-Producing Sectors (Opyt postroenia dinamicheskoy modeli mezhotraslevogo balansa s blokom otraslei nematerialnogo proizvodstva). Institute of Economics and Industrial Production, Novosibirsk (in Russian). - - ( 1 9 9 1 b ) . Investment Lag in the Reproduction of Product and Fixed Capital (Investicionnyi lag v vosproisvodstve producta ifondov). Nauka, Novosibirsk (in Russian). DHRYMES, F. (1971). Distributed Lags. Problems of Estimation and Formulation. Holden-Day, San Francisco, CA. FISHER, I. (1957). 'Note on a Short-cut Method for Calculating Distributed Lags', Bulletin de l'Institut International de Statistique, 29, 323-28. KoNIus, A. (1965). 'Methods of Construction of a Dynamic Model of Interindustrial Balance', in Metody Planirovaniya Mezhotraslevykh Proportsiy. Ekonomika, Moscow (in Russian). KOYCK, L. (1954). Distributed Lags and Investment Analysis. North-Holland, Amsterdam. OZEROV, V. (1984). Analysis of the Dynamics of Socialist Expanded Reproduction (Analiz dinamiki sotsialisticheskogo rasshirennogo vosproizvodstva). Nauka, Novosibirsk (in Russian). PAVLOV, V. (1986). Interindustrial Systems. Mathematical Models and Methods (Mezhotraslevye systemy Matematicheskiye modeli i metody). Nauka, Novosibirsk (in Russian). SEDELEV,B. (1977). Distributed La 9 Estimation in Economic Processes (Otsenka raspredelionnykh lagov y ekonomichskikh protsessakh). Ekonomika, Moscow (in Russian). SHATILOV, N. (1974). Analysis of the Dependences of Expanded Reproduction and Experience of its Modellin 9 (Analiz zavisimostey rasshirennogo vosproizvodstva i opty ego modelirovaniya). Nauka, Novosibirsk (in Russian).
DYNAMIC INPUT-OUTPUT M O D E L T A K I N G A C C O U N T OF THE INVESTMENT LAG ALEXANDER
O. B A R A N O V 1 AND V I C T O R
N. P A V L O V 2
This article describes a variant of the dynamic input-output model that takes account of the investment lag and methods of initial data preparation for this model. The model has been used in analysis and forecasting of the development of the Soviet economy. This article includes results of calculations of distributed lag coefficients for individual sectors over the periods 1976-1980 and 1981-1985. It contains a brief description of calculations for the period 1986-1990.
1. I N T R O D U C T I O N
The Complex Analysis Interindustrial Information System (CAIIS) was created at the Institute of Economics and Organization of Industrial Production of the Siberian Branch of the USSR Academy of Sciences. CAIIS includes a database, several variants of D I O M (a dynamic input-output model) and programs for analytical processing of calculation results (Pavlov, 1986). CAIIS represents the economy as a multipurpose, hierarchical system. The separate models of this system are regarded as specialized subsystems. Introduction of an hierarchical structure for the multipurpose system implies a definite type of subsystem interaction in the system-optimization process. For the optimization of this system numerical methods were elaborated. These methods are described in Pavlov (1986). One of the most important subsystems of CAIIS is the D I O M L (dynamic input-output model taking account of the investment lag). It represents a development of Shatilov's D I O M (Shatilov, 1974; Ozerov, i984) towards a more adequate reflection of the fixed assets formation process. This model has been used by the Institute of Economics and Organization of Industrial Production of the USSR Academy of Science (Siberian Division) in retrospective analysis and in the formulation of forecasts for the Soviet economy's development. The first variants of D I O M L were described in Soviet publications in the 1960s by Konius (1965) and Baranov (1968). But mathematical difficulties in the calculation of the distributed lag coefficients and problems with information for such calculations were the main 1 Scientific Researcher, Institute of Economics and Organization of Industrial Production, Siberian Branch, USSR Academyof Sciences. 2 Leading Scientific Researcher, Institute of Economics and Organization of Industrial Production, Siberian Branch, USSR Academyof Sciences. © Oxford University Press 1994
87
88
A. O. B A R A N O V A N D V. N. P A V L O V
reason why these models remained only theoretical constructions. The DIOML in CAIIS is one of the first lag DIOMs in the Soviet Union to be used for calculations involving real economical data (Baranov, 1985, 1991). A brief description of these data is given in section 3. The production of a considerable proportion of the output of industries that produce capital goods---construction of buildings and structures, and assembly of equipment--takes more than a year (the usual accounting period in many DIOMs). Hence the output of these industries in year t can be grouped under the following headings: (1) output with a production cycle of less than 1 year; (2) output providing the completion in year t of the construction initiated in preceding years; (3) output serving for the continuation of construction works started in preceding years but incomplete as at year t; (4) output required for the start of construction works in year t, to be terminated in the subsequent year. The production of the machinebuilding industry, comprising machines and equipment which do not require assembly, is completed within a production cycle lasting < 1 year and hence is fully covered by the first of the above-mentioned headings (production of trucks, locomotives, tractors, etc.). The other part