Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

A use-side trade margins matrix for the Andalusian economy

By

J. M. Rueda-Cantuche*, A. Titos Moreno* & M. Asensio Pardo*

Abstract
The National Accounting Systems proposed by United Nations (1968, 1993) and Eurostat(1996) establish the concepts of use and make matrices and recommend that production
costs of goods and services should be measured before they are conveyed to the markets(basic values). However, initial survey based use matrices are valued at purchasers' prices
and therefore, trade and transport margins and net commodity taxes matrices are needed.
This paper shows the methodology used presently by the Institute of Statistics of Andalusia
for constructing trade margins matrices, which is based on the use-side procedure from the

ESA-95 Input-Output Manual (Eurostat, 2002). Input-output compilers may profit fromreading this work.

1

Introduction

The 1995 European System of Accounts (ESA 95) integrates use and supply tables as

one of the new features of the system. Only symmetric input-output tables were included as part of it in the former ESA. As a result, the supply-use framework may pro

vide more accurate and disaggregated descriptions of inter-industry flows for future
economic analysis. Hence, many countries adopted the ESA 95 framework to constructsupply and use tables and symmetric input-output tables. Particularly, the recently pub
lished ESA 95 Input-Output Manual - Compilation and Analysis (Eurostat, 2002)

complements the United Nations Manual (UN, 1999), provides a good technical andmethodological basis for low experienced countries in the compilation of input-output

tables, proposes harmonized solutions and describes the best current practices in com
pilation and input-output analysis.

The National Accounting Systems proposed by United Nations (1968, 1993) andEurostat (1996) recommend that production costs of goods and services should be

Received February 2004,final version received November 2006.
* Institute for Prospective Technlogical Studies (IPTS), DG Joint Research Centre, European Commis
sion, Seville, Spain and Pablo de Olavide University, Department of Economics, Quantitative Methods and Economic History, Seville, Spain. E-Mail : jmruecan@upo.est University of Cordoba, Cordoba, Spain.

* Regional Ministry of Economy and Finance, Seville, Spain.

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measured before they are conveyed to the markets (basic values). However, initial sur

vey based use matrices are valued at purchasers' prices and therefore, trade and transport margins and net commodity taxes matrices are needed. At the same time, the ESA

95 Input-Output Manual (Eurostat, 2002) provides a guiding procedure for constructing
the so-called valuation matrices.

A use table comprises commodities i consumed by industries j (intermediateuses), final uses by commodities (final demand, including exports), and value added foreach industry. According to the ESA 95 Input-Output Manual (Eurostat, 2002), the aimof the use table is twofold. Firstly, it presents the input structure of each industry (bycolumn), that is, the cost of production in each corresponding industry; and secondly, itshows the use of different types of commodities (by row) for intermediate or final uses.
The use table is defined at purchasers' values although basic values can be derived
through some valuation adjustments on trade and transport margins and net commodity
taxes§.

A supply table shows the produce of sectors / in terms of commodities j (production matrix), the total imports by products, and some valuation adjustment items totransform the production values from basic prices to purchasers' prices. The purpose of

the supply table is to provide the total supply of goods and services of an economy fora given period of time. The supply table is defined at basic values, which means that
distribution margins (trade and transport) and net taxes on products** are left out of thevaluation of the production.

However, supply and use flows should be valued at basic prices in order to con
struct a homogeneous input-output table, as shown in Eurostat (2002). Other analytical
purposes like constructing technical coefficients are also involved. Because of these
specific requirements, the use table must be transformed from purchasers' values to ba
sic prices and therefore, the so-called valuation matrices must be compiled, i.e. trade
and transport margins matrices, and the net commodity taxes matrix (including non deductible value added tax). A guiding procedure for the Andalusian economy can beseen in ten Raa and Rueda-Cantuche (2007). Particularly, this paper focuses on trade
margins and describes the Andalusian experience in constructing trade valuation matri
ces on the basis of the use-side procedure included in the ESA 95 Input-Output Man
ual.

