Fourteenth International Conference on Input-Output Techniques s1

Fourteenth International Conference on Input-Output Techniques 10-15 October 2002, Montréal, Canada

DERIVATION OF SYMMETRIC INPUT-OUTPUT TABLES FOR ESTONIA

Iljen Dedegkajeva

Statistical Office of Estonia Abstract

This paper presents the results of work on transformation of the supply and use tables into product by product input-output table based on the product technology assumption for Estonia. The product by product input-output table according to the product technology assumption is regarded as the most preferred input-output table in the ESA 1995. It can be applied in various input-output models. Application of the product technology assumption, however, leads often to negative flows in the transformed input- output matrix. The derivation of the product by product input-output table using the product technology assumption in practice is the iterative process, which requires much more time and efforts than construction of the other types of tables based on the application of purely mathematical methods.

This paper provides a description of the supply and use tables from which the input- output table was derived. The preliminary adjustments made to SUT and compilation process of the input-output table are described in detail. The most interesting cases of the largest negatives appeared in the transformed use matrix and their solutions are also explained.

1. Introduction

In year 2002 Input-Output Tables Section of Macroeconomic Division of Statistical Office of Estonia participated in the Eurostat project on “Compilation of Supply and Use Tables and Input-Output Tables for the Baltic States”. The aim of the project was to develop and improve the compilation of the supply and use and input-output tables in the Baltic States.

The main task of the project work for Estonia was to compile the symmetric input-output tables according to the recommendations of ESA 1995. During the project the product by product input-output table based on the product technology assumption for year 1997 was elaborated. The input-output tables for domestic output and imports were calculated as well. The working version of the transformed input-output table contains 112 by 71 products. To calculate the Leontief inverse coefficients aggregation of the input-output table to a square format (71 by 71 products) was made. For the presentation at the 14 th International Conference on Input-Output Techniques input-output table was aggregated to level of 60 products (see Annex 1).

Section 2 of this paper contains a description of the supply and use tables (structure, classifications, statistical units) from which the input-output table was derived. The preliminary adjustments made in the supply and use tables are also given in this section. The derivation process of the input-output table is described in detail in section 3.

2 2. Basic data for the compilation of the input-output table

Input-output table was derived from the supply and use tables for year 1997, which were the first tables compiled according to the concepts and definitions of the ESA 1995. The supply and use tables for base year cover following tables: supply table at basic prices, including a transformation into purchasers prices, use table at purchasers prices, valuation matrices (trade and transport margin matrices, matrices on product taxes and subsidies) and import matrix.

In supply and use tables 91 activities are distinguished, of which 73 market activities, 13 other non-market and 5 activities for own final use. The activity classification used is based on the Classification of Activities of the National Economy (EMTAK), which is consistent with NACE Rev. 1 at 4-digit level. The aggregation level depends on basic statistics, which provide data in general at the 2 or 3-digit NACE level.

On the product side in supply and use tables 119 product groups are distinguished. The product classification used in the compilation of the supply and use tables is based on the Classification of Products by Activity (CPA). The product details are mainly 3-digit level and partly 4-digit level of CPA. Few products are specified at 5-digit level.

The following adjustments to the original supply and use tables were made before the calculations started. In the use table the intermediate consumption is extended by a nominal industry FISIM (i.e. financial intermediation services indirectly measured). FISIM is recorded as the intermediate consumption of this nominal sector. For the input- output purposes, FISIM was aggregated with product and activity J.65 Financial intermediation. This correction increased the total intermediate consumption of this industry by 1 170,9 million kroons and reduced the value added by the same amount. This aggregation did not change total intermediate consumption and total value added.

For input –output analytical purposes the basic price is the preferable valuation concept. Valuation at basic prices is the most homogeneous concept as the trade, transport margins as well as product taxes and subsidies are eliminated. Normally the use table is compiled at purchaser’s prices. To calculate input-output table at basic prices the use table was made according to basic price valuation. The trade and transport margin as well as taxes and subsidies on product matrices were deducted from use table at purchasers’ prices to obtain basic price use table. In basic price use table the margins were treated as products and added to the trade and transport services. Taxes and subsidies on product were recorded as separate rows in the use table.

A major problem in compilation of IOT is the existence of secondary products. The size of secondary production depends on the statistical unit that is used. In case of Estonia data sources provide information on the enterprises as statistical units, not on local kind of activity units. Almost all industries produce not only characteristic product of the industry to which they are classified but also a number of secondary products. For

3 example, the aggregated supply table (71 products by 71 industries) showed that of the total value of production of 149 813,4 million kroons, the amount of secondary production was 17 778,2 million kroons or 11,9% of total value of production. It should be noted that the share of secondary output varies significantly between different industries, for example, from 0,2% in activity E.41 Collection and distribution of water to 81,7 % in D.23 Manufacture of coke and refined petroleum products.

