From an elaborated FSAM to a full CGE model for Germany : a guide to elaborate a financial social accounting matrix and a computable general equilibrium model, with reference to the German economy in 2009

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(2) INSTITUTO TECNOLÓGICO Y DE ESTUDIOS SUPERIORES DE MONTERREY EGAP GOBIERNO Y POLÍTICA PÚBLICA CIUDAD DE MÉXICO. From an Elaborated FSAM to a foil CGE Model for Germany A Guide to elaborate a Financia! Social Accounting Matrix and a Computable General Equilibrium Model, with reference to the German Economy in 2009. -:·-~:,.; , .,· EGAP. ,;t"~;. Gobierno y Polltica Publica. ',;,,,J. TE CNOLÓG ICO DE tv10NT ERR EY. J... m:t«>LéGteo •. DE MONTERREY.. Jens Markus Helbig [email protected]. Biblioteca. c.,,...Cludad•IIMaco. Proyecto de Investigación Aplicada Maestría en Economía y Política Pública Asesor: Dr. Arturo Pérez Mendoza Fecha de término de tesina: Octubre de 20 l 3.

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(4) Table of Contcnts. Table ofContcnts ........................................................................................... 1 List orFigurcs ..................... . ...................................................... ................. 11 List ofAbbrcviations ............ . .... .. ......... .... . ................................................... 111 List or Symbols ....... . .......................... . .... . ... . .... . .... . .......... . ......... . . ............... IV l. lntroduction ....................................................................... ............. ........ ....... ...... .. ...... ......... 1 2. Building the FSAM ................................................................. .............................................. 2 2.1 Classification .................................................................................................................... 3. 2.2 Goods & Services ............................................................................................................. 6 2.3 Production ..................... ....... .............. ...... ...... ............. ....... ....... ............. ...... .................... 8. 2.4 lncome Generation ........................................................................................................... 8 2.5 Allocation of Primary lncome .......................................................................................... 9 2.6 Secondary Distribution of lncome ................................................................................. 1O 2.7 Use of Disposable lncome .............................................................................................. 1O. 2.8 Capital Account and Gross fixed Capital Formation ....... ...... .. ...... ............. .............. ..... 1O 2.9 Financia! Flows and Rest ofthe World .......................................................................... 11 3. Working with Real Data and Assumptions ...................................................................... 11 4. An Alternative FSAM Presentation .................................................................................. 16 5. A Computable General Equilibrium Model Application ...... .. ...... ...... ....... ...... .. ..... ....... 17. 5.1 Statemenl of Problem ..................................................................................................... 18 5.2 Macroeconomic Assumptions ........ ...... ....... ...... ...... .. ..... .. ..... .................... .. ........... .. ...... 19 5.2.1 Scctors· Behavior .................................................................................................... 19 5.2.2 lnstitutions· Behavior .............................................................................................. 23 5.2.3 Detinition of Equilibrium ....... ......................... ....... ...... ........ ....... .................... ........ 27 5.3 Model Calibration .................. .......................... ............ .............. ....... ............................. 32 5.4 Original Equilibrium ...................................................................................................... 34 5.5 Economic Experiment and New Equilibrium ................................................................ 35 5.6 Comparison of Equilibria ............................................................................................... 35 6. Résumé and Conclusions ................................................................................................... 3 7. 7. Appendix ................................................. ...... ............ .......................................................... 39 8. References ......................... ........ ............. .. .................. ...... ....... ....... ............. ............. .. ......... 5 1.

(5) 11. List of Figures. Figure 1: General Outlinc of the f-S/\M Figure2: FSAM ;\ccoun1·s Classification Par! 1/3 Figure 3: FSAM /\ccount"s Classilication Part 2/3 Figure 4: FSAM Account"s Classilicalion Part 3/3 Figure 5: Goocls and Serviccs in the FS/\M Figure 6: Total Explanation of thc FS/\M Figure 7: The lnput-Output Matrix in Million Euros Figure 8: The Alternativc lnput-Output Matrix in Million Euros Figure 9: Seven Basic Steps to conducta succcssful CGE Model Analysis Figure I O: Model Framework of Production and Distribution Figure 11: The whole Modcl Economy Flmv of Funds Figure 12: Values of the Original Equilibrium and Results from the Experiments in Billion Euros Figure AX 1: Financia! Social Accounting Matrix for Germany 2009 in I Os of Millions of Euros Figure AX2: Alternative Design of a Financia! Social Accounting Matrix for Germany 2009 in Billion Euros Figure AX3: The complete CGE Model in GAMS.

(6) 111. List of Abbrcviations. CGE. Computable General Equilibrium. DAX. (icnnan Sharc lndex. Dcstatis. German Federal Statistics Bureau. EC. European Commission. ECB. European Central Bank. EU. European Union. ESA. European System of Accounts. FSAM. Financia! Social Accounting Matrix. GAMS. General Algebraic Modeling System. GFCF. Gross fixed Capital Formation. GTAP. Global Trade Analysis Project. IOT. lnput-Output Table. NAFTA. North American Free Trade Agreement. NPISH. Non-Profit lnstitutions Serving Households. OECD. Organization for Economic Co-operation and Development. ROW. Rest of World. SAM. Social Accounting Matrix.

(7) IV. List of Symbols. Sub-indices are lell out for easy accessibility.. (1. Share ofConsu111er Utility. a. Share Para111eter of V A or 11. A. Factor Productivity. B. Labor Share of Value Addcd. e. Household Consumption. C IN ROW. Net Consumption of nationals in ROW. ChlNV. Change in lnventories. CVA. Costs ofValue Added. CT. Total Costs. 8. Efficency Parameter in the CES function. d. Ratio of Domestic Product to Compound one. D. Domestic Product. DAX. German Share Index. De. Deposits. Depr. Depreciation. e. Export Parameter. E. Exports. EXR. Exchange Rate. FA. Financia( Assets. Fr. Flexible Funds. y. Institution Share Parameter in the Production Process. G. Government Consumption. GFCF. Gross fixed Capital Formation. Id. Disposable Income. ldGT. Final Disposable Income of Government (including Taxes). 11. Intermediate Input. 1,. J. Sectors 1-4. In. lncome. K. Capital. KS. Sum of ali Capital. "-. Share Parameter of FF.

(8) V. L. Labor. (,F¡\. Liabilities of Financia! /\ssets. LDe. Liabilities or Deposits. LS. Sum or ali Labor. LSh. Liabilitics of Shares. ~l. Share Parameter of Domestic Product. M. lmports. G. Elasticity. o. lnstitutions 1-4. p. lndicating Elasticity. p. Price of the Compound Good, Domestic one, lmports or Exports. PE. World Price on Exports. PIX. Consumer Price lndex. PM. World Price on Imports. r. Revenue. s. lnstitutional Savings. Sh. Shares. sr. Household's Savings Rate. T. Tax Rate for Taxes on V A, lmports or lncome. 0. Effect Parameter on DAX. T. Transfers to Government by ROW. TAXES. Taxes. TC. Total Costs. TFA. Total Financia! Assets. TFF. Total Flexible Funds. TGFCF. Total Gross fixed Capital Formation. TL. Total Liabilities. trnsf. Net Transfers. VA. Value Added. VAT. Value Added Tax. w. Wage. X. Compound Product. y. Production.

(9) l. lntroduction. In the light ofrecen! economic crises the necessity or more detailcd and especially linancial invesl igat ions for econom ic poi icy makers and I he majority o f econom ic agents surged imperatively around the world. l 10\vever. one quite popular anal:, sis instrumenl used in many countrics. unfortunately in Cierman/ ancl some othcr members. or the. Luropean lJnion seems. to be lacking its deserved attention. Social Accounting Matrices (Si\Ms) and their respective Computable Equilibrium Models (CGEs) represen! a usel'ul tool ror profound and targeted economic analysis worldwide.~. Basically, observed and selected data of a base year 1s accommodatecl into a matri:-.: presentalion taking into account the douhle-enlry accounting principie of revenues ancl expenditures revealing cross-institutional and cross-sectorial inlúrmation or the mix of hoth. The underlying principie is to connect the producing part oran economy ,vith the national institutions and the rest of the world in order to he a ble to conducl a signi licant analysis through a Computable Equilibrium Model. This model is calibrated and computed to generate the general equilibrium of an economy with the help. or (mostly. neo-classical) economic. equations and assumptions reproducing the same values as observecl in reality. In consequence, it is possible to perform an econom ic experiment preclicting the reactions of the economy under consideration when facing those e:-.:ogenous shocks.. Until now. most SAMs and therefore CGEs have focused on a too limited presentation of the economies ignoring completely the financia! part of it. even though this is an essenlial and in modern economies decisive part of economic life. This paper aims to transmit a step by step illustration of the elaboration of a Financia! Social i\ccounting Matri:-.: (FS/\M) ancl the gradual development ofan economic CGE model written in Cii\MS' ,vhich makes use ofthe same data. 1. Actually. the only rcccntly orticially puhlished SAM for Gcrmany \\as puhlishcd in 2004 for the year 2000 and. was a onetime affair. (Schwar;, et. al. 2004) ~ To mention justa fow. famous examples include the analysis ol' hous..:hold hehavior in the Norwegian MSG-6. Modcl (Byc and Holmoy. 1997). the evaluation ofthe impacts. 011. \ilcxico afkrjoining the NAFTA (Pére1.. 2005). and the CiTAP Project (l lertel. 1997) where research is conducted on a \ arié!y orto pies. A lternati ,ely. any ,rnrk ofThomas F. Rutherford. J. GAMS stands for General Algehraic Modcling System which. \\US. de\ elopcd hy rescarchers at the World Bank. l'or the exact purpose or conducting complex ami large scak mmkl aprlications. S..:..: also Rutherford ( 1998)..

