Compilation of Social Accounting Matrices with a Detailed Representation of the Agricultural Sector (AgroSAM)

Transcription

1 btract ompilation of Social ccounting Matrice with a Detailed Repreentation of the gricultural Sector (grosm) Marc Mueller* and Ignacio Pérez Domínguez European ommiion, Intitute for Propective Technological Studie Social accounting matrice (SM) are a convenient way to repreent the monetary flow between productive ector and intitution and may erve a databae for a large variety of quantitative tool ued for economic analyi. The aim of thi tudy i to contruct conitent and complete SM for the EU27 Member State with a highly diaggregated agricultural ector, which hould erve a a conitent databae for quantitative policy analyi within and beyond the agricultural ector. The main challenge here wa the integration of information from different data ource in everal tep: (1) compilation of upply and ue-table a well a data about monetary flow between intitution into a SM format, (2) diaggregation of the agricultural and food-ector by uing input data from the agricultural ector model PRI, and (3) equential cro-entropy etimation of the final SM in order to map different databae and miing information. The etimation tep were deigned in a way that the final repreentation of the agricultural ector agree with the correponding macro-total while maintaining the core information provided by the PRI databae. Thi reulting databae i meant a a contribution to exiting tool for quantitative policy analyi built on SM, like for example computable general equilibrium model. For thi reaon, we have choen a ectoral claification that i motly compatible with the format of the GTP databae in order to facilitate it potential ue alo in a GTP framework. Moreover, the tool i alo flexible to match different product aggregation and feed partial equilibrium model (e.g. agricultural, foretry or energy model). Keyword: compilation of ocial accounting matrice, data recovery, agricultural ector model, cro entropy etimation * ontact uthor: Dr. Marc Müller, GRITRDE, Edificio Expo / Inca Garcilao, /n - E SEVILL - Tel : Fax :

2 1 Background The P reform of 2003 ha provoked a ignificant change of policie affecting agricultural market in the EU Member State (MS). Thi i of particular relevance for the new MS, in which the agricultural ector ha a comparatively high hare in the generation of national income. Moreover, rural development policie have increaed their weight in the policy agenda. Therefore, the linkage between agriculture and other economic ector, uch a renewable energy and food proceing indutry, a well a the impact of policy change on factor market (labour and land) and farm income, have received pecial attention by policy analyt. Social accounting matrice (SM) are a convenient way to repreent the monetary flow between productive ector and intitution and may erve a databae for a large variety of quantitative tool ued for economic analyi. However, mot of the tatitical department often provide upply and ue table (SUT) and input-output table (IOT) with a highly aggregated repreentation of the agricultural ector, which make it very difficult to analye the economic impact of pecific policie on the agricultural ub-ector and related indutrie. Particularly the change from agricultural ubidie linked to production to a ingle farm payment cheme require databae that contain the flow between and within intitution like private and public budget and productive ector like agriculture and food proceing indutrie. The main aim of thi project wa therefore to contruct SM for the EU27 Member State which would allow analying the economic effect of the P reform within and beyond agriculture. The main challenge here wa the integration of information from different ource, which are neither necearily conitent nor complete, even when coming from the ame data owner (e.g. tructural deviation between P (ommodity Produced by ctivity) and E (Economic ccount for griculture) claification ued by Eurotat). further goal of thi project i to contribute to exiting tool for quantitative policy analyi that are built on SM, like computable general equilibrium model (GE). Therefore the proviion of updated SM for EU MS with a high reolution of agriculture would be beneficial for both, uer and modeller. With thee objective in mind, the following apect are highlighted: The contruction of ocial accounting matrice for the EU27 with a high reolution of the agricultural ector (grosm) hould allow for a proper analyi of agricultural policie. The number of agricultural ub-ector hould allow for (a) a detailed repreentation of the main agricultural policie, (b) the incorporation of dataet from already exiting economic model (e.g. PRI), (c) aggregation algorithm allowing the reuability by other modelling ytem (e.g. GTP, GLOBE), and (d) the utiliation of readily available dataet from tatitical department (e.g. Eurotat, FOSTT) tranparent and automatied routine hould allow the extraction, tranformation and incorporation of new dataet, o that the update cot of the grosm i kept at a low level. 2 Target Structure of the grosm The tructure of the grosm i largely determined by the available data and the deired compatibility with the claification ued in the GTP and PRI model. The upper limit for a diaggregated repreentation of the agricultural ector hould be the "omplete and 2

