From Input-output to SUT Jörg Beutel Productivity in the European Union: A Comparative Industry Approach Workshop Inter-Industry Accounts WP 1 15-16 September.

From Input-output to SUT

Jörg Beutel

Productivity in the European Union: A Comparative Industry Approach

Workshop Inter-Industry Accounts WP 115-16 September 2005, Groningen

From Input-Output to SUT 2

Introduction

Objectives• Outline of present data situation• Discussion of missing data• Transformation of use tables from purchasers’ prices to

basic prices• Transformation of supply and use tables to input-output

tables• The dual approach: Transformation of input-output tables to

supply and use tables• Empirical example of transformation for Austria 1995• Estimation of missing supply and use tables


Data Situation

ESA 1995• Annual supply and use tables starting in year 1995• Five-yearly input-output tables 1995, 2000, 2005, etc.• Submission mandatory for member countries of EU

The tables• Supply table at basic prices, including transformation into purchasers'

prices• Use table at purchasers' prices• Input-output tables for total uses, domestic production and imports at

basic prices

Earlier years 1970-1994• Very few supply and use tables available• SUT mostly internal data for compilation of IOT’s• Various input-output tables with different classifications and price

concepts were published


Period 1995-2002

Code 1995 1996 1997 1998 1999 2000 2001 2002 1995 1996 1997 1998 1999 2000 2001 2002 1995 2000 2001 1995 2000 2001 1995 2000 2001 pp/ii

BE x x x x x x x x x x x x x x x x ppDK x x x x x x x x x x x x x x x x x x iiDE x x x x x x x x x x x x x x x x x x ppGR x x x x x x x x x x x ppES x x x x x x x x x x x x x x x ppFR x x x x x x x x x x x x xIE IT x x x x x x x x x x x x x x x x x x x x ppLU NL x x x x x x x x x x x x x x x x x x x x x x x iiAT x x x x x x x x x x x x x x x x ppPT x x x x x x x x x x 99 99 99 ppFI x x x x x x x x x x x x x x x x x x iiSE x x x x x x x x x x x x x x x x x x ppUK x x x x x x x x x x x x x x x x x ppCYCZEE x x 97 97 97 ppHU x x x x x x 98 x 98 x 98 x pp + iiLTLVMT x x x xPL x x x x x x x x x x x x x x x x SK x x x x x x x x x x x xSI x x x x 96 x 96 x 96 x ppBG x x x x xHR

RO

TR

NO x x x x x x x

Derogation Source: EurostatYY Different yearx under preparation

1500 Supply 1600 Use 1700 Siot 1800 Domest. 1900 Import


Period 1970-1994

1959 1965 1970 1975 1980 1985 1990 1995

1. Belgium x x x x x e e e2. Denmark x x x x e e3. Germany x x x x x x e e4. Greece e (5) e e5. Spain x x x (6) e e6. France x x x x x x e e7. Ireland x (1) x x (7) e e8. Italy x x x x x x (8) e e9. Luxembourg x x (2) x (9) e e10. Netherlands x x x x x x (10) e e11. Portugal x e (11) e e12. United Kingdom x x x x e e13. Austria e14. Finland e15. Sweden e

EU6 x xEU7 xEU9 x x (3) x (4)EU12 e e EU15 e

Legend: x: available e: estimated for R25 by Eurostat Source: Eurostat

Input-output tables by country

Aggregate input-output tables


Challenge

1995-2002• Collect supply and use tables from NewCronos (Eurostat)• Compile missing supply and use tables 1995-2002• Estimate valuation matrices (trade and transport margins, taxes) • Establish supply and use tables at basic prices for total supply, domestic production, imports

Earlier years 1970-1994• Collect existing SUT’s and IOT’s• Estimate supply tables for existing IOT’s• Various price concepts and various classifications• Estimate use tables at basic prices for existing IOT’s• Estimate missing SUT’s at basic prices for other years• Comparison with National Accounts in NewCronos


Valuation matrices

Different valuation matrices• Trade margins (wholesale trade, retail trade)• Transport margins (inland, water, air and other transport)• Taxes on products (product taxes, VAT) • Subsidies on products

Price concept• Transformation of use tables at purchasers prices to use

tables at basic prices• Transformation of input-output tables at producers prices to

basic prices


Access to valuation matrices

• Access to valuation matrices for selected countries in the course of the Eurostat data submission programme

• Germany, Denmark and Austria

• Austria published valuation matrices on CD-Rom in ‘Statistik Austria: Input-Output-Tabelle 1995’

• Tax matrices were published by Eurostat in ‘Input-Output tables 1985’ for Denmark, France, and Ireland covering 59 sectors.


