NEW I-O TABLE AND SAMs FOR POLAND

Łucja Tomasewic University of Lod Institute of Econometrics and Statistics 41 Rewolucji 195 r, 9-214 Łódź Poland, tel. (4842) 6355187 e-mail: tiase@krysia. uni.lod.pl Draft NEW I-O TABLE AND SAMs FOR POLAND XIII International Conference on Input-Output Techniques University of Macerata, Italy, August 21-25, 2 Introduction The national economy is a complicated and complex economic system. Different fields of activity carried by economic units are interlinked to a great extent and it is difficult to understand certain phenomena without attempts to describe them by means of statistical, mathematical or econometric tools taking into consideration, of course, the theory of economy. These tools cannot be used effectively without a good system of statistical accounting, which appears to be a synthetic quantitative reflection of economic processes occurring in the national economy. Economic links between different countries, necessity of assessing their economic situation and comparative needs made it necessary to design standardied systems of collecting, classifying and presenting statistical data at the level of entire national economy. The Material Product of System MPS for short was commonly used in the former socialist countries, while the remaining countries used mainly the system of social accounting otherwise known as the System of National Accounts SNA. Differences between both systems were quite significant. They were reflected primarily in a different approach to defining production activity yielding value added as well as in terminology, definitions of economic categories and their classifications (see, for instance, Tomasewic (1994)). MPS included the concept of material activity as the activity, which produces value added. The so-called non-material services belonged to the sphere of distribution and not production, and the vast majority of them were provided by the government free (education, health services or even services of the financial sector). The necessity of adopting SNA can be explained by a simple fact that MPS is useless in the present situation of a market economy, in which most services belong to the market services, that is, services, whose price covers costs and yields profit. The system has been introduced to the Polish statistical practice changing in this way the methods of material balances followed in Poland for over thirty years. 1

The Social Accounting Matrix (SAM) for 1995 presented in this paper is a synthetic approach to links between accounts. A part of this matrix is the input-output table for 1995. SAM is a statistical model of the national economy, which reflects the main quantitative relations (transactions) occurring in the field of production, consumption and accumulation between economic units (institutions) and production sectors, and it describes flows of incomes between them (see, for instance, a special edition of Economic System Research vol. 3, 1993). The double entry principle is fulfilled automatically in this matrix each element of the matrix is simultaneously an income on a given account (line) and an expenditure on another one (column). The accounts are usually divided into: production accounts, consumption accounts (current accounts) and accumulation accounts (capital accounts). The last mentioned accounts include all transactions changing the level of assets (of physical and financial) of institutional sectors. For comparison of the Social Accounting Matrix and the input-output table a very simplified scheme of the SAM is presented, with no peculiar analytical goal hiding behind this scheme. It is rather an illustration of possibilities of describing the System of National Accounts in the matrix form for the Polish economy. It can be seen from the scheme that apart from production accounts showing creation (columns) and allocation of products (lines) between intermediate and final uses (input-output table) there are additional accounts describing generation and distribution of incomes in the national economy. Scheme 1. Simplified scheme of SAM Product accounts Production accounts (according to NACE) Product accounts Value added accounts Accounts of institutional sectors Current accounts (consumption) Capital accounts (accumulation) Total Value added accounts Current accounts (consumption) Capital accounts (accumulation) Total 2

The SAM opens huge possibilities before the national economy analysts. Application of the multiplier analysis allows to get an answer to the question how a given economic category for instance, growth of final demand for products of a given economic sector or transfers of capital will respond to an impulse sent to the economy in the form of, for instance, increase of direct taxes by unity and, thus, revenues on the government s institutional account. This simple example shows that SAM is a valuable analytical tool, and availability of matrices for successive years creates an opportunity of monitoring the country s economic condition and dynamics of economic growth. The input-output table for 1995 (according to SNA) allowed to build aggregated national accounts in the form of the social accounting matrix for that year in a way making allowances for generation of incomes (value added) also in production sectors (according to NACE). Integration of national accounts of institutional sectors in the form of SAM has been possible since 1992. Statistical data to be found in national accounts provide information about generation of incomes and value added (GDP) in institutional sectors without their division into activity sectors. 1 It was only the input-output table which allowed to include activity sectors, i.e. present income generation processes in these sectors. Unfortunately, no data are available about the cross classification, i.e. about incomes in activity sectors with an additional division into institutional sectors. Expenditures and incomes on particular production and current accounts are shown below by way of illustration. Entries are organied in such way as it is done in publications of the Polish Central Statistical Office, that is, one of expenditure items is treated as a balancing item being simultaneously a revenue (income) on the subsequent account. Entries on accounts showing generation of revenues and primary and secondary distribution, as well as allocation of disposable incomes are presented schematically below. 1. Production accounts (according to NACE) 1. Product accounts Incomes from sales: Expenditures: Total value Material costs Balancing value: value added - Costs resulting from involvement of primary production factors (GDP) 2. Income generation account value added account Incomes: Expenditures: Value added Costs connected with employment (total production material costs) Taxes from producers minus subsidies for producers 1 It can be found primarily in publications of the Central Statistical Office in the series National accounts according to institutional sectors, as well as in statistical yearbooks. 3