Next section discusses the use-side and supply-side procedures described in the
ESA 95 Input-Output Manual for constructing trade margins matrices. Section 3 presents the Andalusian experience and results and section 4 concludes.

2 Methodology
According to the ESA 95, a trade margin is the difference between the actual or im
puted price realized on a good purchased for resale and the price that would have tobe paid by the distributor to replace the good at the time it is sold or otherwise disNotice that for exports the FOB valuation is comparable with purchasers' values.

k Notice that for imports the cif valuation is comparable with basic values.

A use-side trade margins matrix for the Andalusian economy

123

posed of. (...). Trade margins are valued at basic prices.

Thus, trade margins can be derived as the difference between the trade turnover(at basic prices) and the costs of goods purchased for resale adjusted by changes instocks. Recall that trading is defined as resale of goods without any transformation11
and that trading activities are measured regardless whether done as main or secondary
activity.

Trade services are generally divided into wholesale and retail sale. The ESA 95
Input-Output Manual (Eurostat, 2002) states that wholesale consists of re-selling new
and used goods to retailers, industrial, commercial, institutional or professional users,

or to other wholesalers; while retailing includes re-selling of new and used goods
mainly for personal or household consumption. Neither exclusive trade services on sec
ond hand goods, waste and scrap, nor should transit trade be included as trade margins.
Lastly, because of the valuation concepts of imports (cif), no imports of trade margins
need to be considered either.

The compilation of trade margins matrices admits two procedures, either from the
supply side or from the use side. The ESA 95 Input-Output Manual (Eurostat, 2002)

favors the former arguing that data sources can be more likely available**. However, theuse side approach becomes more useful once this issue is solved, at least for the Anda
lusian experience, as we will show later.
Supply-side trade margin matrices

The starting point of this method is trade turnover data derived by surveyed establish

ments, that is, the total trade sales and changing in trading stocks. Sometimes, plausi
ble assumptions should be made to achieve data on total trade margins of the economy(e.g. non-market services industries, recreational and sporting activities, etc.).
The first step would be to distinguish trade revenues between wholesale and retailsale, which can be easy for trade industries but not for the other industries. Even if thatwould be possible, costs of purchased goods for resale may not be required to be sepa

rated between wholesale and retail trade. Hence, the subdivision of trade revenues into
wholesale and retail trade turnover must be done by using again plausible assumptions
when no survey based data are available. For instance, trade sales of restaurants andhotels can be ascribed to retail trade; and trade activities of advertising agents towholesale trade. Whether such trade turnovers correspond to one or to another will depend normally on the kind of industry.
Wholesale industries are classified in the industry classification NACE Rev. 1 under division 51, retail industries under division 52 and a mixture of both wholesale andretail trade activities under division 50, "sale, maintenance and repair of motor vehicles

and motorcycles, and retail sale of automotive fuel".
The second step consists of subdividing trade turnovers by products or group ofn However, certain manipulations such as sorting, mixing, breaking bulk, and repacking for distribution
in smaller lots are included.

** Van den Cruyce (2004) also constructs a use-side trade margins matrix for Belgium but only makes a
distinction between distributive channels (producers, wholesalers and retailers) in the case of imports
and exports. In his approach, the valuation table of trade margins is compiled simultaneously withthe use table of imports.

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Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

products, which would result in two trade turnover matrices industries by products, one

for wholesale activities and one for retail trade. Here, again, plausible assumptions areusually required in case non-trade industries because of their lack of such data. Not
surprisingly, estimating trade turnover by products is also a difficult task for manybranches in the trade industries, generally when a lot of goods are traded (i.e. nonspecialised supermarkets) or in some wholesale cases, due to the higher level of hetero

geneity products sold. A possible solution proposed by the ESA 95 Input-Output Man
ual is to get some information by asking selected units with important trade turnovers.
The following step is to transform the trade turnover matrices by multiplying themby the assumed product margin ratios, which are defined as the share of a trade margin
in relation to the trade turnover. Such ratios can be defined at the level of products (orgroup of products) or at the level of industries. Particularly, the ESA 95 Input-Output
Manual favors the product approach because it seems to be the best approximation toreality.

