PWC Matrices: new method and updated Base Matrices...not optimal for modelling purposes including...

Analysis & Strategy

REPORT

PWC Matrices: new method and updated Base Matrices

Final Report

Christer Anderstig and Moa Berglund, WSP, Henrik Edwards, SWECO, and Marcus Sundberg, KTH

2015-05-18

Title: PWC Matrices: new method and updated Base Matrices – Final Report

WSP Sverige AB

Arenavägen 7

SE-121 88 Stockholm-Globen

Phone: +46 10-722 50 00

E-mail: [email protected]

Corporate identity no.: 556057-4880

Reg. office: Stockholm

www.wspgroup.se/analys

http://www.wspgroup.se/analys

Analysis & Strategy 3

Table of Contents

SAMMANFATTNING ............................................................................... 5

1 BACKGROUND AND PURPOSE ................................................... 7

1.1 Use of PWC matrices ...................................................................... 8

1.2 Matrices currently used ................................................................. 10

1.3 Previous ideas for PWC matrices method ..................................... 12

1.4 Introduction to new suggested method ......................................... 13

2 COMMODITIES AND SECTORS .................................................. 15

2.1 Industry sector classification ......................................................... 15

2.2 Commodity classifications ............................................................. 16

2.3 Deriving the keys ........................................................................... 20

3 METHOD FOR PWC MATRIX GENERATION ............................. 22

3.1 Main data sources ......................................................................... 22

3.2 Methodology .................................................................................. 24

3.3 Estimation of PWC models ............................................................ 27

4 ROW AND COLUMN ESTIMATES ............................................... 34

4.1 Description of data sources ........................................................... 36

4.2 Allocation of production and consumption to municipalities .......... 42

4.3 Price adjustments of estimated consumption ................................ 44

4.4 Estimation of imports ..................................................................... 44

4.5 Wholesale (W) ............................................................................... 44

4.6 Results, total values for P, C, W, exports and imports .................. 49

5 PREDICTION OF BASE YEAR TON MATRICES ......................... 50

5.1 Steps going from value 2010 to weight 2012 ................................ 50

5.2 Commodity flows 2012 .................................................................. 52

6 CONVERSION OF BASE YEAR TON MATRICES INTO

SAMGODS FORMAT .................................................................... 53

6.1 Results .......................................................................................... 54

6.2 Introduction of singular flows ......................................................... 62

6.3 Domestic iron ore PWC-matrix elements ...................................... 64

6.4 Adjustments based on project committee meetings ...................... 65

7 ADDITIONAL ADJUSTMENTS ..................................................... 72

8 CONCLUDING REMARKS ........................................................... 83

4 Analysis & Strategy

REFERENCES ...................................................................................... 84

Appendix 1 Original micro-level approach ....................................... 85

Appendix 2 Proposal to Statistics Sweden ..................................... 88

Appendix 3 Costs, tonne kms and tonnes (all in millions) ............ 100

Appendix 4 Prediction model script for Matlab ............................. 106


Sammanfattning

Syftet med detta projekt har varit att ta fram en ny (uppdaterad) metod för att ge-

nerera de matriser som för ett basår beskriver flöden av olika varugrupper, samt

att ta fram sådana PWC-matriser (”Production – Wholesale – Consumption”) för

basår 2012. I viss utsträckning bygger den nya metoden vidare på både den me-

tod som för närvarande är i bruk, och en tidigare metodansats från 2004. Vidare

har det inom ramen för ett delprojekt även tagits fram en ny modell för att pro-

gnosera varuvärden.

PWC-matriserna utgör huvudsakliga indata till Samgods-modellens prognoser av

godstransporter. Matriserna beskriver efterfrågan på godstransporter från en plats

till en annan, så att matriselementet (r, s) ger mängden varor i ton som transporte-

ras från zon r till zon s. Samgods-modellen allokerar dessa varutransporter till

olika transportlösningar och rutter, baserat på lägsta generaliserad kostnad.

PWC-matriserna avser flöden av varugrupper; för närvarande arbetar Samgods

med 34 varugrupper. För att kunna generera dessa PWC-matriser, exempelvis flö-

den mellan kommuner i Sverige, måste vi emellertid använda datakällor som i hu-

vudsak avser de branscher som genererar produktion, förbrukning och handel av

de olika varugrupperna. För detta ändamål har det tagits fram nycklar på den mest

detaljerade branschnivån (SNI 5 siffror) som länkar varugrupper till branscher.

Föregående PWC-matriser använde grövre nycklar, baserade på SNI 2 siffror.

För produktion och förbrukning inom mineralutvinning och tillverkningsindustri

har Statistiska Centralbyrån (SCB) med stöd av IVP (Industrins varuproduktion)

och INFI (Industrins insatsvaruförbrukning) tagit fram data som omvandlar

(”översätter”) produktion per varugrupp till producerande bransch, respektive för-

brukning per varugrupp till förbrukande bransch, med bransch definierad av

SNI2007 5 siffror.

För övrig varuproduktion och varuförbrukning har översättningen varugrupp-

bransch genomförts i huvudsak med stöd av detaljerade uppgifter hämtade från

SCB:s Nationalräkenskaper. SCB:s Utrikeshandelsstatistik har tillhandahållit data

som för respektive varugrupp ger information om mottagande land för svensk ex-

port och avsändande land för svensk import.

Allokeringen av P, W och C till kommuner kan, med tillgängliga data, uppskattas

med ledning av sysselsättningsdata. Uppskattningen har genomförts med stöd av

data för sysselsatta per kommun och detaljerad bransch, dvs. SNI2007 5 siffror.

För mineralutvinning och tillverkningsindustri används data för sysselsättning

inom varuhanterande yrken, för att göra åtskillnad mellan varuproduktion och

tjänsteproduktion inom respektive bransch.


PWC-matrisernas marginalvillkor, de rad- och kolumnsummor som uppskattats

vid allokering till kommuner enligt ovan, är uttryckta i MSEK. Omvandlingen till

marginalvillkor uttryckta i Ton har genomförts med de varuvärdesberäkningar

som tagits fram inom ramen för arbetet med ny modell för varuvärdesprognoser.

Prediktionen av elementen för basårets PWC-matriser sker med de skattade PWC-

modeller som tagits fram inom projektet. Dessa estimerade modeller använder ti-

digare genomförda varuflödesundersökningar (VFU) som huvudsaklig datakälla.

De modeller som utvecklats kan beskrivas som gravitationsmodeller, där varuflö-

den mellan kommuner förklaras av, t ex, tillgång, efterfrågan, transportkostnader,

tillgänglighet till hamn, storleken på arbetsplatser i olika kommuner, för att nämna

några faktorer som kan påverka flödenas storlek. I modellskattningen används

även noll-observationer som faktiska observationer, i stället för att endast använda

positiva värden (observationer större än noll). Vidare är modellskattningarna ge-

nomförda på flöden i ton. Föregående PWC-matriser var skattade på monetära

flöden, som senare omvandlades till ton, vilket kan vara problematiskt eftersom

VFU-data för handel i värde och handel i ton inte är perfekt korrelerade.

Efter att basårets PWC-matriser har predicerats, med skattade PWC-modeller till-

lämpade på 2012 års marginalvillkor, skall matriserna anpassas till Samgods-

modellen. Anpassningarna avser dels att dela upp efterfrågan i varje relation till

s.k. ”firm-to-firm” = f2f-efterfrågan (= efterfrågan mellan individuella företag i

alla förekommande par av PC-områden), dels att föra in observerade, större, exo-

gena flöden i matriserna. Den senare delen avser främst järnvägsflöden, men om-

fattar även en del kända transitflöden. Exogent införda volymer i matriserna kom-

penserar vi för genom att ta bort motsvarande volymer från den modellberäknade

efterfrågan.

För uppdelning av efterfrågan på f2f-nivå används en kombination av CFAR

(Centrala Företags- och ArbetsställeRegistret), antal anställda i olika SNI-

branscher per kommun, nyckel mellan SNI-branscher och varugrupper i Samgods,

varuflödesundersökningens observerade sändningsstorlekar och antagandet att

sändningsstorlekar väsentligen bestäms av den klassiska kvadratrotsformeln för

att beräkna ekonomiska orderkvantiteter (Wilson-formeln). Företagsstorlekarna

indelas i små, medelstora och stora. På relationsnivå ger det upp till 9 kombina-

tioner. Utöver dessa finns en kategori för mycket stora flöden, s.k. singulära flö-

den.

Den resulterande efterfrågan bedömdes av Trafikverket leda till ett för högt trans-

portarbete jämfört med befintlig statistik. Av detta skäl balanserades vissa varu-

grupper om på ett sådant sätt att genomsnittsavstånden mellan P och C förkortades

en del, med oförändrade marginalvillkor. Efter dessa operationer gjordes en av-

stämning mellan medelavstånden för PWC2012-matriserna och varuflödesunder-

sökningens medelavstånd (beräknat med modellens avståndsberäkningar). Avvi-

kelserna bedöms ligga inom felmarginalerna.


1 Background and purpose

This project aims to produce an updated method to generate Production – Whole-

sale – Consumption (PWC) base matrices, together with a set of PWC matrices for

base year 20121. Apart from the method to estimate the matrices currently in use,

there is an earlier approach from 20042. The new method proposed in this project is

to some extent drawing on both these approaches and aims to make best possible

use of the statistics available on production, trade and consumption of commodities

in Sweden. Furthermore, as a separate part of the project a new model for forecast-

ing average commodity values (1000 SEK per ton) has been developed3.

In this first chapter we start by describing the use of the PWC matrices, implying a

specification of requirements for the matrices. Next follows a discussion on previ-

ous approaches, including the method used to generate current matrices. A short

summary of the ideas from the 2004 project is presented in section 1.3, and section

1.4 gives an introduction to the new suggested method.

Chapter 2 gives a thorough description of the process of generating necessary data

for commodity groups by use of various data sources. More specifically, in order to

make use of available data and for future purposes to estimate forecasting matrices,

we need correspondence tables for allocating production value per industry sector

to commodity classes. Tables previously used are on an aggregate industry sector

classification level, and have been derived from foreign trade statistics, which is

not optimal for modelling purposes including domestic trade. As a part of the PWC

generation method, we derive new correspondence tables.

Chapter 3 gives a more detailed presentation of the new method for generating

PWC-matrices and its background. Data sources are described in section 3.1., the

methodology is discussed in section 3.2, and a thorough description of estimation

procedures is given in section 3.3. As the suggested method can be seen as a “se-

cond-best” approach, we present this project’s original idea – to produce matrix

row and column constraints based on micro-level data – in Appendix 1.

Chapter 4 presents data sources and estimates of the row and column constraints

actually used. Chapter 5 is describing the procedures to apply the estimated row

and column constraints, as input to the estimated PWC matrix models, to get the

predicted base year ton matrices. Chapter 6 is dealing with the conversion of these

matrices into the format used in the Samgods model, taking “singular flows” and

transit into account. Chapter 7 is about the background and ways to make some

required adjustments. Finally, Chapter 8 gives some concluding remarks.

1 When the project started, in early 2013, the base year was 2006.

2 Anderstig et al (2004)

3 ”Nya varuvärden 2040 - data, metod och resultat” (2015-02-06)


1.1 Use of PWC matrices

The PWC matrices constitute the main input data to the Samgods freight transport

forecasting model system. The matrices describe the demand for transport of goods

from one place to another, so that the matrix element (r, s) gives the amount of

goods to be transported from zone r to zone s. The amounts should be specified in

economic value (SEK) as well as weight (tons). The Samgods model is then used

to allocate the goods to different transport solutions on different routes, based on

the lowest generalised cost.

The model operates for 34 commodity groups in parallel, which implies that there

has to be a PWC matrix for each commodity group. The zones r, s are equivalent to

municipalities within Sweden (there are 290). For areas close to Sweden, countries

are divided into zones, while zones in more remote areas consist of several coun-

tries. In total, there are 174 defined zones abroad, ranging in size from counties to

continents. The matrices thus describe domestic as well as border-crossing

transport demand, see Figure 1.

Figure 1 Schematic picture of a PWC matrix

There is also a part describing transit traffic, i.e. transports with origin and destina-

tion outside Sweden, but passing through Sweden. The transit demand primarily

consists of data converted from the old Samgods model that used the STAN model


for network analysis. Some additional demand values have been added to the ma-

trices, but it is an area that needs more attention.

Thus, the sum of all elements in a row of the matrix (D), gives the amount of

commodities produced in the corresponding municipality and consumed some-

where in Sweden. For the import (M) part of the matrix, the row sum gives the

amount of commodities imported to Sweden, produced in the corresponding zone

abroad.

Equivalently, the sum of all elements in a column of the matrix (D) gives the

amount of commodities to be consumed in the corresponding municipality, origi-

nating from somewhere in Sweden. For the export (X) part of the matrix, the row

sum gives the amount of commodities exported from a municipality in Sweden,

and consumed in the corresponding zones abroad.

All traded commodities are not transported directly between the producing unit and

the consuming unit. In that case we would have PC matrices. Instead, the goods are

often traded via a wholesale actor, which in this way acts as well as a consumer as

a producer, but of exactly the same commodity. In the final matrices, no distinction

is made between if the receiving unit is the final consumer or a wholesale actor, but

the distinction is made for the sending unit. Therefore, each element of the matrix

also contains information on whether the sending unit is a producer (P) or a whole-

sale actor (W).

Furthermore, sending and receiving units are divided into small, medium and large

companies. This gives 9 possible types of flows by firm size class. In addition, a

10th type of flows is defined by particularly large single-firm flows. These are iden-

tified and declared separately as “singular flows”. In this way, each element of the

matrix holds the information of

1. Origin zone r

2. Destination zone s

3. P and/or W flow

4. Distribution over 10 firm-to-firm type flows

i.e. up to 20 variables for each matrix element (r, s).


1.2 Matrices currently used

Domestic matrices

The domestic matrices are constructed by combining observed up-scaled values

from CFS and a synthetic matrix. The synthetic matrix for each product is estimat-

ed in four major steps4:

1) First a set of regression models for each product and for row and column

sums are estimated; separate models are estimated for flows from producers

(P) and wholesalers (W). The dependent variable for each model is the row

and column sums that were observed in CFS 2001 and CFS 2004/2005. In-

dependent variables are production, intermediate consumption and final con-

sumption for each zone, calculated from national account data disaggregated

over the zones using employment data for each zone and product. Further,

employment data for different industry and trade sectors are used as inde-

pendent variables.

2) Second, for each product the parameters of a model for the cell values are

estimated. These models are of a “gravity” type. The dependent variable is

the observed CFS-flow for each cell and the independent variables are the

relevant modelled row (supply) and column (demand) values, the network

distances calculated from STAN for each matrix cell.

3) Third, the synthetic domestic product matrices are computed.

4) Fourth, for each product the synthetic matrix is combined with observed val-

ues from CFS according to certain rules designed to avoid generating values

for all cells, since this would lead to too many small values. One further aim

is to ensure that a target value, compatible with National accounts, is met for

each product matrix.

Export and import matrices

Like the domestic matrices, export and import matrices are estimated for each

product (34 products including air freight, number 30 is unused). Data on export

and import in value and weight between Sweden and other countries are available

at a very detailed product level in the foreign trade statistics (FTS). These data are

judged to give reliable estimates of the country to country trade flows per product.

However, there is no information at all in the foreign trade statistics on the region-

al distribution of trade, which is required to make it possible to estimate the export

and import matrices.

4 Large demand flows, “singular flows”, are extracted before carrying out these steps, and

they are subsequently inserted at the end of the process.


Fortunately, the CFS databases also cover export and import flows that to a consid-

erable extent also are coded with location of origin and destination, though there

are flaws in the location coding that have to be addressed. Observations on export

and import flows from CFS (2001 and 2004/2005) therefore potentially provide a

source for information on the domestic and foreign regional distribution of trade

flows.

Therefore, the approach to the export and import matrices has been to use FTS-data

to determine the level of trade, and CFS-data for the regional distribution of the

trade at both ends.

One problem is that the number of CFS-observations on foreign trade is rather

small, with the effect that many trade relations that are present in the FTS are very

sparsely or not at all covered by CFS-observations. To handle this certain supple-

mentary rules have been used, intended to generate reasonable distributions even in

cases where there are only very few or no observations for the particular product

and country to country flow.

Thus the export and import matrices are entirely estimated from available data. Un-

like the domestic matrices, no synthetic (modelled) matrices have been used for the

foreign trade matrices.

Transit matrices

The transit matrices are almost entirely based on the earlier transit matrices for

2001 that were produced for the STAN-product groups in 2004. The STAN orient-

ed transit matrices have been distributed among the 33 new products (not including

air freight and excluding number 30), and the flow values for each product have

been recalculated to 2004 level, using the growth rate for Swedish foreign trade

between 2001 and 2004.

Revision of the 2004/2005 base matrices

In a first revision the base matrices constructed were adjusted with the aid of an

entropy model with the purpose to obtain a better fit of goods flow per STAN

product group and NUTS2 – region. Some further adjustments were made to re-

duce the PC-relations with low demand values.

For the infrastructure planning carried out by the National Road Administration

and other infrastructure authorities a few years back, the PWC-matrices were mul-

tiplied by suitable index factors to reflect the estimated transport volume change

from 2004/2005 to the base year 2006.


Strengths and weaknesses in current matrices

Strengths:

Matrices are constructed for all product groups with a reasonable fit to ob-

served, aggregate entities.

When used with the logistics model the results are relatively easy to cali-

brate to obtain reasonable estimates of the nation transport volumes in

terms of ton kilometres.

Weaknesses:

The demand values are probably too spread out from production zones and

to consumer zones, in particular concerning production.

Total demand volumes should probably be adjusted so that trade flows

through the Swedish ports displays a better fit.

There are in some cases too large deviations in demand distributions in the

PWC-matrices as compared to socio-economic data distributions for the

base year.

1.3 Previous ideas for PWC matrices method

In this section we will give a very short summary of the method proposed in the

report by Anderstig et al (2004). Elements of this proposed method will be referred

to in Chapter 3. First, the construction of row and column constraints starts by us-

ing regional economic data, at the municipality level, derived from the rAps data-

base and from using the rAps model system. This step gives the value of P and C at

the industry level (h).

In the next step P (h) and C (h) are converted to commodities (k), by use of IVP-

data (micro), Foreign Trade Statistics (FTS) and input-output tables. Then data on

wholesale trade, also available for commodity (k), can be added to get the row and

column constraints, P+ and C+, still in value terms. Next, an a priori matrix is con-

structed for each k, both in value and weight. This matrix is a combination of two

different matrices:

A) Matrix elements based on direct observations from CFS; B) Matrix elements

based on a gravity model approach, using CFS, row and column constraints and

data on transportation costs (generalised cost from STAN). The B component can-

not be calculated for the diagonal elements (r, r) for which transportation cost data

are missing.

These diagonal elements are calculated by a specific method, the regional purchase

coefficient (RPC) technique. Given the a priori matrices, by use of entropy maxi-

misation the matrix elements are estimated subject to row and column constraints,

P+ and C+. The estimation of matrices in weight is making use of value/weight re-

lations to get the column (consumption) constraints.


Some comments should be made concerning the row and column constraints to be

used. First, from FTS additional row and column constraints will be defined. As

FTS is given both in value and weight, this information can be described in weight

terms.

FTS gives information on Swedish bilateral export and import of commodity k.

Thus, flows from a region abroad should equal Swedish import from this region,

sQr’s = Qr’.,

and flows to a region abroad should equal Swedish export to this region

rQrs’ = Q.s’.

In case regions abroad represent parts of a foreign country, a summation over r’

R’, s’ S’ is added to get the respective constraint.

Another comment concerns differences in the constraint structure, with respect to

reliability of data. The row constraints for production P are more reliable than the

column constraints for C, since the former are taken from data whereas the latter

are based on model calculations.

This difference in reliability will be handled by introducing ‘soft’ constraints for C.

Soft constraints are also suggested to make use of information from CFS, by ag-

gregating observed flows in CFS to larger regions (NUTS II), the regional level at

which CFS is expected to be reliable.

Finally, part of the trade between foreign regions, Qr’s’ , are possible transit move-

ments through Sweden. Although trade flows between non-domestic regions in

general will be ignored, transit traffic through Sweden is treated in the logistics

project and the corresponding matrices must therefore be provided. Some part of

the transit traffic will be represented in the PWC matrices, namely re-export of im-

ported commodities by wholesalers.

1.4 Introduction to new suggested method

Given the above description of previous methodologies for the generation of PWC

matrices, this section is providing a brief overview of the proposed methodology.

In large, the methodology follows the outline of this report. Basically the follo-

wing steps are developed and described in this report:

Conversion Keys

Estimation of PWC matrix models

Production and Consumption estimates

PWC base year predictions

Disaggregation and post-processing of matrices


Modelling goods flows is complicated. One reason is that the demand for goods

flows may be viewed as a derived demand, i.e. goods flows originates from the

need to move goods from one location to another, based on the locations of the

supply and demand for the good. Thus, the basis for a good flow is differently lo-

cated supply and demand.

Therefore, in addition to data directly related to goods flows, it is also important to

consider data related to supply and demand. Statistics related to supply and demand

typically follows different classification systems than statistics related to goods

flows. Conversion keys are developed in order to be able to transfer data related to

one type of classification to the other classification system.

The main data sources for movements of goods are the commodity flow surveys

performed in Sweden. Using this data, PWC models are estimated. The models that

have been developed and are provided in this report are gravity-like models where

the flows between regions are explained by, e.g., the size of supply, demand, and

transport costs, the accessibility to a port, or the size of workplaces located in dif-

ferent regions and handling a particular type of goods, only to name a few factors

that have an impact on the size of flows.

The newly developed models may be applied in predictions, provided new data

related to the explanatory variables are available. In this report it will be described

how to perform predictions of base year matrices for the year 2012.

Given that goods flows are derived demand, and that the models for the PWC ma-

trices have been estimated, the next step is to provide the models with relevant in-

put data. One of the most critical inputs to the PWC matrix models is supply and

demand data. Therefore, much effort has been put into generating production and

consumption estimates for the base year.

After attaining input data, in the form of production and consumption data, the

PWC matrix models are applied. This application of the models generates predicted

PWC flows, and the resulting matrices are calibrated to satisfy the row and column

constraints given by the production and consumption data.

Finally, the predicted matrices for the base year are disaggregated into flows be-

tween different categories of firms. Post-processing of the matrices related to very

large flows, or singular flows, is also performed in this final stage, as well as stor-

ing the matrices in a format suitable for the Samgods model.


2 Commodities and sectors Generating the PWC matrices is at a basic level equivalent to modelling domestic

and border-crossing trade with commodities. As described above, there has to be

one matrix for each commodity group. In the current version of the Samgods mod-

el, there are 34 commodity groups. This classification, hereafter called Samgods34,

is one of several existing commodity group classifications.

No matter which classification is being used, the matrices model the flows of dif-

ferent commodity types. However, in order to generate the matrices, we need to

make use of various statistical data sources, describing mainly the characteristics of

different industry sectors, producing, consuming and trading the commodities.

Some industry sectors only produce one type of commodity, but, depending on the

detail level on the commodity and industry sector classifications, other industry

sectors produce several commodity types, and some commodity types are being

produced by several industry sectors. Thus, in order to make use of the statistics of

the various industry sectors to draw conclusions on the trade of different commodi-

ty types, we need to associate industry sectors with commodity types in an exact

way.

More specifically, we need a set of correspondence tables, or keys, that for each

industry sector allocates the production value to different commodity types. Using

the keys then allows us to estimate the production levels per commodity type,

based on figures of the production value per industry sector, e.g. in a specific geo-

graphical region such as a municipality. Furthermore, we need an equivalent corre-

spondence table for the use of goods, i.e. which commodities different industry

sectors use as inputs in their production.

At an early stage of this project, the background and alternatives for the derivation

of a new correspondence table was described in a PM. This PM can be found as

Chapter 2 in the supplementary Technical report5. It provides, e.g., a description of

the existing key and different ideas for deriving the key. In this section, only the

parts necessary for understanding the selected method for deriving new corre-

spondence tables are repeated and developed.

2.1 Industry sector classification

In current business and industry statistics, industry sectors are classified according

to SNI (Standard för Svensk Näringsgrensindelning), which is the label for the

Swedish Standard Industry Classification. According to the webpage of Statistics

Sweden6, SNI is based on the EU standard NACE Rev.2.

5 “PWC Matrices: new method and updated Base Matrices, Technical report” (2015-02-06)

6 http://www.scb.se/Pages/List____257409.aspx, 2013-05-02

http://www.scb.se/Pages/List____257409.aspx


Production units (i.e. companies or other units registered as workplaces) are classi-

fied according to the type of activity pursued. A unit can have several SNI codes, if

more than one activity is pursued. In 2008 a new set of SNI codes were introduced;

SNI2007. Earlier versions are SNI2002 and SNI92. There are relatively big differ-

ences between SNI2007 and the earlier versions.

The SNI2007 classification divides industries into 21 sections, denoted by letters.

Those are divided into 88 main groups (denoted by 2-digit codes), 272 groups (3-

digit codes), 615 sub-groups (4-digit codes) and 821 detail groups (5-digit codes).

In order to make use of current statistics, all statistics used for the matrices should

use SNI2007 as a classification for industry sectors. There is a great variety within

the commodities produced in Sweden and in different parts of the country, similar

industries could have distinct product mixes, giving implications for how goods are

being traded and transported.

Thus it is important to make use of information on industries at a level as detailed

as possible. Therefore, the derivation of the matrices will make use of the most de-

tailed SNI classification level, in which industry sectors are represented by 5-digit

codes, as far as possible.

2.2 Commodity classifications

There are several existing commodity group classifications, derived and used for

partly different purposes. Deriving the matrices involves handling more than one

commodity classification. The mostly used classifications are described below.

Samgods34 and NST/R

As described above, the Samgods model operates with 34 commodity groups sepa-

rately. Those 34 groups can be directly aggregated to the 12 commodity groups of

the old STAN model. The Samgods34 commodities are based on the NST/R classi-

fication.

NST/R (Standard Goods Classification for Transport Statistics/Revised) is the ver-

sion of the standard goods classification for transport statistics which was in use

from 1967 to 2007, e.g. by member states of the EU. According to the documenta-

tion7,

7 “Standard goods classification for transport statistics – NST\R”, can be found in “Intro-

duction to the classification” at

http://ec.europa.eu/eurostat/ramon/nomenclatures/index.cfm?TargetUrl=LST_CLS_DLD&

StrNom=NSTR_1967&StrLanguageCode=EN&StrLayoutCode=HIERARCHIC

http://ec.europa.eu/eurostat/ramon/nomenclatures/index.cfm?TargetUrl=LST_CLS_DLD&StrNom=NSTR_1967&StrLanguageCode=EN&StrLayoutCode=HIERARCHIC

http://ec.europa.eu/eurostat/ramon/nomenclatures/index.cfm?TargetUrl=LST_CLS_DLD&StrNom=NSTR_1967&StrLanguageCode=EN&StrLayoutCode=HIERARCHIC


“the NST/R takes the form of a list with 176 headings for goods which are classi-

fied as far as possible on the basis of their nature, processing stage, methods for

transport and total tonnage transported; (…) The analytical structure of the NST/R

divides the 176 headings of the classification into 10 chapters and 53 main groups

according to a system which consists of:

One digit for the chapters,

Two digits for the groups,

Three digits for the headings.”8

More specifically, the Samgods34 classification is an aggregation of NST/R on the

most detailed level – the 176 NST/R headings have been aggregated into 33 groups

(the last group of the 34 is for air freight), but with some modifications. There was

demand for a distinction between round wood and pulp wood in the Samgods mod-

el, which was not provided by the NST/R classification. Therefore, the correspond-

ing product group was split into fractions. Other cases that cannot be directly ag-

gregated from NST/R commodity types are Samgods34-group 7 (Wood chips and

wood waste), 8 (Bark, cork, other wood (…)) and 34 (Used wrapping and packag-

ing materials).

The Samgods34 classification can be found in the Samgods documentation.9

The matrices will use the Samgods34 as a commodity classification. However, for

various reasons described below, a large amount of the data used will also be pro-

duced using the NST2007 classification (at some aggregation level that also may

be slightly adjusted to fit the purposes of the model).

NST2007

In official statistics, the NST/R classification has been replaced by NST2007 (the

Standard Goods Classification for Transport Statistics, 2007), meaning that NST/R

is being abandoned for transport statistics. Therefore it is also interesting to consid-

er NST2007 as a commodity classification, as a future possible commodity classi-

fication for the Samgods matrices.