(10) Thc sccond chaptcr or this papcr c.,plains thc brcakdom1 of my FSAM ,vhich is bascd rccommendation of thc Leadcrship group. 011. 011. thc. Social Accounting Matrices by thc Luropcan. Commission ( Luropcan Commission 2003) taking into accounl the classilication all(f thc circular llo\\ or funds. In thc third chaptcr. thc way of tilling in the theoretically cxplaincd FSAM with real data is shown and ,, hich aspccts havc to be taken into consiclcration. Chaptcr l<rnr in conscqucncc prcscnts bricfly an altcrnativc dcsign for the FSAM paving thc way ror the modcl application in chapter livc. This includcs ali stcps from the intended cconomic analysis through thc spccilication of cconomic cquations and variables to the ful! CGE modcl in Gi\MS. The ceonomic analysis of this model cxample will be about how the German Share lndex DAX influcnces thc institutional savings spcnding. 011. either shares or deposits. Finally.. chaptcr six el oses with a brid résumé and a conc lusion about the FSAMs, the conducted analysis and futurc rcscarch ticlds including FSAMs.. 2. Building the FSAM. The construction of the Financia! Social Accounting Matrix (FSAM) 4 can be quite a timcconsum ing undertaking. beca use thcrc is no global standard on its final design yet. There has bcen done a wholc lot more research ,vith applications of regular Social Accounting Matrices (SAMs) thougi/ which give lcad to the construction of the FSAM. Just recently, a variety of economists have proposed difkrent implemcntations and designs 6 • The main idea of the FSAM is to include the linancial accounts of an eeonomy to get a better impression of who is paying or receiving what kind of (inancial llow. Besides of having only the goods market the financia! market is also inclucled. As a consequence. there can be done a series of more clctailed investigations giving rise to more sophisticatcd recommenclations to economic policy makers. (MPR;\ 2009). In the following I will explain the construction of a FSAM (Figure 1) step by step which is bascd on the recommendation of the Leadership group on Social Accounting Matrices by the European Commission. (European Commission 2003). ~ Thc Lcadcrship group on Social J\ccounting Matrices refers to Lhis design as to a ··Dctailed National J\ccounts. \llalri,··. (Europcan l'ornrnission. 2003) 'For c,amplcs scc Thiclc and l'iazolo (2002). Shantong et al. (2004) or Keuning and Rt\iiter ( 1988). '' For c,amrles sce l ll lBIC (2012). Ml'RJ\ (2009). l lcmúndcz ( 2008) ami ECB (2004 ).. 2.

(11) The advantage of this design is that it is confonning to the European System of Accounts 1995 (ESA95) and includes all major transfers of an economy. (Eurostat 2009) Figure 1: General Outline of the FSAM. Source: European Commission (2003). This is not the only way to design a SAM or FSAM though. There is a plethora of possibilities and depending on the necessities, a SAM should be as simple and practica! as possible. Therefore, Iater on, I will present an altemative design which is particularly suited to fit the specific GAMS model at the end of the paper.. In the FSAM there are eleven different accounts in each row and in each column. In addition, there is one more account in which the totals of each row and column are summed up. It is utterly important that the total of each row matches the total of its respective column to guarantee that an account does not spend more than it receives and that the circular flow of money is complete.. Before explaining every account in detail, it is important to consider that there is a classification for each of them. To understand the different accounts' behavior in a better way, I will first say a few words about their classification.. 2.1 Classification Each of the eleven accounts, symmetrically in both, rows and columns, has its own subaccounts which constitute their classification. So actually the real FSAM will have all the accounts and sub-acconts as shown in Figure 2-4.. 3.

(12) Figure 2: FSAM Account's Classification Part 1/3 Accounts Classification 1.1 Prod. Primary Sector 1.2 Prod. Secondary Sector. Goods & Services 1. 1.3 Prod. Tertiary Sector. 1.4 Prod. Financia! Sector 2.1 Primary Sector 2.2 Secondary Sector. Production. 2. 2.3 Tertiary Sector 2.4 Financia! Sector. 3.1 LabourL Generadon of Income. 3. 3.2 Capital K 3.3 OtherTaxes less Subsidies on Production Source: European Commission (2003). In this vers10n of the FSAM I distinguish between Primary, Secondary, Tertiary and the Financia! Sector. 7 This classification corresponds to the '"Production·· account and represents the different sectors of the economy. The classification for the .. Goods & Services" account would then be their corresponding products, so the goods or services produced by each sector (Figure 2).. Furthermore, the third account "Generation of lncome'' includes the factors of production, which are labor and capital. It also includes other taxes less other subsidies on production, paid by the production. Regarding the institutions, covering accounts 4 to 7, there are Govemment, Households, NonFinancial Enterprises and Financia] Enterprises (Figure 3). In my classification Households include "Non-Private Organizations Serving Households" (NPISH) which can be found separated in the Input-Output Tables.. 7. The Matrix of thc ECs Lcadership group has a different classification: There are six different sectors and. products. In addition. in the income generation account thcy counts .. net mixed income.. separately and differentiate betwcen the institutions ··households.. and ··non-profit institutions scrving households", which are joined togetht:r hcrt:. Throughout the paper 1 will point out ali difft:rt:nct:s to tht: Lcadership group's Matrix. For further details see European Commission (2003).. 4.

(13) Figure 3: FSAM Account's Classification Part 2/3 4.1 Non-Financial Enteiprises NFE 4.2 Financia) Enteiprises FE. Allocation of Prlmary lncome 4. 4.3 Government G 4.4 Households HH & NPISH 5.1 NFE. Secondary Distribution oflncome. 5.2FE. 5. 5.3G. 5.4 HH & NPISH 6.1 NFE. Use of Disposable lncome. 6.2FE. 6. 6.3G 6.4 HH & NPISH 7.1 NFE 7.2 FE. Capital. 7. 7.3G 7.4 HH & NPISH. Source: European Commission (2003). The ··Gross fixed Capital Formation" (GFCF) account 8 in my FSAM has no extra classification, dueto lack of infonnation (Figure 4). So we just know how much GFCF each sector receives, but we do not know which sector pays which part of that amount. With additional infonnation this account could be divided into the different sectors, revealing a little more detail. For our model purposes and for this FSAM exercise, a one dimensional vector is sufficient, though.. Finally, what is new to a regular SAM is the '·Financiar· account 9 (Figure 4), which is divided into its different financia( assets: "Monetary, Gold & SDRs" (Special Drawing Rights), "Currency & Deposits'', "Security other than Shares", "·Loans", "Shares & other Equity"', ··Insurance Technical Reserves" and "Other Accounts receivable or payable". This classification is confonning to the ESA95 and represents the financia! investments of the institutions. (Eurostat 2009). The account '·Currency & Deposits" includes currency, transferable deposits, time deposits, savings deposits and savings certificates. '·Security other than Shares" contains monetary market papers, bonds and financia] derivatives. The "Shares & other Equity'· besides of shares and other equity imply mutual funds shares and '·Loans" counts short-tenn and longer-tenn 5.