Hence, the next step would be to search potential sources of product specific mar
gin ratios, both for wholesale and for retail trade. An easy way to estimate them would

be to use the surveyed margin ratios of single trade branches as proxies. So, one could
use the margin ratio of the retail trade branch with dairy products as the typical retailmargin for dairy products. Of course, very detailed data would be needed. Having es
tablished the product specific margin ratios, it is only a matter of multiplication to ob
tain the trade margins matrix, assuming implicitly that each specific ratio is valid in allindustries trading that product.

The last step would be to compare the above estimated trade margins by industries
with the survey based trade margins by industries. There should be surely differences
between them, which can be ascribed to errors in the assumptions made so far on the
trade turnover matrix, the subdivision between wholesale and retail trading, the productmargin ratios and the product technology assumption. Next, the corresponding com
piler should check the data and the assumptions made accordingly.

It should be noticed that the supply-side method for constructing trade margins
matrices has to deal with some uncertainties such as weak databases, changing formsof supply of tradable goods, e-commerce, etc. Nevertheless, some advantages should berecognized. The supply-side method allows checking trade sales and trade margins byproducts with the respective surveyed supply of these products; and the distributive
channels, the product specific ratios as well as the size of total trade margins by prod
ucts are taken into account.

In short, as stated by the ESA 95 Input-Output Manual (Eurostat, 2002), "thiscompilation method should thus be followed as much as possible depending on thedata sources (...)".
Use-side trade margin matrices

From the use-side means that our main objective is to estimate the share of trade margins included in each cell of the use table at purchasers' prices. These shares depend
mostly on the typical product margin ratio (as in the supply-side method) and on the
distributive channel of each product-flow, which is rarely available by asking establish
ments and other users. Data availability seems to be again crucial. Particularly, fromthe use-side it seems to be even worse because of the ignorance of the buyer about theA use-side trade margins matrix for the Andalusian economy

125

trade margin incorporated and the previous distributive channels involved for eachproduct before the final seller. Notwithstanding the difficult task of finding reliable data
sources, plausible assumptions and the balance with estimated total supply of the trade
margins should be made, as in the supply-side method.
According to the ESA 95 Input-Output Manual (Eurostat, 2002) the following information is needed: (1) for each single element of the use table at purchasers' prices,the distributive channel involved, if that exists; and (2) the relevant margin ratios of the

products. Most of these data are usually unknown for statistical offices and therefore,plausible assumptions are required, particularly, on the distributive channel, on the dif

ferent trade margin ratio of certain products between users, and on the distinction be

tween wholesale and retail trade. For instance, intermediate consumption, capital formation and inventories usually involve mostly wholesale trade margins than private
consumption, which is more likely connected with retail trade margins.

Once the above information is obtained, the resulting use-side trade margins ma

trix must be checked with the total supply of trade margins by products, as in the
supply-side method. Having achieved final use-side trade margins matrices, they only
have to be used for deducting margin values for each industry and final demand com

ponents from the use table at purchasers' prices, and then allocate them to the trade
margin products according to the corresponding classification. Checking overall plausi
bility is advisable.

3 The Andalusian experience
The high availability of data sources from surveyed trade establishments allows the In
stitute of Statistics of Andalusia (IEA) to construct a use-side trade margins matrix.

The IEA's trade survey collected information about 4,858 trade establishments; 2,999
retailers, 1,207 wholesalers, and 652 both wholesalers and retailers of motor vehicles
and motorcycles and retailers of automotive fuel. The aim of this section will be to ex
plain the whole procedure that has been carried out with that purpose.
Estimating specific trade margins ratios