8 The classification can be found at

http://ec.europa.eu/eurostat/ramon/nomenclatures/index.cfm?TargetUrl=LST_NOM_DTL

&StrNom=NSTR_1967&StrLanguageCode=EN&IntPcKey=&StrLayoutCode=HIERARC

HIC

9 See e.g. “Representation of the Swedish transport and logistics system”, VTI notat 17A-

2009, page 14-15 (please note that the NSTR codes given in the table on page 15 do not

equal the official NST\R codes given by Eurostat – the groups are an aggregate of NST\R

but the notation used for the codes is another. The documentation can be found at e.g.

http://www.trafikverket.se/PageFiles/64819/representation-av-det-svenska-godstransport--

och-logistiksystemet-logistikmodell-version-200.pdf

http://ec.europa.eu/eurostat/ramon/nomenclatures/index.cfm?TargetUrl=LST_NOM_DTL&StrNom=NSTR_1967&StrLanguageCode=EN&IntPcKey=&StrLayoutCode=HIERARCHIC



http://www.trafikverket.se/PageFiles/64819/representation-av-det-svenska-godstransport--och-logistiksystemet-logistikmodell-version-200.pdf

http://www.trafikverket.se/PageFiles/64819/representation-av-det-svenska-godstransport--och-logistiksystemet-logistikmodell-version-200.pdf


There is no key available for converting NST2007 data to the Samgods commodi-

ties and vice-versa, and the conversion between NST/R and NST2007 is not

straight-forward, see below. This means that the option to adjust the Samgods

commodity classification in the near future should be considered.

The drawbacks would be that some of the tables and parameter values in the

Samgods model have to be re-calculated, and it will be more complicated to com-

pare new model results to previous results.

In return, new model results may be validated using new transport statistics directly

without the need for transformation between product classifications, but also, extra

uncertainties in the calculation of the PWC matrices due to additional conversion

between product classifications are avoided.

According to the webpage of Eurostat10:

“The Standard goods classification for transport statistics abbreviated as NST

(2007), is a statistical nomenclature for the goods transported by four modes of

transport: road, rail, inland waterways and sea (maritime).

As NST 2007 considers the economic activity from which the goods originate, each

of its items is strongly connected to an item of the European Union product and

activity classifications Classification of products by activity (CPA) and Statistical

classification of economic activities (NACE), which themselves are consistent with

their counterparts at UN level, CPC and ISIC.“

NST2007 divides commodities into 20 main groups and 81 subgroups11 and has

been in use since 2008. As described above, NST2007 is based on the production

process where the goods are originated, while NST/R is based on the physical

characteristics of the goods12. Therefore the conversion between the two versions is

not straightforward, but has to be done via CN and an additional commodity classi-

fication, CPA.

However, the correspondence between NST/R and NST2007 are not 1:1, i.e. one

NST/R code corresponds to several NST2007 codes, and vice-versa. The solution

will be to use detailed information of CN. Each CN8 commodity group only corre-

spond to one group in NST/R and NST2007, hence the correspondence goes from

many to one.

10 http://epp.eurostat.ec.europa.eu/statistics_explained/index.php/Glossary:NST, 2013-04-15

11 The classification can be found at

http://ec.europa.eu/eurostat/ramon/nomenclatures/index.cfm?TargetUrl=LST_NOM_DTL

&StrNom=NST_2007&StrLanguageCode=EN&IntPcKey=&StrLayoutCode=HIERARCHI

C&IntCurrentPage=1

12 http://epp.eurostat.ec.europa.eu/cache/ITY_SDDS/en/road_go_esms.htm, 2013-04-15

http://ec.europa.eu/eurostat/ramon/nomenclatures/index.cfm?TargetUrl=LST_NOM_DTL&StrNom=NST_2007&StrLanguageCode=EN&IntPcKey=&StrLayoutCode=HIERARCHIC&IntCurrentPage=1



http://epp.eurostat.ec.europa.eu/cache/ITY_SDDS/en/road_go_esms.htm


The Eurostat Metadata Server RAMON provides correspondence tables for several

statistical classifications. The NST/R-NST2007 conversion table includes a corre-

spondence table between CN and NST/R, and between CN and NST2007 (via

CPA13) 14.

CN – Combined Nomenclature

The Combined Nomenclature is used by all EU countries in their foreign trade sta-

tistics and common custom tariff. In Sweden it is also used in the Production of

commodities and industrial services statistics, IVP. CN 8 is the most detailed level

of commodity classification consisting of 8 digits. In 2009 the CN 8 consisted of

9 600 commodity groups.

In Sweden a large share of all production and foreign trade is connected to relative-

ly few CN 8 commodity groups, while the rest of the commodity groups have very

small values or are equal to zero. The CN 8 is summed hierarchically to the more

aggregated commodity groups CN 6, CN 4 and CN 2 which consist of 6 respective-

ly 4 and 2 digits.

Every year small changes are made in the description and classification of the CN 8

commodity groups. Approximately every fifth year the CN 6, CN 4 and CN 2 are

revised which implies larger changes to the CN 8 commodity groups. The changes

are made to harmonise the commodity classification with technical development

and changes in trade patterns.

Conclusions for commodity classifications

The ultimate aim of the correspondence keys is to connect production levels per

industry sector, to production levels per

1. Samgods34 commodity group

2. Some aggregation of NST2007 commodity groups (for future purposes)

Figure 2 below summarises the connections between different commodity classifi-

cations. The conclusion is that if we can get production levels per CN 8 category, it

13 CPA – Classification of Products by Activity – is EU’s product classification based on

the production process that results in the products. The products can be goods or services.

The current version is CPA2008. CN on the 8-digit level are linked to the 6-digit CPA2008

codes which are linked to the classification of commodities NST2007on a 3-digit level. The

linkage is done through existing Eurostat correspondence tables. More information and an

index of existing and downloadable correspondence tables can be found at

http://ec.europa.eu/eurostat/ramon/relations/index.cfm?TargetUrl=LST_REL

14 For more information, see “Maintenance of the NST\R – NST2007 conversion table”,

Artemis Information Management, September 2008. The conversion table can be found at

http://ec.europa.eu/eurostat/ramon/relations/index.cfm?TargetUrl=LST_REL&StrLanguage

Code=EN&IntCurrentPage=8 (NST\R 1967 – NST 2007)


http://ec.europa.eu/eurostat/ramon/relations/index.cfm?TargetUrl=LST_REL&StrLanguageCode=EN&IntCurrentPage=8

http://ec.europa.eu/eurostat/ramon/relations/index.cfm?TargetUrl=LST_REL&StrLanguageCode=EN&IntCurrentPage=8


will be possible to reach the aims 1 and 2 above by pure aggregation of different

CN 8 categories. The aggregation to Samgods34 is made via NST/R, after which

some NST/R categories have to be split into fractions again. However, when using

NST/R on the most detailed level (3 digit codes), they can be aggregated directly to

Samgods34, thus avoiding having to split up aggregates.

Eurostat provides official tables on their webpage for aggregating CN 8 categories

to NST/R and NST2007, respectively. For the NST2007 case, the aggregation is

made via the CPA classification, but it is still a pure aggregation without any need

to create fractions of commodity groups. The connection between NST/R and

Samgods34 can be derived from the documentation of the current PWC matrices15.

Figure 2 Connections between commodity classifications

2.3 Deriving the keys

Thus, the aim is two versions of the correspondences tables, both starting from

SNI2007 5-digit industry sector codes, one allocating production value per industry

sector to Samgods34 commodity types, and one allocating the production value to

NST2007 commodity types (by now on the most detailed level, i.e. the 81 3-digit

codes). Moreover, the same types of tables are needed for the (intermediate) con-

sumption side.

Data on the production and intermediate consumption of commodities have been

delivered by SCB, using the statistical data bases Production of commodities and

15 See Technical report, Chapter 3


industrial services statistics, IVP and The Intermediate consumption statistics, IN-

FI. Commodities are mainly produced within sectors

A. Agriculture, forestry and fishing - SNI codes starting with 01-03

B. Extraction of minerals - SNI codes starting with 05-09

C. Manufacturing - SNI codes starting with 10-32

and these are divided into 325 5-digit SNI codes. Data delivered by SCB covers

sectors B and C, i.e. codes starting with 05-32. For sectors 01-03 data has to be

collected elsewhere.16

In IVP and INFI, observations are registered by industry sector SNI2007 5-digit

codes as well as commodity CN 8-digit codes. SCB has aggregated the CN 8-digit

codes to Samgods34 commodities as well as NST2007 3-digit codes. This data

provide correspondence tables connecting 5-digit SNI2007 codes within sector B

and C to the two commodity classifications, to be used for future purposes.

16 See the next chapter for further information on the data sources.


3 Method for PWC matrix generation In this chapter we give an overview of the method suggested for generating the

PWC matrices. We start by describing the main data sources. In section 3.2 we dis-

cuss the view taken on PWC matrices related to previous methodologies. The se-

lected method for estimation of the PWC matrix models is introduced and de-

scribed in section 3.3; the methods for calculating row- and column sums and the

final matrix elements are presented in subsequent chapters.

3.1 Main data sources

The following statistical databases are the main input data for the PWC matrix

generation. It should be pointed out that there is a distinction between PWC matrix

generation and PWC model estimation. The latter only refers to the problem of es-

timating models for PWC flows, and is primarily based on data from the commodi-

ty flow survey, while the former relates to the whole process of generating the final

PWC matrices, where a wide range of sources of data is used.

Industrial goods statistics

The Industrial goods statistics (IVP) is a yearly survey that has been conducted

since 1996, with the purpose to describe the Swedish production of commodities at

a detailed level. The IVP reports production of commodities using CN at an 8-digit

level registered in values and quantities. The population of entities within, or linked

to, the mining and manufacturing sector (SNI codes starting with 05-33) being sur-

veyed is defined by the following criteria

Workplaces with a minimum of 10-20 employees within their main branch

in the sector

Workplaces with their main branch in the sector with less than 10-20 em-

ployees and a net turnover that is 50 million SEK or more per year.

Workplaces with their secondary branch in the sector if the secondary

branch has a minimum of 10-20 employees.

In 2011 the population consisted of approximately 4000 workplaces and the survey

had a weighted response frequency of 99 percentages. The production of commodi-

ties in those workplaces that do not fulfil the criteria’s are model estimated, since

they are not a part of the survey population. For each workplace the main and se-

condary industry branch can be identified at the SNI 5-digit level.

Given that the IVP reports production of commodities at a CN 8-digit level for

each workplace, the data can be aggregated to the desired commodity classification

(Samgods34 or NST2007).

Data at the most detailed level include observations of production values (per CN

8-digit commodity code) per unit, defined by a corporate identity number. For


firms with only one workplace, the production levels could be allocated to the cor-

rect municipality without the need for model estimations.

For firms with multiple workplaces, the production levels could be distributed over

two or more municipalities by e.g. number of employees. However, data at this

detailed level has not been available in this project (see Appendix 1). Only IVP-

data at the national level has been used, but with detailed information on industry

sectors and commodity types. Data for year 2010 is used in this project.

Intermediate consumption statistics

The Intermediate consumption statistics (INFI) is a yearly survey, where one third

of the manufacturing industries are surveyed every year according to a rolling

schedule. The statistics describe the industry’s consumption of input materials, per

industry sector and commodity types. The population of entities that are being sur-

veyed are all units within the manufacturing sector (SNI codes starting with 05-33).

The commodity classifications used do not include all CN 8-digit codes, but is a

collection of appropriate CN codes. Information on the manufacturing sector exists

at a 5-digit SNI2007 level. In this project, statistics from the years 2009-2011 have

been used aggregated to the national level but with detailed information on industry

sectors and commodity types. Just as for the IVP described above, it would be the-

oretically possible to allocate consumption to municipalities guided by the firms’

corporate identity number, if data at that detailed level were available.

Foreign trade statistics

The foreign trade – export and imports of goods statistics (FTS) give information at

a detailed level on import and export of commodities classified with CN 8-digit

codes, specified with receiving country for exports and sending country for im-

ports. The values are also reported with SPIN codes, which is a commodity classi-

fication closely linked to the classification of the industry sector producing the

commodity.

The Swedish Occupational Register with statistics

The Swedish Occupational Register with statistics (YREG) contains, among other

things, information on employment by occupation group and industry. As we have

to use employment figures to estimate the regional distribution of production and

consumption of commodities, YREG can be used to get a more probable distribu-

tion than what will be the case if this estimation is based on the regional distribu-

tion of total employment by industry.

It will be assumed that the regional distribution of the production activity for a spe-

cific industry is the same as the regional distribution of employed persons in

goods-handling occupations.


The commodity flow survey

The Commodity Flow Survey (CFS) describes shipments of goods with Swedish

and foreign recipients and foreign shippers. The survey provides information about

the type of commodities shipped, their value, weight, and transport mode(s) as well

as sending and receiving zones The CFS results are derived using two different

methods. For most sectors, data is collected through a survey based on a method

used for the American CFS, developed by the Census Bureau. The method includes

a three-stage sampling process, where workplaces, time period and individual

shipments are sampled from the population. A shipment is defined as a transport of

a specific commodity type to a unique receiver, from Swedish workplaces within

the manufacturing and wholesale sector and completing import shipments.

The survey is completed using register data for shipments from the agricultural and

forestry and mineral extraction sectors. For the agricultural sector, shipment data at

the municipality level is available for transport of living animals, cereals and raw

milk. For the forest industry sector, shipment data at the municipality level is avail-

able for transports of raw forest materials. For mineral extraction workplaces the

survey was completed with register data on production level permits, for workplac-

es too small to be included in the population. 17

For more information on the CFS, see the method reports (SIKA 2005, 2006).

3.2 Methodology

The original idea of this project was to use a data-driven approach for the row and

columns sums of the matrices, where different statistical data sources are used to

get estimates of production, consumption, export and import at a micro-level, and

aggregating the estimates to the municipality and commodity group level. Thus, the

row and column sums would be estimated using all available statistics and could be

treated as strong constraints to the rest of the matrix elements. “Row and column

sums” is here equivalent with

1. Production per municipality and commodity group

2. Consumption per municipality and commodity group

3. Import and export per origin/destination country and commodity group

(and maybe allocated to Swedish municipalities)

all measured in economic value (SEK) and weight (tons) per year.

A suggested methodology for deriving row and column constraints from micro data

is given in the appendix. However, the project was not allowed to access the data

needed for the derivations, why an alternative approach had to be taken.

17 Information provided by Lars Werke, Statistics Sweden, 2013.


Instead of using micro level data regarding production, intermediate consumption

and foreign trade, as first intended, data is used at a somewhat more aggregate lev-

el. In large, the proposed methodology follows a three stage process, where initial-

ly the PWC-matrix models are estimated primarily using CFS data, then row- and

column marginal information for the PWC matrices are determined, and thereafter

the actual distributions of flows in the matrices cells are predicted and calibrated

using the PWC-matrix models with the new row and column information.

This basic methodology is similar to the one that was proposed by Anderstig el al

(2004), and the one implemented by Edwards et al (2008). This type of approach

relies fundamentally on having good information regarding the locations of produc-

tion and consumption. The proposed methodology relies on highly disaggregate

data from Statistics Sweden for this purpose, while the former implemented meth-

odology relied on the commodity flow surveys.

To fix ideas, one may recapitulate the basic ideas of the original proposal on base

matrix methodology (Anderstig et al, 2004), where one single PWC matrix estima-

tion is considered per commodity. Since the wholesale sector largely does not pro-

duce or consume any commodities, but merely act as a mediator, the “production”

and “consumption” of these warehouse actors can simply be added to the marginal

row and column constraints of a combined PWC matrix.

Finally one single PWC matrix was proposed to be generated by using a gravity

model combining strong constraints on the production marginals while imposing

soft constraints on the consumption marginals, reflecting a greater uncertainty

about the quality of such data.

The implementation by Edwards et al (2008) separates the treatment of PC-flows

and WC flows, basically following how observations are recorded in the CFS. In

principle this separation may be interpreted as disaggregating the domestic PWC

matrix above into on domestic PC matrix and one WC matrix, where each is esti-

mated separately.


This view estimates the row and column constraints separately for the production

and wholesale activities, and then estimates the two separate matrices. It should be

noticed that this approach may violate the assumption that the wholesale sector acts

only as an intermediate, since no constraints are imposed on the relationships be-

tween row and column sum models, they are estimated separately.

One way of keeping the separate modelling of PC- and WC-flows, whilst respect-

ing the intermediate role of the wholesale sector flows, would be to disaggregate

the initially proposed method as PC-flows, including domestic flows and exports.

They may be summed per municipality to provide observations of the production.

The total supply from the wholesale sector in a municipality may likewise be ob-

tained by row-wise summation of observations related to WC-flows.

Final consumption, in the column constraints may partially be satisfied by direct

deliveries from the production facilities, fraction (α), and partially by the wholesale

sector, fraction (1- α). Similarly, the demands by the wholesale sector may be par-

tially covered by PC and WC-flows. This kind of approach would satisfy the same

type of assumptions as the initially proposed methodology since adding the two

matrices will generate marginal row conditions of P+W and marginal column con-

ditions of C+W, for the aggregate matrix. Though appealing, the implemented

methodology rests on the original, combined, PWC-matrix approach rather than

estimating separate PC and WC-matrices, for two reasons. First, a separation re-

quires the identification of two extra parameters (alpha and beta). Second, due to

the rather low number of observations of flows for some commodities, pooling PC

and WC-flow data into PWC-flows will improve the situation for estimating mod-

els. Thus, a combined PWC matrix will be estimated.

In the following section the methodology for generating models for the matrix cells

will be described and in subsequent chapters the marginal constraints and the ge-

neration of the final matrices will be described.


3.3 Estimation of PWC models

The purpose of estimating the PWC trade flow models is twofold. First, inference

regarding trade flows, and how they are affected by factors such as regional pro-

duction, consumption patterns, proximity etc., is required. Second, the resulting

models will be applied in predictions, or in scenario analyses.

The traditional way of thinking of trade flows is that they are primarily derived

from the interaction of supply at one location with the demand at another location.

Thus, the regional distributions of supply and demand should, at least in part, ex-

plain the flows of commodities between regions. Another factor that is thought to

affect the size of flows is transport costs. These factors; supply, demand and

transport costs are the backbones of the well-known gravity model, which has been

very successful, empirically, in explaining international trade flows. This project

will rely on gravity-like models in explaining the PWC-flows. Yet, the developed

models will use a possibly much larger set of explanatory variables in explaining

the PWC-flows, as described later in this section

The estimation of the PWC flow matrices will primarily be based on Swedish

commodity flow surveys, where we have utilized the surveys from 2001 and

2004/05. For each Samgods commodity, the data is used at a municipality level for

domestic flows and at a regional/country level for imports and exports. In total, the

models include 464 regions, which may send or receive commodities, out of which

290 constitute the municipalities of Sweden.

Thus, for each commodity there are approximately 185 thousand potential trade

relations that may be active. Clearly, all those trade relations are not active for each

commodity and furthermore, the CFS’s are sample surveys which do not necessari-

ly cover even the trade relations that are active. Hence, we will have a large pro-

portion of unobserved or zero trades.

Different routes could be taken in dealing with those zeros and unobserved trade

flows. The occurrence of true zeros could be modelled in a Tobit based approach,

the occurrence of zeros due to sampling could be modelled as well, and this might

well be the ideal solution. The issue could be disregarded altogether by simply us-

ing only the positive trade flows which has been observed; this was the route taken

in the previous methodology for PWC-matrices in Sweden. The proposed method-

ology will use the zeros as observations, and is based on a methodology which is

relatively robust to the occurrences of zeros (Santos Silva et al 2014).

Another aspect of the CFS data that should be considered in the choice of estima-

tion methodology is the variance of the observations. It is likely that PWC-data is

heteroscedastic, such that smaller observations of flows are accompanied by a

smaller variance than are the flows which are reported to be orders of magnitudes

larger.


Based on the mentioned considerations, the proposed methodology for estimating

the gravity-like PWC-models, is based on a quasi-maximum likelihood method

called the Pseudo Poisson Maximum Likelihood method which is denoted as

PPML (see Wooldridge 2002, and Santos Silva, J.M.C. and Tenreyro, S. 2006)

Provided that models are required for all Samgods commodities, a robust way of

constructing those models will be employed. The number of observed positive

trade flows, after pooling the 2001 and the 2004/05 CFS’s, ranges from 25 to tens

of thousands. Therefore, a stepwise regression technique will be employed, where

only those explanatory variables that are significant, and thus supported by the

commodity specific data, will enter the final models.

A final remark, before going into the specifics of the estimations is warranted. Pre-

viously the PWC-matrices were estimated using observations of values and the

PWC-matrix was predicted in terms of values, and later converted into tons by ap-

plying a single commodity value. It has been noted through an investigation of the

CFS’s that this may be a problematic approach since for a significant part of the

commodities, the correlation between trade measured in values and trade measured

in weight is not 1. The mean correlation over the commodity groups is 0.65 for the

2004/05 CFS, and for one specific commodity it is as low as 0.03.

Therefore, as one of the main objectives is to generate the PWC-matrixes in tons,

the models for the PWC matrices in tons will be based on observations in terms of

tons.

In the following some notes on the observations are provided; and after that the

actual estimation methodology will be covered; then we provide a description of

the feature selection mechanism or the stepwise regression and the potential ex-

planatory variables that are used; and finally we provide a summary of the models

which have been estimated.

Observations

The observations used are exactly those that were used in the previous PWC-

methodology (see Edwards et al 2008). The difference is that “zero” flows are also

used, but only those zeros regarding municipalities where production and con-

sumption has been observed. As was previously done, very large flows called sin-

gular flows have been removed from the data prior to estimation of the models.

The definition of those singular flows are observations in the CFS which are larger

than “10000 tons per year and more than five standard deviations away from the

average shipment size”, see chapter 4.2 in Edwards et al (2008).

The CFS data from 2001 and 2004/05 have been pooled, such that the regressions

are based on observations from both surveys.


The Exponential Conditional Expectation Model

The models used for the PWC-flows falls into the class of exponential conditional

expectation models. The conditional expectation of a flow from region r to region s

is given by

'x[F | x ] m( ,x ) e rs

rs rs rsE , (1)

where xrs is a vector of explanatory variables and β is a parameter vector. The ex-

pected flow is necessarily a non-negative number and this is guaranteed by the ex-

ponentiation. It may be noted that standard gravity models falls into this class of

models, since they can be written on the form of Equation (1).

Basically, the only assumption that will be imposed on the models for the PWC-

matrices is that of Equation (1). No additional assumptions will be made regarding

the distribution of flows, e.g. its variance or distributional form.

Pseudo Poisson Maximum Likelihood

The PPML method can be found in standard textbooks such as Wooldridge (2002),

chapter 19, and its adequacy in the context of estimation of trade flows has been

illustrated by Santos Silva and Tenreyro (2006). The appropriateness of using the

PPML method for continuous data was first noted by Gourieroux, Monfort, and

Trognon (1984).

Given an observed flowrsf , the pseudo log-likelihood of this observation is

( ) log(m( ,x )) m( ,x )rs rs rsl f

where m is given in Equation (1). Taking the first order condition of l with respect

to the parameter 𝛽, setting it to zero, and summing over all observations, the

following system of equations is satisfied at the optimal parameters

(f m( , x )) x 0rs rs rs

rs Obs

. (2)

That is, solving the system of equations (2) for the parameter vector β provides the

PPML estimates. These estimates are consistent and asymptotically normal under

rather general conditions, see Wooldridge (2002).

In order to calculate the standard errors of the parameters, a robust sandwich esti-

mate of the covariance matrix of the estimated parameters should be calculated.

The robust covariance matrix is calculated as

1 1C A SA (3)

where


( , x ) ( , x )1,

( , x )

, and (f ( , x )) x

T

rs rs

rs Obs rs

T

rs rs rs rs rs rs

rs Obs

dm dmA

m d d

S s s s m

(4)

The standard errors of the estimated parameters are then extracted as the square

root of the diagonal of C.

It should be noted that the PPML estimator can clearly be used under additional

assumptions regarding the distributions apart from the assumptions of Equation (1).

Under such additional assumptions, the expressions for the covariance matrix will

typically be altered. For the remainder of the work presented in this report no such

additional assumptions will be imposed. Therefore, we retain only the assumption

of Equation (1) and utilize the robust sandwich estimator of the covariance matrix

as given in Equation (3) for the sake of inference and model selection. In the next

section the automated model selection mechanism that has been used for the gener-

ation of PWC-models is described.

Stepwise Regression

In order to build the PWC-models for each of the Samgods commodities the PPML

estimator has been integrated into a feature selection, or stepwise regression

framework. A stepwise regression procedure typically starts out with an initial

model, which may be the null model, and then iteratively considers entering or re-

moving possible regressors. If a regressor is not yet included in the model, the null

hypothesis is that if it is included it will be insignificant.

All variables that are not included are scanned by including them separately and

calculating their significance. If any of the non-included variables are significant,

the null hypothesis is rejected and the most significant of the non-included varia-

bles is entered into the model. Correspondingly, for variables already included in

the model, the null hypothesis is that these are significant, and if any included vari-

able is not, remove the one which is least significant. The scheme provided above

is iterated until no more variables can be entered into the model, or removed from

the model.

In the implementation of the stepwise regression technique used for the PWC-

models, variables are entered into the model if they are significant at the 2.5% level

and are removed from the model if they are not significant at the 5% level. Hence

the final models that are generated by the procedure are guaranteed to only contain

variables which are significant at the 5% level.

The regressors used in the stepwise regression are selected from a set of possible

explanatory variables with the intention of finding those which fit the data. Table 2

presents the complete set of possible explanatory variables, together with a short

explanation of each variable. For a more exhaustive explanation of the variables

and their definitions, see the Technical Report.


Table 1 Set of variables used in stepwise regression

Const

Constant, scaling the model

lnP

Log of Production (row sum of PWC matrix)

lnC

Log of Consumption (column sum of PWC matrix)

lnD

Log of distance measure

D

Distance measure

Year01

Dummy for year 2001

Self

Dummy for flows within a municipality

Self_lnP

Interaction between Self and lnP

Self_lnC

Interaction between Self and lnC

Neigh

Dummy for neigbouring municipalities Drs<0.05

Neigh_lnP

Interaction between Neigh and lnP

Neigh_lnC

Interaction between Neigh and lnC

Acc

Accessibility score for production

Agg

Accessibility score for consumption

MainP

Dummy, main production municipalities Pr>0.1*sum(P)

MainC

Dummy, main consumption municipalities Cs>0.1*sum(C)

MainPC

Interaction between MainP and MainC

Big

Dummy, Based on big sized workplaces both in r and s

BigToW

Dummy, Big production sited to warehouse sites Big_FrTo ToPortDom FrPortDom PortToPort

Dummy, Big interacted with FrTo which is 1 if Pr>Cs Dummy, domestic flow to a municipality with a port Dummy, domestic flow from a municipality with a port Dummy, domestic flow between municipalities with ports

Ex

Dummy for export flows if municipality is exporter

Ex_lnP

Interaction between Ex and lnP

Ex_lnC

Interaction between Ex and lnC

Ex_lnD

Interaction between Ex and lnD Ex_D Ex_FrPort

Interaction between Ex and D Dummy, export from a municipality with a port

Im

Dummy for import flows if municipality is importer

Im_lnP

Interaction between Ex and lnP

Im_lnC

Interaction between Ex and lnC

Im_lnD

Interaction between Ex and lnD Im_D Im_ToPort

Interaction between Ex and D Dummy, imports to a municipality with a port

Models Summary

All in all, 32 PWC-models for trade flows expressed in tons are estimated, and

equally many for PWC-matrices in value terms. The results of the estimations are

presented in the supplementary excel files “TonModels.xlsm” and “ValueMod-

els.xlsm”. Samgods commodities 8 and 30 are not estimated simply because there

is no data for these commodities in the CFS’s. The model estimations have been

performed in Matlab, and more information related to the code may be found in the

Technical Report


We will not display all the models in the report, but refer the interested reader to

the mentioned excel spreadsheets. Below, a summary of the PWC-models estimat-

ed in ton terms is provided in Table 2. The table provides the adjusted R-squared

for each model, the correlation between observed and modelled PWC-flows, the

number of observations, and the number of positive observations. As can be seen in

the table the number of observations for the different commodity groups varies

quite substantially, as does the explanatory power.

In Table 3 the resulting models from the stepwise regression are indicated as the

table shows which variables were included in the final PWC-models for ton-flows.

As can be seen from the table, the constant term and the terms lnP and lnC are al-

ways included as explanatory variables in the models. This is actually not a result

of the stepwise regression as these variables were required to be in the models. In

the supplementary material “TonModels.xlsm” it may be noted that these factors

are significant for all estimated models. All the green cells shown in the table rep-

resents significant parameter estimates.

Table 2 PWC models summary

R2 adj Corr Nobs Nobs>0 Description

VG 1 0,87 0,93 55 820 2 094 Cereals

VG 2 0,64 0,81 42 330 1 354 Potatoes, other vegetables, fresh or frozen, fresh fruit

VG 3 0,66 0,81 15 950 2 129 Live animals

VG 4 0,60 0,79 88 50 Sugar beet

VG 5 0,69 0,83 107 846 6 890 Timber for paper industry (pulpwood)

VG 6 0,18 0,43 137 275 7 497 Wood roughly squared or sawn lengthwise, sliced...