(14) loans . Equally, the "lnsurance Technical Reserves" include short-tenn and longer-tenn claims. Finally, "Other Accounts receivable/payable" also implies claims from company pension commitments. (Bundesbank 2013). Figure 4: FSAM Account's Classification Part 3/3 Gross fixed Capital Formation. 8 9.1 Monetary, Gold &SDRs 9.2 Currency & Deposits 9.3 Security other than Shares. Financial (Type of Financia] Asset). 9. 9.4 Loans 9.5 Shares & Other Equity 9.6 lnsurance Technical Reserves 9.7 Other Accounts receivable/payable. 10 Curren!. Rest of the World. 11 Capital Total. Source: European Commission (2003). At last, the "Rest of the World" has two accounts l O and 11, which are a current and a capital account to be able to distinguish between financia) and regular spending.. Having in mind the accounts' classification we can now fill Figure l with infonnation of the circular flow of the economy. In the following I will explain what infonnation the accounts hold and with which other accounts they interact. Meanwhile reading the accounts' explanation, the completed FSAM can be read along in Appendix Figure AXl at the end of this paper. Later on in chapter three, I will illustrate how to fill the FSAM with concrete numbers.. 2.2 Goods & Services Although the production process and the goods and serv1ces could be summarized and represented in one single account, they are separated into two different accounts here. The two accounts are differentiated, because in theory there could be an industry producing more than one of the goods that is represented in the "Goods & Services" account. For exarnple, the 6.

(15) energy sector could produce wind, solar, atomic energy etc. Vice versa there could also be a commodity which is produced by various sectors: Transportation could be provided by a govemment sector and by a private sector or food products by small, medium and big agricultura! enterprises.. The "Goods & Services" receive payments (row) from vanous other accounts which altogether constitute the final demand for domestic goods and services from the four sectors. This can also be seen in distributional tenns and as an inverse flow: Where do the sectors commodities go to? The '·Goods & Services" account itself makes sorne payments (column) to a variety of other accounts, which is its total supply. (Figure 5). The "Production" account pays to the "Goods & Services" account for the intermediate products which are needed as input to conduct the production process (row: 1, column: 2). Furthennore, the institutions households and govemment spend their money on goods and services, which is their consumption ( 1,6). Another part which is paid for is the change in inventories (1,7) carried out mainly by the enterprises and investments are made in fonn of ''Gross fixed Capital Fo1mation" (1,8). Finally, a part of the goods and services are exported to the rest of the world ( 1, 1O).. Figure 5: Goods and Services in the FSAM. Source: Own Constn,ction and European Commission (2003). 7.

(16) Looking at thc column. or the ··Goods and Scrviccs·· account one can see ,, here the suppl:,. of. goods and services comes from: The domestic output comes from the procluction proeess (2.1) which is also the total of"the production column. ami another part is irnported from the rest of the world ( 10.1 ). l lowever, the government charges laxes for the commodities (and at times offers subsidies). so laxes minus subsidies. 011. comJ11odities are paid for by ·'Goocls &. Services·· directly to the government (sub-account ro\v 4.3. colullln 1. AX 1).. The el'fect is that the column·s total is also valued in purchasers· prices. as is the valuation of the row. This irnplies. though, that laxes minus subsidies on commodities also include the value added tax (V AT) and that consuI11ption. etc. is also valued at purchaser·s prices. In my FSAM I separate the VA T to see who pays which part of VAT to the government, making row and colurnn of the --Goods & Services·· valued al producer"s prices.. 2.3 Production. The ··Production·· account in consequence receives the payrnents made for ali domestic output from the "Goods & Services'' account (2, 1) as indicated in Figure 6. To conduct the production process "Production'· spends its funds on the consumption of interrnediate products (1,2), value added to the product (3.2), which is the cost for the assumed factors labor and capital (this also includes other laxes rninus subsidies on production) and finally, for the depreciation (8.2). Depreciation fonns part of the gross fixed capital formation earlier received by the ·'Goods & Services·· account.. 2.4 Income Generation. Although this account could be a part of the next one (as it is in the national account), the generation of income has its own account to connect the producers' realm with the different institutions' behavior through the factors of production. At the same time it connects the input-output table (IOT) of an economy with the national account. If it was not for this separation, one would just know that the sectors pay so much to the institutions, but not through which factor of production, which is a core piece of almost every rnacroeconomic model.. Therefore, the account of the factors receives payments frorn domestic industries (3,2), but also from foreign industries (3, 1O), which is the income inflow. Subsequently, "lncome 8.

(17) Generation" passes on these funds to domestic institutions (4,3) and also to non-residents (10,3), which is the income outflow. As shown in Table AXl, only households and part of the rest of the world receive ali labor payments, whereas capital is distributed between ali institutions. "Other Taxes minus Subsidies on Production" is "received" by the national government, of course, but the rest of the world also benefits from it ( 10,3.3,AXl ).. Figure 6: Total Explanation of the FSAM. Exports. GFCF. Consumption. lncome lnflow. Value Added. lncome. lnter-lnst. Transfers Net National locome. (Product Taxes). (Product Taxes). Transfers lnflow. Redlstr. of Prim. lncome Disposable lncome. Redistr. lnflow Ch. Pension Funds Net loe. Llablllties. Savlngs. Capital lnflow. New lnvestments. Depreclation. lncome Outflow. Transfers Outflow. Redlstr. Outflow. Cons. Abroad - Cons. For.. Net Acqu. Fin. Assets. Net lending/ borrowing. Capital Outflow. Externa! Balance. S011rce: Own Constn1ction and European Commission (2003). 2.5 Allocation of Primary Income The allocation of primary income represents in consequence the inter-institutional transfers of property income which sums interests, dividends, rents, etc. (4,4). This includes tranfers from and to the rest of the world (4, 1O and 10,4 ). In my version of the FSAM, as mentioned earlier, taxes on products are split into taxes on products paid by the sectors (4.3,1,AXl) and taxes on products paid by the consumers households and government (4.3,6,AXl), gross fixed capital formation (4.3,8,AXl) and the rest of the world (4.3, 10,AXl). This seperation makes it possible to see a little clearer who is paying which part to the government. Alternatively, ali taxes on products can be accumulated in (4.3,1,AXI) having the consumption at purchaser prices, as is the case in the FSAM of the European Commission (European Commission 9.

(18) 200] ). Further. 011.. the resling runds ()1· this account ()r the institutions represen! the net. national income (5.4) and are taken to the ne'-.t accounl.. 2.6 Sccondary Distribution oí lnconu.·. l·urthermore. ··Secondary Distribution or lncome·· indicates the redistribution of the primary income within the national institutions (5.5.Figure 6). These redistributions are laxes. 011. income. wealth. etc .. social contributions allll benclits (exccpt of thosc in kind) and other curren! transfcrs. 1-'lows of that lype from allll to the res! of the world are also taken into account here (5.1 O and 10.5 ). The remaining runds are taken to the next account again ami thcy are called disposabk income (6.5).. 2.7 Use oí Disposablc lncome. Govcrnmcnt and households use thcir disposablc incomc for consumption ( l ,6). whereas thc laxes on products of that consumption are countcd in (4.3.6) in my FSAM. Part of household consumption takes also place in the resl of the world. meanwhile foreigners spend money. 011. consumption in Germany. The dilTercnce is counted in ( 10,6) and represents together with domestic consumption and their laxes the total household consumption as it is listed in the national account.. Cell (6,6) then expresses the ad_justment for thc change in net equity of households in pension fu neis which theoretically could also be receivcd from or paid to the rest of the world (6.1 O. ami 10.6). In our particular case. though. thcy are equal to zero. so in Figure 6 they are not mentioned. Saving of ali institutions is expressed in (7.6) and represents the resting funds which are taken to the next. the capital account.. 2.8 Capital Account and Gross fixed Capital Formation. In consequence, the capital account of the institutions receive payments from their 0\vn savings of the disposable income (7,6) and also from their net incurrence of liabilities of the financia! account (7,9). Theoretically. capital transfers of acquisitions less disposals of nonproduced non-financia! assets could be counted in (7,7). but are left in blank because ignored here due to irrelevancy though. In addition, capital transfers could also be received from or paid to the rest of the world (7, 11 and I l. 7), but because of m issing data, they are not fi lled in my FSAM. 10.