3 onitent Databae" (oo) hared by the ector model PRI and PSIM. The lower limit i the repreentation in GTP in order to allow a traightforward many-to-one mapping between the claification. thee requirement are not fulfilled by none of the exiting claification, the formulation of a new one, called "Modified gro-indutrial laification" (M) i purued, which follow in general the commodity claification of the "ombined Nomenclature" (N) and the "ommoditie Produced by ctivitie" (P) ued by Eurotat, but lie within the bound given by oo and GTP 1. For commoditie and activitie, the tructure of the target claification M i largely determined by the ES (European Sytem of National ccount) claification, particularly the NE (Nomenclature of Economic ctivitie) and P (ommoditie Produced by ctivitie) claification at 3-digit level, in which the upply and ue table are provided. griculture and food-indutry are here repreented by one row and one column repectively. more detailed repreentation of thee two ector can be achieved by uing the one provided by the oo databae. further deirable property of the target claification i a correpondence of the activitie with the mot refined NE claification level (5 digit). Regarding primary factor, the available ue table ditinguih between compenation of employee, net operating urplu and conumption of fixed capital. Information about different type of labour i not provided here and oo doe not allow for further ditinction. The taxe and intitution included in the target claification follow thoe featured by ES at the 3-digit level. Thi i a rather coare repreentation a import tariff and dometic taxe on commoditie are ummarized here a indirect taxe on commoditie 2. 3 Dataet The data et ued for the grosm project are decribed in thi ection. The main focu lie on the tructure and availability of thee data ource 3.1 Multi-Sectoral Data Supply and ue table (SUT) are the mot ueful databae in the context of SM contruction a they repreent the full flow of good and ervice within an economy and provide alo information on trade margin and certain type of taxe/ubidie. Eurotat provide SUT in two different file-format: NIO: available a bulk download in 'tab-eparated' file (.tv file) SUIOT: available a country-wie downloadable MS-Excel file (.xl file). Symmetric input-output table in baic price (IOT) are alo provided by the ame ource a the SUT and in the ame format and coverage. lthough IOT are often ued a input for the compilation of SM, they do not provide the ame amount of information a SUT, particularly ince the tranformation of baic price into purchaer price (e.g. trade margin a differential) i miing. In general, SUT are preferable for SM contruction. The macro aggregate provided by Eurotat (NM) have a full coverage of the EU27 Member State and include main indicator like total intermediate demand, compenation of employee, 1 The target claification and the correpondence with other model are not documented here but are available from the author upon requet 2 Land rent would be deirable to include in the lit of primary factor, but we decided not to include them at thi tage of the project. For thi verion of the grosm project, we retrain ourelve to the rather coare repreentation of the primary factor a "operating urplu, gro", and "compenation of employee". Moreover, the diaggregation of import and dometic taxe on commoditie will have priority in the next tage of the grosm project. 3

4 gro value added and net taxe on production, but only for 31 ector and not the 59 which are featured in the SUT framework. The national account by intitutional ector (NS) repreent the monetary flow between the productive ector and the intitution a well a the flow within the intitution. Particularly direct taxe paid by non-governmental intitution (houehold, enterprie) and direct tranfer received, a well a the ditribution of factor income (wage, operating urplu) acro the intitution are relevant to ae the full picture of a national economy in a SM framework. 3.2 gricultural Data The agricultural ector model PRI 3 and PSIM 4 are both baed on a common databae (oo) which wa developed at the Univerity of Bonn and i the ucceor of the formerly ued SPEL databae. Both model and the databae are currently available at JR-IPTS (GRILIFE 5 Unit) and provide a comprehenive picture of the agricultural ector for the EU27 Member State plu the Balkan. The main data ource for the contruction of oo are preented in the following table. Table 1 Data item ctivity level Production Data item and their main ource in oo Farm and market balance poition Sectoral revenue and cot Price Output coefficient Input coefficient ctivity pecific income indicator Policy data Source Land ue tatitic, herd ize tatitic, laughtering tatitic, tatitic on import and export of live animal Farm and market balance tatitic, crop production tatitic, laughtering tatitic, tatitic on import and export of live animal Farm and market balance tatitic Economic ccount for griculture (E) Derived from production and E Derived from production and activity level, engineering knowledge Different type of etimator, engineering function Derived from input and output coefficient and price Variou ource (Official Journal of the EU) Source: Eurotat ( everal bio-phyical econometric tudie and European ommiion ( For the purpoe of the grosm project, oo i fairly detailed and include everal element which are conceptually challenging concerning it tranformation into a SM format (e.g. data on manure production/ue, fertilizer conumption, et-aide, milk quota, activity and product premium). Thi ha to do with the fact that (1) oo doe not trictly follow the "activity from/to commodity" book keeping tructure of ES (ee ection 5, "compilation of prior") and (2) it doe not conider other ector of the economy (e.g. proceing of agricultural product like dairie are preented a end-of-pipe product, with no correponding indutrial activitie to pay for). Moreover, the oo databae include algorithm for data conitency and completene, which are key iue to pick up in the grosm project (ee Britz 2005, pp.15-30). The combination of the SUT and oo i in fact the major challenge of the grosm project. Eventually, other etimation module of PRI might be picked up in later tage of the project (e.g. etimation of labour and energy 3 ommon gricultural Policy Regional Impact nalyi Model, URL: 4 ommon gricultural Policy Simulation Model, URL: 5 griculture and Life Science in the Economy, URL: 4