VG 7 0,26 0,51 56 158 1 124 Wood chips and wood waste

VG 8 0,00 0,00 0 0 Other wood or cork

VG 9 0,48 0,73 115 461 6 052 Textiles, textile articles and manmade fibres, other …

VG 10 0,46 0,68 190 112 17 809 Foodstuff and animal fodder

VG 11 0,67 0,83 182 715 3 829 Oil seeds and oleaginous fruits and fats

VG 12 0,80 0,92 13 201 609 Solid mineral fuels

VG 13 0,50 0,72 146 42 Crude petroleum

VG 14 0,56 0,75 143 188 4 020 Petroleum products

VG 15 0,57 0,76 3 088 185 Iron ore, iron and steel waste and

VG 16 0,90 0,96 991 81 Non-ferrous ores and waste

VG 17 0,65 0,93 177 283 9 476 Metal products

VG 18 0,49 0,71 147 950 8 000 Cement, l ime, manufactured building

VG 19 0,64 0,80 11 636 329 Earth, sand and gravel

VG 20 0,83 0,91 52 142 1 485 Other crude and manufactured

VG 21 0,68 0,83 3 827 237 Natural and chemical fertil izers

VG 22 0,36 0,60 12 140 661 Coal chemicals, tar

VG 23 0,49 0,73 209 330 15 889 Chemicals other than coal chemicals

VG 24 0,51 0,71 8 864 523 Paper pulp and waste paper

VG 25 0,58 0,79 154 270 8 939 Transport equipment, whether or not assembled, and parts...

VG 26 0,89 0,96 263 445 22 702 Manufactures of metal

VG 27 0,33 0,59 100 771 4 036 Glass, glassware, ceramic products

VG 28 0,27 0,52 15 760 1 102 Paper, paperboard; not manufactures

VG 29 0,15 0,40 303 658 38 469 Leather textile, clothing, other manufactured articles than...

VG 30 0,00 0,00 0 0 Mixed and part loads, miscellaneous articles etc

VG 31 0,45 0,67 81 703 2 669 Timber for sawmill

VG 32 0,40 0,65 266 363 28 960 Machinery, apparatus, engines, whether or not assembled...

VG 33 0,37 0,61 179 015 11 879 Paper, paperboard and manufactures thereof

VG 34 0,40 0,64 39 645 1 023 Product wrappings, coverage protection


Table 3 Included variables in the different PWC-models

Ton

ne

VG

1V

G 2

VG

3V

G 4

VG

5V

G 6

VG

7V

G 8

VG

9V

G 10

VG

11V

G 12

VG

13V

G 14

VG

15V

G 16

VG

17V

G 18

VG

19V

G 20

VG

21V

G 22

VG

23V

G 24

VG

25V

G 26

VG

27V

G 28

VG

29V

G 30

VG

31V

G 32

VG

33V

G 34

Co

nst

11

11

11

11

11

11

11

11

11

11

11

11

11

11

11

11

lnP

11

11

11

11

11

11

11

11

11

11

11

11

11

11

11

11

lnC

11

11

11

11

11

11

11

11

11

11

11

11

11

11

11

11

lnD

11

11

11

11

11

11

11

D1

11

11

11

11

1

Ye

ar011

11

11

11

11

11

11

11

Self

11

11

11

11

11

1

Self_ln

P1

11

11

11

11

11

1

Self_ln

C1

11

11

11

11

1

Ne

igh1

11

11

11

11

11

11

11

Ne

igh_ln

P1

11

11

1

Ne

igh_ln

C1

11

11

11

1

Acc

11

11

11

11

11

Agg

11

11

11

11

11

11

1

Main

P

Main

C1

1

Main

PC

11

11

11

Big

11

1

BigTo

W1

11

Big_FrTo

11

1

ToP

ortD

om

11

11

1

FrPo

rtDo

m1

11

11

1

Po

rtToP

ort

11

11

1

Ex1

11

11

11

11

1

Ex_lnP

11

11

1

Ex_lnC

11

11

11

1

Ex_lnD

11

11

11

11

1

Ex_D1

11

11

11

Ex_FrPo

rt1

11

11

11

11

Im1

11

11

11

11

11

Im_ln

P1

11

1

Im_ln

C1

11

11

11

11

11

11

Im_ln

D1

11

11

1

Im_D

11

11

11

11

11

11

Im_To

Po

rt1

11

11

11


4 Row and column estimates Row and column estimates consist of values of production (P), wholesale (W) and

consumption (C), per zone18 and per Samgods commodity. These values are esti-

mated from different data sources.

Figure 3 gives an overview of the various data sources used as input to the genera-

tion of row and column estimates for P and C. Here industries are defined in three

sectors at SNI 2 digits: Agriculture, Forestry and Fishing (01-03), Mining and

Manufacturing (07-32), and Services (33-96). Production of commodities is as-

sumed to take place in sectors 01-03 and 07-32, but not in the Services sectors.

However, intermediate consumption of commodities is included in all sectors.

Moreover, final consumption of commodities, in the form of investments and the

households’ and the public sector’s consumption, is included. In the sections be-

low, the different fields in Figure 3 are described.

In order to get row and column estimates for zones abroad, foreign trade statistics

(FTS) is used, which gives import and export per commodity and sending/receiving

country.

Figure 3 Overview of data input to generate row and column estimates for produc-tion (P) and consumption (C)

18 A zone within Sweden equals a municipality and a zone outside Sweden could be a re-

gion, a country or a several countries/a continent, depending on the distance from Sweden.

01-03 07-32 33-96 CO+CP investm

NR, CFS INFI NR NR NR

Co

mm

od

itie

s fr

om

SN

I2 s

ect

or

C

intermediate final

NR, CFS INFI NR NR NR01-03

07-32

33-96

other

P

IVP


In this section, Samgods commodities are often referred to only with their numbers.

For a description of the commodities, see Table 4 below.

Table 4 Description of Samgods commodities

1 Cereals

2 Potatoes, other vegetables, fresh

or frozen, fresh fruit

3 Live animals

4 Sugar beet

5 Timber for paper industry (pulp-

wood)

6 Wood roughly squared or sawn

lengthwise, sliced or peeled

7 Wood chips and wood waste

9 Textiles, textile articles and

manmade fibres, other raw animal

and vegetable

10 Foodstuff and animal fodder

11 Oil seeds and oleaginous fruits and

fats

12 Solid mineral fuels

13 Crude petroleum

14 Petroleum products

15 Iron ore, iron and steel waste and

16 Non-ferrous ores and waste

17 Metal products

18 Cement, lime, manufactured build-

ing

19 Earth, sand and gravel

20 Other crude and manufactured

21 Natural and chemical fertilizers

22 Coal chemicals, tar

23 Chemicals other than coal chemi-

cals

24 Paper pulp and waste paper

25 Transport equipment, whether or

not assembled, and parts thereof

26 Manufactures of metal

27 Glass, glassware, ceramic prod-

ucts

28 Paper, paperboard; not manufac-

tures

29 Leather textile, clothing, other

manufactured articles than paper,

paperboard and manufactures

thereof

31 Timber for sawmill

32 Machinery, apparatus, engines,

whether or not assembled, and

parts thereof

33 Paper, paperboard and manufac-

tures thereof


4.1 Description of data sources

Mining and manufacturing

Statistics Sweden (SCB) has delivered data concerning Production of commodities

and industrial services statistics, IVP and the Intermediate consumption statistics,

INFI. Those data have been delivered in a form specifying

Production of Samgods commodities per 5-digit SNI sector within the min-

ing and manufacturing sector (IVP)

Intermediate consumption of Samgods commodities per 5-digit SNI sector

within the mining and manufacturing sector (INFI)

Thus, those data sources cover all production of commodities in sector 07-32 and

the intermediate consumption of all types of commodities in the same sector, ac-

cording to Figure 3 above.

In order to allocate this production and consumption to zones (within Sweden),

additional data from the Swedish Occupational Register (YREG), also delivered

from SCB, has been used.

The IVP and INFI data are classified with respect to industry (SNI 2007, 5 digits –

SNI5), and commodity group (Samgods34). By aggregating to the 2 digits level

(SNI2), data on Mining and Manufacturing (industries 07-32) can be compared to

corresponding data in the National Accounts (NR). An overview of production data

is presented in Figure 4.

Figure 4 Production of commodities 2010, National Accounts (NR) and IVP


Since National Accounts are based on detailed data, e.g. IVP and INFI, it is ex-

pected that IVP and NR should harmonize. This is also the case, as shown in Fig-

ure 4. For industries 07-32 the sum of total production value in IVP is 1 366 574

MSEK, which is 91 percent of the corresponding total production value in NR.

The discrepancy between IVP and NR can be explained by two factors. First, NR

relates to products from any industry within 07-32, i.e. also products that are atypi-

cal for the specific industry. The diagonal, i.e. products that are typical for the spe-

cific industry, represents a total value of 1 456 233 MSEK.

Second, products in NR also include services whereas products in IVP are com-

modities. When adding the information from IVP on industrial services, the total

value is 97 percent of the total production value (07-32) in NR, and approximately

100 percent of the value in the diagonal in NR.

In NR production is also reported for industries with SNI2 codes 33-96, i.e. indus-

tries outside the mining and manufacturing sector. This production is marked by an

* asterisk in Figure 4 above. In NR the production value for industries 33-96 repre-

sents an addition about 1 percent to the production value for industries 07-32. As

stated above, this production value also includes services.

IVP also reports on production in industries 33-96. The value of commodity pro-

duction in those industries, as share of total value for commodity groups in

Samgods, is presented in Figure 5.

Figure 5 Value of production in industries 33-96 in percent of total value (IVP) for commodity groups in Samgods

The relative importance of commodity production outside manufacturing industries

is varying between commodity groups. At most this production represents

3,1 percent of the total production value, which is the case for the Samgods group 7

“Wood chips and wood waste”.

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5%

6 Wood roughly squared or sawn lengthwise, sliced or peeled

7 Wood chips and wood waste

9 Textiles, textile articles and manmade fibres,

10 Foodstuff and animal fodder

11 Oil seeds and oleaginous fruits and fats

12 Solid mineral fuels

14 Petroleum products

15 Iron ore, iron and steel waste and

16 Non-ferrous ores and waste

17 Metal products

18 Cement, lime, manufactured building

19 Earth, sand and gravel

20 Other crude and manufactured

21 Natural and chemical fertilizers

22 Coal chemicals, tar

23 Chemicals other than coal chemicals

24 Paper pulp and waste paper

25 Transport equipment, whether or not assembled, and parts thereof

26 Manufactures of metal

27 Glass, glassware, ceramic products

28 Paper, paperboard; not manufactures

29 Leather textile, clothing, other manufactured articles

31 Timber for sawmill

32 Machinery, apparatus, engines,

33 Paper, paperboard and manufactures thereof


However, on the average the non-manufacturing industries represent only 0,4 per-

cent of the total production value for the Samgods commodity groups. Based on

this, the production of commodities in the Services sector (SNI 33-96) is excluded

from the estimation of row and column sums.

The corresponding overview of data on intermediate consumption of commodities

in Mining and Manufacturing is presented in Figure 6.

Figure 6 Intermediate consumption of commodities 2010, National Accounts (NR) and INFI

For industries 07-32 the sum of total intermediate consumption of commodities

(01-32) in INFI is 666 733 MSEK, which is 83 percent of the corresponding total

value in NR, 803 780 MSEK. In comparison with a detailed Use-table, where ex-

plicit services are excluded, INFI represents 84 percent.

This is a lower share compared to production, where IVP represents 91 percent of

the production value in NR, as mentioned above. Again, the intermediate consump-

tion of products in NR also includes services. But, even if the INFI-data on con-

sumption of industrial services is added, INFI represents about 90 percent of inter-

mediate consumption according to NR.

It turns out that the relative big difference between total intermediate consumption

in INFI and NR is mainly due to one specific industry, namely Manufacture of

coke and refined petroleum products (SNI2 = 19; SNI5= 19200). The intermediate

consumption of Samgods commodity group 13, Crude petroleum is 15 269 MSEK

according to INFI, and 77 493 MSEK according to NR.


Obviously there is an error in the delivery of INFI-data, but this error has been easy

to correct, as intermediate consumption of crude petroleum is imports, and deliv-

ered data on imports is correct in this respect19.

Agriculture, forestry and fishing

The production of commodities in the Agriculture, Forestry and Fishing sector

(SNI 01-03) is not covered by the IVP data and thus needs to be estimated from

other sources.

For agriculture, production numbers from the Economic Accounts for Agriculture

(EAA) provided by the Swedish Board of Agriculture is used. The data gives pro-

duction values on a detailed product classification on a national level. Those agri-

culture-specific commodity groups have been manually associated to Samgods

commodities and 5-digit SNI2007 codes (for allocating values to commodities)20.

The connection between EAA commodities and SNI codes was guided by the SNI

code descriptive labels. In cases were several SNI codes could be associated with a

certain EAA commodity, the distribution follows the number of employees in

goods-handling occupations in the different SNI industries, at the national level.

However, for some agriculture commodities, the CFS from 2004/2005 is based on

register data and thus completely covers all flows (for that year). Agriculture statis-

tics indicate that the harvest etc. has not changed exceedingly between 2004 and

2010, why CFS data for commodities 1 (cereals) and 3 (live animals) has been used

for estimation of P and C per municipality. The values have been scaled to 2010

prices.

For forestry, the production value according to CFS is used as well (for the same

reasons), but only for the estimation of P. Related Samgods commodities are 5

(pulp wood), 7 (wood chips and wood waste) and 31 (round wood). The values

from the 2004/2005 CFS have been scaled to 2010 prices.

The reason for not using the CFS for C estimation is that the shipments in the CFS

for forestry products have more of an O/D character, where D often is a terminal.

Therefore C is estimated using INFI, described above.

The fishing sector has been excluded from the calculations, since the produced

commodities are not included in any Samgods commodity.

19 INFI data has been revised by SCB in a second delivery.

20 See Chapter 4 in the Technical report.


National Accounts (NR), detailed

The supply and input-output tables in the National Accounts are based on detailed

tables further specifying the commodities and services included in the NR product

groups. At this level, it is possible to distinguish commodities from services and

moreover, to (manually) allocate each product label to a Samgods commodity.

Thus, services have been excluded and commodities have been aggregated to the

Samgods level21.

In these detailed tables, the intermediate consumption of all 2-digit SNI labels is

given. The information is used for estimating the intermediate consumption in sec-

tors 01-03 (Agriculture and Forestry) and 33-96 (Services) – the mining and manu-

facturing sector is already covered by the INFI at a more detailed level.

Further, final consumption - the consumption of households and the public sector,

and investments - is given at the same commodity classification level (which has

been aggregated to Samgods commodities).

Exports and imports

The FTS data are classified with respect to two different commodity groups, SPIN

2007 (5 digits) and Samgods34. SPIN is a classification of products by activity,

which means that products are linked to activities as these are defined in the classi-

fication of industries, SNI.

IVP and INFI provide data on production/ intermediate consumption of commodi-

ties by SNI code, i.e. the SNI code of industries producing/consuming the specific

commodity. However, the SPIN code provides information on the typical origin of

the exported/imported commodity, with respect to the SNI code of the industry

where the commodity has been produced. The conditions of using FTS data in this

context can be illuminated by some comparisons between foreign trade data in

NR/I-O and the FTS data delivered by SCB.

The I-O tables published by SCB (Symmetric input-output tables 2010 published

December 2012) reports in the table for total supply 2010 that the total exports in

the relevant product groups, i.e. corresponding to industries 07-32, is

1 035 374 MSEK.

In the table for domestic output the corresponding figure for exports is

929 198 MSEK. The difference in exports, 106 176 MSEK, is exports of imported

commodities, which is also reported in the Imports table. For the relevant product

groups (01-32) the total imports in the Imports table is 1 036 723 MSEK. The part

of this which is imports in intermediate consumption in industries 07-32 amounts

to 382 281 MSEK.

21 See Technical report.


Turning to FTS data, the corresponding total for exports of commodities with

SPIN-codes 07-32 is 1 070 011 MSEK, i.e. close to exports reported in the table for

total supply above, which also includes export of imported commodities. The total

imports (codes 01-32) in FTS data is 1 022 076 MSEK, i.e. close to what is report-

ed in the Imports table above.

For several reasons exports in FTS data has to be adjusted to be suitable for the

purpose at hand. First, FTS exports obviously include export of imported commod-

ities. In order to make estimations feasible, exports should refer to domestic out-

put22.

Second, production according to IVP represents less than 100 percent of production

according to NR, which also should be reflected in the estimates.

Third, the SPIN codes are not necessarily the same as the SNI codes of the produc-

ing industry. In which cases the SPIN code can/cannot be assumed to be the same

as the SNI code of the producing industry is unclear. The pragmatic method ap-

plied with respect to this issue is the following.

FTS reports exports for 251 SPIN groups. Preliminary it is assumed that the SPIN

code is the same as the SNI code. For 120 of these SPIN groups the exports are

larger than production in one or two commodity groups (Samgods34), according to

IVP. This reflects the inclusion of imported commodities in FTS data, and possibly

also that the SPIN code is not the same as the SNI code.

The first adjustment to be made is to exclude the part of exports which represent

imported commodities. According to the I-O tables this implies a reduction of FTS

export by about 10 percent. The distribution of this reduction on SPIN groups will

be guided by the I-O table for exports of imported products. Without other infor-

mation the further distribution on commodity groups (Samgods34) will follow the

existing distribution.

A second adjustment refers to cases where FTS exports, reduced by imports, are

larger than production according to IVP for the corresponding Samgods34 com-

modity groups. In these cases exports will be constrained by IVP, i.e. exports =

production.

At this stage there is no reason to adjust FTS data on imports; there is no need to

relate SPIN codes to SNI codes as the aim is to get imports per commodity group,

(Samgods34). However, in a later step some adjustments of imports are made in

order to fulfil the supply balance in Sweden for all Samgods commodities.

22 This argument is related to the P-C part of the estimation, where production (P) reduced

by exports defines consumption (C) of domestic production.


4.2 Allocation of production and consumption to municipalities

Commodities produced/consumed in mining and manufacturing

Estimates of production and intermediate consumption are allocated to municipali-

ties by their share of employment in goods-handling occupations in the respective

SNI5 industry. The Swedish Occupational Register with statistics (YREG) pro-

vides numbers on employment by industry h (5-digit SNI 2007) in goods-handling

occupations g and region r (municipality): 𝑔ℎ,𝑟. The distribution of production and

consumption of commodity k will be estimated as follows:

1. For each SNI5 industry, each municipality’s share of the employment in

goods-handling occupations is calculated: 𝑞ℎ,𝑟 = 𝑔ℎ,𝑟/ ∑ 𝑔ℎ,𝑟𝑟

2. From the various data sources described above, production (P) and con-

sumption (C) values per industry h and Samgods commodity k is given:

𝑃ℎ,𝑘 and 𝐶ℎ,𝑘.

3. Production and consumption values per Samgods commodity k and muni-

cipality r are calculated as 𝑃𝑘,𝑟 = ∑ 𝑃ℎ,𝑘 ⋅ 𝑞ℎ,𝑟ℎ and 𝐶𝑘,𝑟 = ∑ 𝐶ℎ,𝑘 ⋅ 𝑞ℎ,𝑟ℎ ,

respectively.

This is an improvement to previous matrices, where the regional distribution was

estimated by each municipality’s share of total employment (in contrast to em-

ployment in goods-handling occupations) in the respective industry. Figure 7 illus-

trates the difference in results between the two principles.

Figure 7 Estimated total production value MSEK (SNI 07-32) by municipality in year 2010, allocation by employment and by employment in goods-handling occupations.

0

20 000

40 000

60 000

80 000

100 000

120 000

140 000

0 20 000 40 000 60 000 80 000 100 000 120 000 140 000

MSE

K A

lloca

tio

n b

y e

mp

loym

en

t in

go

od

s-h

and

ling

occ

up

atio

ns

MSEK Allocation by employment

Stockholm

Göteborg

Södertälje

Lysekil


The most striking difference concerns the value allocated to Stockholm. The value

allocated by employment in goods handling occupations is less than 30 percent of

the value based on allocation by total employment in the respective industries.

Other commodities and allocation of final consumption

For other commodities the allocation of production and intermediate consumption

is made is made in slightly different way. This is described below, together with a

description of how final consumption is allocated to municipalities.

Forestry: the production values of commodities 05, 07 and 31 are allocated

to municipalities according to CFS 2004/2005 values. The CFS values are

added to any production values originating from the IVP, which have been

allocated as described above.23

Agriculture: Production of commodities 01 and 03 in SNI 01 sectors are al-

located to municipalities according to the CFS.

Intermediate consumption in Agriculture and Forestry: The intermediate

consumption values are given per 2-digit SNI industry, why the allocation

is made by employment in goods-handling occupations per 2-digit SNI

codes (instead of 5-digit).

Intermediate consumption in the Service sector: The intermediate con-

sumption values in the service sector are allocated by total employment per

industry (SNI 2-digit, in some cases 3-digit) and municipality, since the

employment in goods-handling is low and less relevant for estimating the

intermediate consumption of goods in this sector.

Final consumption, households and public sector: The final consumption

of households and the public sector is first allocated to counties by data on

household disposable income, which is available on the county level, but

not on the municipality level. The allocation to municipalities within each

county is made by data on assessed income.

Final consumption, investments: Investments are first allocated to NUTS2

regions24 by published data on gross capital formation. Thereafter the allo-

cation on municipalities within each NUTS2 region is based on published

data on value added/gross regional product.

Total consumption of commodities 01 and 03: The sum of intermediate and

final consumption of commodities 01 and 03, estimated as described

above, is replaced by the consumption according to the CFS including the

allocation to municipalities.

23 This is of importance mainly for commodity 7, which is produced both in manufacturing

and forestry.

24 NUTS = Nomenclature of Units for Territorial Statistics. At the 2-digit level there are 8

regions in Sweden


4.3 Price adjustments of estimated consumption

All data on consumption (NR and INFI) are given in purchaser’s prices, while all

other data (production, import and export) are given in basic prices. Purchaser’s

prices also include trade and transport margins, and the net of taxes and subsidies.

Consumption values thus need to be adjusted to basic prices. This is done with re-

spect to the supply balance for each Samgods commodity.

Estimates are aggregated to total national levels per commodity for

Production (𝑃𝑘) – basic prices

Exports (𝑋𝑘) – basic prices

Consumption (𝐶𝑘) – purchaser’s prices

Imports (𝑀𝑘) – basic prices

The supply balance gives that 𝑃𝑘 + 𝑀𝑘 = 𝐶′𝑘 + 𝑋𝑘 must hold for each commodity

k (𝐶𝑘′ here stands for 𝐶𝑘 in basic prices, which we want to estimate). Note that im-

ports and exports used here are according to the original data delivered by SCB,

before adjustments. 𝐶′𝑘 is given by 𝐶𝑘′ = 𝑃𝑘 + 𝑀𝑘 − 𝑋𝑘 for each commodity k.

The resulting 𝐶𝑘′ (basic prices) is compared to 𝐶𝑘 (purchaser’s prices) resulting

from the estimated consumption in order to get scale factors 𝑞𝑘 = 𝐶𝑘′ /𝐶𝑘 per com-

modity k. The scale factors 𝑞𝑘 are then applied to all consumption estimates (in-

termediate and final consumption per commodity and municipality).

In total, all consumption is scaled by 68 %. Turning to the National Accounts for

validation, the same scale factor is 72 % (but including services), which gives a

hint that the number is reasonable.

4.4 Estimation of imports

The adjustments of the export statistics in order to exclude export of imported

goods have been described above in section 4.1, and the import statistics must be

adjusted accordingly. Using the same notation as in the previous section, import

per commodity k is calculated as 𝑀𝑘 = 𝐶𝑘′ + 𝑋𝑘

′ − 𝑃𝑘. 𝐶𝑘′ are the adjusted con-

sumption values and 𝑋𝑘′ are the export values adjusted as described above.

4.5 Wholesale (W)

The amount of goods passing through wholesale on its way from production (or

import) to consumption (or export), is estimated by the activity in the wholesale

sector. The wholesale sector is represented by SNI codes 45 and 46. SNI 45 is

Wholesale and retail trade; repair of motor vehicles and motorcycles. In this case

we are only interested in the wholesale part of SNI 45, and will try to exclude retail

trade and repair services as much as possible. SNI 46 is Wholesale trade, except of

motor vehicles and motorcycles.


SNI 45 and 46 are handled separately. The activity in (parts of) SNI 45 is assumed

to relate only to the wholesale of Samgods commodity 25 (Transport equipment),

while the activity in SNI 46 is assumed to relate only to other Samgods commodi-

ties (1-7, 9-24, 26-29, 31-33).

Wholesale of commodities 01, 05, 07 and 31 is completely covered by the

CFS2004/2005, why the CFS values are being used for these commodities.

Basic datasets and assumptions

Statistics Sweden provides structural business statistics, where costs for goods for

resale (i.e. purchases of goods with the purpose to be sold) are given per 5-digit

SNI codes, see Table 5 below. For SNI 46 the resulting value is an estimation of

the value of goods handled by the wholesale sector. For SNI 45, however, the re-

sulting value also includes retail trade of motor vehicles. In order to adjust for this,

estimated consumption (C in above sections) of Samgods commodity 25 is sub-

tracted. After these initial steps, the estimations of W in sectors SNI 45 and 46 are

allocated to Samgods commodities and geographical zones (municipalities).

Table 5 Initial steps

SNI sector 45, excluding 45.2 (repair

services)

46

Goods for resale 214 805 888 521

Of which retail trade 142 985 -

Estimation of wholesale trade 71 820 888 521

Wholesale trade covered by

CFS (commodities 1,5,7,31)

- 2 689

Remaining wholesale trade 71 820 885 832

Samgods commodities 25 2-4, 6, 9-24, 26-29, 31-33

In total, the wholesale trade is estimated to 960 341 MSEK in 2010, which equals

42 % of the total supply (production and import) of commodities in Sweden, ac-

cording to the estimations described in previous sections.

In the following sections, the proceeding steps for SNI 45 and SNI 46 values are

described separately.


Wholesale trade of Samgods commodity 25 – Transport equipment

According to the results of the initial steps, the wholesale trade in sector SNI 45 is

estimated to be 71 820 MSEK year 2010, and it is assumed that the total value is

wholesale trade in Samgods commodity 25, transport equipment. Thus, the value is

already allocated to commodities. The next step is to allocate the wholesale trade to

municipalities. The geographical allocation is made in two steps.

1. To counties, by using information on the production value in sector SNI 45

per county, see Figure 8 below. The production value per county is only

available for 2-digit SNI codes, why the entire SNI 45 sector has been used

to allocate wholesale trade of Samgods 25 to counties.

2. To municipalities in each county, by using information on number of em-

ployees in sector SNI 45 (excluding SNI 45.2 – repair services) per munic-

ipality.

Figure 8 Allocation of wholesale trade in Samgods 25 to counties

Wholesale trade of other Samgods commodities

According to the results of the initial steps, the wholesale trade in sector SNI 46 is

estimated to be 888 521 MSEK year 2010, which is to be allocated to the Samgods

commodities 1-7, 9-24, 26-29 and 31-33, and thereafter to municipalities.

Out of this amount, 2 689 MSEK originates from the wholesale trade of commodi-

ties 1, 5, 7 and 31 which is given by the CFS (values are scaled to 2010 prices).

The remaining amount is allocated to commodities and municipalities as described

below.

0%

5%

10%

15%

20%

25%

30%

01

Sto

ckh

olm

s lä

n

03

Up

psa

la lä

n

04

Sö

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man

lan

ds

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05

Öst

ergö

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06

Jö

nkö

pin

gs lä

n

07

Kro

no

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gs lä

n

08

Kal

mar

län

09

Go

tlan

ds

län

10

Ble

kin

ge lä

n

12

Skå

ne

län

13

Hal

lan

ds

län

14

Väs

tra

Gö

tala

nd

s lä

n

17

Vär

mla

nd

s lä

n

18

Öre

bro

län

19

Väs

tman

lan

ds

län

20

Dal

arn

as lä

n

21

Gäv

leb

org

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n

22

Väs

tern

orr

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ds

län

23

Jäm

tlan

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24

Väs

terb

ott

ens

län

25

No

rrb

ott

ens

län

Shar

e o

f p

rod

uct

ion

val

ue

County


Wholesale per Samgods commodity

The allocation is made by connecting 5-digit SNI 46 codes to Samgods commodi-

ties. The connections are based in the description of the SNI code. In some cases

several commodities fit the description of a certain SNI code. In these cases the

connection is split between commodities, with fractions according to the total sup-

ply of the respective commodities25.

The costs for goods for resale are given in the statistics per 5-digit SNI46 code, so

by connecting SNI codes to Samgods commodities, the wholesale trade per com-

modity has been estimated26. The result is shown in the figure below, together with

the total supply for each commodity27.