of the machine-building industry takes its final form only after an additional production stage (assembly). For example, assembly of rolling mills. In this connection, the output of the machine-building industry, which produces the capital goods, is modelled in DIOML in different ways. The manufacture of non-assembled equipment is modelled in the same manner as in Shatilov's (1974) DIOM (without taking account of the investment lag). The production of equipment which will be assembled during the construction period is modelled using the equation with a distributed investment lag. Both these parts form the production of so-called 'fund-forming' machine-building industry. Besides, in the machine-building industry we distinguish the metal fabricating industry and production of components, capital repair of machinery and equipment (see section 2). Similarly, in construction we distinguish a fund-forming sector (construction of buildings and structures) and capital repair of buildings and structures (see section 2). The foundation of our model is the Balance of Economy System. It does not include in the production sphere (sphere of material production) the production of services. The material production sphere includes: industry, agriculture, and forestry, construction, transport, and communication (without passenger transport and communication, which serve the population), trade, procurement, material, and technical supply, and other sectors of material production. This is its main difference from the National Accounting System. The production of services is non-material production (a non-productive sphere in the old Soviet economic terminology). Every sector in our model is divided into two parts. The first part is the production of means of production and the second part is the production of consumer goods. All sectors that produce means of production form the first subdivision in the economy and all sectors that produce consumer goods form the second subdivision. The production of the first subdivision includes: raw materials, semi-manufactured goods (intermediate products) and machines, equipment, building, and structures, which are used in the process of production. The product of the second subdivision
DYNAMIC
INPUT-OUTPUT
MODEL
89
includes all consumer goods but not the services. The Gross Social Product is the sum of the first and second subdivision products. Over the last few years work has begun on the creation of the Soviet National Accounting System. Since 1987 the Soviet Gross National Product has been audited. But our input-output tables until the present time do not include service-producing sectors. In 1990 we began to build a D I O M L incorporating sectors which produce services (Baranov, 1991). 2. THE M O D E L
The model considers an economy with n sectors. The first m industries belong to the first subdivision, including the fund-forming industries 1. . . . . k, and non-fundforming industries k + 1. . . . . m. Among the fund-forming industries, the first 1 , . . . , p turn out buildings, structures, machines, and equipment, that have to be assembled and p + 1. . . . , k non-assembling machines and equipment. Industries m + 1. . . . . n belong to the second subdivision. The following symbols have been adopted for the DIOML: i, j--industry indices; s, z, t , / - - y e a r indices of the period under review; T--number of years encompassed by the period under review; 0ij--length of the capital investment lag of type i in industry j; hi--service life of fixed assets of type i; aij(t)--coefficients of direct expenditure of type i labour objects per output unit of industry j in the year t for non-fund-forming industries of the first subdivision (i = k + 1. . . . . m); cj(t)-- labour intensity coefficients of the output of industry j in year t; Si(t)--export-import balance in industry i in year t; q~i--output growth rate in industry i, of the second subdivision as per 2 scale; L(t)--average annual number of material production sphere employees in year t; Xi(t)--gross output of industry i in year t; K i j ( t - s , t + z ) - value of type i capital investment in industry j in year t - s assigned to projects to be commissioned in year t + z, for p = 0 it is calculated from the formula Kij(t, t + z) = ~O(z)Bij(t + z), where ~ij(z) is a coefficient indicating the average share of fixed assets of type i put into service in industry j in each year of the period under review which is due to capital investments effected z years ago (these coefficients are defined from problem (13)-(17)); ~ij(t)--volume of type i fixed assets in industry j as of the beginning of year t; F q ( t , / ) - - v o l u m e of type i fixed assets (basic production funds, in Soviet economic terminology) in industry j as of the beginning of year t which were made operational l years before; Bij(t)--value of type i fixed assets put into service in industry j in year t; Bij(t ) = Fij(t + 1, I); N i j ( t ) - - v o l u m e of type i incomplete construction in industry j as of the end of year t; bij(t)--fixed assets' intensity of the output of industry j related to type i fixed assets in year t, derived from the formula bij(t ) = tgij(t)/Xj(t). The system of constraints of the D I O M L includes the following. (1) Constraint on the output of fund-forming industries of the first subdivision, producing buildings, structure, machine, and equipment which have to be assembled:
Xi(t ) =
Kij(t, t + z) + S,(t), j=l
~=0
i = 1, p; t = 1, T.