5 input, barrier to trade between the EU and the ret of the world, land price and quota rent for ugar/milk, etc.) 6. The Economic ccount for griculture (E) i a rather extenive dataet for the agricultural ector of the EU27 and the main input for the oo databae. The gricultural Information Sytem (GR_IS) i only ued in the analyi when no information from the E i available (e.g. gro trade of agricultural commoditie). FOSTT own the mot comprehenive databae on trade of agricultural commoditie and input. Thi information i important to determine the import/export ub-matrice of the SM. Since it i already ued by the PRI Model in it market module, the product definition are conitent with the one found in the oo databae (e.g. trade of wheat meaured in term of raw equivalent found in proceed product like beer or pata). Moreover, the gricultural Market cce Databae (MD) ha very detailed information on market policy intrument (e.g. import tariff or tariff rate quota), the OED provide information on conumer/upply upport equivalent (SE/PSE) for different world aggregate and the World Bank periodically publihe population tatitic. Dometic production value of the food indutry and trade data are extracted from PRODOM and OMEX databae. 4 ontruction of SM in ES95 Format The firt tep for the contruction of the grosm databae i the compilation of a comprehenive et of SM according to the ES claification ued by Eurotat. It ditinguihe 59 productive ector and commoditie and, therefore, will be noted here a ESSM. The tylized tructure of the ESSM i mainly haped by the tructure of the main input dataet, namely the SUT (either SUIOT or NIO) and the intitutional account (NS). SM, a depicted in appendix 1, can be directly compiled baed on SUT and NS dataet. SUT are available for 21 MS in 2000, NS data for 23 MS. However, both dataet were only available in 18 cae. The dataet ued at thi tage are in general conitent and the ESSM are in mot cae balanced. However, mall deviation between row- and column-um of the ESSM could be oberved. We need to enure that the ESSM are balanced before entering the next tage of the compilation procedure, therefore we ue a cro-entropy procedure to balance the SM (e.g. Robinon et al 2000). With thi purpoe we employ a multiplicative error term with an expected value of 1 and a range ufficiently large to accommodate poible high deviation between row- and column-um of the ESSM. The error term i defined by a et of upport point and aociated weight. The upport point are arbitrarily defined a hown below (for the cae of five upport point). Thee weight have to add up to unity and hould be a cloe a poible to a et of pre-defined prior weight, for which we aumed a uniform ditribution. [ 3, 1.5,0,1.5,3] b = with W = 0.5 The objective function of the balancing model i to minimize the cro-entropy between prior weight and final weight. The minimization i ubject to the contraint that the weight range between 0 and 1, add up to unity and that the final ESSM i a cloe a poible to the prior SM derived from the NS and SUT dataet, but ha equal row- and column-um. The balancing model i ummarized below 7, more detail on the method can be found in ection 6: 6 The correpondence between the activity and commodity claification in PRI and the modified agroindutrial claification (M) are omitted from thi paper but are available from the author upon requet. 5

6 Eq (1) E = min W ln W W t.., ', ',, ',, ',, ', ESSM, ' = ESSM, ' exp W, ', b, ' W ESSM = 1, 0 W 1 = ESSM, ', ' ' ESSM: Balanced ESSM ESSM : Prior ESSM derived from SUT and NS dataet W: Weight of error upport point E: ro-entropy minimand S: Index for upport point 5 ompilation of Prior for grosm (PriorSM) The objective of etimating a reliable, balanced ocial accounting matrix with diaggregated agricultural and food indutry ector, largely depend on the reliability of the a-priori information drawn from the variou ource. The compilation of the prior SM hould hence be carried out in a careful and tranparent manner. Particularly the tranparency of the datamaaging proce of re-arranging entrie in the parent dataet in order to achieve the required compatibility of format and content i difficult to realize 8. In general, we followed a five tep procedure: (1) derive tax rate, trade margin and input-output coefficient from ESSM, (2) re-arrange the oo data into the SM format (agricultural accounting matrix M), (3) merge the ESSM and M into an unbalanced PriorSM, (4) balance activity and commodity account total, and (5) balance the PriorSM We could rely in mot cae on the information provided by our preferred ource ES and oo, but particularly the food-indutry ector i not covered exhautively in oo 9, uch that we had to incorporate other ource of information a well. The oo databae build upon the meta-databae of the NewRONOS domain manager of EUROSTT (ub-domain: ZP1, OS, PRG). lthough thee raw data i proceed to meet the demand for completene and conitency (Britz et al 2005), it till follow the general accounting principle of the E. Thi "data maaging" property create eriou difficultie when attempting to combine the data with data in ES format (e.g. SUT) a the ditinction between an agricultural commodity and a proceed commodity i not done in the 7 Note: Indice for time (t) and tate (r) have been omitted for reaon of readability 8 The implemented GMS code wa developed ad-hoc a new challenge occurred while including more countrie, year or dataet. However, we will decribe the proce in a manner that allow following the mot relevant tep, but it ha to be noted that it will not be poible to replicate the procedure without conulting the correponding GMS code 9 Thi might change in the near future, ince the PRI Model i currently improving proceing function for dairie, oileed and biofuel it it market module, information which will mot likely be fed into the bae year databae and ued in the contruction of a future PriorSM. 6