Transformation of supply and use tables to basic prices

Supplytable atpurcha-

sers’prices

Supply table atbasic prices

Trans-portmar-gins

Importscif

Use table of importsat basic prices

Whole-saletrademar-gins

Retailtrademar-gins

Taxeson pro-ducts

Usetable atpurcha-

sers’prices

Supply and use tables

Sub-sidies

on pro-ducts

Valuation matrices

Use table at basic prices

Use table of domestic production at basic prices


Price system of the input-output framework

Basic Prices =

+Taxes on products- Subsidies on Products

= Producers’ prices (net of all VAT)+ Non-deductible VAT

= Producers’ prices (net of deductible VAT)+ Trade Margins+Transport Margins

= Purchasers’ prices (net of deductible VAT)


PRICE SYSTEM OF THE INPUT-OUTPUT FRAMEWORK FOR DENMARK 1985 (Mio. DKR)

Industry by industry

Ag

ricu

lture

Ind

ust

ry

Se

rvic

es

Co

nsu

mp

tion

Gro

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ixe

d ca

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tion

Exp

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s to

EU

co

untr

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Exp

ort

s to

th

ird

co

untr

ies

Ou

tpu

t

Industry by

industry

Ag

ricu

lture

Ind

ust

ry

Se

rvic

es

Co

nsu

mp

tion

Gro

ss f

ixe

d ca

pita

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tion

Exp

ort

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EU

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untr

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Exp

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s to

th

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Ou

tpu

t

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

Table 2: Domestic production Basic prices Table 3: Imports Basic prices

1 Agriculture 6 40 1 3 0 7 3 61 1 Agriculture 1 4 0 3 0 1 1 10

2 Industry 10 88 52 60 72 60 82 424 2 Industry 8 86 20 30 27 6 8 184

3 Services 7 53 101 329 10 13 32 546 3 Services 0 2 12 0 0 0 0 15

4 Imports cif 9 92 33 32 27 7 9 209 4 Total 9 92 33 32 27 7 9 209

5 Other taxes linked to production - 1 0 - 1 0 0 0 0 - 2

6 Net taxes on domestic production- 1 1 4 15 1 - 2 - 2 16

7 Non-deductible VAT on domestic production 0 0 11 32 7 0 0 51

8 Net taxes on imports from EU 0 0 1 8 1 0 0 10

9 Non-deductible VAT on imports from EU 0 0 1 4 0 0 0 5

10 Net taxes on imports from third countries 0 1 1 8 1 0 0 10

11 Non-deductible VAT on imports from third countries 0 0 1 4 0 0 0 5

12 Value added 30 149 342 0 0 0 0 521

13 Output 61 424 546 495 120 86 124 1 854

Table 5: Domestic production (5 = 2 + 11 +14) Producers' prices (net of all VAT) Table 6: Imports (6 = 3 + 12 + 15) Producers' prices (net of all VAT)




4 Imports 9 93 34 49 29 7 9 229 4 Total 9 93 34 49 29 7 9 229


6 Net taxes on production - 1 12 5 0 0 0 0 16

7 Non-deductible VAT domestic products 0 0 11 32 7 0 0 51

8 Non-deductible VAT on imports from EU 0 0 1 4 0 0 0 5

9 Non-deductible VAT on imported products 0 0 1 4 0 0 0 5

10 Value added 30 149 342 0 0 0 0 521

11 Output 60 436 550 495 120 86 124 1 870

Table 8: Domestic production (8 = 2 + 11 + 14 + 17) Producers' prices (net of deductible VAT) Table 9: Imports (9 = 3+12+15+18) Producers' prices (net of ded. VAT)