(1)
90 A. O. BARANOV AND V. N. PAVLOV (2) Constraint on the output of fund-forming industries of the first subdivision producing the machines and equipment which take their final form without assembly: Xi(t) = ~
Bii(t) + Si(t),
i = p + 1, k; t = 1, T.
(2)
j=l
(3) Constraint on the output of non-fund-forming industries of the first subdivision: Xi(t ) = ~
aij(t)Xj(t ) + Si(t),
i --- k + 1, m; t = 1, T.
(3)
j=l
(4) Constraint on the output of the second subdivision industries: Xi(t ) = [Xi(t ) - Si(t)-]qi ~ + Si(t),
i = m + 1, n; t = 1, T.
(4)
(5) An equation for yearly recalculation of the stock of machinery and equipment which have to be assembled, buildings and structures: Oij -
t~ij(t ) = ¢~ij(t) +
1
Kig(t -- 1 -- s, t -- 1) -- F/j(t -- 1, hi),
~ s=O
i = 1, p ; j =
l,n;t=
(5)
1, T.
(6) An equation for yearly recalculation of the stock of machinery and equipment which takes its final form without assembly: ¢~i2(t) = ~ij(t -- 1) + Bij(t -- 1) -- F~j(t - 1, hi), i=p+
1, k ; j = 1, n ; t = 1, T.
(6)
(7) An equation for yearly recalculation of the volume of incomplete construction: 0U
Nij(t ) = Nij(t ) +
-- 1
~,
Oij -- 1
Kij(t,t + z ) -
"¢=1
~,
Kij(t-
s,t),
s=l
i = 1,p;j = 1, n ; t = 1, T.
(7)
(8) Constraint on fixed assets production: b~j(t)Xi~(t) = ¢ ~ ( t + 1),
i = 1, k ; j = 1, n; t = I,T.
(8)
(9) Constraint on labour resources: L ( t ) = ~ cj(t)Xj(t), j=l
t = 1, T.