7 ame way. For intance, wine i conidered a an agricultural commodity in E but a a proceed output of the "beverage indutry" in the ES framework (Eurotat 1997). Furthermore, it i unclear how "feed cereal" hould be mapped into the grosm format: either a non-marketed on-farm conumption or a demand of the agricultural ector for product of the "animal feed" indutry, which in turn would demand cereal a intermediate input. The mapping of farm and market balance i alo not traightforward. For intance, eed ue, internal ue and loe on farm are not conidered in the ES framework. The firt tep in utilizing the oo dataet wa to tranform it into an agricultural accounting matrix (M) to facilitate the mapping of oo and M account at a later tage. The M ditinguihe trictly between activity and commodity account and agricultural, proceing, and other indutrial activitie. a conequence, it wa neceary to introduce activity account not included in the oo databae. The commodity 'beef' for intance i produced by the cattle ector, which i not conitent with the concept of the ES account. In there, the tranformation of live cattle into beef ready for human conumption or further proceing i an activity within the food and beverage indutry complex (ES code da15) rather than belonging to agriculture. The ame applie for pork, poultry meat, and wine. n important feature in thi context i that baically two agricultural accounting matrice were created: One in value term (MV) and one in quantity term (MQ). MQ i baically a balance heet for oo commoditie, arranged in SM format, but with empty account for activity expenditure and conequently only with balanced commodity account. MV i the correponding matrix with filled activity account and quantitie on the commodity market meaured at baic price obtained from oo (Unit Value at Baic Price, UVB). Thi treatment of the available data allow controlling the etimate for price and quantitie at a later tage and prevent the creation of un-plauible value, which can occur when uing only value-data for the SM etimation. ppendix 2 illutrate the tructure of the target SM, the acronym ued for the repective entrie, and provide a legend for the operation decribed in the following ection. n outline of the operation to obtain the M from the oo dataet i alo diplayed in appendix ctivity ccount of the gricultural Sector For the agricultural ector, the procedure of re-arranging the oo data i in general traightforward. We ue the oo notation whenever poible to allow the comparion of the computation with the PRI documentation (Britz et al. 2005). Starting with the activity account, the firt tep i the derivation of an aggregate output value of each agricultural activity: Eq (2) MV' Total ', = LV = TOOU LEVL griculture MV: gricultural accounting matrix in value term baed on oo data LV: Total value of activity level TOOU: Total output value per activity level (oo) LEVL: ctivity level (oo) : Index for activitie (here only agriculture) Taxe paid (or received a negative taxe i.e. ubidie) by each activity equal the P premium per activity a indicated by oo time the activity level: 7

8 Eq (3) MV' T _ PRME ', = TX = PRME LEVL griculture TX: PRME: Value of tax or ubidy received or paid by activity P premium effectively paid (oo) The rate for activity-related taxe i here computed a the hare of taxe paid (or ubidie received) in the total output value of the activitie: Eq (4) ta TX = griculture LV Value added at baic price can alo be taken directly from oo: Eq (5) MVF, = VD = GVB LEVL griculture F VD: Value-added per activity GVB: Gro value-added at baic price per activity level (oo) F: Fixed factor (here: labour and capital) wage indicator i alo provided in the oo databae, but the exact unit in which they are meaured i not explained in the documentation (Britz et al. 2005). Furthermore, we are not ure whether thi information wa proceed by the conitency algorithm of oo. However, in the abence of other data, we ued WGE a an intrument for the ditribution of the correponding entry in the ES SM. WGE LEVL ES Eq (6) MV' F_ LB', = LB = LB griculture griculture WGE LEVL ggregate input demand from agricultural activitie i expreed a input demand per unit of activity level time the activity level. Eq (7) MV, = ID = TOIN LEVL griculture ID Vector of aggregate input demand per activity (in million Euro) TOIN Total intermediate input (oo) The reult for the agricultural ector are diplayed againt the correponding ES total in figure 1. It appear that intermediate demand of the agricultural ector a obtained from the oo databae i 21% larger than the correponding figure from the ES account. The reaon behind thi could be that oo provide value alo for non-marketed input like pature and manure. The higher total output value indicated by ES may originate in the fact that agricultural output encompae a wider range of product a are conidered by oo. Taxe on activitie ("Other net taxe on production", d29_m_d39, in ES notation) indicated by ES are coniderably lower (in abolute term) than the aggregate P Premium from oo. gain, the reaon for thi obervation i not clear, ince detail on the compoition of the figure in quetion are not provided by either ource. It eem anyway that ome 8

9 component of the P premium are booked a direct ubidie to agricultural holding in the ES framework rather than a activity-related payment in the oo databae. Figure 1 omparion between ES and MV total, gricultural Sector, Germany year 2000, in Million Euro (current price) 160% % 140% 120% 100% Million Euro, current % 60% 40% Relative deviation ES MV Rel. Dev. 21% 20% % 0% % ID VD TX LV -20% -40% Source: Eurotat, oo, own calculation lthough the two databae preent ubtantial difference in the definition and coverage of featured item, without clear information on the exact nature of thoe deviation, a multitude of component of the oo databae can be conidered a reliable information (e.g. produced and trade quantitie of agricultural and ome proceed commoditie, activity level, outputand input-coefficient, and baic price). Both databae can be harmonized by incorporating the qualitative information about the potential ource of the deviation in the finally choen etimation method. Having derived ID, VD, TX, and LV (ee alo appendix 2), we have obtained the minimum neceary et of item in the activity account to connect it to the correponding commodity account. 5.2 ommodity ccount The oo databae provide information on quantitie of produced and trade commoditie a well a the related price. Thi information i deemed to be of ignificant ue for the final etimation of the monetary flow within the target grosm, ince the uage of quantitie and plauible bound on price etimate can be ued to curb the poible variation of the final etimate and hence avoid everely ditorted reult. We will tart with the tranformation of the quantity-related data of the oo databae into SM format, which will be called MQ (gricultural ccounting Matrix in quantity term) in the following. gain, we ue the oo notation whenever poible to allow the comparion of the computation with the PRI documentation (Britz et al. 2005). Dometic marketed production quantitie QX are computed by: 9