(19) Payrm:nts of thL' capital account are mmk for the change in inventories. or \\ hich the ma_jl1rit~. is paid by the 1H111-fi11a11cial enterprises ( 1. 7). /\nother part of the capital account is thed as linancial investrncnh ami is slHl\\11 in (9.7) as the net acquisition or linancial assets \\hich includc a varicty. or linancial. instrumcnts. Furthermore. the institutions pay. llC\\. irncstments. ,, hich are nceded by thc rm1ductio11 ( 8. 7). These new investments. togcthcr ,, ith the dcprcciation paid by thc procluction itsclf (8.2). is then transferrcd as ··Cross lixed Capital 1-'ormation .. to thc --Goods and Services·· account. so that the industries receivc and use thcse paymcnts ( 1.8). Ir thcre was more detailecl information available. here ,,e could sec ,,hat difieren! produet groups cach sector needs for its investments. Producl laxes 011 gross lixed capital rormation are listcd in (4.3.8.AX 1).. 2.9 Financia! Flows and Rest ofthe World. Thc ··Financia! .. account rcceives payments for net acquisitions of financia! assets frorn rrntiorrnl institutions (9.7) ancl from the rest ofthe world as net lending or borrowing ,vhich is shmvn in (9.11 ). In adclition. payments are made to the capital account or the institutions as the nct incurrence or liabilities (7.9).. Final ly. thc externa! balance is described in ( I I, I O) and is seen from the viewpoint of the rest. or world. So a negative sign reflects a positive current externa( balance for the economy undcr considcration. Furthcrmorc. the externa( balance is a balancing item. like there are many othcrs which I havc not pointecl out yet. I will discuss the function of the balancing items and the transition from real data to the complete FSAM in the next chapter.. J. Working with real Data and Assumptions. Alter having undcrstood the differcnt positions of the FSAM its construction can be complcted by filling it with data of the real economy (Figure AX 1). The main elata source I usecl is Destatis. which is the Federal Statistics Bureau of Germany.. The first step is to choose a base year which will be represented in the FSAM and later on in the model, too. I chose 2009 as base year as this was the year with the newest data publications necessary available. In addition, it will be interesting to conduct an economic analysis in the light ofthe financia( and world crisis which started in 2007.. 11.

(20) Second. there needs lo he galhered all in!'ormation neeessar.' to lill in the 1·si\M. The bes! souree is traditionally the oflieial statisties hureau or the observed econolll.'. hlr (ierman.' this is Destatis. i\llérnatively. Eurostat or the OLCD database could also be usecl. In adclition. lo lill in the data li.)r the financia! account. data !'rom the ((ierma11) Central Bank or the European Central Bank is needecl. The following files are essential:. ,. lnput-output table (IOT) ofthe domestic production \vith imports (Destatis 2013a). ,. National account inclucling sector accounts (prefcrrably conforming to LSJ\95) (Destatis 2013h). ,. Financia! accounts (Bundeshank 2013). When ohtaining the data it is upmost import that all data sets do 11ot only refer to the same hase year. hut also have the same publishing date. ir procurablc. 11' not ohtainable. the numhers might differ ancl then the totals of the FSJ\M \\ill 1101 match anymore and the complete analysis could be distorted. For example. the national accounts ora specific year might be updated on a regular hasis. maybe every year. hut the IOT might only be published once and might not he updated anymore or only once in a \vhilc. Therel'ore. hefore doing the whole exercise one should be aware of the publish ing date and making sure that key 11umbers like the total ofvalue added. intermediate consumptio11. final consumption. etc. concur.. 8. Third. before tilling the FSAM and to make sure that the circular tlow of production is complete and to eraclicate errors early. one should do a prc-exercise lilling out an input-output 1natrix (IOM) like the one in Figure 7. One needs to decide which scctors ofthe economy of the IOT ought to be subject of the observation and all the olher seclors should be put in an aclditional sector. I will observe the primary. secondary. tertiary ami the linancial sector. So after dividing ali sectors into those four. I summarize the IOT putting thc surns of the four sectors· key figures into the IOM. In order to do that. 011e ncccls to know how much each sector is paying to every other sector as intermediate consumption which is pul in the first part of the IOM. Vertically. this is the intermediate consumption and horizontally. this is the intcrrnediate demand.. 8. Ikstatis actually sen! me thc accuratc data on personal inquiry.. 12.

(21) Going down the IOM, the sector totals of the compensation of employees and net operation surplus is put there as "labor'' and "capital"'. Then the sector values for the depreciation, other taxes minus other subsidies on production and taxes minus subsidies on products is recorded there. Those three could altematively be put in a single account which I have not done, because the FSAM requires to put ali of those values in different spaces. As I have mentioned earlier, the FSAM (and therefore also the IOM) can also have a lighter and more summarized design, depending on one's necessities. An example for a slightly condensed IOM can be found in the next chapter (Figure 8). The fields of "lntermediate Consumption", ··Value Added" and the gross value of production "G VP" are calculated automatically and the sum of ali sectors should coincide with the total of ali sectors in the IOT.. Figure 7: The lnput-Output Matrix in Million Euros ISI. 2nd. 3rd. FS. lnt. lkm.. e. G. C hlNV. GFCF. Exp. lmp. FD. GVP. ISI. 3456. 31444. 2063. o. 36963. 16941. o. 39-46. -40. 7487. 23169. 5165. 42128. 2nd. 11679. 732660. 175595. #16. 924350. 366190. 1-4999. .280QS. 305421. 'l!I0911. 68IIOS5. 76107 1. 168542 1. 3rd. 9376. 344758. 654074. 52884. 1061092. 754751. 454071. 6129. 69590. 1611103. 110297. 1340347. 2401439. FS. 1056. 20883. 57206. 79224. 158369. 67574. o. o. o. 20028. 10119. 77483. 235852. lntermediate Consumption. 25567. 1129745. 888938. 136524. Labor. 5652. 376831. 788746. 61201. Capita l. 7344. 85363. 407526. 22397. Depreciation. 7969. 83977. 276350. 62#. Subsidies on Production. -5925. -2615. -4064. 354. Taus - S ubsidies on Products. 1521. 12120. 43943. 9132. Value Addtd. 16561. 555676. 1512501. 99328. GVP. 42 128. 1685421. 2401439. 235852. Other Taxes minus. So urce: Own Constntction and Des/alis (2013a). Going horizontally, there is the total demand for each sector. So after the interrnediate demand is calculated automatically, there is the consumption of the households (C) and the govemment (G), the change in inventories (ChlNV), gross fixed capital forrnation (GFCF), exports (Exp) and imports (lmp). In consequence, the final demand (FO) calculated by excel is the sum of ali those, except of the interrnediate demand, minus imports. At the end, to get to the GVP the interrnediate demand is added to the final demand. The GVP of each row and also their joined total have to coincide with the GVP of each column and also their joined total. If that is not the case a mistake was made in transfering the data from the IOT to the IOM. To detect a potential error one can check the sum of ali (four) sectors of each variable 13.

(22) anti compare it directly ,vith the total or that , aria ble in 1he IOT. Without a consisten! IOM onc ,, ill not gct a co11sisle111 FSJ\M anti hence. 110. rcliablc analysis.. J\licr ali numbers of the IOM match. in a fourth step. the lirst t,\o ro\\s and columns or the FSJ\M can be tillecl with the elata or the IOM \\ ithoul any problems. J\s neither the IOT nor the nat ional account suggest data o r \\ hal inst itul ion pays ,vh ich parl or the change in inventories to what sector I assume at thal poinl thal ali change in invenlories is paid by the non-financia! enterprises. The nalional account artirms that the ma_jority or the change in inventories is paid by non-financia! enterprises and only a marginal part by financia! enterprises and households.. 9. J\nother particularity is. that in my FSJ\M the CiFCF is _jusi a row vector due to the lack of clctaillcd information. With more data it could be classilied inlo the dilTerent sectors. Then one coulcl also observe which instilution is making ne\\ investments to ,vhat sector giving room íor greater analysis.. ;\ 11 resting data comes from thc national account ( Deslatis 2013 b ). excepl for row and column. nine which is based on the financia! accounl published by the central bank (Bundesbank 2013). The necessary data can be taken ami transfcrred directly from thal tile.. What cannot be found in thc national account. however. is the cktaillcd inner-institutional al local ion of primary income (4.4) ami secondary dislribution of income (5.5) lound in Figure 6. Apparently. that data is not publishecl - at !casi for Ciermany - in general due to its delicateness. Payments and receipts or each institution can be extracted. though. For the construction of my FSAM I assume therefore. that in thc case of the allocation of primary income ali transfers are made via households. Ali transfers. go to houscholds first instead of flowing directly to the destined institution. Then. in the same matrix houscholds pay whatcver amount corresponds to each institution. Those transfers also includc the rest of the world.. In thc case of secondary distribution of income ali transfers are made via the government. This makes even more sense as those transfers are mainly income taxes and social transfers. Again, the rest of the world is included in those transfers. Obviously. both distribution " In thc ncxt chaptcr and in thc model I undo this assumption ami use th..: cxact data from th..: national account.. 14.