(9)
A comparison of model (1)-(9) with other models of the same type developed in the USSR has made it possible to establish the following essential features. (1) A differentiated modelling of the production of the means of production for the production of the mean of production (first subdivision for first subdivision) and production of the means of production for the production of consumer goods (first subdivision for second subdivision). This essential peculiarity requires a
DYNAMIC
INPUT-OUTPUT
MODEL
91
separate determination of coefficients aij(t ), b~j(t), cj(t), as well as of the lag value for the specified industries of the first and second subdivisions. The need for additional data is offset by an expansion of the model's analytical potential. (2) In modelling the reproduction of fixed assets, their age structure is taken into consideration. This permits a more accurate reflection of the process of simple and expanded reproduction of fixed assets. For a practical implementation of the DIOML, a 39-industry classification was selected with the following composition. First subdivision--production of machinery and equipment; construction of buildings and structures; electric power industry; ferrous metallurgy; non-ferrous metallurgy; fuel-producing industry; metal fabricating industries and production of components; chemical and petrochemical industries; forest, woodworking, woodpulp, and paper industries; construction materials industry; glass-producing industry; light industry; food processing industry; other branches of industry; capital repair of buildings and structures; capital repair of machinery and equipment; agriculture and forestry; transport and communication; other branches of material production; trade, procurement, and material and technical supply. Second subdivision--production of machinery and equipment; construction of buildings and structures; electric power industry; ferrous metallurgy; non-ferrous metallurgy; fuel-producing industry; metal fabrication and components production; chemical and petrochemical industries; forest, woodworking, woodpulp, and paper industries; construction materials industry; glass-producing industry; light industry; food processing industry; other branches of industry; capital repair of buildings and structures; capital repair of machinery and equipment; agriculture and forestry; transport and communications; other branches of material production. 3. M E T H O D S OF I N I T I A L DATA P R E P A R A T I O N
The main components of the database of DIOML are formed on the basis of information from input-output tables of the Soviet economy, interindustrial fixed capital balances (containing information about the distribution of 26 types of fixed capital between industries of the Soviet economy), dynamic series of investment, fixed capital put into service and incomplete construction. Information from the above-mentioned input-output tables and interindustrial fixed capital balances permits the formation of matrices IIa~j(t)[I, IIbij(t)II. A large number of other statistical sources are employed. It is impossible to give descriptions of all the peculiarities involved in the preparation of information for model (1)-(9) in this paper. Such a description is given in the relevant literature (Shatilov, 1974; Ozerov, 1984; Baranov, 1991). Of special interest are the methods of distributed lag structure determination. The above element of information is used for the formation of DIOML data arrays affording the possibility of modelling fixed capital reproduction with regard to the length of their formation period. The various mathematical methods of distributed lag coefficients determination are covered in numerous literature sources (see, for example, Koyck, 1954; Fisher, 1957; Dhrymes, 1971; Sedelev, 1977).
92
A. O. B A R A N O V
AND
V. N. P A V L O V
The subsystem of the determination of the investment lag length for each DIOML industry has been carried out based on the findings of case studies concerned with the time limits of projects construction conducted by the USSR State Statistical Committee. The lag length O~(t) has been calculated as a weighted average of the construction time limits of project groups within industry j put into operation in year t: Rj(t)
Oj(t) = ~ P~j(t)Of(t),
j = 1, n
(10)
j=l
where Of(t) is the average construction time of t h e f t h project group within industry j commissioned in year t; Rj(t) is the number of project groups within industry j covered by sample study in year t; Psi(t) the share of capital investments in t h e f t h project group brought into service in year t within industry j in the overall volume of capital investments channelled into construction of projects within industry j and put into operation in year t. Pij(t) is computed from the formula below:
(11)
Pfj(t) = Kf(t)/K~(t)