10 Eq (8) MQ, NETF griculture = QX = MPR FoodIndutry MQ gricultural accounting matrix in quantity term baed on oo data QX Dometic marketed production (quantitie) NETF Net trade on farm (oo) MPR Marketed production (oo) : Index for commoditie Import and export are derived in a imilar way: MQ,' ROW' = QE = EXPT griculture, FoodIndutry Eq (9) MQ' ROW ', = QM = IMPT griculture, FoodIndutry QE Export of commoditie (quantitie) QM Import of commoditie (quantitie) EXPT Export total (oo) IMPT Import total (oo) Total dometic upply QDS i compoed of dometic production QX plu import QM minu export QE. On the demand ide, the item ID (dometic intermediate demand for commoditie; note the difference to ID which i the intermediate demand for commoditie by activitie), GVT (governmental conumption), H (final conumption by houehold), ST (tock change), FF (fixed capital formation), and LOS (loe on market) can only partially be derived from the oo. So i invetment demand for agricultural commoditie treated a "on-farm uage" of invetment commoditie like young animal and live plant (e.g. tree for orchard), but not a conumption on market. Dometic demand in the MQ a derived from oo data i conequently repreented by the following entrie: Eq (10) QDD = QX + QM QE = QID + QH + QST + QLOS griculture, Foodindutry With the following correpondence to oo data regarding intermediate conumption, houehold conumption, tock change and loe: Eq (11) MQ, = QID = INDM + PRM + FEDM + SEDM Eq (12) MQ,' _ ' = QH = HOM I HHLD Eq (13) MQ,' _ ' = QST = STM I STH Eq (14) MQ,' _ ' = QLOS = LOSM + SDM T TRD QDD Dometic aborption 10

11 QID QH QST QLOS INDM PRM FEDM SEDM HOM STM LOSM SDM Intermediate demand per commodity Houehold final conumption per commodity Stock change Loe on market Indutrial ue market (oo) Proceing to derived product market (oo) Feed ue on market (oo) Seed ue on market (oo) Human conumption market (oo) Stock change on market (oo) Loe on market (oo) Statitical adjutment on market (oo) Loe on market are here booked in the account for tranaction cot and will erve at a later tage a proxy for the etimation of commodity-pecific trade margin in the grosm. 5.3 Intermediate Input and Output Matrice ccount for activitie and commoditie are linked via two ub-matrice, the input table I and the output table D in appendix 1. oo provide information about the intermediate demand of the agricultural ector in value term (e.g. pharmaceutical input or energy in contant 1995 Euro/ha) and in quantity term (fertilizer in kg/ha), while output (or yield) of each agricultural activity are recorded a quantitie (kg/ha). The ub-matrix for dometic output can be therefore fully derived by multiplying the output coefficient with the activity level: Eq (15) MQ, = QD, = OUTP, LEVL QD OUTP Dometic production quantity by activity Output coefficient (oo) The input matrix I on the other hand ha two repreentation: Eq (16) MQ = QI = INPT LEVL INPT meaured in quantitie,,,, MV = VI = INPT LEVL INPT meaured in value,,,, QI VI INPT Dometic intermediate demand quantity by activity Dometic intermediate demand value by activity Input coefficient 5.4 Splitting griculture and Food Indutry One of the main challenge when attempting to harmonize the oo databae with the upply and ue table in ES format i the fundamental difference in the treatment of proceed agricultural commoditie. Thee are part of the agricultural ector in the E (and 11

12 conequently oo) framework, but belong to the food proceing indutrie in the ES framework. For thi reaon, a new et of auxiliary activitie wa introduced in the SM while proceing the oo data. Thee correpond with the agricultural output in oo conidered a proceed commoditie in the grosm framework, particularly beef, pork, heep and goat meat, and wine. The dometically produced quantitie are here mapped to the correponding indutrial activitie: Eq (17) MQ, = QD, = QX PROUT,, FoodIndutry PROUT Binary aggregator matrix (1 if activity produce commodity, ele 0) Since thee product are not anymore conidered a output of the agricultural ector, the correponding entrie under agricultural activitie have to be et to 0: Eq (18) MQ, = QD, = 0 griculture, FoodIndutry imilar approach i choen for the input demand. The new activity "beef meat" (_BEEF) demand laughtered animal from the agricultural ector, the activity "Rice milled" demand paddy rice, and o on: Eq (19) MQ, = QI, = QX PRINP, FoodIndutry, griculture PRINP Binary aggregator matrix (1 if activity demand commodity, ele 0) Together with the cot-hare coefficient ζ(.) obtained from the ESSM, we can now derive the prior information of the cot tructure of the proceing indutrie. The total output value of the new activitie at baic price i computed by: Eq (20) MV' Total ', = LV = QX PB PROUT, FoodIndutry Expenditure for labour, capital, and intermediate input are derived by multiplying the ES cot hare with the activity output, a following: MV' LB', _ ES = LB _ ES = ζ LB _ ES _ ES LV _ ES Eq (21) FoodIndutry Eq (22) MV' ', _ = P _ = ζ P _ ES _ LV _ P ES ES ES ES FoodIndutry 12