(23) accounts do not n.:,cal authentic information ami could thercl'ore be sumniari/ed into one single vector account callcd net transkrs. This is e.,actly what I have done in my alternative FS/\M presentation (1.-igure i\X2) a111011gst other ehanges to illustratc a complete ditTerent approach or construeting the FS/\M containing the same relevan! information. That transkr account can then also contain the adjustment for the change in net equity or households in pension funds. \\hich in this matri:-.: is cell (6.6).. The advantage or the (irst FS/\M presentation is that the flow of funds is represented e:-.:actly like in the national accounts and can directly be compared ali way long in the balancing cells (5,4). (6.5) and (7.6) which are like ali cells or Figure 6 matrices in the final FSAM (AX 1). Those automat ically calculated balancing matrices. 10. represen! money receivcd from the. previous account minus spendings in the actual one. This is the reason why they have to be diagonal in Figure i\X 1. too. becausc thcy only pay and receive from their own account. So ··Net National lnconH:·· (5.4) shows what cvcry institution receives from its participation in the production process plus property income allocation and in the case of the government this inclucles product ta:-.:es and taxes on production. too. This is the income of the institutions which is principally spent. 011. social transfers and income tax in the secondary distribution of. income account. What is lett is the disposable income (6,5) which is passecl on to thc clisposablc incomc account whcre it is mainly spent on consumption. Matrix (7.6) shows in consequence the saving of the institutions which is passed on to the capital account. In a regular SAM one would jusi know that ali of those savings are spent on investments ancl returned to the industry (saving:s identity). In thc FSAM though. one can surveil whethcr those savings are returned to the industry instantly as change in inventaries or GFCF. or enter the financia! markct tirst. Especially in the light of the rccent financia! crisis. infonnation and investigation of the financia! realm becomes more and more vital to economic policy makers.. Unfortunately. financia! published data of Gcrmany is not congruent in the sensc of closing the tlow of funds, dueto a small difference in the publishing date of the financia! account and. 10. Thcre is another balancing matrix in (2.1) which is thc oulput. Togcther wilh the laxes on producls paid by thc. activities (4.3.1) it represents thc GVP and can be compare<l with the GVP in the IOM. Another one is thc externa! balance in ( 11.10) which <loes not coincide with thc final externa! balance or the national account. becausc it <loes not Lake ali payments ami receipt or Lhe rest or Lhe world in account.. 15.

(24) statistical differences. 11 That gap in the financia! balance forced me to make the assumption that the difference in the financia) balance is absorbed by "other accounts receivable/payable" of the financia) account in (9,7) and by the rest of the world in the column of the financia! account ( 11,9). Making this assumption is unfortunately a loss in the validity of any investigation. This is one of the reasons why it is utterly important to have a clear vision of the objective of ones investigation. In my case, I am not that interested in a financia) analysis in depth, as this would also exceed the limit of this paper. I will concentrate my analysis on the financia! assets '·Currency & Deposits" and '·Shares & Other Equity" and ali other financia) assets will be put in a single account "Financia! Assets''. In the next chapter I will briefly present the alternative FSAM construction which is also suited to the economic model in the subsequent chapter in which I will develop the complete economic model and present the computable general equilibrium model in GAMS.. 4. An Alternative FSAM Presentation For the alternative FSAM there needs to be done the IOM first, too. In that way it can be made sure that key flows are correct and totals of the production process match. Figure 8 shows the IOM for the alternative FSAM which is valued at consumer prices this time.. Figure 8: The Alternative lnput-Output Matrix in Million Euros 1s1. 2nd. 3rd. FS. l nt. Dem.. e. G. C hl NV. GFCF. Ex p. lmp. FD. GVP. 1st. 4368. 37802. 2990. o. 45160. 2S967. o. 3946. -40. 8003. 23169. 14707. 59867. 2nd. 1S828. 8429S6. 22S637. 6019. 1090440. 621977. 33877. -23831. 68905S. 1116423. 2206863. 3rd. 20468. S28091. 34186S. S7089. 9475 13. 636250. 441423. l95S. 61486. 164377. 72456. o. o. FS lntermediate Co nsum ption. 1254. 23771. 59748. 79604. 41918. 1432620. 630240. 142712. Labor. 6080. 401310. 763390. 61650. Cap ital. 7630. 97020. 394000. 23980. Depreciation. 8320. 91280. 267790. 71S0. T ax es. -4081. 184633. S3098. 112S0. VA+ Deor+TAX. 17949. 774243. 1478278. 104030. GVP. 59867. 2206863. 21 085 18. 246742. o. 347204 826251. 130188 110297 116 1005 21085 18 20028. 10119. 82365. 246742. So urce: Own Constniction. Des/alis (20 I 3a). 11. Even in the officially published FSAM of Destatis the financia! part <loes not match perfcctly and the. difference has to be booked to non-financia! enterprises. (Schwar¿ et. al, 2004). 16.

(25) Additionally. taxes are added up to _jusi nne row. Another si111plification \\Ould be to also include the depreciation in the nrn ··Taxes··. but as depreciation will be part or the 111odel. 1 lcti it in the IOM as \\ellas in the alternative l"SNv1 (Figure AX2).. As the data is the foundation of' an CCiI: Model. the FSAM should be constructcd with a lot of care and detail 011 those elcments \\ hich will be acore part of ones economic interests. l lcnce. the FSAM should be customised taking into consideration the upcoming analysis 0111itting unnecessary data and aggregating some where it rnay be needed. Figure i\X2 in the Appendix shows the complete alternative presentation of the FSAM.. There are sorne striking differences to the lirst FSAM. One is that many values which could be found within the first FSAM are now outside. as separate accounts. Whereas the value added was parl or the ··Goods & Services·· account in the first FSAM, in the alternative presentation it has its own account. Importan! sub-accounts were converted into single accounts. like transfers. change in inventories or acquisition of financia! assets. Also intennediate input already inclucks laxes on products paid by the activities making prices being purchaser's prices. The other big difTerence is that the institutions changed from being a sub-account into being a proper acccount with different funds accounts.. In contrast to the first FSAM. in this one all numbers are actually needed in the economic model with sorne rninor cxceptions. Furtherrnore. in this FSAM the flow of funds will be easier to follow \vhen applying the eco1101111c analysis and following the structure of the rnodel in the next chapter.. 5. A Computable General Equilihrium Modcl Application. Making proper use of the data or the FSAM I will write an economic rnodel in GAMS which analyses a certain econornic problem. To successfully conduct the whole investigation it 1s crucial to follow seven basic stcps (Figure 9). Every single one of them is crucial and it 1s indispensable to follow them step by step for the analysis. (Pérez, 2008). 17.

(26) Fi~un· 9: Scnn Ba~ir Stcps to condurt a surcessíul CCE .\lodcl .-\nal_vsis l. Statement of Problem. 2. Model Specification. 3. Calibration. 4. Original Equilibrium. 5. Economic Experiment. 6. New Equilibrium. 7. Comparison. Firsl it is essential lo formulate the econo1111c problem or issue which is the point of investigation. Second. lhere is the necd to specify the problem-suited model"s macroeconomic assumptions deseribing the (neoclassical) environment in which the behavior of the economic agents all(I the industries takcs place. Third, the model has to be calibrated using the real data oflhe FSAM. Fourth. the calibratecl moclel has to be written and run in GAMS. At this point it is imporlant thal il generales the Original Equilibrium retlecting the same bchavior as il is obscrvcd in the economy. Fifth. an cconomic experiment is intcgratcd into thc modcl which com:urs \\ ith thc problem of stcp 011c. Finally, the New Equilibrium is calculatcd and thcn comparcd with thc Original Equilibrium.. 5.1 Statcment of Problem. In this papcr I will analysc the following problem which I chose to intcgrate the financia! part ofthc FSAM. too:. To whal Degree cloes lhe German Stock !ne/ex DAX influence the lnstilltlions · Financia! lnvestments Decision hetween Deposit.1· ancl Shares?. 18.