Surveyed trade establishments were divided into three groups according to the Classifi
cation of Products Activity (CPA) division 50, 51 and 52, that is, both wholesale andretail trade of motor vehicles and motorcycles as well as retail trade for automotive
fuel, wholesalers, and retailers, respectively. They were asked for trade sales and costsof goods for resale by products as well as changes in stocks. Consequently, specifictrade margins ratios for each CPA division were available. They were derived by divid

ing the difference between trade turnover and costs of goods purchased by the total

trade sales for each product and for each surveyed establishment. Of course, some adjustments were needed to ensure full coverage of trade margins supply because of underreporting, sampling, hidden economy and other additional information. Notice thatthese estimated trade margins ratios are assumed to be the same for the trade secondary
activities of the rest of the economy, that is, the specific trade margin ratio for i.e.
shoes is fixed irrespective what kind of establishment may sell them. That seems to be

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TABLE 1

SPECIFIC TRADE MARGINS RATIOS (PERCENTAGES)

Product

Description

1

Fruits and vegetables

2

Olive and vine

CPA

CPA

CPA

Division

Division

Division

50

51

52

n

wi

n

16.23

24.37

3

Other agriculture and related services

19.69

24.71

4

Livestock and hunting

16.08

15.89

5

Forestry and related services

22.77

14.44

6

Fish and fishing products

15.63

20.02

7

Coal mining

34.80

16.60

8

Metallic minerals

25.45

-

9

Non-metallic and non-enegetic minerals

3.30

-

10

Meat and meat products

16.76

24.79

11

Canned and preserved fish

13.72

26.05

12

Canned and preserved fruits and vegetables

13.97

22.49

13

Fats and oils

21.85

17.85

14

Milk and dairy products

14.70

20.45
17.34

15

Grain mills, bakery, sugar mills, ...

18.91

16

Pet food

18.74

12.12

17

Miscellaneous food products. Tobacco products.

12.00

39.64

18

Wines and alcoholic beverages

21.93

16.54

19

Beer and soft drinks

18.14

21.65

20

Textile mill products

25.22

33.49

21

Clothing products

21.15

49.53

22

Leather tanning, leather products and footwear

33.71

35.70

23

Cork and wood products

21.17

29.72

24

Paper and allied products

22.69

28.30

25

Printing, publishing and editing services

20.56

28.96
22.48

26

Petroleum refining products

27

Basic chemical products

13.55

28

Other chemical products

6.72

26.79

29

Rubber and plastic products

23.87

42.75

30

Cement, lime and allied products

21.57

19.14

31

Ceramics, clay, bricks and other products for building

17.80

24.43

32

Stone and glass products

26.83

35.00

33

Primary metal products

13.65

21.85

34

Fabricated metal products

22.19

25.15

35

Machinery and mechanic equipment

19.46

33.34

36

Computers and office equipments

15.74

20.55

37

Electrical and electronic machinery

15.57

21.12

38

Electronic materials, radio and television equipments

15.69

18.70

39

Professional and scientific instruments

22.39

56.60

40

Motor vehicles transportation equipment

36.24

—

41

Naval transportation and repairing services

42

Miscellaneous transportation equipment

43

Furniture

44
45

12.00

19.28

—

24.50

25.25

29.91

Miscellaneous manufactured products

20.40

32.40

Recycling products

25.32

Source: own elaboration_

A use-side trade margins matrix for the Andalusian economy

127

a plausible assumption. Table 1 shows the results for the Andalusian economy in percentages.

Distributive channels

The distributive channels are clearly the unknown component of the required informa
tion for constructing a use-side trade margins matrix. Usually, buyers do not knowwhether a product has been sold through retailers, wholesalers or none of them. How
ever, this lack of available information is solved by an exhaustive study for the Spanish
region Castilla y Leon (CEH, 1990), where for each element of the use table at pur
chasers' prices, the most frequent type of distributive channel is identified. Neverthe
less, Rueda-Cantuche (2005) is proposing in collaboration with the Institute of Statis
tics of Andalusia a new procedure to improve future identifications of distributive channels using survey-based information.
TABLE 2

DISTRIBUTIVE CHANNELS
Description
1

Imports/Producers —► Consumer/Exports

2

Imports/Producers -* Retailer -► Consumer/Exports

3

Imports/Producers —* Wh. on supply —* Wh. on demand —* Retailer —► Consumer/Exports

4

Imports/Producers —► Wholes, on supply —► Wholes, on demand -*• Consumer/Exports

5

Imports/Producers -+ Wholesaler on demand -* Retailer -► Consumer/Exports

6

Imports/Producers —► Wholesaler on demand —* Consumer/Exports

Source: own elaboration.