4 Imports 9 93 36 56 29 7 9 239 4 Total 9 93 36 56 29 7 9 239


6 Net taxes on production - 1 12 5 0 0 0 0 16

7 Non-deductible VAT on production 1 27 23 0 0 0 0 51

8 Value added 30 149 342 0 0 0 0 521

9 Input 61 462 574 495 120 86 124 1 921

Table 11: Net taxes on products (domestic production) Table 12: Net taxes on products (imports)

1 Agriculture 0 0 0 0 0 0 0 - 1 1 Agriculture 0 0 0 0 0 0 0 0

2 Industry - 1 0 2 14 0 - 2 - 2 12 2 Industry 0 1 1 16 1 0 0 20


4 Total - 1 1 4 15 1 - 2 - 2 16 4 Total 0 1 1 16 1 0 0 20

Table 14: Non-deductible VAT (domestic production) Table 15: Non-deductible VAT (imports)




4 Total 0 0 11 32 7 0 0 51 4 Total 0 0 2 7 1 0 0 10


Transformation of supply and use tables to IOT’s

Model assumptions

Product technology assumption (Model A)

Each product is produced in its own specific way, irrespective of the industry where it is produced.

Assumption of fixed industry sales structure (Model B)

Each industry has its own specific sales structure, irrespective of its product mix

Industry technology assumption (Model C)

Each industry has its own specific way of production, irrespective of its product mix.

Assumption of fixed product sales structure (Model D)

Each product has its own specific sales structure, irrespective of the industry where it is produced.


Transformation of supply and use tables to input-output tables

INPUT COEFFICIENTSZ = U * inv(g) Intermediates of industries per unit of outputL = W * inv(g) Value added of industries per unit of output

OUTPUT COEFFICIENTSC = V' * inv(g); Output coefficients for industries by productD = V * inv(q); Output coefficients for products by industry

I. TRANSFORMATION OF SUPPLY AND USE TABLES TO INPUT-OUTPUT TABLES

Model A: Product by product input-output table based on product technology assumption Negativesq = inv(I-Z * inv(C)) * y OutputA = Z * inv(C ) * diag(q) IntermediatesY = Y Final DemandX = L * inv(C) * diag(q) Value added

Model B: Industry by industry input-output table based on fixed industry sales structure assumption Negativesg = inv(I-inv(C ) * Z) * inv(C) * y OutputB = inv(C) * Z * diag(g) IntermediatesE = inv(C) * Y Final DemandW = W Value added

Model C: Product by product input-output table based on industry technology assumption No negativesq = inv(I-Z * D) * y OutputA = Z * D * diag(q) IntermediatesY = Y Final DemandX = L * D * diag(q) Value added

Model D: Industry by industry input-output table based on fixed products sales structure assumption No negativesg = inv(I-D *Z) * D * y OutputB = D * Z * diag(g) IntermediatesE = D * Y Final DemandW = W Value added


Model assumptions for transformation to IOT’s

Product technology assumption (Model A)• Widely used by countries which publish product by product IOT• Belgium, Denmark, Greece, Spain, France, Italy, Austria, Portugal,

Sweden, UK, Estonia, Slovakia, Hungary• Problems with negatives • Analytical tables away from statistical sources

Assumption of fixed product sales structure (Model D)• Widely used by countries which publish industry by industry IOT• Denmark, Netherlands, Finland, Canada, Norway, Hungary• No negatives• Close to statistical sources

Other assumptions• Hybrid technology (UK), Almon procedure (Test version for NL)


Transformation of input-output tablesto supply and use tables

INPUT COEFFICIENTSZ = U * inv(g) Intermediates of industries per unit of outputL = W * inv(g) Value added of industries per unit of output

OUTPUT COEFFICIENTSC = V' * inv(g); Output coefficients for industries by productD = V * inv(q); Output coefficients for products by industry