Note that commodities 24 (paper pulp and waste paper) and 28 (paper, paperboard;

not manufactures) have no wholesale trade. For other commodities wholesale trade

represents from 7 % up to 124 % of the value of total supply. Wholesale shares

exceeding 100 % could be explained in several ways, e.g. too aggregate connec-

tions between SNI codes and Samgods commodities, goods passing through multi-

ple trade steps, and trade with goods from stocks.

However, the wholesale is assumed to not exceed the total supply per commodity

group (production + imports). Therefore, in these cases the wholesale for the total

commodity has been scaled down to 100 % of the total supply of that commodity.

25 A table of the connections can be found in Chapter 5 in the Technical report.

26 After this report was produced, calculations have been adjusted. Commodity 13 (crude

oil) is assumed to not be subject to wholesale. The volumes allocated to commodity 13 in

these results have been reallocated to other commodities, mainly commodity 14 (petroleum

products).

27 Results for Samgods commodity 25, from SNI 45 calculations above, are also included in

the figure.

0

100 000

200 000

300 000

400 000

500 000

600 000

1 3 5 7 10 12 14 16 18 20 22 24 26 28 31 33

MSE

K

Wholesaletrade

Total supply


The resulting value of the total wholesale is 947 097 MSEK. Wholesale per muni-

cipality

In the previous step, wholesale trade was allocated to commodities, by using the

costs for goods for resale at the 5-digit level of SNI 46, which has been connected

to Samgods commodities. The same information is used for allocating the whole-

sale trade to municipalities. For each 5-digit SNI 46 code, each municipality’s

share of the total wholesale is estimated by the percentage of the total number of

employees in that SNI code working in each municipality. The wholesale per SNI

code and municipality is then summed together for all SNI codes connected to a

certain Samgods commodity, to obtain wholesale per municipality and Samgods

commodity.

However, we also have information on the production value of the total SNI 46

sector per county, which could be used as a proxy for the wholesale trade per coun-

ty. Summing the results per municipality to the county level gives the distribution

of the estimated wholesale. These two distributions are shown in Figure 9 below.

Figure 9 Comparison of the fraction of the wholesale sector’s production value per county (statistics) and the estimated wholesale trade per county (summed estimations per municipality)

We see that the distributions are similar, but differ quite much in some cases, espe-

cially for county 14 (Västra Götaland). In order to adjust for the differences, the

estimated wholesale trade values per municipality are scaled with a county-specific

factor. This does not affect the total level of wholesale trade for all commodities

and all counties, but to some extent the distribution over commodities. The effects

on the commodity mix are shown in Figure 10.

.

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

01 03 04 05 06 07 08 09 10 12 13 14 17 18 19 20 21 22 23 24 25

Frac

tio

n o

f to

tal

County

Production value

Resultmunicipalities


Figure 10 Distribution of wholesale trade over Samgods commodities, before and after adjustment to fit distribution of production value per county

4.6 Results, total values for P, C, W, exports and imports

Figure 11 below gives an overview of the estimated total values26.

Figure 11 Estimated P, W, C, exports and imports per Samgods commodity year 2010. Billions of SEK.

0

50000

100000

150000

200000

250000

1 3 5 7 10 12 14 16 18 20 22 24 26 28 31 33

MSE

K

Samgods commodity

After county-spec.adjustm.

Before county-spec.adjustm.

0

50

100

150

200

250

300

350

01 02 03 04 05 06 07 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31 32 33

Bill

ion

SEK

Samgods commodity

Production

Consumption

Imports

Exports

Wholesale


5 Prediction of base year ton matrices Up to this point a description of the data, the general methodology, PWC model

estimation and estimation of production and consumption data has been addressed.

Now, it is time to put the pieces together and make base year predictions of goods

flows for the different types of Samgods commodities for the year 2012.

5.1 Steps going from value 2010 to weight 2012

Upscaling from value 2010 to value 2012

Thus, we have estimates of the value of P, C and W per Samgods commodity and

municipality, in year 2010. From National Accounts (NR) we have data on the

production value per commodity group (n=245) in current prices for year 2010 and

2012. These values are aggregated to Samgods commodity groups. Data from FTS

provides exports and imports, and consumption is derived residually from the sup-

ply balance. We use this information from NR, on growth of national P, C, Exports

and Imports, to upscale our estimates in value from year 2010 to 2012.

Conversion from value 2010 to weight 2010

The next step is to convert our estimates in value 2012 to estimates in weight 2012,

by use of the commodity values (1000 SEK per ton) estimated from the CFS

2004/2005 and the commodity value model in a separate part of the PWC-project28.

From the commodity value model we get the estimated national commodity values

for exports and imports in year 2012, which are applied to the export and import

estimates in order to obtain these numbers in weight.

From this project we also have the estimated commodity values differentiated by

municipality for imports and exports. It is assumed that the regional variation of

export commodity values applies to the production values, and the regional varia-

tion of import commodity values applies to consumption. However, the absolute

level of domestic trade commodity values could differ from corresponding foreign

trade commodity values. Thus, only the relative difference in commodity values

between municipalities has been used to differentiate national production and con-

sumption commodity values.

Thus, national levels of exports and imports per Samgods commodity in tonnes are

estimated directly using the export and import commodity values for 2012. The

procedure for obtaining national levels for production per Samgods commodity in

tonnes is described below. Consumption in tonnes per commodity is derived resid-

ually from the supply balance, and finally wholesale levels per commodity in

28 See report ”Nya varuvärden 2040 - data, metod och resultat” (2015-02-06), ”Varuvär-

desmodellen Bilaga med modellresultat mm_150206.xlsx


tonnes is estimated from total production per commodity, using weight shares from

the CFS 2004/2005. For some commodities (3, 4, 21 and 24) wholesale is missing

or has unreliable values in the CFS. In those cases, the shares of total supply in

value 2010 are applied instead.

National levels for production, consumption and wholesale are allocated to munic-

ipalities according to the same distribution as for value 2010 described in earlier

chapters, except that for production and consumption the regional variation given

by the differentiated commodity values for export and imports are applied as well.

Estimation of national commodity values for production

The CFS for 2004/2005 indicates that domestic trade commodity values could dif-

fer substantially from corresponding foreign trade commodity values. Especially

for commodities with a low degree of foreign trade in relation to the total trade, it

is risky to assume that the foreign trade commodity values apply to all goods. The

only source of information on commodity values except from foreign trade is the

CFS. Thus, commodity values from the CFS 2004/2005 are being used together

with the SCB production price index in order to get values for 2012. Only ship-

ments originating from producers (i.e. not wholesale) in the CFS are considered.

Produced commodities are either consumed in Sweden or exported. Therefore, do-

mestic as well as export shipments in the CFS are included.

For commodities 4 and 28, values are missing in the CFS and the export commodi-

ty values are being used instead. Production commodity values for commodities

with a high degree of export are compared to export commodity values. For ho-

mogenous commodity groups, where large differences cannot be explained by dif-

ferent sub-commodities in domestic and foreign trade, export commodity values

are being used instead of the CFS values. This applies to commodities 6, 15 and 21.

For commodity 22, the CFS value is unreasonable high, and an average of the im-

port and export commodity value is being used instead.

Results

These estimations give the results presented in Table 6 below.

Table 6 Row and column sums 2012 in tonnes

Million tonnes 2012

Production 245.0

Consumption 242.6

Exports 83.1

Imports 80.7

Wholesale 46.6


The sum of the national totals of production, import and wholesale for 2012 is

372.6 Mton. The corresponding sum in CFS for year 2004/2005 is 349.7 Mton.

What would be the corresponding sum of our estimate in year 2004/2005? Assum-

ing that the growth of exports and imports in tons between 2004/2005 and 2012

(9.8 % and 5.3 %, respectively) can be used as a proxy for total growth in tons, the

corresponding sum of our estimate in year 2004/2005 is 346.5 Mton. The conclu-

sion is that our estimate for year 2012 seems to be in agreement with the CFS esti-

mate for year 2004/2005, and definitely within the 95 % confidence interval.

5.2 Commodity flows 2012

The PWC matrix models have been estimated for each type of commodity where

there is CFS data. This data relates to the years 2001 and 2004/05, and provide the

parameter estimates of the models. It is assumed that those parameters are stable

over time, and that predictions can be made based on the estimated regional pro-

duction and consumption patterns according to the description above.

Given the production and consumption of 2012 expressed in tons, the PWC matrix

models are applied to generate predictions of 2012 commodity flows. These predic-

tions are calibrated to exactly reproduce the marginal constraints imposed on pro-

duction and consumption by Swedish municipalities and those restrictions imposed

on exports to and imports from foreign zones.

This calibration is achieved through a RAS balancing procedure, which may be

equivalently thought of as the introduction of origin and destination specific con-

stants which are calibrated such that the marginal constraints are satisfied.


6 Conversion of base year ton matrices into Samgods format

Demand matrices for Samgods are not expressed only in terms of yearly volumes

in tonnes between pairs of PWC-zones, but each demand value is also split into 10

possible categories. These are A) regular flows between pairs of firms at the re-

spective ends being of size small, intermediate or large, all in all 9 different combi-

nations, and B) singular flows that are very large flows of certain product groups in

some relations. Examples are iron ore flows from Kiruna/Gällivare to different

places and steel from Luleå to Borlänge. Also a modelled number of these so called

f2f-flows (firm-to-firm flows) must be provided to Samgods. Exogenous input in

terms large rail transport volumes and of transit flows, primarily related to Norway,

are introduced.

The basic tonne matrices according to Chapter 5 (these are denoted BASEMTX in

short) for Samgods product groups are modified to meet these demands in the fol-

lowing manner:

1. Singular flows introduced. These are observed flows larger than the aver-

age observed CFS-flows plus five standard deviations, and large system

train flows obtained from Trafikverket [2014a]. The total values in the ma-

trix are adjusted so as to preserve the total matrix volume.

2. Transit flows are added according to input data from Trafikverket

[2014b,c].

3. The matrices elements are split into a number of f2f-relations (firm-to-firm

relations) needed for the logistics model approach, see Edwards et al

[2008, Chapter 7]. For product group 15, iron ore, the large demands are

moved into firm-to-firm categories 3, 6, 7, 8, 9 from Pajala and Gällivare

to allow for system trains to be used.

4. All demand values are labelled as P (as in production) in the matrices (in

the 2006 version the demand was split into demand originating from P och

W (as in warehouse).

5. Air freight matrices (product group 35) are constructed from the CFS-data

in the same manner as described in Edwards et al [2008], but they are up-

scaled with the overall growth factors 2006-2012 for domestic, export and

import flows (1.171, 1.024, 1.036).

6. One important technical difference is that with 2010 data there is no data

available for construction of demand matrices for product groups 08 and

34, in addition to number 30 that was not available in the 2006 version. In

order for the logistics model programs to function properly, template ma-

trices are introduced with dummy input values for these product groups.

7. Note that Heby kommun still is referred to as zone 891700 (kommun num-

ber 1917) and not as zone 733100 as it should be according to Samgods

conventions. The reason is that the input data in Samgods is not yet updat-

ed to accommodate this change.


The format for the matrices to Samgods version 1.0 are the same as the one used in

Edwards et al [2008]. For future Samgods versions, Trafikverket will provide a

revised format (in the form of a regular table) to which the matrices will be refor-

matted. For the time being they are delivered according to the format below:

Psite Csite FCat Tonnes #f2f15

711400 961900 2 0.53891E+00 1

711400 963500 2 0.14432E+01 1

711400 969000 2 0.79265E+00 1

711400 969100 2 0.79265E+00 1

711400 972100 2 0.14663E+00 1

711400 972200 2 0.14663E+00 1

711400 972300 2 0.14663E+00 1

711400 972400 2 0.14663E+00 1

Matrices according to the present format are labeled pwc2012_nn.txt where nn is

the product group number with a leading zero for products 1-9. Matrices according

to the new format above are labeled pwc2012_nn_Table.txt.

The BASEMTX matrices are also included as text files mtxnn..dat (regular ascii

files with matrix values in a 464 by 464 matrix. In these matrices Heby kommun is

located as serial number 30.

All these base matrix data is saved in a compressed file BasMatriser2012.zip.

6.1 Results

The base matrices from 2006 are summarized in Table 7 and Table 8. Then new

2012 version is summarized in Table 9 and Table 10, and the growth rates are pre-

sented in Table 11 and Table 12.


Table 7 Base matrix 2006 summary

BASE MATRICES 2006 Domestic eXport iMport Transit

Basematrices 2006 [Mton]

Product D06 X06 M06 T06 Total

Spannmål 1 3.898 1.058 0.258 0.000 5.21

Potatis, andra färska eller frysta köksväxter, färsk frukt2 3.705 0.122 1.077 0.000 4.90

Levande djur 3 0.453 0.004 0.001 0.000 0.46

Sockerbetor 4 2.644 0.151 0.158 0.000 2.95

Rundvirke 5 36.792 1.249 8.234 0.000 46.27

Sågade och hyvlade trävaror 6 3.995 5.788 0.236 0.011 10.03

Flis, sågavfall 7 8.606 0.539 2.455 0.006 11.61

Bark, kork, övr. virke, ved (ej brännved) 8 0.000 0.031 0.067 0.000 0.10

Obearbetade material eller halvfabrikat avs. textil, textilartiklar, konstfibrer och andra råmaterial från djur eller växter9 0.132 0.114 0.308 0.102 0.66

Livsmedel och djurfoder 10 14.787 1.323 3.376 2.240 21.73

Oljefrön, oljehaltiga nötter och kärnor samt animaliska och vegetabiliska oljor och fetter11 9.969 0.306 0.746 0.000 11.02

Stenkol, brunkol och torv samt koks och briketter därav12 1.595 0.203 4.000 0.000 5.80

Råolja 13 0.000 0.000 20.503 0.000 20.50

Mineraloljeprodukter 14 12.141 12.646 9.464 0.001 34.25

Järnmalm, järn- och stålskrot samt masugnsdamm 15 8.660 18.128 0.429 0.006 27.22

Icke järnhaltig malm och skrot 16 1.227 0.629 1.133 0.001 2.99

Obearbetat material eller halvfabrikat av järn eller metall17 7.527 5.898 4.403 1.157 18.99

Cement, kalk och byggnadsmaterial 18 17.948 1.867 1.670 0.002 21.49

Jord, sten, grus och sand 19 15.657 2.288 1.389 0.002 19.34

Annan rå och obearbetad mineral 20 6.432 2.944 3.124 0.004 12.50

Gödselmedel, naturliga och tillverkade 21 0.930 0.271 0.724 0.000 1.93

Kolbaserade kemikalier och tjära 22 0.052 0.631 0.173 0.000 0.86

Andra kemikalier än kolbaserade och tjära 23 3.795 5.000 5.537 0.002 14.34

Pappersmassa, returpapp och pappersavfall 24 3.926 3.777 1.280 0.049 9.03

Maskiner, apparater och transportmedel, samt delar därtill25 1.022 1.497 1.264 0.666 4.45

Arbeten av metall 26 3.877 0.458 0.515 0.235 5.08

Glas, glasvaror och keramiska produkter 27 0.711 0.335 0.275 0.147 1.47

Papper, papp och varor därav 28 1.645 10.414 0.842 0.109 13.01

Diverse andra färdiga varor 29 5.936 1.064 1.477 0.613 9.09

30 0.000 0.000 0.000 0.000 0.00

Rundvirke till sågverk 31 14.348 0.001 0.534 0.000 14.88

Maskinutrustning och motorer, tillbehör 32 3.219 1.937 1.493 0.828 7.48

Papper och pappersprodukter 33 4.360 0.450 0.360 0.008 5.18

Förpackningsmaterial, övrigt avfall 34 2.512 0.187 0.158 0.083 2.94

Air freight (2006 model) 35 0.634 0.256 0.090 0.000 0.98

SUM 203.13 81.56 77.75 6.27 368.72


Table 8 Base matrix 2006 summary – STAN groups

BASE MATRICES 2006Domestic eXport iMport Transit Total

STAN produkt STAN nr Base matrices 2006 [Mton]

Jordbruk 1 20.67 1.64 2.24 0.00 24.55

Rundvirke 2 51.14 1.25 8.77 0.00 61.16

Trävaror 3 12.60 6.36 2.76 0.02 21.73

Livsmedel 4 14.79 1.32 3.38 2.24 21.73

RåoljaKol 5 1.60 0.20 24.50 0.00 26.30

Oljeprodukter 6 12.19 13.28 9.64 0.00 35.11

JärnmalmSkrot 7 9.89 18.76 1.56 0.01 30.21

Stålprodukter 8 7.53 5.90 4.40 1.16 18.99

PapperMassa 9 9.93 14.64 2.48 0.17 27.22

JordStenBygg 10 40.04 7.10 6.18 0.01 53.33

Kemikalier 11 4.73 5.27 6.26 0.00 16.26

Färdiga industriprodukter 12 18.04 5.85 5.58 2.67 32.14

SUM 203.13 81.56 77.75 6.27 368.72


Table 9 Base matrix 2012 summary

BASE MATRICES 2012 Domestic eXport iMport Transit

Basematrices 2012 [Mton]

Product D12 X12 M12 T12 Total

Spannmål 1 2.274 0.938 0.632 0.010 3.854

Potatis, andra färska eller frysta köksväxter, färsk frukt2 10.162 0.075 1.177 0.421 11.835

Levande djur 3 0.744 0.002 0.000 0.000 0.746

Sockerbetor 4 0.294 0.000 0.000 0.000 0.294

Rundvirke 5 45.963 0.527 6.609 0.051 53.150


Flis, sågavfall 7 9.312 0.262 1.064 0.131 10.769




Oljefrön, oljehaltiga nötter och kärnor samt animaliska och vegetabiliska oljor och fetter11 1.190 0.223 0.904 0.206 2.523

Stenkol, brunkol och torv samt koks och briketter därav12 0.732 0.379 5.940 0.015 7.065

Råolja 13 0.000 0.000 20.190 0.000 20.190



Icke järnhaltig malm och skrot 16 1.592 0.395 0.379 0.154 2.521


Cement, kalk och byggnadsmaterial 18 5.932 1.429 1.719 0.235 9.315



Gödselmedel, naturliga och tillverkade 21 0.221 0.426 0.957 0.025 1.627

Kolbaserade kemikalier och tjära 22 0.029 0.000 0.034 0.750 0.813








30 0.000 0.000 0.000 0.000 0.000






SUM 215.05 83.68 80.86 6.89 386.48


Table 10 Base matrix 2012 summary – STAN groups

BASE MATRICES 2012Domestic eXport iMport Transit Total

STAN produkt STAN nr Base matrices 2012 [Mton]

Jordbruk 1 14.66 1.24 2.71 0.64 19.25

Rundvirke 2 58.97 0.55 6.63 0.05 66.20

Trävaror 3 12.90 6.46 1.28 0.70 21.34

Livsmedel 4 15.94 1.87 3.40 2.10 23.31

RåoljaKol 5 0.73 0.38 26.13 0.01 27.26

Oljeprodukter 6 19.85 15.76 9.43 0.76 45.80

JärnmalmSkrot 7 11.73 22.59 0.44 0.44 35.21

Stålprodukter 8 4.20 5.21 4.57 0.00 13.99

PapperMassa 9 7.19 14.31 2.09 0.46 24.05

JordStenBygg 10 47.45 5.63 6.25 0.31 59.64

Kemikalier 11 7.75 4.15 9.61 0.02 21.53


SUM 215.05 83.68 80.86 6.89 386.48


Table 11 Base matrices differences – Ratios 2012 / 2006 [%]

BASMATRICES 2006-2012. Ratio 2012/2006 [%]

Domestic eXport iMport Transit

Base matrices growth [%]

VarugruppI06 X06 M06 T06 Total

Spannmål 1 58.3 88.7 245.5 - 73.9

Potatis, andra färska eller frysta köksväxter, färsk frukt2 274.3 61.7 109.3 - 241.3

Levande djur 3 164.0 61.6 48.3 183.0 163.1

Sockerbetor 4 11.1 0.0 0.0 0.0 10.0

Rundvirke 5 124.9 42.2 80.3 - 114.9


Flis, sågavfall 7 108.2 48.6 43.4 2345.8 92.8




Oljefrön, oljehaltiga nötter och kärnor samt animaliska och vegetabiliska oljor och fetter11 11.9 72.9 121.1 - 22.9

Stenkol, brunkol och torv samt koks och briketter därav12 45.9 186.5 148.5 - 121.8

Råolja 13 0.0 0.0 98.5 0.0 98.5



Icke järnhaltig malm och skrot 16 129.8 62.9 33.5 - 84.3


Cement, kalk och byggnadsmaterial 18 33.1 76.6 102.9 - 43.4



Gödselmedel, naturliga och tillverkade 21 23.7 157.0 132.1 - 84.5

Kolbaserade kemikalier och tjära 22 56.3 0.0 19.6 - 95.0








30 0.0 0.0 0.0 0.0 0.0






TOTAL 105.9 102.6 104.0 109.9 104.8


Table 12 Base matrices differences – Ratios 2012 / 2006 [%] – STAN groups

The distribution among firm to firm relations is presented in Table 13, and the

number of cells in the PWC-matrices can be found in Table 14.

BASMATRICES 2006-2012 Ratio 2012/2006 [%]Inrikes eXport iMport Transit Total

STAN produkt STAN nr Base matrices growth [%]

Jordbruk 1 70.9 75.5 121.2 - 78.4

Rundvirke 2 115.3 44.0 75.6 - 108.2

Trävaror 3 102.4 101.6 46.4 4116.2 98.2

Livsmedel 4 107.8 141.1 100.7 93.7 107.3

RåoljaKol 5 45.9 186.4 106.6 - 103.6

Oljeprodukter 6 162.8 118.7 97.9 - 130.5

JärnmalmSkrot 7 118.7 120.5 28.5 6814.3 116.5

Stålprodukter 8 55.8 88.4 103.9 0.0 73.7

PapperMassa 9 72.4 97.7 84.3 276.3 88.3

JordStenBygg 10 118.5 79.4 101.0 3562.3 111.8

Kemikalier 11 164.0 78.7 153.5 926.2 132.4


TOTAL 105.9 102.6 104.0 109.9 104.8


Table 13 Firm-to-firm flow distributions

F2F-demand distributions (nbrs) in power of 10 classes [10^-6 <= x < 10^-5, etc ] [tonnes]#Tot nbr f2f-relations=19 928 117

0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

1 0 0 0 0 0 0 45 584 37 311 5 425 279 4 0 0

2 0 0 0 927 10 030 49 020 82 616 274 417 12 015 789 25 0 0

3 0 0 0 0 6 642 7 387 12 239 5 008 1 071 90 7 0 0

4 0 0 0 0 0 6 036 4 184 1 883 372 47 0 0 0

5 0 0 0 1 657 11 345 70 668 82 500 206 826 58 762 6 119 270 3 0

6 0 0 0 4 876 16 119 81 594 189 390 84 629 13 850 1 299 7 0 0

7 0 0 0 0 0 60 253 78 556 50 541 15 314 1 451 47 0 0

8 0 0 0 0 0 1 0 0 0 0 0 0 0

9 0 0 0 40 542 163 078 277 549 40 415 3 022 96 0 0 0 0

10 0 0 0 596 7 318 1 755 032 923 967 214 949 29 549 1 737 26 0 0

11 0 0 0 0 14 693 55 683 55 269 22 317 6 280 35 5 0 0

12 0 0 0 0 0 68 337 51 144 19 452 5 461 948 83 2 0

13 0 0 0 0 0 271 120 29 13 101 150 46 2

14 0 0 0 0 13 993 29 206 29 425 39 323 12 721 4 002 643 51 0

15 0 0 0 0 3 201 2 759 1 014 328 252 39 3 0 0

16 0 0 0 0 0 12 413 7 136 3 040 1 087 271 40 1 0

17 0 0 0 20 058 31 010 59 092 139 331 62 727 13 876 1 497 57 0 0

18 0 0 0 8 376 19 671 97 823 425 271 100 650 11 576 634 15 0 0

19 0 0 0 0 0 13 049 14 657 71 937 37 528 6 375 504 0 0

20 0 0 0 0 13 373 55 613 78 457 47 003 9 587 1 187 41 0 0

21 0 0 0 0 0 0 24 914 12 790 2 262 199 4 0 0

22 0 0 0 7 547 16 843 24 994 7 714 1 956 0 0 0 0 0

23 0 0 0 6 049 14 166 116 341 279 889 163 136 30 909 2 357 37 0 0

24 0 0 0 0 8 618 8 619 4 953 3 240 2 209 809 87 1 0

25 0 0 0 21 061 44 366 217 425 165 058 29 308 3 365 242 3 0 0

26 0 0 0 5 638 19 585 194 494 1 869 579 21 029 71 0 0 0 0

27 0 0 0 29 053 30 463 176 894 64 301 8 561 456 10 0 0 0

28 0 0 0 0 0 24 925 23 709 19 505 4 767 1 276 74 0 0

29 0 0 0 1 530 6 796 2 247 242 1 084 559 179 476 12 643 255 0 0 0

30 0 0 0 0 0 0 0 0 0 0 0 0 0

31 0 0 0 0 0 29 984 24 372 20 210 37 298 1 573 38 0 0

32 0 0 0 5 222 19 539 2 713 042 774 952 101 870 6 413 58 0 0 0

33 0 0 0 5 212 24 637 895 414 418 675 71 823 9 339 661 0 0 0

34 0 0 0 0 0 1 0 0 0 0 0 0 0

35 0 0 0 13 934 213 162 373 583 52 647 6 198 173 0 0 0 0

SUM 0 0 0 172 278 708 648 9 724 744 7 056 597 1 884 494 344 740 34 340 2 170 104 2

% 0 0 0 0.9 3.6 48.8 35.4 9.5 1.7 0.2 0.0 0.0 1.0036E-05


Table 14 PWC-cell flow distributions

6.2 Introduction of singular flows

Singular flows and transit flows from the cited sources, Trafikverket [2014a-c] and

the CFS’s, are introduced after construction of the PWC-matrix elements according

to Chapter 5 (these are denoted BASEMTX in short). The data is aggregated into

Table 15 in which you can see that they will have a very considerable impact on

PWC-matrices for some product groups, e g product 15 where the exogenous input

is much larger for the domestic flows than what is inside the modelled matrix. Fur-

ther, a particular issue is that a large fraction of the exogenous system train input

regarding ore stops in Narvik, which in reality has destinations around the world.

This has been dealt with in a special manner.

Total demand distributions (nbrs) in power of 10 classes [10^-6 <= x < 10^-5, etc ] [tonnes]#Tot nbr PC-relations= 5 572 762

0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

1 0 0 0 0 0 0 45 584 26 176 2 109 130 2 0 0

2 0 0 0 927 10 030 49 020 82 616 67 957 3 494 262 8 0 0

3 0 0 0 0 6 642 7 387 6 683 2 106 491 41 2 0 0

4 0 0 0 0 0 6 036 4 184 1 883 311 46 0 0 0

5 0 0 0 1 657 11 345 70 668 82 500 78 186 17 791 3 237 188 3 0

6 0 0 0 4 876 16 119 81 594 138 983 63 100 13 113 1 292 7 0 0

7 0 0 0 0 0 60 253 78 556 50 541 14 961 1 402 46 0 0

8 0 0 0 0 0 1 0 0 0 0 0 0 0

9 0 0 0 40 542 64 317 39 847 8 088 1 111 34 0 0 0 0

10 0 0 0 596 7 318 156 062 135 151 74 640 16 282 983 21 0 0

11 0 0 0 0 14 693 55 683 55 269 22 317 3 543 6 1 0 0

12 0 0 0 0 0 68 337 51 144 19 433 5 457 948 83 2 0

13 0 0 0 0 0 271 120 29 13 101 150 46 2

14 0 0 0 0 13 993 29 206 29 425 25 490 8 253 2 645 435 42 0

15 0 0 0 0 3 201 2 759 1 014 307 111 31 3 0 0

16 0 0 0 0 0 12 413 7 136 3 040 1 087 271 40 1 0

17 0 0 0 20 058 31 010 51 202 58 384 29 044 9 359 1 423 57 0 0

18 0 0 0 8 376 19 671 97 823 147 757 27 519 4 709 336 8 0 0

19 0 0 0 0 0 13 049 14 657 24 462 9 576 1 850 137 0 0

20 0 0 0 0 13 373 55 613 78 457 45 448 9 279 1 150 41 0 0

21 0 0 0 0 0 0 24 914 12 790 2 262 199 4 0 0

22 0 0 0 7 547 16 843 24 994 7 615 849 0 0 0 0 0

23 0 0 0 6 049 14 166 69 459 106 050 73 772 21 133 1 942 37 0 0

24 0 0 0 0 8 618 8 619 4 953 3 240 2 209 809 87 1 0

25 0 0 0 21 061 44 366 87 348 41 355 16 492 2 597 236 3 0 0

26 0 0 0 5 638 19 585 144 728 313 736 1 874 14 0 0 0 0

27 0 0 0 29 053 30 463 71 723 12 321 2 345 172 5 0 0 0

28 0 0 0 0 0 24 925 21 694 10 761 3 935 1 250 73 0 0

29 0 0 0 1 530 6 796 213 279 220 236 94 707 8 129 168 0 0 0

30 0 0 0 0 0 0 0 0 0 0 0 0 0

31 0 0 0 0 0 29 984 24 372 14 314 7 041 220 4 0 0

32 0 0 0 5 222 19 539 277 832 103 462 21 236 1 347 13 0 0 0

33 0 0 0 5 212 24 637 141 410 56 518 19 706 3 165 221 0 0 0

34 0 0 0 0 0 1 0 0 0 0 0 0 0

35 0 0 0 13 934 29 886 25 855 3 504 430 21 0 0 0 0

SUM 0 0 0 172 278 426 611 1 977 381 1 966 438 835 305 171 998 21 217 1 437 95 2

% 0 0 0 3.1 7.7 35.5 35.3 15.0 3.1 0.4 0.0 0.0 3.5889E-05

Sum % 0 0 0 3.1 10.7 46.2 81.5 96.5 99.6 100.0 100.0 99.9999641 100


The singular matrices from 2001 and 2004/05 used in the 2006 version are consid-

ered too old (at least for the time being). Introducing these values obviously will

have a considerable impact on BASEMTX-elements, and at least some original

marginal values for rows and columns will be changed dramatically – in some case

all elements in a category (Domestic, eXport or iMport) will be set to zero with the

exception of the singular flows of course.