13 MV' ', _ = ID _ = ζ ID _ ES _ LV _ Eq (23) ID ES ES ES ES FoodIndutry The thu derived value are compared with the ES total in figure 2. It appear that, in contrat to the agricultural ector, the food indutry ector i only repreented to a limited extent in the oo databae and conequently in the agricultural accounting matrix. Figure 2 omparion between ES and MV total, Food Indutry Sector, Germany year 2000, in Million Euro (current price) % % % Million Euro, current % -40% -50% Relative deviation ES MV Rel. Dev % % 0 ID VD LV X M E -80% Source: Eurotat, oo, own calculation Becaue of the ubtantial deviation between ES and M value in the food proceing ector, we have to include additional information from PRODOM and OMEXT dataet. The account for export, import, and dometic production were adjuted a hown below: VX = { Beef, Pork, Poultry, Dairy} Eq (24) VX = PRODOM = { nimalfeed, Beverage} ES VX VX = { Otherfood} Otherfood VM = { Beef, Pork, Poultry, Dairy} Eq (25) VM = OMEXT = { nimalfeed, Beverage} ES VM VM = { Otherfood} Otherfood VX VM Export by commodity Import by commodity 13

14 5.5 Price and Value The ES upply and ue table ditinguih between baic price and purchaer' price. We will introduce export and import price in addition to account for deviating weighted average price when aggregating group of oo commoditie at a later tage. Thi can happen when merging comparatively heterogeneou type of product, e.g. cheee, milk-powder, and cream, into a dairy aggregate, with a different compoition of the individual commoditie in each group. However, a a tarting point we ued unit value at baic price (UVB) to determine tarting value for dometic, import, and export price. In cae they were not available from oo for certain proceed commoditie (e.g. oilcake or molae), we had to rely on other ource, among which FOSTT appeared to be the mot appropriate for the commodity group ditinguihed in oo. It hould be emphaized at thi tage that the price entering the following computation are bet firt guee, which will be altered in the ubequent balancing tep. The tarting value for baic price are: UVB griculture, FoodIndutry Eq (26) PB = FOPRI if not UVB PB Starting value for baic commodity price UVB Unit value at baic price (oo) FOPRI Price for proceed commoditie from FOSTT With thi price vector at hand, we can now connect the two agricultural accounting matrice: Eq (27) M M, ' MV, ' if MV, ' = MQ PB if not MV, ', ' gricultural accounting matrix in baic price 6 Balancing the grosm The balancing procedure propoed here to conolidate oo and ES data i plit into two tep. Firt, we balance only the ub-vector of the target-sm (grey entrie in appendix 2), before we include the matrice of dometic production by activity and intermediate demand. There are two reaon for thi. Firt, we reaoned that the explicit incorporation of price and quantity data (intead of uing only value when directly working on a SM) allow for a better incorporation of qualitative knowledge about the reliability of the underlying information. We may have, for intance, high trut in the balance-heet data for dairy product but a lower trut in the correponding price. The choen approach allow expreing thi trut in term of lower and upper bound on the deviation between prior and balanced data. Second, we experienced rather long computation time when olving the balancing problem in one tep. It turned out that we could balance alo the rather large ub-matrice (intermediate demand, dometic output) when firt deriving their row- and column-um by balancing the market item and then uing the thu obtained, pre-balanced value a tarting point for the 14

15 econd tep. In general, the problem at hand may be ummarized a the need to find a et of quantitie and price (and value) that are a cloe a poible to the prior data but atify a number of accounting contraint. The choen approach ha to allow the incorporation of qualitative information, like the degree of aumed reliability of the prior data, and whether an entry i poitive or negative. We decided to expre the relation between prior and balanced data via a correction coefficient kappa (κ): Eq (28) Y = Y κ, with the propertie Y Y κ [ ] = 1 E κ 0 < κ Balanced value for quantitie (Q), price (P), and value (V) Prior value for quantitie (Q), price (P), and value (V) orrection coefficient The expected value hould be 1 (in which cae the balanced value equal the prior), and it hould not aume negative value in order to avoid the change of the ign of any prior entry. Furthermore, it hould not be equal to zero a we aume that once there i a prior entry, there hould alo be a non-zero entry in the balanced dataet. The aumed reliability of the prior data hould alo influence the poible outcome for kappa. Thee deired propertie made u chooe a cro-entropy approach imilar to the one applied for the balancing of the ESSM, but with ome modification. Kappa i here expreed a an exponential function of upport point ( b ) and their aociated weight ( W ).Thee weight have to add up to unity and hould be a cloe a poible to a et of pre-defined prior weight. Eq (29) κ = exp W b The upport point are arbitrarily defined according to the 3-igma rule (in the cae of five upport point). SIG i a variance parameter and prior weight are computed according to Robinon (2007), thu auming a non-uniform, ymmetric ditribution ymmetric around 0. b = [ 3, 1.5, 0,1.5,3] SIG W = Eq (30) 162, 81, 81, 81, 162 The cro-entropy minimization model can be ummarized a follow: Eq (31) E = min W ln W W t.. κ = exp W b W = 1 Y = Y κ accounting identitie for Y 15