Balancing value: gross operating surplus Taxes from products minus subsidies for products 4

2. Current accounts 3. Primary distribution of income account (according to NACE and institutional sectors) Incomes: Expenditures Gross operating surplus Ownership incomes Costs connected with employment Taxes from producers minus subsidies for Producers Taxes from products minus subsidies for products Ownership incomes Balancing value: gross primary incomes 4 Secondary distribution of income account (according to institutional sectors) Incomes: Expenditures: Gross primary incomes Income and property tax Income and property tax Social insurance benefits and other social transfers Social insurance benefits and other social Various current transfers transfers Various current transfers Remaining current transfers Remaining current transfers Balancing value: gross disposable incomes 2. SAM' 95 Before passing to the presentation of SAM 95 I would like to characterie briefly Polish accomplishments concerning construction of such matrices for our economy and statistics of national accounts in general. The first works in this field are connected with the person of Professor L. Zienkowski from the Department of Statistical-Economic Studies, Central Statistical Office in Poland, who pioneered and continued consistently the introduction of the system of national accounts to the Polish statistical accounting. The first Polish social accounting matrices built according to the SNA standards were published, for instance, in a book edited by S.I. Cohen (1993). The work contains a comparative analysis based on national accounts and SAM. Cohen submits to analysis the economies of countries undergoing economic transformation (Hungary, Poland), which are compared with the economies of Western European countries such as the Netherlands, Spain, Germany and Italy. Co-authors of chapters dealing with Poland are: L. Zienkowski, Z. Żółkiewski and A. B. Cyżewski. 5

The book edited by Cohen provides social accounting matrices for Poland for the years 1987 and 199. The matrices for those years were presented in an aggregated and desegregated form. Only aggregated variants are presented below. The matrices presented below do not contain information about shares of transactions in incomes (expenditures) on particular accounts, but they show the structure of transactions, with the sum total of all elements of the matrix of accounts being treated as equal to 1. This sum does not have a direct economic significance, but it allows to compare in an accessible manner money flows on different accounts and make comparisons over years and according to countries (matrices for all analyed countries of Western and Central-Eastern Europe are presented in a standardied system in Cohen s book). It should be remembered in these comparisons that these money flows are present in current prices. For comparative purposes with an aggregated version of SAM 95 built by me I made an additional aggregation of SAM 87 and SAM 9 bringing down all matrices to possible comparable shares. Table 1. Structure of SAM for Poland for 1987 (sum of all matrix elements equals 1) 1 2 3 4 5 6 7 8 9 Total 1 Consumer goods & services 9,4 9,4 2 Labor 9, 9, 3 Capital 8, 8, 4 Households 7,2,9 1,7,4 1,2 5 Firms 6,,3 6,4 6 Government 1,7 1,,2 2,8,1,1 5,9 7 Accumulation,7 3,6 -,2 1,2 -, 5,3 8 Activities 9, 3,2 4,8 2,8 3,8 41,5 9 Rest of the World,4,9,5 2,5,1 4,4 Total 9,4 9, 8, 1,2 6,4 5,9 5,3 41,5 4,4 1 Source: On the basis of Cohen (1993) p.29 some items were additionally aggregated for the purposes of this paper 6