Then, we distinguish six different distributive channels (see Table 2). Notice thatchannel 1 does not imply trade margins at all, since no trade activities are involved. On
the contrary, channel 3 implies three steps before the product is purchased by the con
sumer. Notice that we distinguish specifically two types of wholesalers only in agricul
tural products. For instance, fruits and vegetables may be gathered and sold by awholesaler situated next to producers (on supply) and be delivered later on by anotherwholesaler located next to final consumers (on demand). This is the main reason to include channels 3 and 4. Channels 4 and 5 involve two steps and channels 2 and 6,
only one step. The Castilla y Leon's study (CEH, 1990) provides us with the most fre
quent kind of channel involved in each element of the use table at purchasers' prices.

Hence, the total share of trade margins for each one of the elements can be estimatedas follows.

Estimating total share of trade margins

Let us denote u% as the use of product / by industry j at purchasers' prices; and r, andWi as the specific retail and wholesale trade margin ratios for product i, respectively.

Since trade margins are included in purchasers' values accumulatively, in the case of
three-step distributive channels, we have that:

Kg - Kg r, = k5 (1 - r,)

(1)

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Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

would correspond to the price paid by retailers to those wholesalers situated next to fi
nal consumers. Analogously,

i4 (1 - r,) - *4(1 - r,) wi = i4 (1 - r,)(l - Wi)(2)would represent the price paid by the wholesaler placed on demand to the wholesaler

situated next to producers. And lastly, uH} (1 - r,)(l - w,)2 will stand for the price paidby the wholesaler on supply to the producers. Moreover, if this expression is operated
mathematically, we can obtain that:uS (1 - r,)(l - Wi)2 = ii& (1 - r,)(l - (2wi - w2)) =(3)= ug (1 - r,)(l - Wi (2 - Wi)) == 4 (1 - (n+Wi (2-wd - Wi n (2 - w,))) == ii5(1 -(r,+(l - r,) (2 - wd Wi)).
Hence, the total share of trade margins for the use of a product that has been delivered through channel 3 would be r, + w, (1 - r,)(2 - wi). From this total, r, would be
ascribed to retail trade and the rest w,(l - r,)(2 - wi) to wholesale trade.
The case of two-step distributive channels admits two different types. Channel 4 isbasically a particular case of the three-step procedure but with r, = 0. Therefore, the resulting formula would be wt (2 - wi). In case channel 5, it can be obtained that wg (1 ri) is the price paid by retailers to wholesalers and furthermore, ug (1 - r,)(l - wi)stands for the price paid by wholesalers to producers. Let us operate with this last ex
pression, it yields:

u% (1 - r,)(l - wd = uSr (1 - (r, + Wi - w,))

(4)

which accounts for the total share of trade margins of a product that has been deliveredby channel 5. That is,r, + Wi - nwh where r, would be ascribed to retail trade and therest Wi - nwi to wholesale trade.

One-step distributive channels can be considered particular cases of the two-stepprocedure. Channel 2 can be derived just when r, = 0, and analogously, channel 6 canbe obtained when wt = 0. In the first case, all trade margins must be ascribed to retailtrade and in the second, to wholesale trade exclusively. A brief summary of the resultspresented so far can be seen in Table 3.

TABLE 3

VALUES FOR COMBINED AND SINGLE TRADE MARGINS RATIOS^,,,
Channelrw.
Type

Total share of trade.

