PWC Matrices: new method and updated Base Matrices Final Report

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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

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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: info@wspgroup.se Corporate identity no.: 556057-4880 Reg. office: Stockholm

www.wspgroup.se/analys

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Analysis & Strategy 3

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.

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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.

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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 2012

¹

. Apart from the method to estimate the matrices currently in use, there is an earlier approach from 2004

²

. 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 developed

³

.

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)

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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

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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 10

^th

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).

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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 steps

⁴

:

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.

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

they are subsequently inserted at the end of the process.

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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.

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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.

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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,



s

Q

r’s

= Q

r’.

,

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



r

Q

rs’

= 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, Q

r’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

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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.

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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 report

⁵

. 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 Sweden

⁶

, 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

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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- tion

⁷

,

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

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“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

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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 Eurostat

¹⁰

:

“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 subgroups

¹¹

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 goods

¹²

. 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.

10http://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

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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 CPA

¹³

)

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)

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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 matrices

¹⁵

. 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

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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.

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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

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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.

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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.

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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.

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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.

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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.

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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.

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Analysis & Strategy 29 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

[F | x ]

_rs _rs

m( , x )

_rs

e

'x^rs

E   

^

, (1)

where x

rs

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 flow f

_rs

, the pseudo log-likelihood of this observation is ( )

_rs

log(m( , x )) m( , x )

_rs _rs

l   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

_rs

m( , x )) x

_rs _rs

0

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.

PWC Matrices: new method and updated Base Matrices Final Report

Analysis & Strategy REPORT