16 When olving the problem above for different value for kappa and SIG, we obtain (by neglecting the accounting identitie for Y) a plot of the objective function a hown in figure 3: Figure 3 ro-entropy Function of Kappa E Kappa Source: Own calculation SIG=0.1 SIG=1 SIG=2 In fact, the value for SIG (0.1, 1, and 2) a ued in figure 3 were choen to expre the trut we had in the different prior data. It ha to be noted here that the deciion, which value to chooe for SIG i a qualitative judgement and not upported by a ytematic quantitative aement of potential variance of the prior data 10. Intead of deriving any other quantitative indicator like variance over time, or EU27 member tate, we reaoned that dometic production and trade of cereal, oileed, and dairy product are comparatively well monitored, wherea "fodder crop", "other crop", or other "animal" where derived a reidual or according to aumption about input coefficient in the raw dataet that had entered the oo procedure in the firt place. 6.1 Balancing the ccount Total The balancing model for the account total i ummarized in table 6. It wa implemented in GMS and put to work a a non-linear optimization problem, olved with the numerical olver ONOPT3. The model in table 2 deviate in ome repect from the general tructure outlined above. We allow for intance for a change of ign in the cae of tax rate on activitie and commoditie (Eq 5 and 6 in table 2), mainly becaue the fact that we had only the average tax rate a prior, which may change from a tax to a ubidy depending on the commodity in quetion. Equation 13 and 14 in table 2 repreent the commodity balance 10 We aume that knowledge about the variance obtained in the original oo etimation procedure would improve the quality of the deciion made here, but have not been ued for thi tudy. 16

17 equation, either in value-term or in quantitie. The important difference i that loe on market (LOS) are part of the quantity balance, but not of the value-balance. Thu, the difference have to be compenated during the balancing proce by adjuting trade margin and tax rate accordingly 11. Table 2 Equation of the firt balancing model No. Equation Decription 1 itm itm ro-entropy min I( W) = Wac, ln ( Wac, W ) W minimand itm ac citm 2 citm citm Qc = Qc κ Definition of final c commodity quantitie pitm 3 pitm pitm Pc = Pc κ Definition of final c commodity price aitm 4 aitm aitm Va = V a κ Definition of final a activity value 5 ta ta taa = taa + Wa, b Definition of final a, activity tax rate 6 tc tc tcc = tcc + Wc, b Definition of final c, commodity tax rate 7 tc tc Definition of final hmc = hmc exp Wc, bc, trade margin κ κ κ = exp W b citm citm citm c c, = exp W b pitm pitm pitm c c, = exp W b itm itm itm, Definition of the correction term for commodity quantitie Definition of the correction term for price Definition of the correction term for activity value X M ID GVT H ST FF E LOS 13 Q + Q = Q + Q + Q + Q + Q + Q + Q Balance for commodity quantitie 14 X X M M P Q + P Q 1 + hm + tc Balance for commodity value = DD ID DD GVT DD H DD ST DD FF E E P Q + P Q + P Q + P Q + P Q + P Q 15 LV ID VD V 1 ta = V + V ctivity value balance VD LB P 16 V = V + V Definition of Value dded (.) 11 (.) W, = 1 with 0< W, < 1 Sum of weight 11 It would be preferable to aociate only the trade margin (when interpreted a tranaction cot on market) with the loe, but we found no way to iolate the effect of trade margin in the dometic tranmiion of baic into purchaer' price for each commodity. Detailed data on tax rate would mitigate thi problem, but that would require the incorporation of additional dataet, which were not available yet. 17

18 No. Equation Decription (.) (.) 12 W, = 1 with 0< W, < 1 Sum of weight ES,(.) (.) 17 V ES = M ES V, ES,(.) (.) (.) 18 V ES = M ES Q, P ctivity value add up to ES total ommodity value add up to ES total 6.2 Balancing the Sub-Matrice In a econd tep, we ue the obtained balanced vector a tarting value for the etimation of intermediate demand and output matrice. The prior for tau and iota were computed from the prior data for VD and VI a decribed in chapter 5.3 (ee Eq. (16)): VD, VI, Eq (32) τ, = and ι, = LV ID The model i olved again with equation 1b replacing 1a and four additional contraint 19 to 22 (ee table 3). Table 3 Equation of the econd balancing model No. Equation Decription 1b min I( W, τι, ) = New ro Entropy W, τι, Minimand itm itm Wac, ln ( Wac, W ) itm ac + τ ln τ τ a c ( ),,, ( ) + ι ln ι ι a,,, c ID ID DD ι, = V Q P Intermediate demand by activity an for commoditie LV X X V τ, = Q P Link between activity ι, = 1 with ι, τ, = 1 with τ, value and commodity price time quantitie 0< < 1 dding-up condition for ι 0< < 1 dding-up condition for τ 18

19 7 Some oncluion The tak to combine the databae of an agricultural ector model with upply-and ue table from Eurotat (oo and ES) confronted u with a huge number of methodological and data-handling challenge. We tried to ue the information from both databae a exhautively a poible, but we had at ome tage (e.g. in the cae of food indutry) to rely on additional ource. It wa poible to compile a prior dataet which we conidered a ufficiently reliable to apply a cro-entropy balancing method. Thi wa implemented a a two-tep procedure, which firt produced a balanced et of ub-vector of the target SM and then a fully balanced matrix. Uing thi procedure, we were able to compile grosm for three Member State: zech Republic, Germany and Spain. Thee are currently under internal validation. Neverthele, there i till a huge potential for improvement. Our original intention wa to create a databae which can be mapped (many-to-one) into the format required by GTP. Thi tak could not be fulfilled totally. lthough it wa poible to repreent the agricultural and food-indutry ector in a way that i compatible with GTP, we could not obtain data for a required plit of the oil and ga ector, the ferrou and non-ferrou metal ector, and a few other. ll attempt to acquire at leat information about dometic production were not ucceful. lat reort would have been to ue the GTP databae itelf. However, we decided to leave the deciion, which dataet to ue for the plit of the repective ector to the uer, in cae he intend to run GTP on our databae. n additional hortcoming of the procedure decribed in thi report i the lack of detailed information on policy meaure like taxe on commoditie, for which we only had the average rate from the upply and ue table. Here there i certainly room for ignificant improvement. The current tate of our approach allow a fully flexible incorporation of additional data, for which we will continue to earch. The procedure decribed in the previou chapter repreent a firt tep, and further improvement will be made according to the comment of the intereted reader and uer of the grosm. 19