Table 2. Structure of SAM matrix for Poland for 199 1 2 3 4 5 6 7 8 9 Total 1 Consumer goods & services 8,6 8,6 2 Labor 7,2 7,2 3 Capital 1,6 1,6 4 Households 5,5 3,2 2,,5 11,2 5 Firms 6,5 6,5 6 Government 1,7,9,1 3,6,3,3,1 6,9 7 Accumulation 2,4 3,,4 1,1 -,8 6, 8 Activities 7,9 3, 5,3 17. 5, 38,2 9 Rest of the World,7 1,2,7 2,1 4,8 Total 8,6 7,2 1,6 11,2 6,6 6,8 6, 38,2 4,8 1 Source: on the basis of Cohen (1993), p.29 some items were additionally aggregated for the purposes of this paper. Table 3. Structure of SAM for Poland for 1995 1 2 3 4 5 6 7 8 9 1 11 12 Total Labor 1 7, 7, Taxes from producers 2,2,2 Capital 3 7,5 7,5 Taxes from products 4 2,2 2,2 Ownership incomes title 5,1 2,2 1,1 3,4 Households 6 5, 4, 1,6,1 3,3,1,8 14,9 Firms 7 3,2 1,5,1,1 4,9 Government 8 2,,2,2 2,2,1 1,8,7 7,2 Non-commercial institutions 9,1,1,1,3 Accumulation 1 1,6 1,6,1,1 1,5 4,9 Activities 11 1,3 2,6,2 3,3 19,9 4,3 4,7 Rest of the World 12,2,9,2 1,5 3,9 6,7 Total 7,,2 7,5 2,2 3,4 14,9 4,9 7,2,3 4,9 4,7 6,7 1, Source: own estimates made in co-operation with B. Frascyk (M.A. dissertation). 7

Table 4. Share of main transactions in all transactions Gross output Intermediate deliveries Incomes from labor Incomes from capital Disposable incomes Household consumptio n Total investment 1 2 3 4 5 6 7 1987 41,5 2,8 9, 8, 1,2 9,4 5,3 199 38,2 17, 7,2 1,6 11,2 8,6 6, 1995 4,7 19,9 7, 7,5 14,9 1,3 4,9 Average for 4,1 19,2 7,8 8,7 12,1 9,4 5,4 Poland Average for selected EU countries 31, 15, 9,9 5,7 17,1 11,6 3,9 Source: Own estimates based on SAM 95 for Poland, SAM 1987 and 199 for Poland and EU countries published in Cohen S.I. (1993). A number of clear differences was pointed out both in Cohen s book (1993) and in other publications containing macroeconomic comparisons of western economies with Central and Eastern European economies. SAM 95 covers, to some extent, the results of five years of the Polish economic transformation and it seems to be a valuable analytical tool from this point of view. Among differences the authors would most frequently mention low effectiveness of the economy (big share of raw materials and materials, low value added), a bigger share of consumption in household expenditures than in western countries, a low share of transactions connected with the sector of households, which was translated directly into lower transactions reflecting disposable incomes of this sector than in western countries. A comparison of SAM for particular countries creates further analytical possibilities. These possibilities can be seen from Table 4 already presented in a synthetic form. The shares reflecting transactions in the field of household consumption in all transactions in the national economy are characteried in the years 1987, 199 and 1995 by respective figures 9.4; 8.6; 1.3. These figures in the analyed Western European countries in the 198s had an average value at the level of 11.6 (average for Poland 9.4). Personal income expenditures in Poland represent a considerable part of disposable incomes. The share of transactions covered by disposable incomes amounted, however, in western countries in the 198s on average to 17.1 as compared with only 12.1 for Poland in the analyed period. It could be seen that the share of transactions in this field rose in 1995. Although the share of consumption in disposable incomes is really quite big, the shares of transactions concerning personal income expenditures are still smaller than in western countries in the 198s. The role of transactions between households and the government institutions tended to grow visibly along with the transformation of our economy into a market economy. The shares of transfers from households to government institutions in the analyed years were:.2;.1; 1.8 respectively, while transfers from the budget to households were: 1.7; 2.; 3.3, which makes the latter closer to those observed in western countries in the 198s (4-5). The shares of transactions connected with indirect deliveries continue to be much bigger than in western countries. The average for Poland reaches 19.2 as compared with the average of 15. for western countries in the 198s. 8