_._
Retail„„ ,Wholesale1

No trade

0

0

0

2

Single

r,

n

0

3

Combined

rrhWi(l-n)(2-wdnWi(l-n)(2-wd

4SingleWi{2-wi)0

Wi(2-wi)

5

Combined

n+ Wi - n winWi-nwi6SingleWi

0Wi

Source: own elaboration.

margins (m£ or mi)A use-side trade margins matrix for the Andalusian economy

129

Adjusted estimated shares of trade margins

However, intermediate uses rarely involve retail trade activities and it would be too rig
orous to admit no retail trade sales at all in such product flows. With respect to final
consumption, it would be the opposite way. A product would be rarely delivered to fi

nal consumption through exclusively wholesale trade activities. With the purpose ofsolving this issue, we have designed the following adjustment procedure to add retailtrade margins to each element of the use table and to deduct retail trade margins toeach element of the final consumption vector. Recall that in intermediate consumption,

capital formation, inventories and exports, wholesale margins can be involved but notretail sale margins§§ and that private consumption performs the other way round.
Hence, let us divide our six distributive channels into two different groups: thosewhich combine wholesale and retail trade margins (combined channels); and those,which do not combine them (single channels) but they should be. If we denote etc as
the share of u% which is delivered through combined channels; and as as the share of w£

which is delivered through single channels, such that ac + a$ = 1, then the total single

channel share of trade margin flows would be astn^uf^ with raj as the total share of
trade margins included in the use flow (wj) in the case of single channels, i.e. regarding
channel 4, it yields raj = w, (2 - wl) and, raj = r, and raj = w, in the cases of channels 2

and 6, respectively. Notice that the value of raj will depend on the corresponding single
channel involved (see Table 3).

Regarding combined channels, the total share of trade margins included in intermediate uses, acm-jUfj can be expressed as"*:acm*ut= (raj - raj) ctcH*+m$acut,(5)with raj as the total share of trade margins included in i& in the case of combined
channels. This time, raj = r,+w,(l - r,)(2 - w,) for channel 3 and raj = r&wi - r,w, forchannel 5. Notice also that raj will depend on the particular case of combined channel
involved for each element of the use table (see Table 3).

If, for instance, we assign single channels to wholesale trade, as mostly for intermediate uses, the total of wholesale trade margins flows of tig would be:

asmfjUfj + actntutj = (as + ac) m*ji4 = n%v5h(6)since ac + as = 1. And the total of retail trade margins flows of uHj would be then (raj raj) acifij.

Finally, the total trade margins incorporated to each element of the use table
would be the sum of retail and wholesale totals of trade margins flows, that is, rajwg +(raj-raj) acvHh

Consequently, by choosing a proper ac some additional retail trade margins will

be included in the corresponding use flow and therefore, in the total use-side estimatedsupply of trade margins. Our starting point would be the case where ac = 0 and as = 1.

Notice that the total amount of wholesale trade margins won't change because, though
we have assumed a new step further on the distributive channel, wholesale trade activi§§ There could be exceptions like petroleum refining products, where retailers can play an importantrole.

*** Notice that for all i andy, it is verified that m% > mij.

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Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

ties are always present for every element of the use table.
In case of intermediate uses (see Table 4), combined channels remain unchanged
because they indeed include retailers and not only wholesalers within the transactions.

The single retailer distributive channel (channel 2) and the one with no trade marginincorporated (channel 1) also has no variation at all. Hence, only in the cases of channels 4 and 6, we find that the (r, - nwi (2 - w,)) etc and (r, - nwi) etc elements, respec

tively, would stand for the additional retail trade margin that has been incorporated tothe corresponding distributive channel as a result of the adjustment procedure. For detailed formulation see Table 4m.
TABLE 4

ADJUSTED VALUES FOR COMBINED AND SINGLE TRADE MARGINS RATIOS(INTERMEDIATE USES)_.
_
Channel_Type

Total adjusted share of trade.

_ A ..
Retail__„ .
.
Wholesale1

No trade000margins2

Single

r,

n

0

3

Combinedr,+w,(l-r,)(2-w)

nw/(l-n)(2-w,-)

4

Single(n -n Wi (2-wd) ac +wt (2-w,)(r;-nwi(2-Wi))ac

w,(2-w/)

5

Combined

n +Wi - n winWi-nwi6Single(n—r<Wi)dc+Wi(n-hwdac

Wi

Source: own elaboration.