Figures 1 and 2 present the structure of the supply and use tables from which the input- output table was derived. The same symbols were used as in Eurostat Input-Output Manual.

Figure 1. Domestic supply table at basic prices

Industries Total Products V´ q

119 x 91

Total g

V´ - domestic supply matrix product by industry g - the row vector of the total output by industry q - the column vector of the total domestic supply by product

Figure 2. Use table at basic prices

Industries Final use Total Products

119 x 91

Net taxes on products Total use at purchasers prices Value added Y Total g

4 U - intermediate use matrix product by industry Y - value added matrix component by industry E - final use matrix product by category g - the row vector of the total output by industry q - the column vector of the total supply by product

3. Derivation process of the input-output table based on the assumption of product technology

The construction of the input-output table from the supply and use tables was carried out in several steps.

The first step was to transform the supply and use tables into input-output table by applying mathematical methods. To perform the operations with matrices such as, matrix inverse, multiplication, aggregation and the calculation of multipliers the special programs were implemented for Windows application (EXCEL) using the Microsoft Visual Basic (VBA) language. Procedures and formulas used for calculations are described in subsection 3.1.

As a result of the first step the initial input-output matrix was obtained. Application of the product technology assumption in practice leads often to negative flows in the transformed matrix. In our case it showed quite large number of negative values; however, many of which were very small.

The next stage in the compilation process was analysis of the negative flows concentrating firstly on the largest negative flows. For each of the largest negative flows a solution was found and the respective corrections were made to the supply and use tables. Imputations and other adjustments made to the original supply and use tables at that stage are explained in more detailed in section 3.2.

To deal with the problems of negatives the various methods exist. However, for the treatment of negatives in construction process of the input-output table the few restrictions were imposed. The ESA requirement is that between the input-output and the supply and use tables should be consistency in terms of values and classifications. It means that the total values of the input-output table should be the same as in the supply and use tables. And second, no changes to classifications at the publication level of 60 products should be introduced.

At the final stage of the compilation process the remaining negatives were eliminated in order to derive the non-negative input-output table. The final balancing was done using the mathematical RAS method. Brief description is presented in section 3.3. After RAS procedure the final checking of the results was made.

5 3.1. Calculation of the input-output table by applying of the mathematical methods

The application of product technology assumption requires that domestic supply matrix has to be square as it involves the inverse of the supply table. It can be possible to perform the transformation procedure if intermediate use matrix remains rectangular.

While the original supply table was a rectangular matrix to obtain the square format the aggregation was made. The project work started with the calculation of the input-output table aggregated to level of 60. To improve the quality of calculations and because the results obtained from the more detailed table were expected to be more reliable it was recommended by expert to perform the further calculations at the most detailed level possible.

The number of product and industry groups in supply table was aggregated to level of 71. At this stage the use matrix remained rectangular. However, the number of product groups in use table was decreased from 119 to 112, since some products were considered not relevant for input-output purposes. Aggregation of the input-output table to a square format was made after the compilation of the final version to calculate the Leontief inverse coefficients.

Calculations were performed using the formulas presented in Eurostat Input-Output Table Manual. Procedures were as follows: first, the inversion of domestic supply matrix V 1 was performed. Then the intermediate input-output coefficient matrix A was calculated by multiplying the use table U with the inverse of the domestic supply table:

A  U V 1

The primary input coefficient matrix W was similarly derived by multiplying the value added matrix Y with the inverse of the domestic supply table:

W  YV 1

The input-output matrix was obtained by multiplying the coefficient matrices A and W with the matrix of total supply of products on the diagonal diag(q):

Z  U V 1 diag(q) K  YV 1 diagq

In Figure 3 the input-output tables scheme is presented.

 Eurostat Input-Output Manual (draft), pages 239-241

6 Figure 3. Product by product input-output table at basic prices

Products Final use Total Products

112 x 71

Net taxes on products Total use at purchasers prices Value K added Total q

Z - transformed intermediate part of the use table by product K - transformed value added part of the use table by product

3.2. Analysis of the initial input-output table

To understand the causes of negatives we have first started with the analysis of the supply and use tables. Furthermore, information available from basic statistics on the level of enterprises was also examined. Due to limited time for the project work the analysis of the problematic values appeared in input-output table was focused mainly on the significant negatives those values were higher than 50 million kroons.