3. Multiplier analysis To remind of some problems of the multiplier analysis we will start with input-output multipliers in the input-output model. In this model final demand is exogenous and gross output of particular activity sectors is endogenous, i.e. 1 ( I A) Y = X where Y final demand vector and X gross output vector (by activity sectors). 1 The sum elements of the matrix ( I A) = [ α ] is the production multiplier T M j = i α j 1 where α j - are elements of column j of the matrix ( I A), and i T is a summing up vector (row of unities). Multiplier M j indicates how much gross output in the whole economic system will increase if final demand for products of sector j increases by unity (e.g. by 1 PLN) Let us divide the accounts shown in SAM into endogenous and exogenous ones. Let endogenous accounts be production accounts (generation of incomes) and institutional current and capital accounts apart from the government and rest of the world sectors. The last two sectors will belong to exogenous accounts. 2 ij Scheme 2. SAM in division into endogenous and exogenous accounts* Expenditures Endogenous accounts Exogenous accounts Total Incomes Exogenous accounts Z = A x Y ˆ x 1 x 2! x n Exogenous accounts R = A x W r ˆ r 1 r 2! r s Total x1 x 2... xn r 1 r 2... rs *Source: According to notation used in Pyatt and Round (1985). 2 Not distinguishing particular analytical goals in this paper, I accepted usually used divisions see, for instance (Pyatt, Round (1985)), (Cohen (1993)). 9

Square Z matrix shows transactions between endogenous accounts. It is a product of matrix A - shares of particular expenditures on endogenous accounts in total expenditures (incomes) by these expenditures (incomes) presented in the form of the diagonal matrix: Z = A x and, thus A = Zxˆ 1. Matrix R, which is not generally a square matrix, is a product of matrix A r of shares of remaining expenditures ( transfers to the government sector and abroad) in expenditures on endogenous accounts by the vector of total expenditures: R = A x r ˆ and, thus A = Rxˆ 1 r. Unit changes in elements of matrix Y (which formally are incomes on endogenous accounts from transfers coming from exogenous accounts) are treated as impulses producing corresponding changes on endogenous accounts. Square matrix W shows transfers between exogenous accounts. Introducing a notation y = Yi vector of exogenous values (where i is a summing up vector with dimensions r 1 composed of unities) we obtain the relation: (1) x = A x + y. After transformations we get: 1 (2) x = ( I A ) y 1 on condition that ( I A ) exists. 1 Denoting matrix ( I A ) with a symbol of M a multiplier we obtain: (3) x = M a y. The element m ij of M a informs how endogenous variable x i will change (incomes on account i) under an influence of a change in exogenous variable y j by unity (increase of incomes on account j). In the case of SAM 95 version shown in Table 5, A matrix was divided into submatrices within appropriate groups of accounts to allow an appropriate interpretation of this matrix elements 3. Matrix A is presented in the scheme below: 3 A consequence of accepting a definite division is the structure and values of A matrix elements. 1

Scheme 3. Matrix A divided into submatrices according to appropriate groups (subsystems) of accounts A 13 A = A 21 A 22 A 32 A 33 A 13 matrix of shares of particular items of the income generation account in total supply of products by NACE activity sectors; A 21 matrix of shares of primary income elements of endogenous institutional sectors in total primary incomes of these sectors; A 22 matrix of shares of ownership incomes and redistribution transfers (current and capital transfers of incomes) in disposable incomes of endogenous institutional sectors; A 32 matrix of shares of particular items of final demand in disposable incomes of endogenous institutional sectors; A 33 matrix of shares of intermediate demand in total supply of products matrix of input-output coefficients - by NACE activity sectors. Following the transformations given in Pyatt and Round (1985) we will exclude from matrix A block matrix A. Scheme 4. Structure of matrix A A = A 22 A 33 Equation (1) is then equivalent to equation: (4) x = ( A A ) x + A x y + Transforming (4) gives: 1 1 (5) x = ( I A ) ( A A ) x + ( I A ) y A 1 ) 1 let A* = ( I A ) ( A ) (6) x = A * x + ( I A y Multiplying both sides by A* it can be noticed that: 2 1 (7) A* x = A* x + A* ( I A ) y It results from (6) that 2 1 (8) x = A * x + ( I + A*)( I A ) y A x x I A 1 * = ( ) y. Substituting it to equation (7) gives: 11