Final consumption admits no such results (see Table 5). In this case, a combined
channel is the point of departure because it is generally assumed that households

mostly buy to retailers and not directly to wholesalers, as in intermediate uses. Then,by choosing a proper as we will deduct some retail trade margins by removing the last

step of the corresponding distributive channel and consequently, the initial use-side es
timated total supply of trade margins will be reduced as well.
Let us define dcm%u\ as the total share of trade margins included in each of theelement of the final consumption element, in the case of combined channels. Noticealso that the total share of trade margins included in single channels would be asrrijuSj

for final consumption. Hence, the total trade margins to be incorporated in each ele
ment of the final consumption vector would yield: acrrijuSj + asrrijuly, where the second
term can be expressed as: asmyi4 - Orij - mj) otsifih and consequently,
ctsrrijuHj + asmijitfj - (m^ - mj) tfswj = mM - (m^ - m£) asifv(7)

For combined and single distributive channels, the total adjusted shares of wholesale and retail trade margins of u% can be seen in Table 5. In the case of final consump
tion, single channels remain unchanged because the adjustment procedure only aims to
deduct retail trade margins from combined channels. Channel 1, where no trade mar-tnFor interpretation purposes, we have dropped m)c and mjs symbols from Tables 4 and 5.

A use-side trade margins matrix for the Andalusian economy

131

gins are included, also has no change at all. However, in case of channels 3 and 5, ther,(l - as) element would represent a lower value for the corresponding retail trade mar
gin.

Furthermore, an additional result can be derived from our approach. That is, thetotal trade margins associated to each element of the use table (intermediate uses and
TABLE 5ADJUSTED VALUES FOR COMBINED AND SINGLE TRADE MARGINS RATIOS(FINAL CONSUMPTION)r^o««oi
Channelt\
Type

Total adjusted share of trade
J.

RetailWholesale1

No trade000margins2

Single

r,

n

0

3

Combinedn(l-as) + Wi(\-n)(2-Wi)

nil-as)w,(l-r,)(2-w/)

4

Singlew/(2-w,)

0w,(2-w,)

5

Combinedn(l-as) + Wi-nwin(\-as)w.-nwi6Singlew,

0w,

Source: own elaboration.

final consumption) can be expressed as a weighted average of the corresponding trade
margins of both single and combined channels, respectively. The proofs can be seen in
Appendix 1.

Constructing a use-side trade margins matrix

Once specific retail and wholesale trade margins ratios are estimated by products andonce distributive channels are identified for each element of the use table at purchasers'
prices, a use-side trade margins matrix thus can be estimated by multiplying each cor

responding share*1* of either retail or wholesale trade margins by their respective uses.
The final results consist of two different trade margins matrices; one for retail trade
margins and other for wholesale trade margins, both by products and industries (seeAppendix 2 for a non-adjusted numerical example).

4 Conclusions
The main purpose of our work has been to develop a more detailed procedure to con
struct a trade margins matrix, particularly for the Andalusian economy, and which isbased on the use side method proposed by the ESA 95 Input-Output Manual (Eurostat,2002). Solving the data availability problem stated in Eurostat (2002) and assuming
usual errors involved in trade databases (e-commerce, changing forms of supply, etc.),
mFor the Andalusian Input-Output Framework 2000, the final adjustment procedure assumed 1% of re
tail deliveries in case of intermediate uses and 1% of exclusively wholesale deliveries in the final
consumption vector, except for petroleum and refining products.

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Journal of Applied Input-Output Analysis, Vol. 11 & 12,2006

the Institute of Statistics of Andalusia has constructed a use-side trade margins matrix.

Perhaps, it could have been interesting to compare the results with the supply-side ap
proach but, in any case, this may be a matter for future research.

Finally, the resulting use-side trade margins matrix will be used to transform theuse table from purchasers' prices to basic values within the Andalusian Input-Output
Framework 2000. Input-output compilers may profit from reading this work.