Table 15 Base matrix summary and values on exogenous input values from TRV and from the CFS:s 2001 and 2004/2005.

The reallocation due to introduced singular flows is described below in short. Nota-

tion used is:

B = matrix with elements as in BASEMTX

Sij = singular flow from zone i to zone j (i=P/W-zone and j=C-zone)

rB = partial row sum in B

cB = partial column sum in B

zoneX = set of indices for export-zones in a foreign country

zoneM = set of indices for import-zones in a foreign country

Base SingularTRV TransitTRV SingularVFU

Product D X M T D X M T T D X M

1 2.273 0.938 0.633 0 0 0 0 0 0.01 0.151 0.108 0.03

2 10.162 0.075 1.177 0 0 0 0 0 0.421 0 0 0

3 0.744 0.002 0 0 0 0 0 0 0 0 0 0

4 0.294 0 0 0 0 0 0 0 0 0 0 0

5 45.963 0.527 6.609 0 5.988 0 0.946 0 0.051 3.103 0 1.013

6 3.591 6.2 0.216 0 0 0 0 0 0.567 0.03 0.394 0.019

7 9.312 0.262 1.065 0 0.247 0 0 0 0.131 0.426 0 0.3

8 0 0 0 0 0 0 0 0 0 0 0 0

9 0.003 0.031 0.247 0 0 0 0 0 0.058 0 0 0

10 15.939 1.867 3.401 0 0.065 0 0 0.452 2.099 0.847 0.049 0.044

11 1.19 0.223 0.904 0 0 0 0 0 0.206 0.951 0 0.092

12 0.732 0.379 5.94 0 0 0 0 0 0.015 0 0 2.206

13 0 0 20.19 0 0 0 0 0 0 0 0 4.168

14 19.822 15.755 9.4 0 1.183 0 0 0 0.009 7.572 10.76 5.742

15 0 22.198 0.065 0 13.763 18.375 0 0 0.286 0 0 3.355

16 1.592 0.395 0.379 0 0 0 0 0 0.154 0 0.039 0.3

17 4.203 5.214 4.573 0 2.933 0.028 0.189 0 0 1.271 1.297 0.921

18 5.932 1.429 1.719 0 0.289 0 0 0 0.235 1.056 0.583 0.827

19 38.645 1.511 1.678 0 0 0 0 0 0.03 0 0 0

20 2.871 2.693 2.85 0 0 0 0.523 0 0.046 0.479 0.053 1.227

21 0.223 0.425 0.954 0 0 0 0 0 0.025 0.055 0 0.031

22 0.029 0 0.034 0 0 0 0 0 0.75 0 0 0

23 7.527 3.72 8.653 0 0.005 0 0 0 0 0.197 0.819 2.605

24 1.074 3.483 0.577 0 0 0 0 0 0.363 0.22 0.543 0

25 0.11 1.345 1.404 0 0 0 0 0 0.149 0.033 0 0

26 2.399 0.492 0.788 0 0 0 0 0 0.308 0 0.044 0

27 0.085 0.206 0.325 0 0 0 0 0 0 0 0 0.049

28 1.125 6.049 0.945 0 4.004 0 0 0 0.094 0.05 1.745 0

29 7.153 1.606 3.526 0 0.478 0 0 0 0.602 0.052 0.232 0.147

31 13.002 0.022 0.022 0 0 0 0 0 0 1.096 0 0.817

32 3.853 1.594 1.915 0 0 0 0 0 0.227 0 0.049 0.104

33 2.11 4.777 0.57 0 0 0 0 0 0 0.23 2.133 0

34 0 0 0 0 0 0 0 0 0.056 0 0 0.011

SUM 201.958 83.418 80.759 0 28.955 18.403 1.658 0.452 6.892 17.819 18.848 24.008


6.2.1 Domestic flow reallocation

When introducing a singular flow Sij (kept in a separate matrix) we reallocate B

according to:

rB = sum(B(i, 1:290))

rC = sum(B(1:290, j))

B(i,1:290) = max(0, rB – Sij) * B(i,1:290)/rB

B(1:290, j) = max(0, rC – Sij) * B(1:290, j) /rC

An exception is made for product group 15 (iron ore) for which all domestic trans-

ports has been replaced by exogenous input.

6.2.2 Export flow reallocation

When handling export relations we lack details about distribution among munici-

palities in Sweden of export flows, and we lack even more information regarding

the distribution among zones in foreign countries. Thus, we limit the reallocation of

flows to stay within the zones of the specific country, i e only a row allocation.

rB = sum(B(i, zoneX))

B(i,1: zoneX) = max(0, rB – Sij) * B(i, zoneX)/rB

As mentioned the iron ore distribution according to input data stops in Narvik for a

few huge volumes (> 100 000 tonnes). This is not a C-zone, and these volumes

must be considered to be aimed for the whole world. Therefore these are distribut-

ed to all zones in the world (in BASEMTX) with a yearly demand over 100 000

tonnes in proportion to their estimated column values.

6.2.3 Import flow reallocation

Import flows are managed in analogy with export flow, i.e.

rC = sum(B(zoneM, j))

B(1: zoneM, j) = max(0, rC – Sij) * B(zoneM, j)/rC

6.3 Domestic iron ore PWC-matrix elements

As shown in Table 15 the exogenous input of domestic flows (13.763 Mton) ex-

ceed the estimated a priori flows (5.73 Mton). For the discussion we show the de-

tails in

Table 16. All in all 5.54 Mton of the domestic flows ore in-zone transports in Kiru-

na. It is perfectly possible that the volume 3.33 Mton from Kiruna is included in

the 17.1 Mton flow to Narvik. The 2.21 Mton to the zone Kiruna seems odd. All

the 7.25 Mton from Gällivare to Luleå constitutes more than half of the domestic

volume. A question is whether some of it may be aimed for export? Finally there


are smaller volumes destined for Skellefteå port (0.28 Mton), that possibly should

continue as export volumes.

Table 16 Exogenous input of iron ore transports.

Based on e-mail correspondence with TRV on the above matters we have decided

to add the in-zone iron ore transports in Kiruna to the domestic part of the PWC-

matrix, and 50 % of the 7.25 Mton domestic volume from Gällivare to Luleå is

considered to be export.

The 0.52 Mton import to Kiruna via Narvik (olivin) is considered to belong to

product group 20. Narvik is regarded as the P-zone here.

Table 17 Exogenous input of iron ore transports after adjustments

D X M T

Revised 15 11.273 22.198 0.064 2.080

Difference to a priori mtx 5.543 0.000 0.000 2.080

DXM From To NSTR SAMGODS Yearly

volume STAN From To

D 952311 948221 110 15 5 000 7 Rail:_Gällivare Sea:_Skellefteå

D 952311 948221 110 15 270 000 7 Rail:_Gällivare Sea:_Skellefteå

D 958411 958012 110 15 420 000 7 Rail:_Kiruna_C Rail:_Luleå

D 958411 958400 110 15 2 213 000 7 Rail:_Kiruna_C Zone:_Kiruna

D 958012 958411 110 15 279 000 7 Rail:_Luleå Rail:_Kiruna_C

D 952311 958012 110 15 7 246 000 7 Rail:_Gällivare Rail:_Luleå

D 958400 958411 110 15 3 330 000 7 Zone:_Kiruna Rail:_Kiruna_C

SUMMA 13 763 000

X 958411 960700 110 15 17 139 000 7 Rail:_Kiruna_C Zone:_Narvik

X 952311 960700 110 15 1 236 000 7 Rail:_Gällivare Zone:_Narvik

SUMMA 18 375 000

M 960700 958411 110 15 523 000 7 Zone:_Narvik Rail:_Kiruna_C


6.4 Adjustments based on project committee meetings

The railway transit flows are all but one considered to belong to product group 29,

Other manufactured articles. The exception is a railway transit flow, 454 803

tonnes, from Narvik to Oslo which is considered to be product group 10, Foodstuff

and animal fodder.

Comparisons of the results from the Samgods model with PWC-matrices from

2006 and 2012 respectively in terms of domestic transport work, tonne kms, are

presented below. We first show a summary of results by mode and by port areas in

Table 18 and Table 19.

Comparisons with the tonne volume growths at 111 % for domestic demands and

107 % for the totals with a tonne km growth at 117 % indicates that the tonne km

growth is approximately 1 % higher than the tonne volume increase (tonne increase

is 1.6 %/year, tonne km increase is 2.6 %/year).

Table 18 Results from the Samgods model with 2012 and 2006 matrices respec-tively.

Note: Standard logistics model results and results after the first iteration, LP0, with the railway ca-pacity management module. Model settings are the same as the calibrated model but without the port calibration factors.

Table 19 Results by port area. Same terms as for results in Table 18. Statistics Source: Sjötrafik 2012 Statistik, Trafa 2013:11

STD chg RCM chg

STD logmod RCM LP0 STD logmod RCM LP0 2012/2006[%] 2012/2006[%]

Mtonkm Mtonkm Mtonkm Mtonkm

Road 41 466 45 959 42 069 45 724 99 101

Rail 40 779 26 180 33 507 23 874 122 110

Sea 38 335 46 361 38 820 44 581 99 104

Air 0 0 0 0 102 102

SUM 120 580 118 501 114 397 114 179 105 104

PWC2012 (as 2006R62 without

port calib) PWC2006 (2006R62)

PortArea Statistics 2012 RCM_LP0

Samgods 12

/Statistics [%]

Samgods 06

/Statistics

[%] RCM LP0 Statistics 2006

Haparanda-Skellefteå 1 9 197 7 769 84 80 9 265 11 586

Umeå-Sundsvall 2 7 809 6 554 84 85 7 955 9 363

Hudiksvall-Gävle 3 5 772 8 533 148 92 6 708 7 257

Norrtälje-Nynäshamn 4 10 282 26 636 259 102 13 241 13 007

Uppsala-Eskilstuna (Mälaren) 5 2 012 231 11 68 2 389 3 532

Södertälje-Norrköping 6 11 466 20 677 180 106 12 127 11 417

Västervik-Kalmar 0 - 80 3 575 4 443

Visby (Gotland) 0 - 66 3 839 5 808

Karlskrona-Trelleborg 7 20 798 3 204 15 39 9 891 25 274

Malmö-Helsingborg 8 16 085 22 161 138 63 11 049 17 572

Halmstad-Varberg 9 3 818 597 16 68 3 393 5 013

Göteborg(nedanför Trollhätte kanal) 10 38 313 26 872 70 102 40 784 40 061

Stenungsund-Strömstad 11 22 563 7 210 31.95 55 13 255 24 002

Trollhättan-Kristinehamn (Vänern) 12 1 741 2 797 160.64 145 3 497 2 413

SUMMA 149 856 133 241 89 78 140 969 180 747


The distributions of transport work among product groups 2006 and 2012 respec-

tively are shown in

-Figure 15. To summarize the results, the total results in terms of transport work

are similar to the ones for 2006.


Figure 12 Transport work by road 2006 and 2012 [billion tonne kms]

Figure 13 Transport work by rail 2006 and 2012 [billion tonne kms]


Figure 14 Transport work by sea 2006 and 2012 [billion tonne kms]

Figure 15 Transport work totals 2006 and 2012 [billion tonne kms]

Transport costs and volumes are presented in Appendix 3 for different distance

classes, split into domestic and international transports. Average transport costs and

distances are also shown there. Average transport distances for domestic transport

are summarized in Figure 16. Average transport costs for both domestic and inter-

national transports are shown in Figure 17.


Figure 16 Average distances for domestic transports29

Figure 17 Average costs per tonnekm (a cut off has been inserted at 50 SEK/tonnekm)

As expected the correlations between the matrices and the CFS-data at the PC-

relation level are not as good as the ones for the marginal values, cf. Table 20. The

entrance of exogenous input in some cases increase the correlation (ex P17), and in

some other the opposite (ex P15). The correlations with the marginal values from

the CFS 2004 are lower than those from the estimation since these marginal values

differ from those by construction. As a result, the correlations for the matrix ele-

ments naturally will be lower.

29 PC-4716\...\PWC2012-statistik_2015-04-17.xlsm


Table 20 Correlation between CFS-data and PWC-matrices and PWC-matrices before adding exogenous entries. The correlations with the marginal val-ues are shown in the four columns to right.

Commodity 19

Commodity 19 displayed a too large tonne km volume in the calibrated Samgods

model for 2006 compared to statistics. One reason was that the marginal condi-

tions, production and consumption, derived with the same method as for the other

products resulted in erroneous results. A probable reason is that the marginal con-

straint method does not regard inventory holding (e g at gravel and sand pits and

mines where large volumes are extracted).As a consequence production and con-

sumption were geographically spread widely which lead to many tonne kms. The

domestic transport work was estimated at a 4 times higher level than expected from

statistics. For these reason the predictions of the PWC 2012 matrix for commodity

19 has been adjusted according to properties of the 2006 matrices.

Product

Correlation

PWC-CFS

Correlation

TON2012-CFS PWC TON2012 PWC TON2012

1 0.564 0.564 0.874 0.875 0.797 0.798

2 0.070 0.070 0.540 0.539 0.191 0.191

3 0.280 0.280 0.410 0.410 0.687 0.687

5 0.406 0.549 0.729 0.725 0.426 0.322

6 0.265 0.265 0.628 0.630 0.690 0.685

7 -0.002 -0.006 0.305 0.301 0.220 0.219

9 0.025 0.025 0.000 0.279 0.113 0.132

10 0.351 0.351 0.279 0.652 0.820 0.869

11 0.109 0.109 0.604 0.153 0.170 0.174

12 0.833 0.833 0.146 0.818 0.764 0.764

13 0.680 0.680 0.819 0.506 0.939 0.939

14 0.189 0.206 0.506 0.690 0.320 0.317

15 0.504 0.668 0.692 1.000 0.563 0.645

16 -0.040 -0.040 0.981 0.437 0.582 0.584

17 0.973 0.170 0.435 0.551 0.911 0.318

18 0.397 0.398 0.863 0.847 0.662 0.685

19 0.379 0.379 0.844 0.403 0.377 0.377

20 0.126 0.130 0.403 0.206 0.145 0.190

21 0.028 0.028 0.216 -0.049 0.033 0.037

22 0.031 0.031 -0.049 0.048 0.412 0.257

23 0.207 0.207 -0.045 0.594 0.300 0.300

24 0.442 0.442 0.594 0.905 0.514 0.522

25 0.364 0.364 0.902 0.770 0.554 0.571

26 0.008 0.008 0.756 0.055 0.073 0.077

27 0.300 0.300 0.049 0.679 0.361 0.361

29 0.017 0.029 0.679 0.172 0.207 0.202

31 0.286 0.286 0.000 0.715 0.345 0.345

32 0.100 0.100 0.176 0.353 0.421 0.419

33 0.214 0.214 0.715 0.532 0.682 0.682

Row sums Column sums


The original production 2012 is provided in a vector P and the consumption by a

vector C. Corresponding values for 2006 was obtained from the PWC 2006 matrix

for commodity 19 (�̂�, �̂�). Linear combinations of P and C that best resembled the

2006 matrix were found by

�̂� = 𝑎𝑟𝑔𝑚𝑖𝑛𝑎 (∑(𝑎𝑃𝑟 + (1 − 𝑎)𝐶𝑟 −

290

𝑟=1

𝑃�̂�)2)

�̂� = 𝑎𝑟𝑔𝑚𝑖𝑛𝑏 (∑(𝑏𝑃𝑟 + (1 − 𝑏)𝐶𝑟 −

290

𝑟=1

𝐶�̂�)2)

New marginal conditions for production and consumption 2012 then were obtained

as:

�̌�𝑟 = (�̂�𝑃𝑟 + (1 − �̂�)𝐶𝑟), 𝑟 = 1, … ,290

�̌�𝑟 = �̂�𝑃𝑟 + (1 − �̂�)𝐶𝑟 , 𝑟 = 1, … ,290

Finally they were rescaled to reach the total domestic production and consumption

llevels for 2012.

�̃�𝑟 = �̌�𝑟

∑ 𝑃𝑠290𝑠=1

∑ �̌�𝑠290𝑠=1

, 𝑟 = 1, … ,290

�̃�𝑟 = �̌�𝑟

∑ 𝐶𝑠290𝑠=1

∑ �̌�𝑠290𝑠=1

, 𝑟 = 1, … ,290.

After this the revised marginal conditions were applied in the matrix element mod-

el (m) for commodity 19 providing a preliminary prediction.

𝐹𝑟�̃� = 𝑚(𝛽, 𝑥𝑟𝑠)𝟏{𝑑<150} = exp(𝛽𝑥𝑟𝑠) 𝟏{𝑑<150}

where x are explanatory variables as e g �̃�, �̃�, and the interzonal distances. An ex-

ogenous assumption was that none of these transports exceeds 150 kms (based on

CFS-data).The assumption was made to obtain a reasonable total domestic

transport work volume.

Finally the matrix {𝐹𝑟�̃�} was balanced to assume the marginal constraints provided

by �̃� och �̃�. The final matrix provides an average transported distance per tonne

close to the CFS 2006-data.

The calculations were made in Matlab with the script file PWCPredict.m and the

function RePredictQP() therein, see Appendix 4.


7 Additional adjustments For a number of reasons The Transport Administration (TRV) requires a Samgods

result with a domestic tonne-kilometre volume at an upper limit of 115 billion

tonne kms. The most important reason is that reported statistics indicate a total

transport volume in year 2012 at approximately 98-99 billion tonne kms, whereas

the 2006 value is 100 billion. However, when considering the uncertainties in-

volved in these estimates, with a coefficient of variation at perhaps 10 % (standard

deviation over estimated mean) it is not really possible to say in which directions

the transport volume has changed.

Anyhow, in a small follow up mission we have suggested a rebalancing of the pre-

dicted matrices, before adding the exogenous inputs, according to the following

model:

0[ ]min ln( ) 1

0

ij

ij ij iji jij

ij ij

ij ji

ij

xBALANCE z c d x x

x

subject to x P i marginal conditions onthe supply side(production,import)

x C j marginal conditions onthe demand side(consumption,export)

x

0 0, 0ijif x otherwise

where

xij = demand values from the prediction model

Pi and Cj = marginal constraints. These are applied to the matrix sections domestic,

export and import flows as required.

c = distance aversion coefficient

dij = domestic lorry distances from zone i to zone j with lorry type 104 in Samgods.

For the case when the distance parameter concerns export/import flows we have

used the domestic distances obtained from the logistics model in Samgods for the

concerned export/import flows.

Should the rebalancing be carried out due to other changes, the model [BAL-

ANCE] is applied with a distance aversion c = 0.

During the rebalancing runs made we came across situations where many interme-

diate row and column sum values got quite small. Such situations occur of course

and to avoid division by small numbers these rows/colums were set to zero during

the balancing. However, in order to reduce this from happening too often the pre-

dicted matrices were analysed with respect to volumes and frequency of occurrenc-

es in various demand classes. Based on this it was decided to aggregate all de-

mands amounting to a cumulative sum of tonnes at approximately 1 % of the total


volume (with a minimum of 1 tonne)30. The sums were distributed over the remain-

ing demand values, leading to an unchanged total demand. Conceivably a higher

value than 1 % could be used without making the model misrepresentative.

Changes are made in four steps, of which number 4 actually comprises a number of

consecutive small changes. Step 4 was performed mainly to keep the rebalancing

down to the lowest possible level (considering the project budget).

1. Revision of import destinations for raw oil (P13) and production sources

for refined products (P14). The four revised zones are Stockholm,

Nynäshamn, Göteborg and Lysekil. Rebalance with the model BALANCE

using c = 0. Product 34 is taken out (not included among PWC 2012 esti-

mates). Approximate impact: -2 billion tonne kms. Rather large raw oil

flows related to Härjedalen were removed31. According to exogenous sys-

tem train input those are represented by system train flows between Här-

jedalen-Uppsala and Tomteboda-Härjedalen of commodity 12 (earlier

available as a commodity 18 flow).

2. Using model [BALANCE] to rebalance domestic PWC-relations for a

small set of commodities with c = 0.04. Approximate impact: -3 billion

tonne kms (1+2: in total -5).

3. Using model [BALANCE] to rebalance domestic and import/export PWC-

relations for a wider set of commodities with varying c-values. Approxi-

mate impact: -7 billion tonne kms (1+2+3: in total -12).

4. Using model [BALANCE] to fine tune the changes needed to meet the ob-

jective while considering average distances from CFS-data 2005 derived

with the logistics model solution for 2006. The final result is 115+ billion

tonne kms after standard logmod and 114+ billion tonne kms after rail ca-

pacity management (LP0).

In Table 21 the settings used for producing the desired result are shown, and in

Table 22 we find the corresponding results with the calibrated Samgods model for

2006. Figure 18 holds the cumulative total tonne kms by commodity.

30 It should be kept in mind that these demand values in subsequent steps of the disaggrega-

tion may be split into a number of so called firm to firm flows.

31 The background of this bug is that the industry 10302 Extraction and agglomeration of

peat for energy purposes, according to the previous industry classification SNI 2002, is

included in 19200 Manufacture of refined petroleum products, according to SNI 2007,

which is the current industry classification being used. Thus, the allocation of production

and consumption to municipalities, according to the method described in chapter 4.2, has

become erroneous in this case.


Table 21 Parameter settings and adjustments made to reach the target < 115 bil-lion tonne kms..

Product group

Lower limit for the predicted demand

Distance aver-sion coefficient c

Matrix part revised Comments

1 10

2 10 0.01 Domestic

3 10

4 4 0.01 Domestic

5 10

6 10

7 10

8 1 Not included in PWC 2012 data

9 1

10 10

11 2

12 10 0.01 Domestic

13 100

imports from 971000 and 977100 for 718000 and 791200 redirected to 848000 (to avoid rail transports via Narvik and Haparanda to Stlm/Nynäshamn) + destinations in Sweden are restricted to 718000, 719200, 848000 and 848400

14 100 0.01

Domestic with 0.04 left + domestic and export from right

Production sites in Sweden are restricted to 718000, 719200, 848000 and 848400

15 100

16 10

17 10

18 5

19 100 0.01 export and import

20 5

21 3

22 1

23 10

24 10

25 2

26 3

27 1

28 10

29 10

30 1 Not included

31 100 0.08 Domestic

32 4

33 5

34 1 Not included in PWC 2012 data

35 5


Table 22 Results from the Samgods model with 2012 adjusted and 2006 matrices respectively.

Table 23 Results by port area. Same terms as for results in Table 18. Statistics source: Sjötrafik 2012 Statistik, Trafa 2013:11

In summary the revised matrices satisfy the conditions for the mission with a small

margin, as desired.

STD chg RCM chg

STD logmod RCM LP0 STD logmod RCM LP0 2012/2006[%] 2012/2006[%]

Mtonkm Mtonkm Mtonkm Mtonkm

Road 41 627 45 812 42 069 45 724 99 100

Rail 38 411 25 469 33 507 23 874 115 107

Sea 35 344 43 020 38 820 44 581 91 96

Air 0 0 0 0 102 102

SUM 115 382 114 301 114 397 114 179 101 100

PWC2012 (with 2006R62 setup) PWC2006 (2006R62)

PortArea Statistics 2012 RCM_LP0

Samgods 12

/Statistics [%]

Samgods 06

/Statistics

[%] RCM LP0 Statistics 2006

Haparanda-Skellefteå 1 9 197 7 199 78 80 9 265 11 586

Umeå-Sundsvall 2 7 809 8 946 115 85 7 955 9 363

Hudiksvall-Gävle 3 5 772 3 341 58 92 6 708 7 257

Norrtälje-Nynäshamn 4 10 282 23 806 232 102 13 241 13 007

Uppsala-Eskilstuna (Mälaren) 5 2 012 1 411 70 68 2 389 3 532

Södertälje-Norrköping 6 11 466 14 305 125 106 12 127 11 417

Västervik-Kalmar - 80 3 575 4 443

Visby (Gotland) - 66 3 839 5 808

Karlskrona-Trelleborg 7 20 798 8 798 42 39 9 891 25 274

Malmö-Helsingborg 8 16 085 13 447 84 63 11 049 17 572

Halmstad-Varberg 9 3 818 2 748 72 68 3 393 5 013

Göteborg(nedanför Trollhätte kanal) 10 38 313 38 098 99 102 40 784 40 061

Stenungsund-Strömstad 11 22 563 14 170 62.80 55 13 255 24 002

Trollhättan-Kristinehamn (Vänern) 12 1 741 2 095 120.32 145 3 497 2 413

SUMMA 149 856 138 364 92 78 140 969 180 747


Figure 18 Transport work totals 2006 and 2012 adjusted [billion tonne kms]

Setting the distance aversion parameters in the [BALANCE]-model has been done

by using comparisons of average transport distances derived with the PWC 2012 –

matrices and with the CFS 2005-data applying the Samgods 2006-solution data in

the derivation. The final results are shown in Figure 19 and Figure 26 for domestic

demand and for export/import-demand, respectively.

As shown in these figures the average model distances are higher than the CFS-

correspondences for all recalibrated matrix parts (domest/export/import) with posi-

tive distance aversion coefficients.

Figure 19 Average transport distances for domestic transports with PWC 2012 adjusted and CFS 2005 respectively.


Figure 20 Average transport distances for export/import transports with PWC 2012 adjusted and CFS 2005 respectively

The results are also presented in emme-format link files (extension 211). They are

derived with the aid of the spanning tree data. Two results are presented in Figures

21 – 25.

(Source files: EMME_NET_Base2006R62_Slct_FIN_YY_(01-00-P13)__N999111.211 - EMME_NET_Base2006R62_Slct_FIN_YY_(01-00-P17)__N999111.211).

The user data ui2 and ui3 holds the marginal values for domestic and export/import

flows respectively (the integer parts are the row sums in ktonnes, and the fractions

are the column sums in ktonnes/1.0E6).

In enif and emme they can be showed in the node displays using the syntax:

int(ui2),(ui2-int(ui2))*1000000,int(ui3),(ui3-int(ui3))*1000000

Colors used for zone circle sector markings in Figures 21-25 are:

1. Light green: Row sum domestic demand

2. Pink: Column sum domestic demand

3. Dark green: Row sum export demand

4. Lilac: Column sum import demand

Link user data ul2 and ul3 holds the flows related to domestic demand and all other

flows respectively. In enif and emme they can be showed in the node displays us-

ing the syntax:

ul2*(modes ~ "c"),ul2*(modes ~ "h"),(ul2+ul3)*(type<500 && modes ~

"y"),ul3*(modes ~ "c"),ul3*(modes ~ "h"),(ul2+ul3)*(type > 500 && modes ~ "y")


Sea flows are presented as flows on domestic and international links respectively

whereas road and rail flow are split into domestic and export/import-related de-

mand.

Colors used for link flow bars in Figures 21-25 are:

1. Light green: Road transport domestic demand

2. Dark green: Road transport export/import-demand demand

3. Red:: Rail transport domestic demand

4. Lilac: Rail transport export/import-demand demand

5. Light blue: Sea transport on domestic links

6. Dark blue: Sea transport on international links

Figure 21 Example of commodity 13 result with Samgods 2006 settings.










8 Concluding remarks The aim of this project, to produce an updated method to generate PWC base ma-

trices, and on this basis to predict actual PWC matrices for base year 2012 has been

achieved. In comparison to the previous method, the updated method means im-

provements in two main respects.