Multiplying (7) by A* and substituting for A * 2 x an expression from (8) yields: 3 1 2 1 (9) x = ( I A * ) ( I + A * + A * )( I A ) y assuming that matrix ( I A* 3 ) 1 exists. Comparing equation (3) with equation (9) it can be seen that algebraic transformations presented above have led to decomposition of M a into three independent matrices. It shows that equation (9) can be written using symbols of multipliers, i.e.: (1) x = M M M x, assuming that: - M a3 a2 a1 1 a1 = ( I A ) 2 - M a = ( I + A* + * ) - 2 A 3 1 M a 3 = ( I A* ) Further algebraic transformations aimed at calculating matrices of multipliers M M M are also shown in Stone (1985). a1, a2 i a3 Decomposed multiplier M a can be presented in an additive form, which will make it more useful and will allow to determine the role of particular decomposed parts in the whole. Stone (1985) showed that multiplier M a can be expressed as 4 : (11) (a) M a = I + (M a1 I) + (M a3 I)M a1 + (M a2 I)M a3 M a1 (c) (d) (b) Particular elements of the sum are explained in the following way: (a) initial impulse (injection); (b) intragroup multipliers; (c) intergroup multipliers; (d) extragroup multipliers. Thus, the above denotation shows how the matrix of multipliers can be decomposed into particular elements (multipliers), with each of them referring to definite interrelationships (links) in the entire system. In our case we are dealing with three endogenous subsystems: primary incomes according to types and institutional sectors, primary and secondary division of incomes according to institutional sectors, and manufacturing of products (generation of incomes) according to NACE. A unit impulse on the exogenous account, for instance, growth of government transfers to households by 1 PLN, can: 4 It follows from (11) that M a = M 2 M 3 M 1 = M 3 M 2 M 1, which is in conformity with the relationship obtained by Stone (1985, p. 162), namely * * *3 1 1 x = ( I + A + A )( I A ) ( I A ) y. 12