20 8 Reference Britz, W. (editor) (2005): PRI Modelling Sytem Documentation. URL: Univerity of Bonn. Eurotat (1997): Manual on the Economic ccount for griculture and Foretry E/EF 97 (Rev. 1.1) Golan,., G. Judge, and D. Miller (1996): Maximum Entropy Econometric: Robut Etimation with Limited Data, New York. Golan,. and S. J. Vogel (2000): Etimation of Non-Stationary Social ccounting Matrix oefficient with Supply-Side Information. In: Economic Sytem Reearch, (12). Heckelei, T., R. Mittelhammer, and W. Britz (2005): Bayeian lternative to Generalized ro Entropy Solution for Underdetermined Model. Selected paper preented at the 89th EE Sympoium Modelling agricultural policie: tate of the art and new challenge" Parma, Italy, February 3-5, Robinon, S.,. attaneo, and M. El-Said (1998): Etimating a Social ccounting Matrix uing ro Entropy Method, International Food Policy Reearch Intitute (Ifpri), Trade and Macroeconomic Diviion (Tmd), Dicuion Paper No. 33, Wahington, D.. Robinon, S.,. attaneo, and M. El-Said (2000): Updating and Etimating a Social ccounting Matrix Uing ro Entropy Method, International Food Policy Reearch Intitute (Ifpri), Trade nd Macroeconomic Diviion (Tmd), Dicuion Paper No. 58, Wahington, D.. McDonald, S. (2006): ompiling National, Multiregional and Regional Social ccounting Matrice for South frica. PROVIDE Project Technical Paper 006:1, Elenburg. Jut, R. E., D. Zilberman, E. Hochman, and Z. Bar-Shira (1990): Input llocation in Multicrop Sytem. In: merican Journal of gricultural Economic (72). Lence, S. H. and D. J. Miller (1998): Etimation of Multi-output Production Function with Incomplete Data: Generalied Maximum Entropy pproach, in: European Review of gricultural Economic (25). Theil, H. and.s. Goldberger (1961): On Pure and Mixed Statitical Etimation in Economic. In: International Economic Review (2). Greene, W. H. (2003): Econometric nalyi, fifth edition, New York. 20

21 9 ppendice ppendix 1 Stylized SM and Sub-Matrice E x p e n d i t u r e ctivitie ommoditie Factor Tranactio n Intitution Total ctivitie griculture _GR Indutry _IND Service _SER D R e v e n u e ommoditie Factor Tranaction Intitution griculture _GR Indutry _IND Service _SER Labour F_LB apital F_P I E Fd Trade T_TRD HM Taxe T_TX Ta Tc Ti Enterprie I_ENT Houehold I_HHD F Government I_GOV Saving- Invetment Ret of the world I_S-I S I_RoW M F Total V VQ F T Fe 21

22 Where the following legend can be followed: Decription ode Source Dometic production by ector D Supply Intermediate demand I Ue Dometic final conumption Ue Export E Ue Dometic factor payment (value added) Fd Ue Factor revenue from abroad Fe NS Trade margin H Supply Taxe and ubidie on production Ta Ue, NS Taxe and ubidie on product Tc Supply, NS Direct taxe paid by intitution Ti NS Ditribution of factor income acro intitution F NS Ditribution of taxe and tranfer acro intitution T NS Import M Supply Saving of intitution S Reidual Total dometic production by activity V Ue/Supply Total dometic production by commodity VQ Supply 22

23 ppendix 2 Target tructure of the M ctivitie Σ ommoditie Σ Intitution ctivitie griculture _GR Indutry _IND τ LV Service _SER Total Σ X ommoditie griculture _GR Indutry _IND ι ID GVT H ST FF E Factor Service _SER Total Σ ID Labour F_LB LB apital F_P P Total Σ VD Trade T_TRD hm Taxe T_TX TX tc Ret of the world I_RoW M Total LV 23

24 ppendix 3 Summary of Operation from oo to M ctivitie Σ ommoditie Σ Intitution _GR _NG I_GVT I_HHD I_ST I_FF I_RoW ctivitie griculture _G R Non-agriculture _N G [LOSF -SEDF -INTF ] SHR, LEVL IO, - LOSF - SEDF - INTF MPR SHR, TOOU LEVL Total Σ NETF, MPR griculture _G R ommoditie Non-agriculture (including _N proceed G commoditie) LEVL IO,, LEVL IO, NETF / SHR, FEDM + SEDM INDM + PRM + HOM STM EXPT Total Σ LEVL TOIN Factor Labour F_LB LEVL WGE apital F_P Total Σ LEVL * GVP Trade T_TRD -LOSM SDM Taxe T_TX LEVL * PRME Ret of the I_RoW IMPT Total LEVL * TOOU 24