Acknowledgements
The suggestions of referees are gratefully acknowledged and all remaining errors are
exclusively owned by the authors. We also acknowledge the helpful comments of atten
dants to the Input-Output and General Equilibrium Modeling: Data, modeling and Pol

icy Analysis Conference held in Brussels in 2004 and to the 31st Meeting of Regional
Studies held in Alcala de Henares (Madrid) in 2005. The views expressed in this paper
belong to the authors and should not be attributed to the European Commission or its
services.

Appendix 1
Total trade margins associated to each element of the use table (intermediate uses andfinal consumption) can be expressed as a weighted average of the corresponding trade
margins of both single and combined channels, respectively.
ProofIntermediate uses

Let us define the total trade margins incorporated to each element of the use table as:m\ju% + (ml - m*j) ctcuij, then it is straightforward that:ug + (ml - m\i) otcuij = rajwg + mUfltcuHj - m^fltcu^(8)

pij^ (I-etc) mlu%

D
Final consumption

The total trade margins incorporated to each element of the final consumption vector
is: m£< - (ml - mj) tf«i& and then:- (ml - ml) Q>suHj = mSwg - miflsifij + mJffsKg(9)

1j + (1 - as) mlu%

Appendix 2
Non-adjusted Numerical Example for the Estimation of a Trade Margins Matrix
Let us suppose a fictitious economy with two industries and three tradable commodi

ties. Intermediate uses (m?), specific trade margins ratios (r, and wi) and the corresponding distributive channels are shown in the following tables:A use-side trade margins matrix for the Andalusian economy

133

TABLE 6

Use Table at Purchasers' Prices
Industry A

Industry B

Commodity 1

10

20

Commodity 2

5

15

Commodity 3

15

5

TABLE 7

Specific Trade Margins Ratios
RetailWholesaleCommodity 1

0.2

0.1

Commodity 2

0.5

0.3

Commodity 3

0.1

0.2

TABLE 8Distributive channels
Industry A

Industry B

1

5Commodity 2

3

6

Commodity 3

42

Commodity 1

Hence, if industry A buys commodity 1 through channel 1, no trade margins
would be involved. On the contrary, the purchases of commodity 2 by industry A are

made through channel 3, which includes two wholesalers and one retailer. Then, the total trade margins incorporated within this transaction would be, according to Table 3:
0.5 + 0.3 (1 - 0.5)(2 - 0.3) = 0.755, where 0.5 corresponds to wholesale and 0.255 toretail.

Another example would be the consumption of commodity 3 by industry B

through channel 2. There, only retail trade margins are included (0.1). In case of transactions of commodity 2 by industry B, only wholesale trade margins are involved (0.3)

and therefore, no retail trade margins are taken into account. Lastly, the purchases ofcommodity 1 by industry B and of commodity 3 by industry A, are analogous. Bearing

these results in mind, the resulting total, wholesale and retail trade margins ratios
would yield:
TABLE 9Total Trade Margins Ratios (m«)
Industry A

Industry B

Commodity 1

0

0.28

Commodity 2

0.755

0.3

Commodity 3

0.36

0.1

134

Journal of Applied Input-Output Analysis, Vol. 11 & 12, 2006

TABLE 10Retail Trade Margins Ratios
Industry A

Industry B

Commodity 1

0

0.2

Commodity 2

0.5

0Commodity 3

00.1

TABLE 11Wholesale Trade Margins Ratios
Industry A

Industry B

Commodity 1

0

0.08

Commodity 2

0.255

0.3

Commodity 3

0.36

0

And finally in absolute terms,
TABLE 12

Total Trade Margins (absolute values)
Industry A

Industry B

Commodity 1

0

5.6

Commodity 2

3.775

4.5

Commodity 3

5.4

0.5

TABLE 13Retail Trade Margins (absolute values)
Industry A

Commodity 1

0

Commodity 2

2.5

Commodity 30Industry B

0.5

TABLE 14Wholesale Trade Margins Ratios (absolute values)
Industry A

Industry B

Commodity 1

0

1.6

Commodity 2

1.275

4.5

Commodity 3

5.4

0

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