Table 5. SAM'95 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 28 29 3 31 32 RAZEM labor costs 1 2 581 463 71 621 8 44 61 33 526 24 3 953 879 8 848 239 1 57 554 1 26 118 6 481 247 3 747 463 9 383 327 13 879 352 9 82 855 8 417 277 8 699 759 128 25 959 producers taxes 2 321 542 8 198 52 565 1 174 359 343 736 344 33 699 887 36 468-43 973 897 949 572 939 16 749 11 333 341 226 4 417 11 operating surplus 3 17 237 598 2 723 859 456 22 641 516 taxes on products 4 5 815 979 12 295 1 935 883 81 76 383 ownership incomes 5 26 4 2 141 9 12 127 7 27 291 5 4 192 279 1 525 141 49 946 756 471 944 1 994 43-53 285 84 1 44 32 9 98 21-2 25 1 11 77 313 762 456 66 5 1 17 51 4 717 148 133 835 818 295 271 462 662 6 275 933 565-3 419-4 32-67 475 39 814 534 19 233 9 1 295 9 62 297 3 non-profit institutiones 6 1 646 8 511 6 1 412 1 13 4 116 4 789 8 households 7 72 436 29 6 14 23 268 517 91 673 1 13 4 2 631 57 462 1 759 936 9 3 395 5 financial corp 8-2 86 6 22 898 2 49 1 36 2 568 2 2 921 8 26 828 8 non-financial corp 9 59 128 282 3 89 9 21 6 489 9 63 53 682 non-profit institutions 1 673 2 673 2 households 11 857 6 28 857 28 6 financial corp 12 7 151 1 7 151 1 non-financial 13 41 26 278 corp 21 425 1 175 3 18 425 478 5 A 14 16 487 322 325-687 956 162 13 44 2 98 16 996 2 234 2 229 21 384 2 887 318 56 498 3 87 18 29 596 298 31 42 118 433 519 24 46-3 487 1 789 69 56 649 823 846 721 74 B 15 9 17 2 6 1 469 156 134 9 215 475 15 476 5 4 623 659 1 19 2 854 3 851 988 6 398 397 3 876 525 83 C 16 1 733 55 15 476 46 233 836 972 711 2 595 366 8 45 183 6 217 53 996 195 792 283 44 677 597 548 589 515 747 15 661 47 3 171 559 137 865 3 668 454 26 568 422 D 17 94 13 3 128 779 99 17 19 98 1 175 15 732 3 863 64 114 831 4 847 469 16 292 15 856 736 34 962 31 128 799 227 383 979 993 31 367 466 96 64 88 5 53 78 365 42 7 416 5 2 2 1 5 28 1 885 259 738 995 612 993 528 752 151 E 18 7 14 789 186 554 847 187 2 983 988 871 5 723 445 2 89 959 43 668 1 635 299 24 859 1 32 312 116 445 3 54 21 613 2 326 782 349 864 424 78 248 69 25 833 813 F 19 3 249 149 2 84 592 1 32 913 18 66 328 G 2 24 88 896 274 429 926 382 659 1 647 73 44 542 6 347 547 494 956 7 465 373 12 4 721 1 188 457 1 356 671 415 476 252 178 525 942 5 245 948 6 785 51 589 93 35 555 16 217 482 158 7 271 259 317 4 76 252 47 216 1 468 99 3 421 625 26 13 1 25 49 519 91 1 642 763 1 119 63 313 927 212 936 338 375 49 77 4 438 42 H 21 2 14 771-18 -54 51 433 296 8 728 468 991 16 53 144 722 194 393 281 633 798 426 79 192 78 271 95 53 77 155 73 258 36 255 686 349 5 231 357 I 22 9 365 97 574 1 714 61 796 19 735 494 457 6 975 97 1 59 13 1 695 618 3 211 7 333 418 7 783 468 351 798 1 186 663 646 416 332 339 283 6 334 776 2 7 298 188 42 184 917 J 23 2 254 124 87 44 75 6 326 1 562 838 114 324 115 9 266 975 1 51 145 836 1 91 228 71 348 8 799 52 714 83 751 18 491 2 141 8 12 779 K 24 11 345 354 319 975 115 156 2 9 195 64 28 4 54 561 89 8 453 651 786 31 2 264 617 3 265 946 161 927 1 438 323 457 493 9 293 494 83 127 84 984 613 232 353 89 584 851 1 5 1 787 941 47 222 457 L 25 22 636 497 22 636 497 M 26 397 515 2 1 627 1 946 5 813 7 27 57 6 34 91 632 16 159 12 511 25 189 2 567 25 29 31 483 28 231 19 339 72 898 3 464 11 824 1 588 976 31 5 13 381 334 N 27 195 958 1 82 696 163 488 6 269 26 11 14 119 289 4 422 12 851 74 161 12 629 11 579 28 455 19 741 22 178 1 791 332 522 7 94 12 786 87 21 867 14 986 9 O 28 2 25 927 9 817 757 2 27 59 83 17 634 4 94 689 652 936 67 511 11 947 191 446 217 246 334 56 11 745 21 951 239 25 68 994 196 855 586 548 1 653 9 193 592 17 37 345 goverment cap. acc 29 3 426 8 64 7 12 3 7 goverment current 3 36 577 4 417 2 73 4 39 814 2 79 1 32 766 2 534 4 rest of the world current 31 3 28 7 4 16 51 9 rest of the world cap. acc. 32 673 2 22 172 Total 128 25 959 4 417 133 855 818 *) minus subsidies Source: own calculations 39 814 534 62 297 3 4 789 8 268 517 395 4 392 6 9 72 718 2 133 845 434 26 828 5 3 422 14 3 492 26 17 266 6 386 398 52 84 665 63 53 682 673 2 28 857 6 2 862 252 419 3 953 33 2 365 788 1 53 76 38 323 12 263 51 693 828 7 94 525 14 5 13 7 27 858 9 7 151 1 41 26 278 56 649 823 525 83 26 568 422 365 42 151 25 833 813 51 589 93 4 438 42 5 231 357 42 184 917 8 12 779 47 222 457 22 636 497 13 381 334 14 986 9 17 37 345 12 3 7 133 845 48 94 55 69 27 858 9 13