First, to estimate the row and column constraints, i.e. the production P and con-

sumption C of each commodity group, the new method makes use of data on com-

modities, industries and correspondence keys at a much more detailed level than

previously. For example, the allocation of P and C to municipalities is estimated by

using data on employment by industry defined at the detailed 5 digit level, and also

by using data on the share of employment representing goods-handling occupations

– to separate goods (commodity) production from service production in the respec-

tive industry. In short, one could state that by using data at more detailed level var-

ious aggregation biases have been reduced significantly.

Second, the estimation of PWC-matrices is based on a methodology which is im-

proved in several respects. One example is allowance for using trade flows with the

value zero as actual observations, instead of using only positive trade flows in the

estimation. Further, the estimation is made on observations of trade flows in

tonnes. The previous PWC-matrices were estimated using observations in values

and the PWC-matrix was predicted in terms of values, and later converted into tons

by applying a single commodity value. This may be problematic since there is no

perfect correlation between trade measured in values and trade measured in weight.

However, the generation of actual base matrices for base year 2012 has not been

achieved without several adaptations, corrections and adjustments – as revealed in

the two preceding chapters. In many cases the need of revising preliminary results

is due to the fact that the estimates still suffer from aggregation problems; e.g. the

abovementioned inclusion of peat within production of refined petroleum products,

generating upward biased trade flows.

Ideally it should be possible to validate the predicted PWC-matrices for year 2012

by comparing the aggregate result with corresponding data from official statistics.

Such comparisons have also been guiding the revisions of preliminary results, alt-

hough official statistics on total million tonnes of goods and million tonne-

kilometres in some respects suffer from uncertainty.


References Anas, A., (1983), “Discrete choice theory, information theory and the multinomial

logit and gravity models”. Transportation Research Part B: Methodological,

17(1):13–23.

Anderstig, C., Scheele, S., Eriksson, J., Vik, L.H., Stokka, A (2004) “D1 Final re-

port of methodology for the generation of P/C matrices for the Swedish National

freight model system”. Report commissioned by SIKA on behalf of the Samgods

group.

Edwards, H., Bates, J., Swahn, H. (2008), “Swedish Base Matrices Report. Esti-

mates for 2004, estimation methodology, data, and procedures”. SIKA.

Edwards, H. (2008), “Update of Samgods Base Matrices 2008”. SIKA.

Gourieroux, C., A. Monfort, and A. Trognon (1984), “Pseudo Maximum Likeli-

hood Methods: Applications to Poisson Models,” Econometrica 52, 701–720.

Imbens, G.W., Lancaster, T. (1994), “Combining Micro and Macro Data in Micro-

econometric Models”, The Review of Economic Studies, 61(4):655-680.

SIKA (2005), “Varuflödesundesökningen 2001”. SSM 071:0201, Stockholm.

SIKA (2006), “Varuflödesundersökningen 2004/2005”, SIKA Statistik report

2006:12, Stockholm.

Silva, J. S., & Tenreyro, S. (2006), ”The log of gravity”, The Review of Economics

and statistics, 88(4), 641-658.

Trafikverket (2014a), ”Systemtågstransporter i Sverige” (Excelfil: Systemtrans-

porter 2012_2014-12-12.xlsx), Borlänge

Trafikverket (2014b), ”PWC-matrisinformation från Norge” (Excelfil: Trans-

it_Norge_Statistik_2012.xlsx), Borlänge

Trafikverket (2014c), ”Information om transit-järnvägstransporter” (Excelfil: Jvg

Annex A 2012_Transit_flik_A3.xlsx), Borlänge

Wooldridge, J.M. (2002), “Econometric Analysis of Cross Section and Panel Da-

ta”, The MIT Press, Cambridge, Massachusetts, London, England (in particular ch.

19)

http://www.sciencedirect.com/science/journal/01912615


Appendix 1 Original micro-level approach

The original idea of this project was to use a data-driven approach for the row and

columns sums of the matrices, where different statistical data sources are used to

get estimates of production, consumption, export and import at a micro-level, and

aggregating the estimates to the municipality and commodity group level. Thus, the

row and column sums would be estimated using all available statistics and could be

treated as strong constraints to the rest of the matrix elements. “Row and column

sums” is here equivalent with

1. Production per municipality and commodity group

2. Consumption per municipality and commodity group

3. Import and export per origin/destination country and commodity group

(and maybe allocated to Swedish municipalities)

all measured in economic value (SEK) and weight (tons) per year.

Below, our suggestion on how this could be calculated based on existing statistics

from Statistics Sweden, is described. The proposal made to Statistics Sweden along

with a more detailed description of the suggested method then follows (in Swe-

dish)32.

A1.1 Industrial production and use

The idea was to combine the Statistical Business Register (FDB), containing de-

tailed information on workplaces, with Industrial goods statistics (IVP), Interme-

diate consumption statistics (INFI) and The Swedish Occupational Register with

statistics (YREG), described above. Through the businesses’ registered corporate

identity number, FDB could be used to link observations in the other data sources

together, and allocate them to municipalities, since FDB also contains geographical

information for the different workplaces of firms. In the cases where firms have

several workplaces in different municipalities, YREG can be used to allocate pro-

portions of the observations by the number of employees in commodity handling

occupations in the different workplaces. In this way, FDB and YREG together

could constitute a key, by which data on production (from IVP), consumption

(from INFI) and imports/exports (from FTS) could be allocated to municipalities.

32 It should be noted that the information gathered by Statistics Sweden, concerning produc-

tion, consumption and foreign trade, refer to very detailed data from which it would be

technically feasible to get very precise aggregate measures at the municipality level, to be

used as input data to PWC-matrices and the subsequent freight transport modelling. This

information gathered by Statistics Sweden, aggregated in the National Accounts, is basical-

ly determined by the demands from the Ministry of Finance to produce data and forecasts

of a very high quality.

As the Ministry of Finance, and the Ministry of Transportation, put similar demands on the

transportation planning to produce transportation forecasts of a very high quality, it is un-

fortunate that it, mainly for secrecy reasons, has not been possible to follow the micro-level

data approach in this project.


Figure 26 Schematic picture of the allocation of observations to municipalities us-ing FDB and YREG data

Figure 26 shows an example of how observations at a micro-level in IVP and INFI

could be allocated to workplaces and afterwards aggregated to the municipality

level.

The first observation, to the left, is for firm X, whose activity is classified to indus-

try sector SNI1. Firm X is a single workplace firm, so the observation can in full be

allocated to the municipality S where the workplace A is located (the geographical

information is given by FDB).

To the right we have two observations for firm Y; one observation for the activity

in sector SNI2 and one for sector SNI3. Firm Y has three workplaces B, C and D,

situated in two different municipalities T and U.

The observation for firm Y and SNI2 thus has to be distributed over two workplac-

es; B and D (workplace C only has activity within sector SNI3), while the observa-

tion for firm Y and sector SNI3 has to be distributed over workplaces C and D.

The YREG data gives us that workplace B has 50 employees and workplace D has

100. FDB gives us that workplace B has all activity within SNI2, which then is rep-

resented by all 50 employees. Workplace D however, only has 60 % of its activity

within sector SNI2, which is represented by 0,6 * 100 = 60 employees. In total, we

have 50 + 60 = 110 employees within SNI2 in firm Y; 50/110 = 45 % of the obser-

vation is thus allocated to workplace B and the remaining part to workplace D. The

same procedure is carried out for the observation for firm Y, sector SNI3, which is

distributed over workplaces C and D.


In the last step, the values allocated to workplaces in the same municipality are ag-

gregated, that is in the example, observations allocated to workplaces B and C are

summed together. By “number of employees” we here mean the number of full-

time equivalents within commodity-handling professions, se the section about the

YREG statistics above.

A1.2 Import and export

The Foreign Trade Statistics (FTS) can give us total national import and export of

commodities per county. Furthermore, we need information on how the import and

export is distributed over Swedish municipalities. There are two ideas for how to

achieve this.

Since also FTS includes information on corporate identity number, a similar ap-

proach as for the production and consumption described above could be used. The

corporate identity numbers for firms exporting a specific commodity can be

matched to firms producing the commodity, identified in the estimation of produc-

tion values described above, and the export levels could be allocated according to

the production levels to different workplaces and thereafter aggregated per munici-

pality. A similar approach could be used for allocating the import, according to the

already estimated consumption. A problem with this idea is that we only target the

industry’s direct import and export and not the trade passing through the wholesale

sector.

An alternative approach would be to estimate export and import fractions per

commodity on a detailed level, between Sweden on a national level and all other

countries. Then these fractions can be applied to the estimated production and con-

sumption per municipality. A problem with this approach is that we expect all

firms to be equally prone to export/import, and all firms to export to/import from

all countries trading with the specific commodity. However, the fractions would be

calculated at the very detailed CN 8-digit level, why the problem probably is slight-

ly smaller than one first can imagine.

Another issue with both approaches, regarding the import is that we do not target

import for consumption outside the industry sectors, i.e. private and public con-

sumption and use within other non-manufacturing sectors.


Appendix 2 Proposal to Statistics Sweden

Stockholm, 2013-07-12

Förfrågan om bearbetad statistik för framtagande av indata till

Trafikverkets transportprognosmodell

Bakgrund

Regeringen har i den aktuella Infrastrukturpropositionen (Prop. 2012/13:25) lyft

fram betydelsen av hög kvalitet på de indata som används vid de trafikprognoser

som ligger till grund för Trafikverkets planering av transportinfrastrukturen. Kvali-

teten på de indata som för närvarande används vid dessa prognoser är avsevärt

bättre för persontrafik än för godstrafik.

För prognoser av godstrafiken behövs framför allt indata som anger start- och mål-

punkter för olika godsflöden, dvs. var produktion respektive förbrukning äger rum.

Kvaliteten på dessa indata, enligt nuvarande skattningar, kan starkt ifrågasättas.

Exempelvis har produktionen av olika varugrupper fördelats på kommuner med

ledning av antalet sysselsatta i motsvarande näringsgrenar på en alltför aggregerad

nivå.

Detta är bakgrunden till denna förfrågan, som gäller datamängder för att ta fram så

kallade PWC-matriser (Production-Wholesale-Consumption) till Trafikverkets

godstransportprognosmodell Samgods. PWC-matriserna utgör indata till modellen i

form av efterfrågan av godstransporter mellan olika zoner och av olika typer av

varor. Modellen uppskattar sedan resultatet av denna efterfrågan i form av trafik-

flöden på vägar, järnvägar, på vattnet och i luften.

Mer specifikt utgörs indata av 34 PWC-matriser, för lika många varugrupper. I

varje matris anger element (i, j) mängden varor som ska transporteras från zon i där

produktionen sker, till zon j där varan konsumeras eller används som insatsvara.

Inom Sveriges gränser är en zon ekvivalent med en kommun. I utlandet är zonerna

större – från delar av länder till hela kontinenter, mer aggregerade områden ju

längre från Sverige området är beläget.

KTH deltar nu i ett FOI-projekt för Trafikverkets räkning med syfte att ta fram

bättre PWC-matriser för ett basår (matriser för prognosår tas fram med annan me-

tod). En ny metod för att beräkna basårsmatriserna specificeras och tillämpas på

data för att ta fram PWC-matriser för år 2006.

Den föreslagna metoden utgår från statistik för att beräkna matrisernas rad- och

kolumnsummor som så mycket som möjligt baseras på verkliga data. Matrisele-

menten modelluppskattas sedan med rad- och kolumnsummorna som bivillkor.

Projektet är nu i fasen att beräkna rad- och kolumnsummor och detta är en förfrå-

gan om beräkningshjälp från SCB. Förslag till specifikationer för beräkningarna

ges nedan.


Översikt

Basmatriserna som ska tas fram inom projektet gäller år 2006. Samtidigt ska den

metod som tas fram i projektet kunna tillämpas på nytt för nya basår längre fram

och vi vill därför använda så uppdaterade standarder som möjligt, till exempel nä-

ringsgrensindelningen SNI 2007. Därför bör statistik för år 2008 användas i beräk-

ningarna.

Slutmålet för beräkningarna är följande:

1. Produktion (mätt i ton samt SEK) per kommun i Sverige uppdelat per va-

rugrupp enligt nedan

2. Konsumtion/Förbrukning (mätt i ton samt SEK) per kommun i Sverige

uppdelat per varugrupp enligt nedan

3. Import/Export (mätt i ton samt SEK) uppdelat per bestämmelse/avsändar-

land och varugrupp enligt nedan samt eventuellt dessutom fördelat över

kommuner.

4. Nycklar som fördelar produktionsvärdet per näringsgren på olika varu-

grupper

Varugrupperna behöver delas in efter två olika klassificeringar – dels den europe-

iska standarden för transportstatistik NST2007 (på den mest detaljerade nivån som

ges av 3-siffriga koder) och dels Samgods egna varugruppsindelning Samgods34

som består av 34 olika aggregat av varor och baseras på den äldre standarden

NST/R.

För var och ett av de ovan beskrivna slutmålen (1-4) specificeras nedan en föresla-

gen beräkningsmetod, samt dimensioner och andra förutsättningar. De metoder

som presenteras beskriver i huvudsak hur vi tänker oss att hantera information

inom SNI 05-33, avslutnings vis i detta dokument undrar vi om det är görligt att

finna motsvarande arbetssätt för att hantera andra näringar.

Förslag till arbetsgång

Vi presenterar här olika förslag till arbetsgång för att få fram efterfrågade data.

Förslagen skall ses just som förslag, och är tänkta att illustrera hur vi tänker oss att

olika datakällor som IVP, FDB, YREG, INFI och UH kan kombineras på mikro-

nivå för att sedan aggregeras upp till efterfrågade storheter. (Förslagen bygger vi-

dare på den information som lämnades vid ett möte med SCB i Örebro 23 april).

Här hoppas vi att SCB kan bidra med att bedöma om arbetssättet är rimligt eller om

det finns bättre sätt att komma fram till de resultat vi vill uppnå.

Genomgående, för denna arbetsgång, är att vi vill fördela ut observationer på

kommun-nivå. Därför tänker vi oss FDB som ett nav genom vilken vi kan koppla

observationer tillhörande olika företag till företagets arbetsställen (vars kommuner

är kända). I det fall ett företag har fler arbetsställen ger YREG möjlighet att fördela

observationer med ledning av hur många som jobbar inom ”varuhanterande” yrken

på respektive arbetsställe. Vi tänker oss sedan att IVP, INFI och UH kan användas


som källor för företagens produktion, förbrukning och handel, vilka kan kopplas

ned till kommunnivå med hjälp av FDB och YREG.

Produktion

Målet är att få fram uppgifter för produktionsvärden och kvantiteter per aggregerad

varugrupp (NST2007 eller Samgods34) och kommun. Vår förhoppning är att det är

möjligt att kombinera IVP, FDB och YREG på mikronivå, och därmed fördela

produktionen etc. på arbetsställen, för att sedan aggregera resultaten per varugrupp

och kommun.

Vår förståelse av IVP är att den rapporterande enheten kan vara ett helt företag, en

grupp av arbetsställen eller ett enskilt arbetsställe, men att det saknas någon direkt

koppling till vilken kommun som varuproduktionen sker i. Enligt de variabelför-

teckningar som vi har tillgång till så är en observation i IVP tillskriven en Närings-

gren (5-ställig SNI2007) och ett Person/Organisationsnummer (Org.nr.).

För att komma fram till en regional fördelning av IVP-observationen (Ex. produkt-

ionsvärde för en vara på KN 8-ställig) tänker vi oss att man kan använda FDB för

att finna arbetsställeenheter kopplade till Org.nr och att med ledning av SNI-koden

från IVP finna de arbetsställen som har motsvarande Näringsgrensklassificering

enligt variabeln Näringsgren i FDB, där flera SNI-koder kan finnas rapporterade.

Därefter,

för IVP-observationer vars Org.nr enbart har ett arbetsställe kan produkt-

ionen tillskrivas detta arbetsställe, och därmed kan en kommun tillskrivas

IVP-observationen m.h.a. FDB.

om ett Org.nr har flera arbetsställen i FDB, då behöver vi fördela den i IVP

observerade storheten på ett antal arbetsställen. Genom att använda den i

IVP observerade SNI-koden och matcha den till arbetsställen med samma

rapporterade variabel ”Näringsgren” i FDB identifieras potentiella arbets-

ställen där varan kan ha producerats. Med hjälp av ex. arbetsställets

CFAR-nummer kan statistik ifrån YREG kopplas till arbetsställena. För att

få en rimlig fördelning av den fysiska produktionen över kommuner är an-

tal anställda troligen en för grov proxy för att göra fördelningen mellan ar-

betsställen inom ett Org.nr, därför vill vi istället använda heltidsekvivalen-

ter inom ”varuhanterande” yrken (t.ex. Yrkesområden 6-9 enligt SSYK96)

för att fördela IVP-observationen till arbetsställen.

I Figur 1 nedan illustreras hur beräkningsgången skulle kunna se ut för att distribu-

era IVP-observationer till arbetsställen.


Företag X: ett och samma org.nr

Observation 1: SNI 1Org.nr X

Observation 2: SNI 2Org.nr X

30 helt.ekv 300 helt.ekv

Från YREG. Endast varuhanterande yrken (Yrkesomr 6-9), heltidsekvivalenter eller liknande

30/230= 13 %

87 %

Från FDB

Från IVP

Org.nr X, SNI1 (100% )

CFAR A, kommun K

Org.nr X,

SNI2(100%)CFAR B,

kommun K

Org.nr X, SNI1 (66%) SNI2 (33%)

CFAR C, kommun J

Från YREG

50 helt.ekv

Värde, kvantitet per varuslag(KN 8-ställig)

Fördelning på arbetsställen

M.h.a. YREG

Figur 1. Flödesschema för att distribuera observationer ifrån IVP till arbetsställen.

Detta förfaringssätt för att fördela ut IVP-observationerna bygger på att kombinera

YREG med FDB. Ifrån YREG används i detta fall bara heltidsekvivalenter inom

varuhanterande yrken (6-9) per arbetsställe. Därefter kan dessa heltidsekvivalenter

fördelas ut på arbetsställets SNI-koder enligt variabeln ”Procent efter tid eller om-

sättning” i FDB. Heltidsekvivalenter bör kunna beräknas ifrån YREG med hjälp av

variablerna ”Tjänstgöringsomfattning” för de personer som arbetar på det aktuella

arbetsstället och inom varuhanterande yrken.

Vi är inte säkra på att kopplingen i termer av SNI-kod mellan IVP och FDB är rim-

lig att göra. Kan det exempelvis vara så att en rapporterad SNI-kod i IVP inte mot-

svaras av något arbetsställes SNI-koder i FDB i.s.f. är koppling omöjlig. Är detta

ett problem? (Som ett alternativ skulle man kunna skippa matchningen i termer av

SNI-koder och bara distribuera IVP-observationerna proportionellt mot antalet hel-

tidsekvivalenter till alla företagets arbetsställen.)

Efter att ha fördelat ut IVP-observationernas värden på arbetsställen tänker vi oss

att vi har sammanställt/distribuerat en rad variabler på arbetsställena. Exempelvis

kommer ett visst arbetsställe att ha blivit tilldelad produktionsvärden för de varu-

grupper på KN-8 som har kopplats dit.


Slutligen vill vi erhålla följande variabler aggregerat från arbetsställen upp till

kommun och varugruppsnivå (NST2007 och Samgods34)

Efterfrågade storheter relaterade till IVP:

Produktion Värde

Leveranser Värde

Leveranser Vikt

Värde av de Leveranser som rapporteras med Vikt

Efterfrågade storheter relaterade till FDB

Andelar, av ”IVP-variablerna” över ”Storleksklasser efter antal anställda” ifrån

FDB

Den sista variabeln kräver en liten förklaring. Som en del i att modellskatta PWC-

matriserna ingår att PWC-modellen skall generera resultat inte bara för handel mel-

lan regioner per varugrupp, utan även att dessa disaggregeras vidare till handel

mellan företag i tre olika storleksklasser. I FDB är arbetsställena klassificerade ef-

ter antal anställda. Här tänker vi att denna distribution skulle kunna användas för

att approximera handelsmönster mellan företag i de tre storleksklasserna.

Förbrukning

Målet är att få fram uppgifter kring förbrukning per aggregerad varugrupp

(NST2007 eller Samgods34) och kommun. I detta fall är det användandet av INFI

som vi har i åtanke.

I INFI finns kostnaden för insatsvaror inom industrin (SNI 05-33). INFI gick över

till SNI2007 år 2009 vilket innebär att först 2011 kommer hela tillverkningsindu-

strin ha undersökt enligt SNI2007, eftersom INFI rullar på ett treårsschema där

bara en del av SNI täcks varje år.

Ifrån INFI är det möjligt att få värdet av insatsvaror på KN-baserade nivåer. De

variabelförteckningar vi har tillgång till ger inte ett entydigt svar om vilka varu-

gruppsindelningar som finns tillgängligt i INFI. Är det KN 8-ställig?

Precis som i fallet med produktion tänker vi oss att industrins förbrukning av in-

satsvaror först kan disaggregeras ned till arbetsställen för att sedan aggregeras upp

till kommun och varugrupp (NST2007 eller Samgods34) . I INFI finns variabler för

Org.nr och SNI-kod enligt ”Näringsgren för statistiken”. Med hjälp av dessa kan vi

koppla INFI-observationer till potentiella arbetsställen i FDB där förbrukningen

skett. Återigen använder vi heltidsekvivalenter inom varuhanterande yrken för att

fördela INFI-observationen till de aktuella arbetsställena. I stora drag skulle be-

räkningarna ske på samma sätt som för produktionen.

Frågor: Går det att använda SNI-koden i INFI på detta sätt för att koppla till mot-

svarande post i FDB? Anledningen att vi är osäkra på detta är att INFI rullar över

tre år. Antag att vi försöker göra en sådan koppling för år 2009, då har cirka en

tredjedel av SNI2007-koderna täckts in, vad gäller för resterande 2/3 kan dessa


kopplas mot SNI2007 i FDB för år 2009? Är de äldre observationerna omklassifi-

cerade till SNI2007 i 2009 års INFI?

Alternativ:

1. Använd INFI för det tidigaste år som Alla data finns på SNI 2007 enligt

ovan.

2. Slopa användandet av SNI och gå enbart på Org.nr, fördela förbrukningen

enligt heltidsekvivalenterna från YREG per arbetsställe.

Efter att ha fördelat ut INFI-observationernas värden på arbetsställen tänker vi oss

att vi har sammanställt/distribuerat insatsvaruvärden per KN till arbetsställen. Vi

skulle även vilja beräkna en proxy för vikt för dessa insatsvaror genom att använda

vikt/värde-relationen för leveranser i IVP på KN8-nivå.

Slutligen vill vi erhålla följande variabler aggregerat från arbetsställen upp till

kommun och varugruppsnivå (NST2007 och Samgods34)

Efterfrågade storheter relaterade till INFI:

Kostnad /Värde

Vikt (baserad på värde/vikt-relation ifrån IVP)

Värde av den förbrukning som beräknats en Vikt

Efterfrågade storheter relaterade till FDB

Andelar, av ”INFI-variablerna” över ”Storleksklasser efter antal anställda”

ifrån FDB

Fråga: INFI täcker endast industrins förbrukning, hur kan vi komma åt övrig för-

brukning på samma aggregeringsnivå? Exempel på övrig förbrukning är pri-

vat/offentlig konsumtion av varor, förbrukning inom övriga näringsgrenar (ej SNI

5-33).

Export/Import

Målet för beräkningarna som beskrivs ovan är att få fram uppgifter kring produkt-

ion och förbrukning per aggregerad varugrupp (NST2007 eller Samgods34) och

kommun i Sverige. Dock behövs även information om handel mellan kommuner i

Sverige och utlandet. I detta fall är det användandet av Utrikeshandel med varor

(UH) som vi har i åtanke. Vi tänker oss att data, per varugrupp (NST2007 och

Samgods34), kan erhållas på två olika nivåer:

1. Total (nationell) import samt export uppdelat på avsändar- respektive mot-

tagarland

2. Eventuellt även Import samt export enl. 1) fördelat på svenska kommuner

Beräkningsgång för båda nivåerna beskrivs nedan. För 2) har vi två förslag på be-

räkningsmetoder.


1 ) Nationell Import/Export

Zonindelningen för utlandet består av 174 zoner. I närområdet, t.ex. norra Europa,

är länderna uppdelade på flera zoner, medan avlägsna länder aggregeras till hela

eller delar av kontinenter. I detta scenario är vi intresserade av den totala importen

samt exporten mellan Sverige och varje sådan zon. Från statistiken för utrikeshan-

del kan vi endast få ut uppgifter per bestämmelse/avsändar-land, därför kommer vi

själva utföra aggregering/disaggregering av uppgifter från UH till de zoner vi är

intresserade av.

Vi tänker oss att UH används för att ta ut den totala exporten per land i både vikt-

och värdetermer, per varutyp (KN 8-ställig). Samma sak görs för den totala impor-

ten. Slutligen aggregeras KN8-varorna till NST2007 samt till Samgods34.

Efterfrågade storheter relaterade till UH:

Export

Statistiskt värde per varukod och bestämmelseland

Fakturerat värde per varukod och bestämmelseland

Vikt per varukod och bestämmelseland

Statistiskt värde per varukod och bestämmelseland för de observationer

som har Vikt angiven

Fakturerat värde per varukod och bestämmelseland för de observationer


Andelar av export-variablerna ovan som härrör från företag som inte tillhör

SNI 1-33, vi vill komma åt hur mycket av handeln som gått via ”detaljhan-

del/grossister”.

Import

Statistiskt värde per varukod och avsändningsland

Fakturerat värde per varukod och avsändningsland

Vikt per varukod och avsändningsland

Statistiskt värde per varukod och avsändningsland för de observationer


Fakturerat värde per varukod och avsändningsland för de observationer


Andelar av import-variablerna ovan som härrör från företag som inte till-

hör SNI 1-33, vi vill komma åt hur mycket av handeln som gått via ”de-

taljhandel/grossister”.

2) Fördelning av Import/Export per kommun

Utöver Sveriges totala export/import per aggregerad varugrupp och land så vore

det önskvärt om vi kunde beräkna ifrån/till vilken kommun denna export/import

härrör. Ett förslag till att skapa en proxy för hur en sådan regional fördelning ser ut

kan vara att använda ett liknande förfaringssätt som för produktion och förbruk-

ning.


Proxyn för fördelningen av export tänker vi oss att vi kan åstadkomma genom att

återigen fördela ned observationerna till arbetsställen. I UH har observationerna

bl.a. variablerna Varukod enl. KN 8, Org.nr, Landskod, Statistisk värde, Fakturerat

värde, Vikt.

Förslag a) Industrins Direkta import/export

Genom Org.nr i UH kan vi identifiera potentiella arbetsställen som genererat ex-

porten via FDB. Eftersom vi tänker oss att vi redan har distribuerat produkt-

ions/leveransvärden av varor på KN8-nivå ner till arbetsställen kan de arbetsställen

som har produktion av den exporterade varan identifieras. Detta resonemang gäller

endast de företag som ingår i IVP. Sedan fördelas exporten för denna vara över de

aktuella arbetsställena proportionellt mot deras produktions/leveransvärden för den

specifika varan. Detta betyder att vi på arbetsställenivå skulle ha en proxy för hur

mycket som exporteras av varje varugrupp på KN8 och till vilket land dessa varor

exporteras. Dessa resultat kan sedan aggregeras till efterfrågad varugrupp, kom-

mun, och mottagande land.

På motsvarande sätt kan importen hanteras, men istället för att använda produktion

som fördelningsnyckel mellan arbetsställen så används förbrukningen. Förbruk-

ningen har fördelats ned på arbetsställen per KN8 för företagen som finns med i

INFI. D.v.s. för ett givet Org.nr. identifieras arbetsställen som förbrukar den impor-

terade varan på KN8, därefter fördelas importen proportionellt mot förbrukningen

av denna vara mellan företagets arbetsställen. Aggregera pss som för exporten,

d.v.s. för varje aggregerad varugrupp har vi en matris som approximerar import

från länder till kommuner.

Ett problem med denna ansats är att vi endast kommer åt direkt export/import i

meningen att vi, via Org.nr, matchar observationer i UH till både FDB och IVP,

men fångar därmed i princip bara den handel som det varuproducerande företaget

självt står för, inte handel som går via partihandel exempelvis.

Fråga: Hur kan vi regionalisera de observationer i UH som inte kan matchas till

FDB/IVP/INFI?

Förslag b) Total import/export via kvoter

Ett alternativt förfaringssätt är att på KN8-nivå bestämma export/import-andelar

per varugrupp och land för Sverige som helhet. Sedan tillämpa dessa på produktion

och förbrukning, på KN8-nivå, som fördelats ned till arbetsställen och därefter ag-

gregera. Detta innebär dock att man går miste om att olika företag kan vara olika

export/import-benägna. Dessutom skulle en sådan nationell fördelningsnyckel in-

begripa att man tvingas använda samma fördelning av import/export över länder

för alla arbetsställen.