(27) 5.2 Macrocconomic Assumptions. To deline a general equilibrium 111oclcl for this econolll) the sectors· behavim. instilutions· behavior. prices ami equilibrium conditions h,ne to be clcar ami be suited lo lit the econo111ic problem. The part of the economy \\ hich is the subject of invesligalion should be the bes! thought through and contain the best data availablc. In the 1·ollm\ing 1 \\ill jusi mention once the meaning of the variables usecl - in !he texl or directly alier the equations.. 5.2.1 Scctors' Behavior. There are four clifferent sectors which are indicated by the subset i = j = ( 1.2.}.4 l 1~ \\hich conduct the production of the commodities maximizing their profits in minimizing thcir total costs (re·,) subject to their techonlogy nest. TC are Value Addcd ( l A,). lnlcrmcdiatc Input of 1. ali l'our scctors. (¿j= 1 1/iJ), the. Dcpreciation (/Jc¡w,) all(I Value Added Tax (V.17;). which is a. percent share of VA. Ali of those inputs are combined as a Lconticf function in fixed proportions by each sector to conduct thc production proccss. cxcept for the dcprcciation which I assume to be fixed.. Depr¡. =. Depr¡. 11; 1 = aiJ(Y¡ - Depr;) VA¡= av 11 ¡(Y; - Depr;) VAT¡. =. T;. VA;. Where: Y,. ~. Procluclion in 5,'ec/or i. = Value Added Tax Rate av 11 i = Amount of VA needed far each Unit of Production in Seclor i a¡ 1 = //111011111o/111/w/ demancls Scclor i_ji-0111 .\ec/orjjiw cuch Unil of Pmduclion in Sector i. T¡. V A itself is a nested Cobb-Douglas function reprcsenting the possiblc substitution between Labor (l,) and Capital (K,) with elasticity I and constan! returns to scale. The offer of those factors of production is inelastic which implies that thcy are homogcnous. The cost of VA (CVA,) also has to be minimized by the sectors:. 12. Thc suhsct i (andj) in this papcr \\ÍII always rcprcscnt onc ol"thc four scctors or ihcir rcprcscntativc products.. 19.

(28) = wl,¡ +. Mi11 CV !I¡. s. t. VA¡. =. rK¡. A;f,/; K/-fl;. Where: 11·. l.uhor ( ·us/ rlL1geJ/or euch. o/Iuhor neeclecl. (;17¡¡. r = ( 'upitul ( 'ns/ (Re,·<'111tcJ ji 11' ('Uch Unil o/( ·upitul net'dccl A,= Fuctor f'r11cl11cti1·it_¡- o/Sec!or i. /f, '- Luhour ,",'hure o/ Vulue 1lcld<'cl 11/.1ec/11r i ll'ilh. If=. 1. {3¡. = 1 allll. O <. /J, < /. In consequence. the optim ization problem or each sector can be representas following:. 4. Min CT¡. = (1 + r;). (wL;. + rK¡) +. L. P/l;j. + Depr¡. j=l. .. VA;. 11; 1 11;,. lli3 11¡ 4 a¡ 1 a¡,. ai3 a¡ 4. s.t. Y¡= m m [ - - , - , - , - , - ] avA;. Where: Pi = PriccfrJr une Unil o/Ciouclj T¡. = Value Added Tax in sector i. In addition. perfect competition is assumecl. so the sectors do not have any intluence on prices and their prolits equal zero. This also implies that each sector and its behavior is representative for a variety of lirms within that sector.. P¡Y¡. = (1 + r¡) (wl¡ + rK;) + 11; 1 + 11¡ 2 + lli3 + 11¡ 4 + Depr¡. The whole production process can be visualised in Figure I O in which the distribution is also recorded. So the output of the national sectors is Y, and is distributed as Exports (E,) to the rest of the world and to the Domestic Market (D,). The output of the domestic sectors to the Domestic Market D; forms together with the lmports (M,) the Compound Product (X;). That Compound Product X; is demanded by the households as their Consumption ( C,). the Government (G,), the sectors as lntermediate lnputs (//1,), by the Change in lnventories (Ch!NV,) and by Total Gross fixed Capital Formation (TGFCF,). TGFCF itself is the sum of. the depreciation paid by the sectors and the investments of G FCF O paid by the institutions, in. 20.

(29) \\hich o. : 11. (i. \JI l .. 11. rclating to l lousd1olds. (ion:rnmcnt. \io11-l·i11a11cial l.ntcrpri~cs. allll linancial l.11lcrpriscs.. Fi~un· 10: \lodl'I Framl'wor·k of l'rnduction and Distrihution. ·\. ¿111j i=. 1. I ,, ·1. 1;. Dcpr,. i=I. V/\1, Source: (hrn ¡wcsellfuli1J1/ 0(1/ie ( iouds .\ lurÁ,·1. lhe co111hi11atio11 of D, ami M, to rorm the Compound Product X, is done through a CLS (constant-elasticity) function for every sector i. This implies that the elasticity values di rkrent lhan O ( l.eonticl) or. 1. 0. 1. can takc. (Cobb-Douglas). Each X, is dclincd by thc follo\\ ing. function ami has a homogcneity of thc dcgrcc I applying thc Armington condition (/\rmington 1969).. X,. = ó¡ [ µ¡(D¡rp, + (1 -. l. ¡i¡)(M¡)-Pi ]-Pi. \Aihcre:. = Efficiency Parmneter ¡1 1 = Slwre Parameter of the Domestic Product p¡ = Exponent Parameter indicating the Elasticity of Substitution O'¡ o'¡. with O'. 1. '. 1. 1 = -l-p¡ -u. l·or cas~ prcscntation purposc: 1 \I ill so111c:timcs use: p, instcad. or 0'1. 21.

(30) For !he consurner the perlccl combination. or good X, lherel'ore i~ 1he 111ini111i/atio11 of i1s price. sub_ject to thc CES function.. Min prl D1 1. = Ó¡. s. t.X¡. l,1.1;(D;)-Pi. + pm M 1. + (1. l. 1. - ,1.1;)(M;)-1i,. ,-/Ji. Where:. = Price.fár Domestic Goocl i P/11 = Price f or lmported Good Pt. with. p."1 l. = PM. 1. EXR (1. + rm) 1. Where:. PM¡. = World. Price of Goods from Sector i. LXR = Exchange Rafe. r¡11. = Tarif f. Rate on Goods f rom Sector i. So the lmport Prices Pf11 take into consideration the World Priccs (PM;). lhe Exchange Rate (EXR) and the lmport Tax (r¡11). To solve this probkm thc ratio between Domcstic and. Compound Good can be obtained representing. the Proportion of Domestic Use (d,t:. Furthermore. Prices P; of the compound good are given solving. lhe minimization problem of the consumer by:. 1. P;. =;. [µ¡1'i (Pn1-a¡. + (1. - µ¡)ªi (P/11)1-a;r-rr¡. l. Ali further definitions, conditions and assumptions concerning the institutions like import and export quantities, etc. will be stated in chapter 5.2.3 in which ali final general equilibrium 14. For fü11hcr dctail scc Pércz (2006).. 22.

(31) equations required are stated. The same applies l'or the institutions· bchavior in \\hich 1 \\ill jusi describe their behavior. but not every single equation until chaptcr 5.2.J. To be ablc to visualise the compkte. tlO\\. of funds I illustrated the \\holc modcl econom) in Figure 11 at the. end of thc nc:--t chapter.. 5.2.1 lnstitutions' Bchavior. Rcgarding thc institutions I assume that thc clasticity of substitution betwecn the compound products is 1. so a Cobb-Douglas 11.mction with homogencity of the degrce I can be used to model consumer behavior. Then: is onc representativc and rational acting household \vhieh rctlects the eeonomic decisions of all households of the economy. For this model this is sufficicnt to analyse the economic problcm. howevcr thcre could be added more types of households. Furthermorc. the Cobb-Douglas houschold function is maximized subjcct to its budget res tri et ion.. Where: e,= 1-/ousehold Con.wmplion o//'roduc/ i r1. 1. = Slwre ofCon.,wner U1ili1_1· o/e, 1i-ith. O<. r1. 1 <. I. !'rice r!f" Produc/ i. !',. ld11 =. sr. Il=i a:¡ = 1 ancl. 00. Disposahle lncome of flouseholds. 1/ousehold Saving.,· Rute. C_IN_ROWfl. = H. Consumption Abroad minus that of Foreigners in Germany. The Disposable Income (/c/ 11 ) minus thc part of it that households save (sr) ancl minus the amount households spend abroad (in their vacations etc.) plus that of foreigners in Germany ([_IN_ROWH) is spent. 011. all four compound products to their respective prices. Thc. Disposable lncome equals the household"s income (/n 11 ) minus a share of it which is income tax (r~) plus net transfers (trnsf11 ). For all institutions Disposable lncome can be described by ld 0 •. ,..,.,. ~-'.