Table 5. Matrix of multipliers 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 28 1 1,2753,,33883,,27773,63166,38515,2517,28485,,143,13646,45291,34725,447,56957,32952,5925,561 1,1599,61889,54218,7835,61947 1,4 1,3819,92652,88351 2,1239 1,,1493,,1235,2335,1733,94,1224,,442,572,1911,197,3199,1232,1367,2966,234,5633,2466,425,13862,3127,1725,1732,1675,3627 3,4243, 1,47386,,39596,58162,563,2871,37694,,13441,1784,57576,77287,39274,35416,37691,64619,72911 2,52245,87147,77642,11945,83313,647,5595,56721,7932 4,4853,,8673 1,,5985,3962,6789,5656,1146,,5957,7762,25843,25275,38429,1629,369,15293,18182-1,1364,1173,1864 -,4227,9487,4335,5821,9975,2712 5,11135,,3598, 1,35345,25,15577,6513,63932,,3357,4271,14388,192,9962,9177,9456,16242,1825,6297,2172,19325,376,2779,1575,14654,14714,219 6,1534,,3928,,2643 1,1936,2147,162,348,,387,493,166,2126,1183,1135,199,1895,296,6946,2486,2211,614,2388,1949,1846,1823,2387 7 1,1894, 1,22844, 1,9856 1,1428 1,66396,7389,73753,,16484,21256,71133,76661,57989,64763,48951,8588,8918 2,51476 1,2855,9972,64542 1,338 1,12853 1,1234 1,4756 1,16723 8,4741,,12662,,5459,796,6632 1,24499,24712,,1234,1573,5294,6824,3754,3572,352,633,669,2229,7941,765,1847,7622,6134,5794,5737,7574 9,18568,,67589,,26874,27126,25977,1924 1,2111,,6171,7844,26434,35459,1844,16288,1738,29676,33474 1,1573,44,3564,555,38247,27814,25745,2688,36434 1,216,,552,,371,14327,32,225,489 1,,54,69,233,299,166,159,155,266,295,976,349,311,86,336,274,26,256,336 11,12782,,1322,,1186,11868,17883,7855,7926, 1,1771,2284,7645,8239,6232,696,5261,9229,9576,2726,1154,9777,6936,1783,12128,1269,11258,12544 12,1264,,3375,,1345,217,1768,33185,6587,,329 1,419,1411,1819,11,952,933,168,1783,5941,2117,1883,492,232,1635,1544,1529,219 13,6262,,22794,,963,9148,8761,6416,4841,,281,2645 1,8915,11958,685,5493,5837,18,11289,3929,13491,1219,1872,12899,938,8682,8798,12287 14,18124,,2593,,1747,18481,25356,12196,15472,,5946,5785,22428 1,45643,14177,12634,19311,17563,19479,57541,21424,18423,1217,19378,22115,1971,22847,2237 15,146,,167,,141,154,24,11,127,,43,55,186,172 1,42437,19,198,153,174,412,31,164,122,173,195,171,225,169 16,6522,,7697,,6419,7864,9125,4677,6192,,2262,2856,9656,899,5898 1,1713,8132,37465,1692,22811,1668,1276,5564,11591,9541,88,9622,9471 17,94569, 1,15619,,94748 1,279 1,3232,715,9937,,38542,49864 1,6662 1,11,9956,84592 1,98212 1,21721 1,41564 3,921 1,2787 1,2446,7899 1,23347 1,22959 1,1297 1,1991 1,16964 18,838,,954,,7739,999,11245,5459,6636,,2123,2737,916,9185,6784,142,7322 1,21582,9951,26922,1543,11977,8195,17824,12727,1289,11649,12131 19,8355,,17714,,1156,1239,11688,11979,25871,,13364,1922,6149,1174,6729,893,6547,1253 1,24926,3525,14384,1252,4574,15628,17443,13652,11862,15699 2,14721,,15966,,1398,15652,2595,9561,1816,,3128,3916,13297,1259,1734,1267,8842,14916,16553 1,44277,241,16836,17215,18762,2897,17747,15931,1777 21,1535,,1675,,1456,1714,2148,16,1149,,331,432,1437,1317,1131,149,18,1522,1823,4433 1,7417,3846,2297,1798,2174,2265,288,1918 22,169,,12114,,1323,12492,14955,7328,913,,2932,383,12737,1846,13983,199,933,16661,15844,3878,2678 1,33871,1459,15825,16283,1576,13921,14724 23,1917,,2117,,1827,239,2681,1275,1496,,455,589,1968,182,1328,1329,1682,2361,222,5698,2328,2349 1,16855,2225,2557,2498,2637,2231 24,13155,,15946,,13143,15733,1844,984,13461,,54,6748,2212,13315,1743,12165,11442,187,221,46842,19691,18927,17378 1,3959,2241,22454,19325,17962 25,,,,,,,,,,,,,,,,,,,,,,,, 1,,,, 26,192,,1338,,1116,9449,1528,735,919,,188,234,796,845,615,669,548,969,968,2765,1138,133,153,1124,1196 1,1639,155,124 27,662,,797,,669,4861,927,445,55,,121,153,516,652,388,447,376,589,621,1858,936,637,85,73,167,688 1,2912,763 28,5834,,7259,,616,53578,8162,3968,582,,19,1312,4543,4796,444,3912,387,537,5422,15313,151,6341,3524,632,7154,6465,6999 1,993 Source: own calculations. 14