The analysis of the largest problematic values showed that the main reasons for the appearance of negative elements were as follows: heterogeneity in data and classifications, misclassifications, vertically integrated production process, errors in the supply and use tables, product technology assumption is not valid, existence of by- products. To fix the problems of negatives several methods were used such as creation of new products, subdividing products and industries, transfers of output and corresponding industry inputs, correcting errors in the supply and use tables and finally manual adjustments in input-output table.

For each of the biggest negative flows a solution was found and the respective corrections were made to the supply and use tables. After each adjustment to the supply and use tables the recalculation of the input-output table was performed. In all the fifthteen versions were produced until the value of the negative elements became acceptable.

The initial version of input-output table showed (see Figure 4) that the total amount of negative values in transformed intermediate part of the input-output table was 4 212,8

7 million kroons or 2,8% of total value of production. It should be noted that 38,5% of total negative value constituted of large negatives those absolute values were over 100 million kroons. Although, compared to the total negative numbers of 2 365, such elements was just 8.

Figure 4. Results of the initial input-output table 112 by 71 products

Value, % % Number Million of kroons elements 1 2 3 4 5 Negative elements in intermediate part of IOT: Under – 100 1 621,3 1,1 38,5 8

- 100 < zij  -50 204,3 0,1 4,8 3

- 50 < zij  - 2 1 882,1 1,3 44,7 251

- 2 < zij  0 505,1 0,3 12,0 2 103 Total 4 212,8 2,8 100 2 365

Total production 149 813,4 100 7 952

As regards the medium and small negative elements, their number was quite big (251 and 2 103 respectively) compared to the number of the largest negative elements. However, the total value of medium and small size negatives (between 0,1 and 50,0 million kroons) was 2 387,2 million kroons or 56,7% of total negative value.

The most interesting cases of the largest negatives appeared in the transformed intermediate use matrix and their solutions are explained below.

Agricultural products CPA A.01

One of the largest negative values of 131,2 million kroons in the Z matrix arose for the use of live animals and animal products by agricultural products. In the supply and use tables agricultural industry was defined as one column. It had primary output of 7037,7 million kroons and also a secondary production of 281,3 million kroons of the meat products. Live animals produced by agricultural industry and then used in the production of meat products was not recorded as inputs of this industry in the supply and use tables and caused a large negative value in the transformation process.

This situation is the classical example of vertically integrated production process, which in practice could lead to the negative elements. In this case the application of product technology assumption was not correct. To solve this problem it was decided to introduce a new product called “meat products produced by agriculture” in the supply and use

8 tables and to subdivide the agricultural industry into two industries. For this new product the input structure was estimated on the basis of the input structure of agricultural industry. However some adjustments to input structure were made. For example, some typical inputs of agriculture (like seeds, fertilise, etc.) were excluded, since these products were not used for meat production.

Textile products CPA D.17

Few not very large negative elements in the transformed intermediate use matrix appeared for the inputs of products of agriculture and chemicals by wearing apparel products CPA D.18. In the supply and use tables wearing apparel industry was defined as one column. This industry produced, as secondary products, 146,7 million kroons of textile products CPA 17.

In textile industry that is a primary producer of textiles products there is a big manufacturer, which uses mainly imported raw cotton, basic and other chemical products as inputs for the production. Analysis of the input structure of wearing apparel industry in the use table showed that neither cotton nor chemical products were used as intermediate consumption.

The product technology assumption is not valid in case of existence of more than one way to produce a product and created negatives in the transformation process. To solve this problem of negatives we decided to divide manufacture of wearing apparel into two industries. A new product called “textiles produced by wearing apparel” was introduced in supply and use tables. For this new activity input structure based on available production statistics was estimated.

Refined petroleum products CPA D.23

The next large negatives in the intermediate part of the input-output table appeared for the inputs of three products, which were used by refined petroleum products. The amount of negative values of these elements was quite big – 544,8 million kroons and comprised 12,9% of total negative value. The negative elements also appeared in the transformed value added part of the use table by this product.

Further analysis showed that in activity of refined petroleum products the secondary production exceeded primary production due to misclassification of activities and moreover, some 96,7% of refined petroleum product’s output were produced outside and came from the chemical industry. This strange situation led to big negative flows in the input-output table. The manual transfer of the primary products and the corresponding inputs to its characteristic industry solved this problem (see explanation for chemical products below).