II. TRANSFORMATION OF INPUT-OUTPUT TABLES TO SUPPLY AND USE TABLES

Model A2: Use table from product by product IOT based on product technology assumption No negativesU = A * inv(diag(q)) * C * diag(g) IntermediatesY = Y Final DemandW = X * inv(diag(q)) * C * diag(g) Value added

Model B2: Use table from industry by industry IOT based on fixed industry sales structure assumption No negativesU = C * B IntermediatesY = C * E Final DemandW = W Value added

Model C2: Use table from product by product IOT based on industry technology assumption NegativesU = A * inv(diag(q)) * inv(D) * diag(g) IntermediatesY = Y Final DemandW = X * inv(diag(q)) * inv(D) * diag(g) Value added

Model D2: Use table from industry by industry IOT based on fixed products sales structure assumption NegativesU = inv(D) * B IntermediatesY = inv(D) * E Final DemandW = W Value added


Transformation of input-output table to use table

Data situation• For earlier years often supply and use tables are not available• If they exist they internal data of Statistical Offices for the compilation of IOT’s.

Required input data• Input-output table and supply table• Supply table can be derived from benchmark years and official national accounts data.• The structure of supply tables is rather stable in time.


Model assumptions for transformation to SUT’s

RecommendationUse the complements of Model A for product by product IOT’s and Model D for industry by industry IOT’s.

Product technology assumption (Model A2)• Widely used by countries which publish product by product IOT• Transformation to SUT is not creating negatives

Assumption of fixed product sales structure (Model D2)• Widely used by countries which publish industry by industry IOT• Transformation may create negatives.• If negatives are generated Model B2 is an option.


Transformation of SUT 1995 to IOT 1995 for Austria

Statistik Austria• Product by product IOT‘s were compiled which are based on

product technology assumption (Model A)• In the course of the transformation numerous small negative

elements were generated.• Large negatives are an indication for the mismatch of statistical

sources with the technology assumption.• The negatives were deleted in a manual balancing procedure.

EUKLEMS transformation• All 4 transformation models were compiled using SAS software

with dynamic data exchange with Excel files• The results of Model A were very close to the published IOT’s.


Transformation of IOT 1995 to SUT 1995 for Austria

EUKLEMS transformation

• Required inputs are IOT 1995 and supply table 1995

• All 4 transformation models were compiled using SAS software with dynamic data exchange with Excel files

• The results of Model A2 were close to the published SUT.

• The manual balancing caused minor deviations for value added and intermediate inputs for most sectors.

• In some cases larger differences were caused which can be revised in a manual balancing procedure.

• GDP and components of value added and final demand are correct.


Projection of SUT‘s and IOT‘s

Requirements

• Supply and use tables or input-output table at basic prices for base year

• Real growth rates for valued added of industries (EUK60)

• Real growth rates for final demand (private consumption, government consumption, gross fixed capital formation, change in stocks, exports)

• Real growth rate of imports


Updating input-output tables

Agri-cul-ture

En-ergy

In-dustry

Ser-vices

Total 1-25

Pri-vate con-

sump-tion

Go-vern-ment con-

sump-tion

Gross fixed

capital for-ma-tion

Chan-ge in

stocks

Ex-ports

Total 27-31

Output 26+32

1 : : 25 26 27 28 29 30 31 32 331 Agriculture : Energy : Industry

25 Services 26 Total 1-25 27 Agriculture : Energy : Industry

51 Services 52 Total 27-51 53 Capital consumption 54 VAT 55 Other taxes 56 Salaries and allowances 57 Operating surplus 58 Value added 53-57 59 Input 26+52+58

= Real growth rates for value added by sector

= Real growth rates for components of final demand

Production activities

Do-mestic

pro-duction

Imports

Value added

Final use of goods and services


Inpu t-ou tpu t tab le 1992

V a lue added 1992F ina l dem and

1992

M acroeconom ic fo recas t 1995

F ina l dem and1995

V a lue added 1995

G row th ra tes 1992 /95 fo r va lueadded and fina l dem and

G row th ra tes 1992 /95 fo rac tiv ities and com m od ities

Inpu t-ou tpu t tab le 1995(incons is ten t)