1) release direct and indirect reactions (feedbacks) within an account of a given subsystem similar to those which find reflection in the matrix of full outlays in the input-output analysis, 2) release reactions with the remaining subsystems through shifting an impulse onto the remaining subsystems and returning to the account of initial subsystem; 3) release a reaction passing through all subsystems, which produces a change on an account of another subsystem. Table 5 contains SAM 95 and Table 6 presents corresponding multipliers. Due to limited frames of this paper we do not include elements (b), (c) and (d) see: (11). For illustration purposes we are giving these elements in the case of household accounts. Let us take into account several elements of the multipliers matrix column corresponding to household accounts. Element: m 77 = 1,66396 = 1 +,17 +,65388 + (a) (b) (c) (d) which means that the primary impulse in the form of government transfers to households by 1 PLN gives the income (as the result of direct and indirect reactions within the subsystem of income distribution) of 11.7 PLN and of 653.88 PLN as a result of indirect reactions with other subsystems (e.g. additional income earned by households due to the loop: the higher the income, the higher the demand for products, the higher the primary incomes, the higher incomes as a result of distribution processes. Element: m 97 =,25977 = +,134 +,25843 + (a) (b) (c) (d) This multiplier concerns the account of firms classified in the same subsystem, i.e. subsystem the redistribution of incomes. It means that primary impulse in the form of growth by 1 PLN of government transfers to households raises firms income by 259.77 PLN as the result of intra- and inter groups effects. Element: m 15,7 =,24 = + + +,24 (a) (b) (c) (d) means that primary impulse by 1 PLN to the household sector raises household spending on construction services by only 2 PLN. Element m 15.7 belongs to an external subsystem (the account of construction products). Summing up, the well known restrictions of SAM and the multiplier analysis should be pointed out: 15

1. Relations between particular categories have a linear character. 2. They are static, that is, there are no lags showing multiplier reactions. 3. Division into exogenous and endogenous parts will be always controversial. 4. No distinction is made between quantitative and ad valorem variables these are multipliers assuming constant prices (with a bigger income either more money can be spent on purchasing a definite product if its price is the same or the same quantity (or less) can be purchased when prices rise. These restrictions cause that more developed models are built on the basis of SAM, which are of a wide spectrum starting with simple attempts at modeling transactions of generation and distribution of incomes and ending with sophisticated general equilibrium models. The structure and way of construction of SAM 95 presented here fits, first of all, the needs of multisectoral model of the Polish economy IMPEC, which is regularly used as a tool of simulation and forecasting analyses. The identities used in IMPEC characteriing the main income flows by institutions in the transformed Polish economy are almost entirely based on SAM 95. References Cohen S.I. Patterns of Economic Restructuring for Eastern Europe, Avebury. Input-output table for 1995 (1999), Central Statistical Office, Warsaw (in Polish). National accounts according to institutional sectors and subsectors 1993-1998 (2), Central Statistical Office, Warsaw (in Polish). Pyatt G., Round J.I (1985) Accounting and Fixed-Price Multipliers in a Social Accounting Matrix Framework in: Pyatt G., J.I. Round (eds.) Social accounting matrices: a basis for planning, Washington DC, World Bank. Stone R. (1985), The Desegregation of the Household Sector in the National Accounts in: Pyatt G., J.I. Round (eds.) Social accounting matrices: a basis for planning, Washington DC, World Bank. Tomasewic Ł. (1994), Input-Output Methods, Polish Economic Editor, Warsaw. 16