Chemical products CPA D.24

9 The three large negative elements in the transformed intermediate input part of the input- output table appeared for the inputs of other mining, chemical products and business services by chemical products. These negative items with amount of 721,2 million kroons produced around 17% of total negative value. The chemical industry is regarded as the one of the most difficult industries to describe in an input-output table2. The chemical companies usually produce different products in interrelated production process and the separation of the production process for each product is not possible.

In Estonia there is a big producer in chemical industry, which besides the primary output of chemical products also had a secondary production of refined petroleum products (oil shale). The production process of chemical products and oil shale is technologically linked that it is difficult to separate. In this case the application of the product technology assumption created a big problem. To fix this problem it was assumed to treat oil shale as by-products and to transfer output of oil shale to the primary industry D.23 by given the same input structure as the main chemical products.

Recovered secondary raw materials CPA D.37

Another negative elements in the transformed intermediate use matrix arose for the use of the few products such as basic chemicals and metals, electricity and renting services by recovered secondary raw materials product CPA D.37. Analysis of the supply and use tables indicated that secondary production in recycling activity constituted 74,4% of total value of production. Information from production and foreign trade statistics showed that one enterprise classified in recycling industry was engaged in contract processing of basic metal products.

This situation caused negative values in the transformation process, because inputs corresponding to the transferred secondary output were determined by the input structure of the basic metals industry as a primary producer. The basic statement of the product technology assumption is that the secondary product is produced in the same way as in the industry producing it as its primary product3. To solve this problem it was decided to transfer the output and corresponding inputs of that enterprise to its characteristic basic metals industry. Output and input structure was estimated on the basis of information available from basic statistics.

Hotel services H.551

Few negative elements which values were not too large arose for the use of food products by the hotels. After examining of this situation we made a conclusion that negative results were caused by errors in the supply and use tables. Further adjustments to input of industry hotels H.55 in the supply and use tables were made.

2 P.J.A. Konijn. On the compilation of input-output data from the National Accounts, Universiteit Twente, Enschede, 1994, page 205

3 Eurostat Input-Output Manual (draft), page 226

10 3.3. RAS procedure

RAS method was used at the latest stage of the compilation process when problems with largest negative values were manually solved. When the total amount of negative value reduced to 1 496,4 million kroons or 1,0% of total value of production (see Figure 5) we considered to apply RAS. It was assumed that size of negative values became acceptable.

Figure 5. Results of the input-output matrix before applying of RAS

Value, % % Number Million of kroons elements 1 2 3 4 5 Negative elements in intermediate part of IOT: Under – 100 0,0 0 0 0

- 100 < zij  -30 0,0 0 0 0

- 30 < zij  - 2 1 040,7 0,7 69,5 170

- 2 < zij  0 455,7 0,3 30,5 2 022 Total 1 496,4 1,0 100 2 192

Total production 149 813,4 100 8 322

To perform the RAS procedure a special program was developed. At first, all negative elements were set to zero and then matrix of the intermediate use was adjusted with multipliers to match the given totals for intermediate inputs matrix Z. Same procedure was applied to value added matrix. RAS method is an iterative procedure. The number of iterations depends on the scale factor’ value, for example, the final balancing with scale factor 0,0001 was done with 46 iterations.

4. Conclusions

The construction of the product by product input-output table based on product technology assumption was our first experience in this field. The derivation of such type of the input-output table in practice was not an easy task. Due to limited time for the project work we concentrated mainly on the analysis of the largest negatives. Of course, much more time was needed to solve the major part of negative elements appeared in transformed version. We think that some further improvements in the input-output table can be made.

11 5. References

Commission of the European Communities, International Monetary Fund, Organisation for Economic Co-operation and Development, United Nations, World Bank: System of National Accounts1993, Brussels/Luxembourg, New York, Paris, Washington D.C. 1993.

Eurostat: European System of Accounts (ESA 1995), Luxembourg 1996.

Eurostat Input-Output Manual (draft), Luxembourg 2001.

United Nations: Handbook of Input-Output Table Compilation and Analysis, Studies in Methods, Series F, No.74, New York 1999.

Marco De March: The Eurostat ESA95 Input-Output Manual: General outline and aims of the Manual, presented at the 13th International Conference on Input-Output Techniques, 21-25 August 2000, Macerata, Italy.

P.J.A. Konijn: On the compilation of input-output data from the National Accounts, Universiteit Twente, Enschede, 1994.

Norbert Rainer: Derivation of Input-Output Matrices from Supply and Use Tables in the 1993 SNA/ 1995 SNA, presented at the 12th International Conference on Input-Output Techniques, 1998, New York.