(32) Whcn:: /11 0. = Generntion. r:,' = In come Tax trnsr;,. of lncome by lnstitution o Rate far lnstitution o\\ ith. rtJ = O. = Fixecl Net Transf ers far lnstitution o. Thc institutions· incomc (In,,) is ddincd by what they carn for thcir labor ami capital participation in thc production process.. Whcrc:. = lnstitution Share Parameter: Labor Participation in the Production Proccss YoK = lnstitution Share Parameter: Capital participation in the Production Process With Y1-T ,. = YN1-T 1. = Yr; 1. = O. y 01 _. Thc linal disposable income. or government (/c/G7). includes ldc; and in adclition ali rcvcnues. rrom ta:-.cs.. ldGT =!de+ TAXES \\ ith 4. TAXES. =. L. 4. rgld 0. o=1. +. L. r¡VAi. i=L. 4. +. L. r['1M¡ EXR PM¡ + TRow. i=l. Whcrc: T110 w. = Taxes paid by the. Rest of the World to the Nacional Government. Finally. the linancial part of the model belongs to the savings (S. 0 ).. 1-Iouseholds as well as the. othcr institutions can decide \vhether to invcst the saved money (of their capital account) in shares or _just deposit it at the bank. A fixed amount of the capital account goes as ne,v invcstmcnts to GFCF (GFCF0 ) and to the Change in lnventories (ChlNV0 ). A part of the rest gocs to Financia( Assets (FA. 0 ). and to any money left over which I cal! Flexible Funds (FF,,).. So there is a Leontief function combining in fixed proportions investment spending. 011. FA. and FF. Flexible Funds itself is a function which contains Shares (Sh,) and Deposits (De whereas Sh 0 depends. 011. 0 ),. the German Share lndex DAX .. 24.

(33) S0. = GFCF;, + Ch!NV,, + ¡:r,;, + FA. 0. Where: A0. = Share Parameter indicating Spencling of s·auings on ¡:¡: of lnstitution o. with Sh 0 De 0. = fJ. 0. = FF,. DAX. 1 -. Sh 0. Where:. = Parameter describing the eff ect the DAX has 011 Sh DAX = German Share lndex 00. 0. Ali important transfers are illustrated in Figure 11 on lhe ncxt pagc. Thcrc. onc can observe !he whole circular flow of funds which is in cin:ulation in the economy. The arrows indicate in what direction the payments go. From the production process moncy llows to their inputs which are the deprcciation. intermediate consumption ancl to the foctors of procluction which is value adclecl. In adclition, the production has to pay laxes to the governrnent which are re\a\ecl to the value added. The institutions receive Lhc money from the f'actors of production labor and capital. and then pass. 011. the funds to thcir savings account atier paying their. particular income tax lo the governmenl. What is lclt alter ne! transfers is the disposable income of' the institutions which is passed on to their savings account all(l. in thc case of the government ami the households. is also used for consumption on !he compouncl goocl before.. Afterwards, savings are spent on financia! asscts ami. 011. llexible l'unds. which are shares or. deposits. whereas ali of thosc threc ··return" nct liabilitcs. A part of savings is also rcturncd back to the industry as consumption of thc compound good in form of the change in invcntories and gross fixed capital formation which forms thc total gross fixccl capital forrnation together with the depreciation paymcnts from !he industry. The compound good itself consists of the domestic good which comes from thc industry and the irnportcd good which comes from the rest of the world. As therc are tariffs on the importcd good. it pays the import tax directly to thc government. Final ly. thc rest of thc world buys a part of the national production, too, which are the exports. At this point the cicle of the circular tlow is complete, which can be casily tracked with the altcrnative presentation of thc FSAM (AX2).. 25.

(34) Figure 11: The whole Model Economy Flow of Funds. -8-[~. I I. ----fil-+. H. NFE. Depr, - - - - - - ~. Ch/NV 0. So urce: Own Presenta/ion of the Model Economy. Having clear the behavior of institutions and sectors, now ali equilibrium conditions can be forrnulated.. 26.

(35) 5.2.3 Definition of Equilibrium. A general competctive equilibrium consists of' priccs (R, W, P;, Pr Pt, PE, PM, DAX, EXR) and quantitics: ( C;, G;, /11 0 , ld 0 , ldGT, S0 , FA 0 , Ff~, Sh 0 , De 0, Y;, E;, D;, M;, X;, L;, K;, VA;, ll;j) i=j={ 1.2,3.4] ando={ 1,2.3.4} so that. 1) The demanded Quantities of each Goocl by l louseholds (C,) solve the Problem of the Consumer: C;. a·. =/. [ldH(l - sr) - C_IN_ROWH]. l. With. I1=i a; = l. and O<. a¡. < 1. Where Prices are given by:. 1. P¡. = ; (µ/i (PnI-a¡ + (1 -. µªª¡ (Pt)l-a¡]l-a¡. l. Where. pm l. = PM. l. EXR (l. + r:TI) l. And Disposable Income for ali lnstitutions is given by:. Where. ln 0. With ¿¿=1 Yo. L. =. ¿¿=1 Yo K. = YaiWLS + YoKrKS. = 1. And Household Saving is given by: SH. = sr ldH. 2) The demanded Quantities of the Government for each Good (G;) satisfies:. G;. = G¡ 27.

(36) J\ncl the Disposabk lnrnme orthe Government is given by: l:i. = ldr; + TAXES. ldGT. Wherc 1. TAXES. =. 4. L. rgln 0. +. ¿. 4. r¡VA¡. +. i=l. o=l. L. r;nM¡ EXR PM¡. + TRow. i=l. And the Public Saving is given by: 4. L. Se= ldGT-. P¡G¡. i=l. 3) Financia! ancl Non-Financia! Enterprises don not consume and therefore their Saving is given by:. = ldFE SNFE = ldNFE SFE. 4) Saving distribution of all institutions o is given by: 16. Whcre FF0 FA 0. = il. 0. = (1 -. (S 0. -. il 0 )(S0. GFCF0 -. -. GFCF0. Ch!NV0 -. + TL 0 ). Ch!NV0. + TL 0 ). In which. T L0. = Total Liabilities o f. lnstitution o. "Altcrnativcly. thc govcrnmcnt could be excluded from the institutions and its disposable income detincd in onc single cquation avoiding having to put its tax paymcnts and capital particaption equal to zero. 1 ". This cquation can be lcli out in thc GAMS modelas thc ncxt two cquations implicate its content.. 28.

(37) With. Whcre:. LFA 0 LDe 0 LSh 0. = Liabilities of Financia[ Assets of Institution = Liabilities of Deposits of Jnstitution o = Liabilities of Shares of lnstitution o. o. And Flexible Funds Spending is a nested function detinccl hy:. With. Sh 0 De 0. =0. 0. DAX. = FF. 0 -. Sh 0. 5) Gross fixed Capital Formation to each sector is givcn by: ll/. GFCF;. = GFCF;. And equals the GFCF paid by the institutions and the dcpreciation paid by thc sectors: 4. L. 4. GFCF¡. =. 1. L. Depr¡. i=l. i=l. +. L. GFCF0. o=l. 6) The Change in lnventories received by each sector is:. Ch/NV¡. = Ch/NV¡. And equals the Change in lnventories paid for by thc lnstitutions: 4. L i=l. 4. Ch!NV¡. =. L. Ch/NVO. o=l. 17. TL will just be fixed in GAMS.. 18. Can be omitted in GAMS.. 19. The equations in 5) and 6) do not have to be stalcd in GAMS. bc1,;ausc 1hcy are jusi fixed al 1hcir obscrved. valuc.. 29.

(38) 7) Thc ckmandcd Quantities olTactors \\hich sol ves thc Problcm or the Producer in each sector is given by:. L1. -. VA-)[ /3· r]l-/?; ( A; (1 - /3;) w _1. ,. K; = (VA;) [(1 - f]¡) w]/?; /3;. A¡ With. ¿f=l /3; = 1 ancl. O,,., /1,. <e. r. I. Where the Dernand of Value Added satisties:. And the Demand for lntennediate Input is given by:. ll;J. =. With the Depreciation corresponding to:~. Depr¡. =. a¡ 1Y¡ 11. Depr¡. And profits in each sector equal zero:. P¡Y¡. = (1 + r¡) (wl¡ + rK;) + ll1 ¡P1 + ll 2¡P2 + ll 3 ¡P3 + ll4¡P4 + Depr¡. 8) The Dernand for the Domestic Goods is given by:. D¡. = d¡( C¡ + G¡ + GFCF¡ + Ch/NV¡ + 111 ¡ + 112¡ + 113 ¡ + ll4¡). Where. 9) National Demand for imported Goods is defined by:. M¡. 20. = P¡~ [P;(C¡ + G¡ + GFCF¡ + Ch/NV¡ + 111 ¡ + 112 ¡ + 113 ¡ + 114 ¡) -. P¡dD¡]. Also rcdundant in GAMS.. 30.