where Kf(t) stands for the investments in the f t h group projects of industry j put into service in year t; finally, K~?(t) stands for the total volume of investments within industry j in projects made operational in year t throughout their construction time. Since in their economic sense the values of PIj(t) are not negative, Rj(t)
Pij(t)>~O
(j=l,n;f=l,
gj(t))
and
~ Pfj(t)=l, f=l
they may be interpreted as the probability of a randomly selected rouble out of the total sum of capital investment in industry j projects put into operation in year t throughout their construction time, thus being included in the sum of capital investments in the f t h project group. If Of(t) denotes a discrete, random-value construction time of projects in industry j put into service in year t, then Oj(t) stands for the mathematical expectation of that discrete random value. The relation of the value of capital investments in year t to the values of fixed assets put into operation in years t, t + 1 , . . . , t + 0 - 1 is derived from the equation below: 0-1
K(t) = ~ ~(z)B(t + z) + e(t),
t = 1, T
(12)
~=0
where ~(z) is a coefficient indicating the average share of fixed assets put into service in each year of the period under consideration which is due to capital investments effected ~ years ago; and ~(t) is the equation error corresponding to factors that are not accounted for. In order to define the parameters of equation (12) for each DIOML industry, the following problem is to be solved (Baranov, 1991):
DYNAMIC
INPUT-OUTPUT
MODEL
93
Oj
~j(~)Bj(t + z) + aj(t) = Kj(t), Oj - 1
2
Oj-
~)(z)B*(z)
-
-
1
~j(t) = Z Kj(t - z) - Nj(t),
~=0
(13)
t = 1, T; t = 1, T;
(14)
~=0
Oj
(15)
~ ( v ) + ~ j = 1; ~=0
(16)
~(~) < ~(~1 < ~(~); T
2 t=l
T
Gj(t)[aj(t)]2 + ~ ~j(t)[~j(t)]2 + ~j#2 __~ min;
(17)
t=l
where (certain coefficients)_G(t) >~ O;f_(T), f(~) are lower and upper coefficient limits, such that ~(~): 0 ~
B*(t) =
~
B(t - 1 ) ;
l=O
and aj(t), fly(t), 8j are discrepancies in the equations 4. S O M E R E S U L T S O F C A L C U L A T I O N S
For an approximate computational solution to the problem (13)-(17), the conditional gradient method was used. The calculations were performed for the periods 1971-1975 1976-1980, and 1981-1990. The coefficients of the temporal development structure of the value of putting buildings and structures into operation (Table 1)/md of putting machines and equipment into operation (Table 2) were determined individually for each industry. Based on these results, the temporal development structure of the aggregate volume of fixed assets put in.to operation was also computed. Imposing restriction (14) on problems (13)-(17) was necessary because of incomplete construction statistics, along with the dynamic series of the values of putting into service of fixed capital and capital investments, when determining the distributed lag coefficients. It follows that restriction (14) represents a transformed equation relating each year's incomplete construction value to the volumes of capital investment and putting into service of fixed assets in the same year or the preceding years. Retrospective and forecast analyses using the DIOML open new opportunities for a researcher as compared with the 'lagless' models. Inasmuch as the output of machine-building industries and civil engineering in year t is only partially included in the putting into service of fixed assets in the same year, while a considerable share (about 50~) is added to the volume of incomplete construction, it is only in part that it enters the composition of the utilized gross social product. The putting into service of fixed capital derives to the extent of more than 40~o (see Table 3) from the machine-building and civil engineering output of past years. The results are significant for identifying the natural composition of the utilized gross social product and its distinction from the product made in the same year.
94
A. O. B A R A N O V
AND
V. N. P A V L O V
c~
r~ t"q
~
~
('-,1(',1
t'q',"-~
',--~',',-~
II
~
~','-~
oo
II
II
II
II
IIII
t~
IIII
II
II
II
I1~1
II
IIII
I~ I I
IIII
II
II
II
II~l
II
Illl
I~
II
llll
II
II
~1
II~l
II
Illl~
II
t111
It
II
h D,...
I
',o
I
I
~ I I ~
I I I I ~ 1
I I I I I I I I
0
0
I
',~C5
,...~',~"
~t
'~--
r-.-o
',o,'n,~¢,~
ooC:~
,.-~oo
',~-t'---,,,n,-n
~,--~
.,-~oo
r.-'.o
r'--
~
,..j
C.) P-
~'~ ,,-~ ¢'~
( ' ~ ("-,I
.--~('~
c-.1 ('~1
t.~ t'.4
~
('~1 c'4 c,4 c'-,I c-,I.,,-,~
c'4 ("-4
cQ("-,l¢~lt'~l
t-4 c,~
~ ~
o
"' ,-., ~
~
c-,,~ e,~
c~1 (",q
' ~ t ¢',,I
, , -
~
2 "~ .~
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e,,h e ~
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DYNAMIC
INPUT-OUTPUT
MODEL
95
TABLE 2. Rated average temporal development structure o f the putting into service o f the equipment, which has to be assembled, in U S S R industries durin 9 the lOth and l l t h 5-year plan periods (%)
Sector
Plan no.