På produktions/export-sidan får vi då en proxy för total export från de varuprodu-

cerande arbetsställena. All export fördelas regionalt proportionellt mot regionens

produktion. På förbrukningssidan kvarstår den problematik som berördes under


rubriken förbrukning, nämligen att vi missar den del som består av privat/offentlig

konsumtion, och förbrukning inom icke varuproducerande näringsgrenar. All im-

port skulle fördelas regionalt enlig den varuproducerande industrins förbrukning.

Återigen vore det önskvärt att ha en uppfattning av förbrukningen, på kommun-

nivå, inom näringar/konsumtion som inte under undersöks i INFI för att kunna för-

dela UH-observationer regionalt.

Sammanfattningsvis vill vi erhålla följande variabler aggregerat från arbetsställen

upp till land, kommun och varugruppsnivå (NST2007, Samgods34)

Efterfrågade storheter relaterade till UH:

Export

Statistiskt värde per varukod, kommun och bestämmelseland

Fakturerat värde per varukod, kommun och bestämmelseland

Vikt per varukod, kommun och bestämmelseland

Statistiskt värde per varukod, kommun och bestämmelseland för de obser-

vationer som har Vikt angiven

Fakturerat värde per varukod, kommun och bestämmelseland för de obser-


Import

Statistiskt värde per varukod, kommun och avsändningsland

Fakturerat värde per varukod, kommun och avsändningsland

Vikt per varukod, kommun och avsändningsland

Statistiskt värde per varukod, kommun och avsändningsland för de obser-


Fakturerat värde per varukod, kommun och avsändningsland för de obser-


Nycklar mellan näringsgren och olika varugruppsindelningar

Om beräkningar kan utföras enligt ovan, kan rad- och kolumnsummor för matriser-

na (total produktion respektive konsumtion per kommun samt import/export) erhål-

las direkt indelat per varugrupp – dels enligt indelningen Samgods34 och dels en-

ligt NST2007. Med hjälp av dessa kan basmatriser för år 2006 tas fram.

Dock ska prognosårsmatriser som tas fram hädanefter vara konsistenta med gäl-

lande basårsmatriser. Framskrivningen av produktionen till prognosår görs med

hjälp av statistik som redovisas per näringsgren. För att kunna tillämpa denna sta-

tistik på matriser indelade efter varugrupp, kommer konverteringstabeller, eller

nycklar, för att översätta värdet av varuproduktionen per bransch till värdet av va-

ruproduktionen per varugrupp vara nödvändiga.

IVP redovisas med både näringsgren (SNI 2007) och detaljerad varutyp (Kombine-

rade Nomenklaturen, KN) för varje objekt. Den informationen kan användas till att

konstruera en nyckel, som fördelar ut värdet av varuproduktionen i varje närings-


gren (SNI 2007) på varugrupper (KN). KN-varugrupperna kan sedan aggregeras

till dels NST2007, dels Samgods34, med hjälp av befintliga tabeller.

Det första steget i beräkningarna är alltså att gå från näringsgren SNI till varugrupp

KN. Varor produceras av näringsgrenar inom

A. jordbruk, skogsbruk och fiske – SNI-koder som börjar på 01-03

B. utvinning av mineral – SNI-koder som börjar på 05-09

C. tillverkning – SNI-koder som börjar på 10-33

IVP täcker näringsgrenar inom SNI 05-33. För de areella näringarna 01-03 finns

registerdata. Från dessa data kan en nyckel för den totala produktionen tas fram,

här kallad 𝑆𝑁𝐼𝐶𝑁, som översätter produktionsvärdet per näringsgren (SNI 2007,

01-33, 5-ställig nivå) till produktionsvärdet per varutyp (KN, 8-ställig nivå). Det

finns 325 stycken 5-ställiga SNI-koder (ℎ, ℎ = 1: 325) bland de aktuella närings-

grenarna och 9 600 stycken 8-ställiga KN-varor (𝑢, 𝑢 = 1: 9 600). 𝑆𝑁𝐼𝐶𝑁 skulle

då utgöras av en matris med 325 rader och 9 600 kolumner, där elementet (ℎ, 𝑢)

ger andelen av produktionsvärdet i näringsgren ℎ som utgörs av vara 𝑢, så att

∑ 𝑆𝑁𝐼𝐶𝑁(ℎ, 𝑢)𝑢=1:9600 = 1 för alla ℎ = 1: 325.

Nästa steg i beräkningarna är att gå från varugrupp KN till en mer ändamålsenlig

varugruppsindelning. I detta fall behövs två olika aggregeringar av KN – NST2007

och Samgods34.

NST2007-varianten, här kallad 𝐶𝑁𝑁𝑆𝑇, ska vara på den mest detaljerade nivån,

som utgörs av 81 olika varugrupper (𝑧, 𝑧 = 1: 81) som beskrivs med 3-siffriga ko-

der. Dessa kan aggregeras från KN med hjälp av den konverteringstabell Eurostat

redovisar i metadataservern RAMON på sin hemsida33. 𝐶𝑁𝑁𝑆𝑇 blir således en ma-

tris med 9 600 rader och 81 kolumner, där elementet (𝑢, 𝑧) ∈ {0,1} anger huruvida

KN-vara 𝑢 ingår i NST2007-vara 𝑧 eller ej, så att ∑ 𝐶𝑁𝑁𝑆𝑇(𝑢, 𝑧)𝑧=1:81 = 1 för

alla 𝑢 = 1: 9 600.

Den ”totala” översättningstabellen från SNI till NST2007 (kallad 𝑆𝑁𝐼𝑁𝑆𝑇) fås se-

dan genom 𝑆𝑁𝐼𝑁𝑆𝑇 = 𝑆𝑁𝐼𝐶𝑁 𝐶𝑁𝑁𝑆𝑇.

Samgods34 baseras på NST/R-klassificeringen, med vissa justeringar. NST/R kan

aggregeras från KN på den mest detaljerade nivån, även den med hjälp av Eurostats

konverteringstabell. Dock behöver vissa NST/R-grupper delas upp för att erhålla

Samgods34-varugrupper34, varför det kan finnas en poäng i att aggregera direkt

från KN 8-ställig till Samgods34. Utgångspunkten blir då Eurostats konverte-

ringstabell tillsammans med Samgodstabeller. Samgods34-varianten, här kallad

𝐶𝑁𝑆𝐺, utgörs alltså av en matris med 9 600 rader och 34 kolumner, där elementet

33 http://ec.europa.eu/eurostat/ramon/relations/index.cfm?TargetUrl=LST_REL

34 Det gäller varugrupperna 7 (Flis, sågavfall), 8 (Bark, kork, övrigt virke, ved (ej bränn-

ved)) samt 34 (Tomemballage, förpackningar, begagnade).



(𝑢, 𝑘) ∈ {0,1} anger huruvida KN-vara 𝑢 ingår i Samgods34-vara 𝑘 eller ej, så att

∑ 𝐶𝑁𝑁𝑆𝑇(𝑢, 𝑘)𝑘=1:34 = 1 för alla 𝑢 = 1: 9 600.

Den ”totala” översättningstabeller för konvertering från SNI till Samgods34 (kallad

𝑆𝑁𝐼𝑆𝐺) fås sedan genom 𝑆𝑁𝐼𝑆𝐺 = 𝑆𝑁𝐼𝐶𝑁 𝐶𝑁𝑆𝐺.

Efterfrågade nycklar:

Översättningstabell från SNI till NST2007 (”𝑆𝑁𝐼𝑁𝑆𝑇”) – en matris med

325 rader och 81 kolumner, med varje radsumma = 1.

Översättningstabell från SNI till Samgods34 (”𝑆𝑁𝐼𝑆𝐺”) – en matris med

325 rader och 34 kolumner, med varje radsumma = 1.

Andra näringar?

Vi har redan ställt frågor kring exempelvis om det går att regionalisera förbruk-

ningen av varugrupper inom näringsgrenar som inte finns undersökta i INFI. En

relaterad fråga rör produktionen, framförallt ”areella” näringar (SNI 1-3), hur

kommer vi åt dessa? Vid kontakt med SCB angående tidigare Varuflödesundersök-

ningar har vi fått intrycket att speciellt VFU 04/05 skall vara avstämd mot register-

data för varor som är ”areella”. Här är vi dock inte på det klara med vad detta inne-

bär. Betyder det att VFU är avstämd mot registerbaserad produktions och konsumt-

ionsdata per region, import/export? I sådana fall finns det ingen anledning för oss

att försöka hantera dessa varor på något annat sätt utan direkt förlita oss på VFU’n

i dessa fall. Eller, är VFU till och med avstämd på handelsnivå, dvs hur mycket av

en vara som transporteras från en kommun till en annan för de areella varorna?


Med vänlig hälsning

Marcus Sundberg

Ph.D., Forskare

KTH/ Inst. för Transportvetenskap/Avd. för Transport och Lokaliseringsanalys

Teknikringen 10

100 44 Stockholm

08 790 96 32

[email protected]

mailto:[email protected]

WSP Analysis & Strategy Arenavägen 7 SE-121 88 Stockholm-Globen Phone: +46 10-722 50 00 www.wspgroup.se/analys

Appendix 3 Costs, tonne kms and tonnes (all in millions)

Costs, tonne kms and tonnes (all in millions) split into domestic (1) and interna-

tional (2) transports in different distance classes.

Prod Dom/Int Label Total 0-100_km 100-200_km 200-300_km 300-400_km 400-500_km 500_km_++