Inpu t coe ffic ien ts

Inve rse F ina l dem and

Inpu t-ou tpu t tab le 1995(cons is ten t)

V a lue added 1995 F ina l dem and1995

D iffe rence to fo recas tA d jus tm en t fac to rs fo r g row th ra tes

D ifference > 1%

S top

D ifference <1%


Eurostat method

The main advantages of the Eurostat update procedure

• Robust update procedure at low costs• Limited data requirements• Only official sources from New Cronos are used.• Integrated estimation of all four quadrants of IOT• No arbitrary changes of input coefficients as in RAS• Row and column totals for intermediates derived not given• Structure of final demand estimated during the iteration• Consistency of supply and demand provided by io-model.• Successfully implemented for DG Regio• Evaluation of the European Structural Funds in Greece, Portugal, Ireland, Germany, Italy, and Spain• Documentation of updating procedures in Eurostat Input-Output Manual


Updating supply and use tables

Imported products

Domestic products

IndustriesFinal

demandTotal

Ud Yd qdDomestic products

qmImported products Um Ym

Ud Yd qdDomestic products

qmImported products Um Ym

VIndustries g

qm' mw

qd' qm' y

= Real growth rates for value added by sector

= Real growth rates for components of final demandV' = Supply matrix

qd = Product output domestic production V = Transposed supply matrix (make matrix)

qm = Imported products Ud = Use matrix for domestic intermediates

m = Imports Ud = Use matrix for imported intermediates

g = Industry output domestic production Yd = Final demand for domestic products

w = Value added of industries Ym = Final demand for imported productsy = Final demand W = Value added of industries

Imports W

Total g'

VIndustries g

Value added


Recommendations

• ClassificationData base of EUKLEMS should cover all 60 individual industries (A60) of ESA 1995. EUK60 requires the disaggregation of 10 additional industries. In consequence the supply and use tables will comprise 70 industries. The data base will always allow to aggregate the results to A60.

• Input-output tablesCollect all input-output tables, also if supply and use tables are available. The input-output tables may be the only reliable source of import matrices.

• Transformation of use tables at purchasers’ prices to use tables at basic pricesEstablish a standard procedure for the transformation of use tables at purchasers’ prices to use tables at basic prices. Estimate or collect all recommended valuation matrices.


Recommendations

• Valuation matricesIf valuation matrices are missing use reference year or reference country to blow up the valuation vectors of the supply table to a full size valuation matrix.

• Transformation of supply and use tables to input-output tables and vice

versaUse appropriate technology assumption for the transformation of input-output tables to supply and use tables and the transformation of input-output tables to supply and use tables.

• Compilation of missing supply and use tables

Use a projection model to compile the missing supply and use tables. The main aggregates (GDP, value added by industry, components of final demand) shall be compared with the macroeconomic data in NewCronos of Eurostat.


Software for transformation

Excel• Restrictions for calculation of an inverse (maximum matrix size 52x52)• No programme code• Not transparent for other users

SAS • No restrictions for calculation of an inverse• Documentation of programme code• Easy search for programming errors• Three windows document the program code (Program), errors in the compilation

procedure (Log) and the results (Output)• Dynamic data exchange with Excel for input and output

Excel and SAS• Powerful tool for complex macroeconomic models• Professional documentation• Easy generation of tables and figures for publication


Documentation

• Compilation of supply and use tables at basic pricesPaper for the Amsterdam meeting of the Data C-ordination GroupDC note1beutelc WP1.doc

• Transformation of supply and use tables and symmetric input-

output tablesNumerical examples with Excelhybridrev8.xls

• Transformation of supply and use tables and symmetric input-output tablesEmpirical application for Austria 1995 with SAS and dynamic data exchange with Excel filesausut95sept05b.xls

From Input-output to SUT Jörg Beutel Productivity in the European Union: A Comparative Industry Approach Workshop Inter-Industry Accounts WP 1 15-16 September.

Documents

yearly inputoutput tables

input data inputoutput

sut16 transformation

sut15 transformation

iots estimate supply

supply table supply

tables available sut

negatives analytical