Share of puttin O into service of equipment, which has to be assembled, in year t formed out of investment of year
Vh (%)
Vk (%)
t
t--1
t--2
2
3
4
5
6
7
8
1. Machine building
X XI
63.2 71.1
20.0 15.6
11.7 13.3
5.1 --
8.8 7.0
10.5 9.1
2. Civil engineering
X XI X XI
82.0 65.2 52.3 39.8
18.0 34.8 22.2 25.8
--14.0 18.8
--11.5 15.6
13.8 26.8 24.0 20.6
10.7 1.9 7.4 8.9
X XI X XI X XI X XI X XI
52.6 45.0 42.2 35.4 56.7 37.8 64.1 52.6 72.7 54.4
25.4 29.8 31.0 32.7 23.3 33.3 19.5 22.2 14.8 24.5
22.0 25.2 26.8 31.9 20.0 28.9 16.4 13.8 12.5 21.1
-------11.4 ---
6.4 12.9 %9 9.1 21.0 19.2 13.1 19.4 8.1 22.6
17.3 9.9 7.1 7.6 18.2 19.6 27.4 20.3 11.7 7.4
X XI X XI X XI
79.1 78.6 50.4 63.2 43.4 57.2
20.9 21.4 49.6 36.8 56.6 42.8
-------
-------
20.6 " 14.5 0.7 18.3 8.9 18.4
0.5 3.5 9.2 3.1 5.1 5.5
12. Transport, communication
X XI
62.6 26.1
37.4 45.2
-28.7
---
5.0 19.8
7.5 8.3
13. Trade, procurement, material and technical supply
X XI
90.3 56.4
9.7 43.6
---
---
8.1 28.8
7.7 6.1
1
3. Electric power industry 4. Ferrous metallurgy 5. Fuel-producing industry 6. Chemical industry 7. Forest and wood-working industry 8. Construction materials industry 9. Light industry 10. Food processing industry 11. Agriculture and forestry
From
t h e d a t a o f T a b l e 3, it c a n b e d e d u c e d
product
was formed
industries 1985--14%;
from
of the previous and, according
'utilized final product'
the output
t-3
that in the USSR
of machine-building
and
years in the following proportions:
the utilized final civil e n g i n e e r i n g in
to our estimate, this share has continued
here stands for the value of consumer
1980--11%;
in
to grow. The
goods consumed
and
fixed assets put into service over the year, while the utilized gross social product, stands for the aggregate of final product process in the specified year (intermediate
and labour objects used in the production products).
96
A. O. B A R A N O V
AND
V. N. P A V L O V
TABLE3. Structure of the formation of 'puttin9 into service' of fixed capital, final product and 9ross social product from the output of different years in 1980, 1985, and 1990 (%) Index
Share o f the previous year's output in the value o f each index o f year t
Share o f the same year's output in the value o f each index o f year t
t = 1980
t = 1985
t = 1990
t = 1980
t = 1985
t = 1990
55.0
Fixed capital put into service
43.0
45.0
45.0
57.0
55.0
Utilized final social product
11.0
14.0
17.2
89.0
86.0
82.8
Utilized gross social product
4.7
4.9
5.1
95.3
95.1
94.9
The share of the previous year's product in the utilized gross social product is not considerable, amounting to approximately 57o. However, expressed in absolute terms in the prices of 1983, this value adds up to an amount exceeding 70 billion roubles. Calculations performed on the basis of the DIOML make it possible to ascertain the degree of capital investment utilizations3 within and without the period under consideration.This permits the assessment of the possibility of manipulating investment resources beyond the planned period subject to the continuation of projects initiated at an earlier stage. The analysis of calculations performed for the 12th 5-year plan period indicates that in some industries the degree of investments engagement at the beginning of the 13th 5-year plan period will amount to 95~. This means that a large scale manoeuvre of investment resources within these industries can only be effected through discontinuation of part of the construction projects launched earlier. In lagless models, the determination of the national income assimilation norm and accumulation value in each year is accomplished irrespective of the investment volume in the preceding and subsequent years. DIOML provides for rectification of this oversimplified technique. The accumulation value in each given year and, accordingly, the accumulation norm are determined depending on the investments of the past years and the values of putting fixed assets into operation in the years to follow. In this context, it may be worth considering the results of variant calculations with regard to the 1985-1990 period. These calculations indicate that in the event of a 2 year gradual reduction of average construction time in all of the USSR economy, other conditions being equal, the consumer goods production growth rate would increase by about 57o. The additional volume of consumer goods production in the 5 year period would be in this case approximately 80 billion roubles. This provides a vivid demonstration of the impact exerted by the shortening of construction times and, accordingly, the reduction of the volume of incomplete construction, on the growth rate and consumption volume. 3 By degree of year t investment engagement we mean the ratio of the investments assigned in year t to the continuation of construction initiated earlier to the total volume of capital investments.