1 1 Cost 527.80 283.30 117.70 53.95 36.57 19.96 16.22

1 1 Tonkm 166.60 59.86 48.51 25.10 16.95 8.32 7.91

1 1 Ton 2.27 1.74 0.35 0.10 0.05 0.02 0.01

1 1 E[SEK/Tonkm] 3.17 4.73 2.43 2.15 2.16 2.40 2.05

1 1 E[km/Ton] 73.29 34.43 138.90 241.00 339.40 442.50 598.70

1 2 Cost 2 900.00 11.25 16.32 19.43 28.02 30.47 2 795.00

1 2 Tonkm 2 864.00 5.50 11.09 16.39 30.43 35.80 2 765.00

1 2 Ton 1.58 0.08 0.08 0.06 0.09 0.08 1.19

1 2 E[SEK/Tonkm] 1.01 2.05 1.47 1.19 0.92 0.85 1.01

1 2 E[km/Ton] 1 813.00 72.65 141.40 252.90 342.60 450.50 2 318.00

2 1 Cost 3 271.00 507.10 363.60 475.90 451.30 337.10 1 136.00

2 1 Tonkm 3 247.00 116.80 166.10 344.60 343.60 323.90 1 952.00

2 1 Ton 10.16 3.49 1.14 1.41 1.00 0.72 2.41

2 1 E[SEK/Tonkm] 1.01 4.34 2.19 1.38 1.31 1.04 0.58

2 1 E[km/Ton] 319.50 33.49 146.00 244.70 343.70 449.70 810.50

2 2 Cost 3 856.00 0.03 1.25 3.20 8.66 12.67 3 830.00

2 2 Tonkm 6 389.00 0.00 0.27 1.51 4.66 7.81 6 374.00

2 2 Ton 1.67 0.00 0.00 0.01 0.01 0.02 1.64

2 2 E[SEK/Tonkm] 0.60 8.03 4.59 2.12 1.86 1.62 0.60

2 2 E[km/Ton] 3 818.00 85.35 148.80 264.20 355.60 442.20 3 899.00

3 1 Cost 244.00 80.14 67.22 42.18 24.93 16.07 13.50

3 1 Tonkm 84.79 15.00 25.24 20.20 11.02 7.04 6.29

3 1 Ton 0.74 0.43 0.17 0.09 0.03 0.02 0.01

3 1 E[SEK/Tonkm] 2.88 5.34 2.66 2.09 2.26 2.28 2.15

3 1 E[km/Ton] 114.00 35.00 147.20 235.90 349.10 434.70 616.40

3 2 Cost 9.13 0.00 0.06 0.15 0.26 0.21 8.43

3 2 Tonkm 4.17 0.00 0.00 0.02 0.04 0.03 4.09

3 2 Ton 0.00 0.00 0.00 0.00 0.00 0.00 0.00

3 2 E[SEK/Tonkm] 2.19 184.50 25.51 9.67 6.81 7.46 2.06

3 2 E[km/Ton] 1 592.00 87.12 155.10 256.10 351.00 449.40 1 725.00

4 1 Cost 79.30 17.25 5.46 8.56 9.02 8.31 30.71

4 1 Tonkm 64.91 7.06 2.30 5.54 5.31 5.47 39.23

4 1 Ton 0.29 0.17 0.02 0.02 0.02 0.01 0.06

4 1 E[SEK/Tonkm] 1.22 2.45 2.37 1.55 1.70 1.52 0.78

4 1 E[km/Ton] 220.50 41.90 142.70 256.00 337.80 455.40 649.30

4 2 Cost 0.00 0.00 0.00 0.00 0.00 0.00 0.00

4 2 Tonkm 0.00 0.00 0.00 0.00 0.00 0.00 0.00

4 2 Ton 0.00 0.00 0.00 0.00 0.00 0.00 0.00

4 2 E[SEK/Tonkm] 0.00 0.00 0.00 0.00 0.00 0.00 0.00

4 2 E[km/Ton] 1.00 1.00 1.00 1.00 1.00 1.00 1.00

5 1 Cost 4 387.00 1 387.00 1 648.00 698.70 328.00 168.20 157.90

5 1 Tonkm 5 349.00 982.10 2 094.00 956.40 516.10 285.50 515.00

5 1 Ton 45.96 23.92 15.16 3.91 1.53 0.66 0.78

5 1 E[SEK/Tonkm] 0.82 1.41 0.79 0.73 0.64 0.59 0.31

5 1 E[km/Ton] 116.40 41.06 138.10 244.50 336.60 431.40 662.50

5 2 Cost 2 470.00 0.11 62.69 34.72 115.30 107.50 2 149.00

5 2 Tonkm 6 464.00 0.08 110.60 55.00 212.70 214.40 5 871.00

5 2 Ton 7.19 0.00 0.59 0.22 0.64 0.48 5.26

5 2 E[SEK/Tonkm] 0.38 1.34 0.57 0.63 0.54 0.50 0.37

5 2 E[km/Ton] 899.40 91.30 186.30 255.50 333.80 447.00 1 116.00

6 1 Cost 2 403.00 265.20 332.50 333.30 321.30 289.90 860.80

6 1 Tonkm 1 249.00 35.54 96.79 125.70 135.00 141.50 714.00


6 1 Ton 3.59 0.88 0.65 0.50 0.39 0.32 0.85

6 1 E[SEK/Tonkm] 1.93 7.46 3.44 2.65 2.38 2.05 1.21

6 1 E[km/Ton] 347.60 40.29 148.50 249.30 347.70 448.30 840.40

6 2 Cost 6 238.00 0.38 7.23 22.59 48.64 80.25 6 079.00

6 2 Tonkm 39 390.00 0.04 3.49 16.48 40.46 81.53 39 240.00

6 2 Ton 6.98 0.00 0.02 0.07 0.11 0.18 6.60

6 2 E[SEK/Tonkm] 0.16 9.91 2.07 1.37 1.20 0.98 0.15

6 2 E[km/Ton] 5 640.00 82.05 166.50 252.60 354.60 452.90 5 944.00

7 1 Cost 2 829.00 346.00 510.20 488.80 397.70 270.30 815.60

7 1 Tonkm 2 318.00 130.50 351.90 442.40 360.80 186.30 846.50

7 1 Ton 9.31 2.62 2.40 1.81 1.05 0.42 1.01

7 1 E[SEK/Tonkm] 1.22 2.65 1.45 1.11 1.10 1.45 0.96

7 1 E[km/Ton] 249.00 49.79 146.80 244.90 342.70 444.30 835.20

7 2 Cost 1 140.00 0.16 15.30 16.21 25.33 53.09 1 030.00

7 2 Tonkm 2 620.00 0.05 10.80 12.99 21.78 72.17 2 502.00

7 2 Ton 1.46 0.00 0.07 0.05 0.06 0.16 1.11

7 2 E[SEK/Tonkm] 0.44 3.31 1.42 1.25 1.16 0.74 0.41

7 2 E[km/Ton] 1 798.00 89.81 165.40 249.20 352.60 443.00 2 245.00

8 1 Cost 0.00 0.00 0.00 0.00 0.00 0.00 0.00

8 1 Tonkm 0.00 0.00 0.00 0.00 0.00 0.00 0.00

8 1 Ton 0.00 0.00 0.00 0.00 0.00 0.00 0.00

8 1 E[SEK/Tonkm] 23.76 23.76 0.00 0.00 0.00 0.00 0.00

8 1 E[km/Ton] 60.42 60.42 1.00 1.00 1.00 1.00 1.00

8 2 Cost 0.00 0.00 0.00 0.00 0.00 0.00 0.00

8 2 Tonkm 0.00 0.00 0.00 0.00 0.00 0.00 0.00

8 2 Ton 0.00 0.00 0.00 0.00 0.00 0.00 0.00

8 2 E[SEK/Tonkm] 0.00 0.00 0.00 0.00 0.00 0.00 0.00

8 2 E[km/Ton] 1.00 1.00 1.00 1.00 1.00 1.00 1.00

9 1 Cost 124.50 20.90 22.77 23.54 17.24 14.01 26.07

9 1 Tonkm 0.82 0.04 0.10 0.15 0.12 0.14 0.28

9 1 Ton 0.00 0.00 0.00 0.00 0.00 0.00 0.00

9 1 E[SEK/Tonkm] 152.50 576.30 237.70 162.20 139.40 101.40 93.98

9 1 E[km/Ton] 265.90 45.39 148.50 248.20 344.70 446.70 743.50

9 2 Cost 3 211.00 5.94 24.57 33.55 51.70 75.13 3 020.00

9 2 Tonkm 954.90 0.09 0.53 0.86 1.69 3.00 948.70

9 2 Ton 0.34 0.00 0.00 0.00 0.00 0.01 0.32

9 2 E[SEK/Tonkm] 3.36 66.92 46.38 38.96 30.52 25.01 3.18

9 2 E[km/Ton] 2 843.00 81.89 163.50 256.10 351.50 452.50 2 996.00

10 1 Cost 50 410.00 8 409.00 8 145.00 7 484.00 5 484.00 4 347.00 16 540.00

10 1 Tonkm 3 714.00 226.30 436.00 470.50 395.60 369.50 1 816.00

10 1 Ton 15.94 6.96 2.99 1.90 1.15 0.82 2.13

10 1 E[SEK/Tonkm] 13.57 37.15 18.68 15.91 13.86 11.77 9.11

10 1 E[km/Ton] 233.00 32.55 145.80 247.50 344.80 451.90 853.50

10 2 Cost 23 060.00 47.62 173.90 252.00 390.90 579.60 21 620.00

10 2 Tonkm 21 590.00 2.65 10.84 26.86 67.89 99.87 21 390.00

10 2 Ton 7.37 0.03 0.07 0.11 0.19 0.22 6.74

10 2 E[SEK/Tonkm] 1.07 17.96 16.03 9.38 5.76 5.80 1.01

10 2 E[km/Ton] 2 931.00 77.14 155.50 255.50 348.30 453.30 3 172.00

11 1 Cost 1 274.00 311.10 233.00 163.00 179.60 147.20 239.80

11 1 Tonkm 129.00 22.32 40.31 21.48 19.88 10.82 14.16

11 1 Ton 1.19 0.71 0.29 0.09 0.06 0.02 0.02

11 1 E[SEK/Tonkm] 9.88 13.94 5.78 7.59 9.03 13.60 16.93

11 1 E[km/Ton] 108.30 31.39 141.30 244.70 337.20 441.00 622.00

11 2 Cost 3 494.00 2.48 18.42 32.59 45.86 83.15 3 312.00

11 2 Tonkm 4 660.00 0.23 3.68 11.20 18.15 47.55 4 579.00

11 2 Ton 1.33 0.00 0.02 0.04 0.05 0.10 1.11

11 2 E[SEK/Tonkm] 0.75 10.74 5.01 2.91 2.53 1.75 0.72

11 2 E[km/Ton] 3 497.00 76.88 161.20 255.50 348.50 453.60 4 140.00

12 1 Cost 217.20 17.80 18.07 23.91 30.00 30.40 97.01

12 1 Tonkm 267.30 4.97 14.11 19.76 27.46 33.31 167.60

12 1 Ton 0.73 0.21 0.09 0.08 0.08 0.07 0.20


12 1 E[SEK/Tonkm] 0.81 3.58 1.28 1.21 1.09 0.91 0.58

12 1 E[km/Ton] 365.20 23.31 154.10 250.70 351.40 447.30 858.00

12 2 Cost 4 628.00 0.01 1.26 3.08 6.23 26.74 4 590.00

12 2 Tonkm 63 530.00 0.00 0.59 2.54 6.50 39.11 63 480.00

12 2 Ton 6.33 0.00 0.00 0.01 0.02 0.09 6.22

12 2 E[SEK/Tonkm] 0.07 5.09 2.12 1.22 0.96 0.68 0.07

12 2 E[km/Ton] 10 030.00 75.28 160.80 259.30 360.60 451.20 10 210.00

13 1 Cost 0.00 0.00 0.00 0.00 0.00 0.00 0.00

13 1 Tonkm 0.00 0.00 0.00 0.00 0.00 0.00 0.00

13 1 Ton 0.00 0.00 0.00 0.00 0.00 0.00 0.00

13 1 E[SEK/Tonkm] 0.00 0.00 0.00 0.00 0.00 0.00 0.00

13 1 E[km/Ton] 1.00 1.00 1.00 1.00 1.00 1.00 1.00

13 2 Cost 7 268.00 0.07 47.24 60.06 85.08 117.80 6 958.00

13 2 Tonkm 63 900.00 0.02 80.84 125.10 234.60 371.50 63 080.00

13 2 Ton 20.19 0.00 0.44 0.48 0.71 0.89 17.68

13 2 E[SEK/Tonkm] 0.11 3.98 0.58 0.48 0.36 0.32 0.11

13 2 E[km/Ton] 3 165.00 75.28 185.60 260.50 331.90 418.30 3 568.00

14 1 Cost 2 615.00 564.60 434.20 374.30 342.80 328.50 570.70

14 1 Tonkm 4 169.00 273.70 619.30 621.40 652.30 669.40 1 333.00

14 1 Ton 19.82 7.94 4.37 2.47 1.86 1.47 1.71

14 1 E[SEK/Tonkm] 0.63 2.06 0.70 0.60 0.53 0.49 0.43

14 1 E[km/Ton] 210.30 34.48 141.70 251.40 351.40 454.30 778.00

14 2 Cost 7 372.00 2.24 51.31 94.18 181.80 396.80 6 646.00

14 2 Tonkm 44 340.00 0.99 43.97 144.40 313.10 1 213.00 42 630.00

14 2 Ton 25.16 0.01 0.27 0.59 0.90 2.57 20.84

14 2 E[SEK/Tonkm] 0.17 2.26 1.17 0.65 0.58 0.33 0.16

14 2 E[km/Ton] 1 762.00 77.46 163.00 246.80 349.60 472.80 2 046.00

15 1 Cost 308.30 213.20 0.00 63.69 31.38 0.00 0.00

15 1 Tonkm 1 131.00 69.07 0.00 745.30 316.50 0.00 0.00

15 1 Ton 10.14 5.54 0.00 3.62 0.97 0.00 0.00

15 1 E[SEK/Tonkm] 0.27 3.09 0.00 0.09 0.10 0.00 0.00

15 1 E[km/Ton] 111.50 12.46 1.00 205.70 325.00 1.00 1.00

15 2 Cost 3 188.00 0.00 0.19 1.62 4.36 148.60 3 033.00

15 2 Tonkm ######## 0.00 0.11 1.91 9.79 788.90 ########

15 2 Ton 22.55 0.00 0.00 0.01 0.03 1.85 20.66

15 2 E[SEK/Tonkm] 0.02 0.00 1.76 0.85 0.45 0.19 0.02

15 2 E[km/Ton] 5 666.00 1.00 176.00 255.90 379.00 425.60 6 145.00

16 1 Cost 450.00 98.23 35.22 40.37 35.61 33.74 206.80

16 1 Tonkm 590.30 11.77 17.75 20.52 24.35 42.52 473.40

16 1 Ton 1.59 0.80 0.10 0.08 0.07 0.10 0.44

16 1 E[SEK/Tonkm] 0.76 8.35 1.99 1.97 1.46 0.79 0.44

16 1 E[km/Ton] 370.70 14.64 171.00 255.50 371.70 417.40 1 083.00

16 2 Cost 818.00 0.01 0.08 0.10 1.54 2.73 813.60

16 2 Tonkm 5 048.00 0.00 0.00 0.00 1.34 2.33 5 045.00

16 2 Ton 0.93 0.00 0.00 0.00 0.00 0.00 0.92

16 2 E[SEK/Tonkm] 0.16 205.20 61.40 71.36 1.15 1.17 0.16

16 2 E[km/Ton] 5 438.00 77.24 151.10 265.00 345.30 481.40 5 486.00

17 1 Cost 1 038.00 56.94 112.60 143.00 116.80 115.00 493.50

17 1 Tonkm 2 975.00 14.59 72.33 156.10 121.90 90.91 2 519.00

17 1 Ton 4.20 0.26 0.43 0.57 0.36 0.20 2.38

17 1 E[SEK/Tonkm] 0.35 3.90 1.56 0.92 0.96 1.27 0.20

17 1 E[km/Ton] 707.80 57.19 166.60 274.50 337.50 444.00 1 059.00

17 2 Cost 8 361.00 1.15 7.82 29.98 53.04 99.40 8 170.00

17 2 Tonkm 41 540.00 0.29 2.59 27.22 38.05 105.50 41 370.00

17 2 Ton 9.79 0.00 0.02 0.10 0.11 0.23 9.32

17 2 E[SEK/Tonkm] 0.20 4.00 3.01 1.10 1.39 0.94 0.20

17 2 E[km/Ton] 4 244.00 88.82 153.80 268.90 349.50 452.40 4 437.00

18 1 Cost 1 985.00 266.40 274.40 274.40 333.90 204.60 630.90

18 1 Tonkm 1 876.00 62.87 141.00 183.20 364.70 210.30 914.20

18 1 Ton 5.93 1.60 0.95 0.74 1.03 0.48 1.14

18 1 E[SEK/Tonkm] 1.06 4.24 1.95 1.50 0.92 0.97 0.69


18 1 E[km/Ton] 316.30 39.25 148.40 248.50 354.60 441.20 803.20

18 2 Cost 3 390.00 0.86 13.67 32.39 49.18 69.73 3 224.00

18 2 Tonkm 7 801.00 0.17 7.35 25.87 54.27 80.06 7 634.00

18 2 Ton 3.38 0.00 0.05 0.10 0.16 0.18 2.90

18 2 E[SEK/Tonkm] 0.43 5.11 1.86 1.25 0.91 0.87 0.42

18 2 E[km/Ton] 2 306.00 81.72 157.50 251.50 346.50 448.50 2 636.00

19 1 Cost 2 005.00 1 341.00 663.90 0.14 0.04 0.01 0.00

19 1 Tonkm 2 095.00 941.10 1 154.00 0.05 0.02 0.00 0.00

19 1 Ton 38.65 29.31 9.34 0.00 0.00 0.00 0.00

19 1 E[SEK/Tonkm] 0.96 1.43 0.58 2.74 2.48 1.81 0.97

19 1 E[km/Ton] 54.21 32.11 123.50 242.90 325.00 414.60 547.00

19 2 Cost 2 156.00 0.22 5.61 6.43 8.60 38.91 2 096.00

19 2 Tonkm 9 896.00 0.11 6.17 7.67 11.32 76.73 9 794.00

19 2 Ton 3.22 0.00 0.03 0.03 0.03 0.17 2.95

19 2 E[SEK/Tonkm] 0.22 2.12 0.91 0.84 0.76 0.51 0.21

19 2 E[km/Ton] 3 074.00 88.22 177.50 245.90 339.70 450.10 3 321.00

20 1 Cost 667.40 98.93 94.29 95.29 80.12 70.15 228.60

20 1 Tonkm 629.30 40.70 72.14 83.51 68.85 64.42 299.70

20 1 Ton 2.87 1.34 0.50 0.34 0.20 0.14 0.35

20 1 E[SEK/Tonkm] 1.06 2.43 1.31 1.14 1.16 1.09 0.76

20 1 E[km/Ton] 219.20 30.48 144.70 245.60 346.20 447.60 846.70

20 2 Cost 4 521.00 1.76 63.49 30.90 73.78 109.10 4 242.00

20 2 Tonkm 11 330.00 0.92 111.80 34.80 110.60 182.90 10 890.00

20 2 Ton 5.59 0.01 0.57 0.13 0.32 0.41 4.15

20 2 E[SEK/Tonkm] 0.40 1.91 0.57 0.89 0.67 0.60 0.39

20 2 E[km/Ton] 2 027.00 78.21 194.80 265.80 351.20 448.90 2 624.00

21 1 Cost 76.68 8.95 15.84 13.38 12.09 8.10 18.32

21 1 Tonkm 56.42 2.47 10.98 8.81 9.09 5.77 19.30

21 1 Ton 0.22 0.05 0.07 0.04 0.03 0.01 0.03

21 1 E[SEK/Tonkm] 1.36 3.63 1.44 1.52 1.33 1.40 0.95

21 1 E[km/Ton] 255.80 50.19 151.50 249.90 352.70 448.30 771.80

21 2 Cost 2 240.00 0.77 4.92 12.24 15.91 22.40 2 184.00

21 2 Tonkm 6 574.00 0.38 3.14 11.84 19.08 25.04 6 515.00

21 2 Ton 1.41 0.00 0.02 0.04 0.05 0.06 1.23

21 2 E[SEK/Tonkm] 0.34 2.02 1.57 1.03 0.83 0.89 0.34

21 2 E[km/Ton] 4 673.00 88.96 147.00 271.10 354.50 453.40 5 303.00

22 1 Cost 1 736.00 211.90 236.80 308.80 249.50 261.60 467.90

22 1 Tonkm 11.82 0.12 0.60 1.24 1.32 1.99 6.54

22 1 Ton 0.03 0.00 0.00 0.00 0.00 0.00 0.01

22 1 E[SEK/Tonkm] 146.90 1 761.00 394.30 248.30 188.80 131.30 71.52

22 1 E[km/Ton] 403.00 26.35 151.70 251.00 348.80 451.30 855.20

22 2 Cost 8 473.00 2.07 3.22 41.36 24.74 53.47 8 349.00

22 2 Tonkm 1 629.00 0.00 0.01 0.36 0.22 0.66 1 627.00

22 2 Ton 0.78 0.00 0.00 0.00 0.00 0.00 0.78

22 2 E[SEK/Tonkm] 5.20 495.70 386.70 115.80 113.30 81.01 5.13

22 2 E[km/Ton] 2 077.00 78.45 145.60 261.40 343.80 454.30 2 085.00

23 1 Cost 5 037.00 471.70 518.90 716.50 594.00 657.60 2 079.00

23 1 Tonkm 3 187.00 55.01 130.60 291.10 302.80 463.90 1 943.00

23 1 Ton 7.53 1.25 0.86 1.17 0.87 1.03 2.34

23 1 E[SEK/Tonkm] 1.58 8.58 3.98 2.46 1.96 1.42 1.07

23 1 E[km/Ton] 423.40 44.11 151.30 248.60 346.70 450.50 829.70

23 2 Cost 13 360.00 9.23 30.45 67.47 169.80 211.70 12 870.00

23 2 Tonkm 47 120.00 1.40 7.62 33.99 119.50 164.40 46 800.00

23 2 Ton 12.37 0.02 0.05 0.13 0.34 0.36 11.47

23 2 E[SEK/Tonkm] 0.28 6.57 3.99 1.99 1.42 1.29 0.28

23 2 E[km/Ton] 3 809.00 75.60 148.30 256.80 354.80 452.10 4 080.00

24 1 Cost 224.80 13.98 18.96 25.70 35.18 31.03 99.95

24 1 Tonkm 425.20 6.20 17.69 33.71 62.97 61.69 242.90

24 1 Ton 1.07 0.17 0.12 0.14 0.18 0.14 0.32

24 1 E[SEK/Tonkm] 0.53 2.25 1.07 0.76 0.56 0.50 0.41

24 1 E[km/Ton] 396.00 37.07 145.60 239.50 344.60 447.40 751.20


24 2 Cost 2 886.00 0.00 1.30 3.67 7.76 16.71 2 857.00

24 2 Tonkm 21 390.00 0.00 1.38 4.46 11.50 26.63 21 340.00

24 2 Ton 4.42 0.00 0.01 0.02 0.03 0.06 4.31

24 2 E[SEK/Tonkm] 0.13 0.00 0.94 0.82 0.67 0.63 0.13

24 2 E[km/Ton] 4 836.00 1.00 179.30 234.20 358.40 451.20 4 958.00

25 1 Cost 1 041.00 123.70 135.80 135.40 146.80 126.20 372.70

25 1 Tonkm 55.98 0.62 2.12 2.90 5.15 6.07 39.14

25 1 Ton 0.11 0.02 0.01 0.01 0.01 0.01 0.04

25 1 E[SEK/Tonkm] 18.59 200.90 64.20 46.73 28.52 20.80 9.52

25 1 E[km/Ton] 510.70 39.12 153.30 251.00 348.40 450.30 971.80

25 2 Cost 9 891.00 1.06 12.24 45.69 101.50 155.40 9 575.00

25 2 Tonkm 13 120.00 0.01 0.63 4.02 17.62 21.75 13 080.00

25 2 Ton 2.90 0.00 0.00 0.02 0.05 0.05 2.78

25 2 E[SEK/Tonkm] 0.75 75.55 19.39 11.36 5.76 7.15 0.73

25 2 E[km/Ton] 4 527.00 78.77 170.90 249.30 335.80 459.30 4 706.00

26 1 Cost 8 241.00 1 095.00 1 095.00 1 141.00 1 057.00 920.80 2 932.00

26 1 Tonkm 1 074.00 14.87 48.63 82.68 103.00 112.90 712.20

26 1 Ton 2.40 0.43 0.32 0.33 0.30 0.25 0.77

26 1 E[SEK/Tonkm] 7.67 73.65 22.51 13.80 10.27 8.16 4.12

26 1 E[km/Ton] 447.80 34.75 150.20 250.70 348.80 446.70 925.20

26 2 Cost 7 182.00 1.56 13.28 25.67 54.12 116.50 6 971.00

26 2 Tonkm 6 624.00 0.03 0.66 2.05 6.38 15.69 6 599.00

26 2 Ton 1.59 0.00 0.00 0.01 0.02 0.03 1.52

26 2 E[SEK/Tonkm] 1.08 49.49 20.09 12.55 8.48 7.43 1.06

26 2 E[km/Ton] 4 169.00 78.37 167.00 255.10 365.20 452.00 4 329.00

27 1 Cost 155.30 15.73 21.66 24.98 20.01 18.31 54.64

27 1 Tonkm 35.90 0.51 2.17 3.34 3.59 4.14 22.16

27 1 Ton 0.09 0.01 0.01 0.01 0.01 0.01 0.03

27 1 E[SEK/Tonkm] 4.33 30.99 9.98 7.49 5.58 4.43 2.47

27 1 E[km/Ton] 420.40 41.98 153.60 251.70 348.00 451.50 838.40

27 2 Cost 1 118.00 1.00 3.82 8.01 15.92 18.22 1 071.00

27 2 Tonkm 2 191.00 0.08 0.51 2.49 5.33 7.99 2 174.00

27 2 Ton 0.53 0.00 0.00 0.01 0.02 0.02 0.48

27 2 E[SEK/Tonkm] 0.51 13.09 7.51 3.21 2.99 2.28 0.49

27 2 E[km/Ton] 4 127.00 82.18 157.60 264.30 351.30 444.10 4 492.00

28 1 Cost 386.90 23.17 0.00 133.30 0.00 128.60 101.70

28 1 Tonkm 1 813.00 11.39 0.00 425.10 0.00 432.50 944.50

28 1 Ton 4.00 0.44 0.00 1.79 0.00 0.95 0.82

28 1 E[SEK/Tonkm] 0.21 2.04 0.00 0.31 0.00 0.30 0.11

28 1 E[km/Ton] 452.90 25.64 1.00 237.70 1.00 453.10 1 155.00

28 2 Cost 5 436.00 0.52 4.81 16.50 29.94 68.81 5 316.00

28 2 Tonkm 33 890.00 0.08 3.45 14.56 25.93 84.18 33 760.00

28 2 Ton 7.09 0.00 0.02 0.06 0.07 0.19 6.75

28 2 E[SEK/Tonkm] 0.16 6.38 1.39 1.13 1.16 0.82 0.16

28 2 E[km/Ton] 4 781.00 82.01 177.60 253.50 347.00 451.10 5 002.00

29 1 Cost 10 250.00 1 413.00 1 524.00 1 504.00 1 180.00 1 155.00 3 473.00

29 1 Tonkm 2 696.00 62.40 164.30 304.30 252.00 325.60 1 588.00

29 1 Ton 7.15 1.60 1.11 1.19 0.72 0.72 1.82

29 1 E[SEK/Tonkm] 3.80 22.64 9.28 4.94 4.68 3.55 2.19

29 1 E[km/Ton] 376.90 39.13 148.70 254.90 349.60 452.00 873.00

29 2 Cost 9 197.00 3.56 19.82 47.23 146.80 258.00 8 721.00

29 2 Tonkm 22 210.00 0.20 2.71 11.75 57.79 120.40 22 020.00

29 2 Ton 5.73 0.00 0.02 0.05 0.17 0.27 5.23

29 2 E[SEK/Tonkm] 0.41 17.48 7.32 4.02 2.54 2.14 0.40

29 2 E[km/Ton] 3 874.00 69.43 162.60 260.70 344.50 448.80 4 208.00

31 1 Cost 1 582.00 296.50 370.90 298.40 176.20 116.50 323.70

31 1 Tonkm 2 721.00 163.20 511.40 545.80 372.90 261.60 866.20

31 1 Ton 13.00 4.37 3.55 2.22 1.07 0.59 1.21

31 1 E[SEK/Tonkm] 0.58 1.82 0.73 0.55 0.47 0.45 0.37

31 1 E[km/Ton] 209.30 37.37 144.10 245.60 348.90 445.40 716.80

31 2 Cost 35.41 0.00 0.43 0.56 0.27 0.26 33.88


31 2 Tonkm 248.90 0.00 0.42 0.63 0.23 0.26 247.40

31 2 Ton 0.04 0.00 0.00 0.00 0.00 0.00 0.04

31 2 E[SEK/Tonkm] 0.14 0.00 1.04 0.89 1.20 1.02 0.14

31 2 E[km/Ton] 5 645.00 1.00 164.70 235.70 347.20 453.70 6 572.00

32 1 Cost 13 690.00 1 872.00 1 730.00 2 272.00 1 850.00 2 020.00 3 952.00

32 1 Tonkm 1 499.00 23.68 66.62 146.00 150.20 275.00 837.60

32 1 Ton 3.85 0.83 0.44 0.58 0.43 0.60 0.97

32 1 E[SEK/Tonkm] 9.14 79.05 25.97 15.56 12.32 7.34 4.72

32 1 E[km/Ton] 389.10 28.41 153.00 252.80 348.60 455.90 860.90

32 2 Cost 11 830.00 9.19 15.57 66.08 182.30 238.20 11 320.00

32 2 Tonkm 18 520.00 0.20 0.64 7.16 24.46 37.13 18 450.00

32 2 Ton 3.74 0.00 0.00 0.03 0.07 0.08 3.55

32 2 E[SEK/Tonkm] 0.64 46.38 24.30 9.23 7.45 6.42 0.61

32 2 E[km/Ton] 4 958.00 75.72 153.50 268.00 342.20 459.50 5 197.00

33 1 Cost 2 634.00 261.10 306.60 397.30 356.00 344.50 968.30

33 1 Tonkm 935.00 11.34 38.71 76.76 96.49 119.70 592.00

33 1 Ton 2.11 0.29 0.25 0.30 0.28 0.27 0.72

33 1 E[SEK/Tonkm] 2.82 23.02 7.92 5.18 3.69 2.88 1.64

33 1 E[km/Ton] 443.20 38.58 155.30 252.00 345.70 450.40 825.90

33 2 Cost 5 878.00 4.23 14.24 41.02 70.75 102.20 5 645.00

33 2 Tonkm 20 460.00 0.32 3.85 13.75 32.20 51.54 20 360.00

33 2 Ton 5.35 0.00 0.02 0.05 0.09 0.11 5.06

33 2 E[SEK/Tonkm] 0.29 13.21 3.70 2.98 2.20 1.98 0.28

33 2 E[km/Ton] 3 826.00 76.78 170.80 255.70 357.60 454.30 4 020.00

34 1 Cost 0.00 0.00 0.00 0.00 0.00 0.00 0.00

34 1 Tonkm 0.00 0.00 0.00 0.00 0.00 0.00 0.00

34 1 Ton 0.00 0.00 0.00 0.00 0.00 0.00 0.00

34 1 E[SEK/Tonkm] 62.82 62.82 0.00 0.00 0.00 0.00 0.00

34 1 E[km/Ton] 15.90 15.90 1.00 1.00 1.00 1.00 1.00

34 2 Cost 26.86 0.00 0.00 0.00 0.00 0.00 26.86

34 2 Tonkm 80.16 0.00 0.00 0.00 0.00 0.00 80.16

34 2 Ton 0.06 0.00 0.00 0.00 0.00 0.00 0.06

34 2 E[SEK/Tonkm] 0.34 0.00 0.00 0.00 0.00 0.00 0.34

34 2 E[km/Ton] 1 427.00 1.00 1.00 1.00 1.00 1.00 1 427.00

35 1 Cost 4 159.00 384.10 504.30 1 061.00 440.60 1 225.00 543.70

35 1 Tonkm 25.36 0.18 0.81 6.25 1.20 13.66 3.26

35 1 Ton 0.08 0.01 0.00 0.02 0.00 0.03 0.00

35 1 E[SEK/Tonkm] 164.00 2 089.00 624.60 169.80 368.20 89.69 166.70

35 1 E[km/Ton] 326.60 19.41 173.60 250.30 341.90 450.30 692.00

35 2 Cost 44 470.00 0.68 14.58 89.61 182.80 329.80 43 860.00

35 2 Tonkm 2 695.00 0.00 0.01 0.16 0.49 1.07 2 693.00

35 2 Ton 0.35 0.00 0.00 0.00 0.00 0.00 0.35

35 2 E[SEK/Tonkm] 16.50 7 870.00 1 387.00 554.40 373.90 309.60 16.29

35 2 E[km/Ton] 7 652.00 70.86 156.70 258.60 342.40 446.00 7 746.00


Appendix 4 Prediction model script for Matlab function main() clear all; close all;

% % % Loads and saves Prediction data in workspace PWCDataForPrediction. % display('Loading and saving data for prediction') % LoadAndSaveDataForPrediction(); % display('data loaded and saved')

% Load the matlab saved data display('loading data') load PWCDataForPrediction display('data loaded')

display('starting predictions') TON2012=PredictQP(PTon,WTon,CTon,D,BIG,Ports,VGTon); display('Predictions completed')

display('Restarting predictions for vg 19') TON2012(:,:,19)=RePredictQP(PTon,WTon,CTon,D,BIG,Ports,VGTon,19); display('RePredictions for vg 19 completed')

% model predicts in kTON, rescale to Ton TON2012=1000*TON2012;

display('Save Predictions in workspace TON2012') save TON2012 TON2012 display('Prediction completed and saved in TON2012.mat')

function PWC=PredictQP(PTon,WTon,CTon,D,BIG,Ports,VGTon) load PWCData oPC4T oPC1T oWC1T oWC4T PWC=zeros(464,464,34); T0104=[reshape(sum(sum(oPC1T+oWC1T)),[34 1]) reshape(sum(sum(oPC4T+oWC4T)),[34 1])]; I0104=T0104>0; for v=1:34 if ismember(v,VGTon); id=find(v==VGTon);

scale=sum(sum(oPC4T(:,:,v)+oWC4T(:,:,v)+oPC1T(:,:,v)+oWC1T(:,:,v)))./(sum(I0104(v,:))*s

um(sum(PTon(:,id)))); D12=Predictiondata(scale*PTon,scale*WTon,scale*CTon,D,v,BIG,Ports,VGTon); PWCPred=DataAndModelPrediction(D12,v)/scale; id=find(v==VGTon); PWC(:,:,v)=RASBalancing(PTon(:,id),CTon(:,id),PWCPred); end end

function PWC=RePredictQP(PTon,WTon,CTon,D,BIG,Ports,VGTon,v) load PWCData oPC4T oPC1T oWC1T oWC4T load('TON2006/TON2006','TON2006'); id=find(v==VGTon); P=PTon(:,id); C=CTon(:,id)'; P06=sum(TON2006(1:290,:,v),2)/1000; C06=sum(TON2006(:,1:290,v),1)/1000; ap=fminunc(@(a) sum((a*P(1:290)+(1-a)*C(1:290)'-P06).^2),0.5); Ptmp=ap*P(1:290)+(1-ap)*C(1:290)'; Ptmp=Ptmp*sum(P(1:290))/sum(Ptmp); PTon(1:290,id)=Ptmp; ac=fminunc(@(a) sum((a*P(1:290)+(1-a)*C(1:290)'-C06').^2),0.5); Ctmp=ac*P(1:290)+(1-ac)*C(1:290)'; Ctmp=Ctmp*sum(C(1:290))/sum(Ctmp); CTon(1:290,id)=Ctmp;

% a=fminunc(@(a) sum((a*P(1:290)+(1-a)*C(1:290)'-P06).^2)+sum((a*P(1:290)+(1-

a)*C(1:290)'-C06').^2),0.5); % PTon(1:290,id)=a*P(1:290)+(1-a)*C(1:290)'; % CTon(1:290,id)=a*P(1:290)+(1-a)*C(1:290)';

PWC=zeros(464,464,34); T0104=[reshape(sum(sum(oPC1T+oWC1T)),[34 1]) reshape(sum(sum(oPC4T+oWC4T)),[34 1])];


I0104=T0104>0; % for v=1:34 if ismember(v,VGTon); id=find(v==VGTon);

scale=sum(sum(oPC4T(:,:,v)+oWC4T(:,:,v)+oPC1T(:,:,v)+oWC1T(:,:,v)))./(sum(I0104(v,:))*s

um(sum(PTon(:,id)))); D12=Predictiondata(scale*PTon,scale*WTon,scale*CTon,D,v,BIG,Ports,VGTon); PWCPred=DataAndModelPrediction(D12,v)/scale; id=find(v==VGTon); PWCPred(1:290,1:290)=PWCPred(1:290,1:290).*(D(1:290,1:290)<0.15); PWC=ReRASBalancing(PTon(:,id),CTon(:,id),PWCPred); end % end

function PWC=RASBalancing(PTon,CTon,PWCPred); % Performs RAS-balancing with PWCPred as apriori matrix % Returns matrix calibrated to the row and col constraints i PTon and CTon. ip=PTon>0; ic=CTon>0; sP=sum(PTon); sC=sum(CTon); CTon=CTon*sP/sC;

M=PWCPred(ip,ic);

ds=1;s=1;r=1; while ds>1e-12 sold=s; rold=r;

r=PTon(ip)./(sum(M,2)); M=diag(r)*M;

s=CTon(ic)./(sum(M,1)'); M=M*diag(s);

ds=norm(s-sold,2)+norm(r-rold,2); end PWC=0*PWCPred; PWC(ip,ic)=M;

function PWC=ReRASBalancing(PTon,CTon,PWCPred); % Performs RAS-balancing with PWCPred as apriori matrix % Returns matrix calibrated to the row and col constraints i PTon and CTon. ip=PTon>0; ic=CTon>0; sP=sum(PTon); sC=sum(CTon); CTon=CTon*sP/sC;

M=PWCPred(ip,ic);

ds=1;s=1;r=1; while ds>1e-12 sold=s; rold=r;

r=PTon(ip)./(sum(M,2)); M=diag(r)*M;

s=CTon(ic)./(sum(M,1)'); M=M*diag(s);

ds=norm(s-sold,2)+norm(r-rold,2); end PWC=0*PWCPred; PWC(ip,ic)=M;

function Data=Predictiondata(PTon,WTon,CTon,D,v,BIG,Ports,VGTon)

id=find(v==VGTon); P=PTon(:,id); C=CTon(:,id)'; r=length(P); c=length(C);


Wr=0*P; Wr(1:290)=WTon(:,id)>0; Wr(291:end)=false; Wc=Wr';

r4=P*ones(1,c); r4(291:end,291:end)=0; c4=ones(r,1)*C; c4(291:end,291:end)=0; wr=Wr*ones(1,c); wc=ones(r,1)*Wc;

%iC=C>0; %iP=P>0;

E=eye(length(P)); E(291:end,291:end)=0;

N=D<=0.05; N=N-diag(diag(N));%remove diagonal which is covered by E N(291:end,291:end)=0; N(291:end,1:290)=0; N(1:290,291:end)=0;

Data.Edom=E;%(iPdom,iCdom); Data.Ndom=N;%(iPdom,iCdom); Data.dist=D;%(iPdom,iCdom);

Data.r4dom=r4;%(iPdom,iCdom); Data.c4dom=c4;%(iPdom,iCdom); Data.wr=wr;%(iPdom,iCdom); Data.wc=wc;%(iPdom,iCdom); Data.Exdum=zeros(r,c);Data.Imdum=Data.Exdum; Data.Exdum(1:290,291:end)=1; Data.Imdum(291:end,1:290)=1; Data.dom=0*Data.Exdum; Data.dom(1:290,1:290)=1;

rs=P(1:290); cs=C(1:290); fr=(rs.*(rs>3*mean(rs)))>cs'; to=rs'<(cs.*(cs>3*mean(cs))); fr=(rs)>cs'; to=rs'<(cs); frto=(1*fr)*(1*to); FrTo=zeros(r,c); FrTo(1:290,1:290)=frto; Data.FrTo=FrTo;%(iPdom,iCdom);

mainp=(rs>0.1*sum(rs))*ones(1,290); %main production regions >10% of national mainc=ones(290,1)*(cs>0.1*sum(cs)); %main consumption regions >10% of national MP=zeros(r,c); MP(1:290,1:290)=mainp; MC=zeros(r,c); MC(1:290,1:290)=mainc; Data.MainP=MP;%(iPdom,iCdom); Data.MainC=MC;%(iPdom,iCdom);

big=zeros(r,c); big(1:290,1:290)=BIG(:,:,v); big=big-diag(diag(big)); big=100*big;%(iPdom,iCdom); Data.Big=big; Data.Bigwc=1*(sum(Data.Big,2)>0)*(sum(Data.wc,1)>0);

% imid=(sum(Data.PCdom.*Data.Imdum,1)>0); imid=(sum(1*Data.Imdum,1)>0); Data.IMP=0*Data.Imdum; Data.IMP(291:end,imid)=1; % imid=(sum(Data.PCdom.*Data.Exdum,2)>0); imid=(sum(1*Data.Exdum,2)>0); Data.EXP=0*Data.Exdum; Data.EXP(imid,291:end)=1;

P=zeros(r,1); P(1:length(Ports))=Ports; Ports=P>0;


FrPortDom=zeros(r,c);FrPortEx=FrPortDom;ToPortDom=FrPortDom;ToPortIm=FrPortDom;PortToPo

rt=FrPortDom; FrPortDom(Ports,1:290)=1; FrPortEx(Ports,291:end)=1; ToPortDom(1:290,Ports)=1; ToPortIm(291:end,Ports)=1; PortToPort=FrPortDom.*ToPortDom; Data.FrPortDom=FrPortDom;%(iPdom,iCdom); Data.ToPortDom=ToPortDom;%(iPdom,iCdom); Data.FrPortEx=FrPortEx;%(iPdom,iCdom); Data.ToPortIm=ToPortIm;%(iPdom,iCdom); Data.PortToPort=PortToPort;%(iPdom,iCdom);

function PWC=DataAndModelPrediction(D4,v) [r4,c4]=size(D4.r4dom); sr=1; sc=1; if r4>0 sr=sum(D4.r4dom(:,1)); sc=sum(D4.c4dom(1,:)); end a=log(sum(exp((log(D4.r4dom)/sr-1*log(D4.dist))/1),1)); Agg=1*ones(r4,1)*((a-

mean(mean(a)))./std(a)); b=log(sum(exp((log(D4.c4dom)/sc-1*log(D4.dist))/1),2)); Acc=1*((b-

mean(mean(b)))./std(b))*ones(1,c4);

dat=[ones(size(D4.r4dom(:))) log(D4.r4dom(:)) log(D4.c4dom(:)) log(D4.dist(:))

D4.dist(:)]; [r,c]=size(dat); % r4=r;

nE=not(D4.Edom(:)); Y01=zeros(size(D4.Edom)); % With Port xall =[dat Y01(:) D4.Edom(:) D4.Edom(:).*log(D4.r4dom(:))

D4.Edom(:).*log(D4.c4dom(:)) D4.Ndom(:) D4.Ndom(:).*log(D4.r4dom(:))

D4.Ndom(:).*log(D4.c4dom(:)) Acc(:).*nE Agg(:).*nE D4.MainP(:) D4.MainC(:)

D4.MainP(:).*D4.MainC(:) D4.Big(:) D4.Bigwc(:) D4.Big(:).*D4.FrTo(:) D4.ToPortDom(:)

D4.FrPortDom(:) D4.PortToPort(:) D4.EXP(:)*ones(1,c).*dat D4.FrPortEx(:)

D4.IMP(:)*ones(1,c).*dat D4.ToPortIm(:)];

[betanum,txt]=xlsread('\Models\TonModels.xlsx',['VG ' num2str(v)]); beta=betanum(1:35,1); ib=find(beta); PWC=exp(xall(:,ib)*beta(ib)); %tag:PWCPrediction PWC(isnan(PWC))=0; PWC=reshape(PWC,[r4 c4]);

function LoadAndSaveDataForPrediction() % Load Distance matrix D = load('DataForPrediction\VFU_UHM_2001_to_2004\dist_km.dat'); Dreg=D(3,1:end); Dreg2=D(1:end,2); i=find(Dreg==1917); i2=find(Dreg==330); tmp=D(:,i); D(:,i)=[]; D=[D(:,1:i2) tmp D(:,i2+1:end)]; i=find(Dreg2==1917); i2=find(Dreg2==330); tmp=D(i,:); D(i,:)=[]; D=[D(1:i2,:); tmp; D(i2+1:end,:)]; i=find(D(3,:)==1917); D(3,i)=331; %Heby i=find(D(:,2)==1917); D(i,2)=331; %Heby D=D/1000; % models are estimated in kkm D=D(4:end,3:end);

% Create dummy for BIG workplaces in sending and receiving regions [dC tC]=xlsread('\DataForPrediction\Större arbetsställen 2004 och 2010 - bearbet-

ning.xlsx','2010 C'); [dP tP]=xlsread('\DataForPrediction\Större arbetsställen 2004 och 2010 - bearbet-

ning.xlsx','2010 P');


BIG=zeros(290,290,34); for i=1:34 mp=dP(4:end,i); mp=mean(mp(mp>0)); % more than average employed in prod mc=dC(4:end,i); mc=mean(mc(mc>0)); % more than average employed in cons BIG(:,:,i)=(1*(dP(4:end,i)>=mp)*(dC(4:end,i)>=mc)'); end

% Dummie for domestic Ports [Ports,t]=xlsread('\DataForPrediction\Hamnar.xlsx','Hamnar');

% [PTonf,PTontxt]=xlsread('\DataForPrediction\PCData\Skattning TON

2012_ForPrediction.xlsx','Produktion 2012 (TON)'); % [WTonf,WTontxt]=xlsread('\DataForPrediction\PCData\Skattning TON

2012_ForPrediction.xlsx','Partihandel 2012 (TON)'); % [CTonf,CTontxt]=xlsread('\DataForPrediction\PCData\Skattning TON

2012_ForPrediction.xlsx','Förbrukning 2012 (TON)'); [PTonf,PTontxt]=xlsread('\DataForPrediction\PCData\omtag varuvärden 2012 2015-03-

29.xlsx','Produktion 2012 (TON)'); [WTonf,WTontxt]=xlsread('\DataForPrediction\PCData\omtag varuvärden 2012 2015-03-

29.xlsx','Partihandel 2012 (TON)'); [CTonf,CTontxt]=xlsread('\DataForPrediction\PCData\omtag varuvärden 2012 2015-03-

29.xlsx','Förbrukning 2012 (TON)');

VGTon=PTonf(1,2:32); PTon=PTonf(2:466,2:32); PTon(291,:)=[]; %size(PTon) WTon=WTonf(2:291,2:32); CTon=CTonf(2:466,2:32); CTon(291,:)=[]; %size(CTon)

PTon(1:290,:)=PTon(1:290,:)+WTon(1:290,:); % Add warehouse to row constraint CTon(1:290,:)=CTon(1:290,:)+WTon(1:290,:); % Add warehouse to col constraint

PTon=PTon/1000; % models are estimated in kTon CTon=CTon/1000; % models are estimated in kTon

tmp=PTon(291:end,:); %reorder, PTon should contain imports as row constraints for

non-domestic regions PTon(291:end,:)=CTon(291:end,:); CTon(291:end,:)=tmp;

save PWCDataForPrediction

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