DYNAMIC
INPUT-OUTPUT
MODEL
ev~
I I I I I I~l
I I i I I
t I i I I I~L
I I I h t
I I I I I I~1
I I I I I
I I I I I I~l
I I I I I
q~
t~
"O "O ,~
~'~~
~i ~ ©
97
98 A. O. B A R A N O V A N D V. N. P A V L O V
DIOML equation (7) shows that this model is instrumental in simulation of the dynamics of the value of incomplete construction and its structure in terms of age and technology. The age structure of incomplete construction denotes the division thereof into projects differing in the duration of their actual construction time. The technological structure stands for the proportions in division thereof into incomplete buildings and structures and equipment. By way of example we cite the D1OMLcalculated incomplete construction age structure in the USSR as at the end of 1990 (Table 4). An analysis of this structure by industries in conjunction with the estimation of the volumes of incomplete construction in the same year affords the possibility of assessing the investments in the period after 1990 required for completion of the projects incomplete as at the end of 1990. The DIOML herein described was applied in calculations based on actual information designed for simulation of different variants of the expanded reproduction process in the USSR in the periods 1986-1990 and 1991-1995. The general conclusion from the results of these calculations is that this model enhances the potentialities of the economic analysis of reproduction processes over lag-exclusive models, and thus contributes to a more adequate modelling of the reproduction process of an economic system. REFERENCES BARANOV,E. (1968). 'Problems of Development of a Scheme of the Dynamic Model of Interindustrial Balance' (Problemy razrabotki skhemy dinamicheskoy modeli mezhotraslevogo balansa), Ekonomika i Matematicheskiye Matody, 4(1). BARANOV,A. (1991a). The Experience of Construction of Dynamic Input-Output Model of Soviet Economy with the Block of Services-Producing Sectors (Opyt postroenia dinamicheskoy modeli mezhotraslevogo balansa s blokom otraslei nematerialnogo proizvodstva). Institute of Economics and Industrial Production, Novosibirsk (in Russian). - - ( 1 9 9 1 b ) . Investment Lag in the Reproduction of Product and Fixed Capital (Investicionnyi lag v vosproisvodstve producta ifondov). Nauka, Novosibirsk (in Russian). DHRYMES, F. (1971). Distributed Lags. Problems of Estimation and Formulation. Holden-Day, San Francisco, CA. FISHER, I. (1957). 'Note on a Short-cut Method for Calculating Distributed Lags', Bulletin de l'Institut International de Statistique, 29, 323-28. KoNIus, A. (1965). 'Methods of Construction of a Dynamic Model of Interindustrial Balance', in Metody Planirovaniya Mezhotraslevykh Proportsiy. Ekonomika, Moscow (in Russian). KOYCK, L. (1954). Distributed Lags and Investment Analysis. North-Holland, Amsterdam. OZEROV, V. (1984). Analysis of the Dynamics of Socialist Expanded Reproduction (Analiz dinamiki sotsialisticheskogo rasshirennogo vosproizvodstva). Nauka, Novosibirsk (in Russian). PAVLOV, V. (1986). Interindustrial Systems. Mathematical Models and Methods (Mezhotraslevye systemy Matematicheskiye modeli i metody). Nauka, Novosibirsk (in Russian). SEDELEV,B. (1977). Distributed La 9 Estimation in Economic Processes (Otsenka raspredelionnykh lagov y ekonomichskikh protsessakh). Ekonomika, Moscow (in Russian). SHATILOV, N. (1974). Analysis of the Dependences of Expanded Reproduction and Experience of its Modellin 9 (Analiz zavisimostey rasshirennogo vosproizvodstva i opty ego modelirovaniya). Nauka, Novosibirsk (in Russian).