(39) 10) 1:xports or Good i are givcn by: E - f1 ,,. -. PE1 ( Pt /EXR. )'I¡. Whcrc. E;= Value of Exports of Goocl i if P/1 /EXR is the same as PE¡ r¡¡. = Elasticity of Export Demand of Good i. PE;= World Price of Exports of Good i P/1/EXR. = Domestic Price of Good i in Foreign Currency. 1 1) And Savings of the Rest of the World is given by their commercial dclicit rninus labor paymcnts (LRow ). transfcrs to the national government (TRow) and ne\ translcrs. (trns fRow) plus consumption paid by nationals. 1. Srow. =. ¿. in. the. rcst. of the. world. 4. PM;M; EXR -. i=l. ¿. P¡dE¡ - LRow - TRow - trnsfRow. + C_IN_ROWH. i=l. 12) The Goods Markct is equilibrium:. D; +E¡= Y;. 11) The Factor Markct is in cquilibrium:. Li. + L,. + L3 + L4 + LROW = LS K1 + K2 + K3 + K4 = KS. 14) The Financia! Markct is in Equilibrium 4. TFA. = FARow +. ¿. FAo. o=l 4. TFF = ShRow. + DeRow +. ¿. FFo. o=l. With. TFA. = Total Financia[ Assets. TFF. = Total Flexible Funds 31.

(40) 15) The Consumer Price Inde., can be representcd as fó lltrn ed: 4. =. PIX. L. P¡ªi. i= 1. There is a system of 84 Equations wilh 84 endogenous variables.. To be a ble to sol ve this system one needs to knmv the value of the 81 Paramders: (a;, Yo. 1_,. Yo K• sr, rg, T¡, r;r1, 00 , {3¡, a¡, avA ;, a;¡, r¡¡, O;, a;, fl;, f;, A0 ). And the 45 exogenous variables:. (C_I N _ROW11 , PM¡, PE¡, trnsf0 , GFCF;>, Ch/ N½¡, TL 0 , KS, LS, Depr¡, GFCF;, Ch! NV¡, TRow, LRow, trns fRow, FARow, ShRow, DeRow). 5.3 Model Calibration. The data for the Model Calibration comes mainly from lhe lnput-üutput Matrix or is calculatcd in GAMS. Alternatively. some data can be laken from outsidc sourccs. too. Actually. the elasticities should be takcn from oulsidc which I have not. bccause above ali this paper aims to be a guide explaining the general approach. 1 picked the elasticities to be close to l. but not 1 so they could be represented by a CI·:S function. but act similar to a CobbDouglas one.. To calibrate the model parameters. basically. the equations are turned around to single out the parameter we are looking for. These are the most importan! emes:. C;P¡. a------------1 [/du(l - s) - C_IN_ROW1¡] A-= 1. Vi i. Lf/; K i-fJ; 1. {3¡. =. 1. wl¡ wl¡ + rK¡ S11. sr=ldu. ,,...,. J~.

(41) Y11. =. K. ln 11. - wl,S KS. Sh 0. 0 =-. (). = 1. ó·. DAX. -. D +PMM. [. 1. 1. µ¡D¡ i-a;. µ¡. =. + (1. 1. l,t-1. 1. 1. - µ¡)M¡. ,_a;. Pt ) (J¿_)~ ( P/11 M¡. Utilizing numbers from Germany of the real economy in 2009 using the data of the FS!\M. the valucs can be calculated easily. The parameters can be calculated by G!\MS with the equations mentioncd rclcring to the base year data. Then only the elasticity has to be clelined in tcrms of numbers ,vhich I e hose to be close to 1. but not I to maintain the CES function in the model. Thc best way though is to take a wel I estimated elasticity from an outside so urce or to estimate it oneselr. In addition. for the import tax I calculated the overall import tax ror all industries. A more accurate way would be lo investigate further for exact values. In the following. the used order still applies for the sectors i = j = ¡ 1,2.3,4} and for the inslitutions o= [H. G, NFE. Fll.. = {0.019, 0.458, 0.469, 0.053} sr = 0.109 Y11 L = 1 Ye L = YNFE L = YFE =O Yo K = {0.384, -0.008, 0.59, 0.035} a¡. 1,. rg = {0.155,0,0.129,0.408} = {14.15,25.391,37.946, 19.564} A. = {0.496, 0.4 72, 1.494, -88} T¡ = {-0.298,0.371,0.046,0,131} rt = {0.02}. 00. 0. ..... -'.).

(42) = {1.987, 1.637, 1.899, 1.809} {]¡ = {0.443, 0.805, 0.66, o. 72} Cl¡,;1; = {0.229, 0.226, 0.549, 0.347} o,. n; 1. = {0.073, 0.264, 0.342, 0.021}. = {0.017, 0.382, 0.239, 0.01 l} nu = {0.001, 0.107, 0.162, 0.028} a; 4 = {O, 0.024, 0.231, 0.323} Cl¡ = {1.01} µ¡ = {0.689, 0.665, 0.946, 0.956} ó¡ = {1.868, 1.903, 1.234, 1.196}. Cl¡2. f;. = {8.003, 826.251, 130.188, 20.028} (fixed to r¡¡. E;). = {1}. 5A Original Equilihrium. i\lkr putting ali equations into Gi\MS the original equilibrium is calculated. Additionally. the variation of'the variables shoulcl be calculated to be able to observe any possible differencc ot' thc original cquilibrium to the clatasct. Naturally. thc output of GAMS has to match thc real lik observations. lt has to be pointed out that in my 111odel thcre was a very marginal variation \\ ith livc to se\'Cll digits behind thc comma regarcling 111ost variables. which I accepl lo be tolerable. Thcrefore I rounded thc variations to two cligits after the com111a so they appear to be zero. The only s111all variation lcft is the one. or the. government in its cleposits (0.1 1).. ti11a11cial asssts (0.02) and flexible funds (-0.0l) which I also accept. as this analysis does 1101 locus 011 the govcrn111c11t in particular.. Thc complete GAMS moclel can be found in the Appenclix Figure AX3. Brief commenls are insertecl throughout the \\hole program to indicate the meaning ofeach section. which will nol be discussed in detail in this paper. Basically. GAMS~ 1 enables the user to calibrate the parameters and calculate the general equilibrium taking into account a multitude of equations. Alter the successful cxecution ofthe model the economic experiment is conductecl.. :i. 1\noth<.:r lamous program 11hi<.:h can also he uscd is GEMl'i\CK.. 34.

(43) 5.5 Economic Expt•rimcnt :tll(I i\l.'w Equilibrium The economie experimenl consisls ol' a slighl change. 111. lile value. PI'. a ,ariablc. ,,hich. represenls an exogenous shock. This change is applied lo the ,ariahlc ol' the (ierlllan Share lnde., DAX. lnslead of assullling lhe value or lhe base :~·ar. \\hich represents lhe DAX. performance in that ycar of 28.55 %. it takes lhe value ora dillerent pcrli.innance. ::. In my model the following economic experiments are observed: DAX Performance of -28.55 % DAX Performance or O % DAX Performance or 18.55 % DAX Performance of 38.55 % DAX Performance of 100 %. Obviously. thcre could be conclucted a lot more econolllic e.,¡JCriments ,,ith this same moclel like altering labor or capital supply. changing any ol' the prices. etc .. which clepends on the focus of the analysis.. 5.6 Comparison of Equilibria. Colllparing the model output or the original equilibrium ancl the new equilibriurn. one can observe the impulse response ol' the economic endogenous variables confronling the shock. Figure 12 shows the change or relcvant endogenous variables in lhe ne,, equilibria in comparison to the original equilibriurn.. Comparing these valucs revea! some important aspects. Firsl of ali. the modcl limitations become clear when looking at R. TFA and TFF. The values or those variables do not change in the moclel, even though in real lite we woulcl expect sorne kincl ora change. for exarnple. when the German Share lndex hadan outstanding performance or 100% lo mention a drastic example. The limitation of the model lies in the savings of lhe institulions which can not be affected by the DAX. Therefore. no matter how good or bad the DAX is. ali institutions are limited to the amount of their savings of which they spencl some fixcd amount to the change in inventories and to the gross fixed capital formation. Further on. as 1am bda is fixed in the institutions' savings equation. too, there will only be spent lambda percent on flexible funds 22. The performance of thc DAX is takcn from thc oficial lndc., Wcbsitc. ( Da,-lndiccs. 201 3). 35.

(44) and one minus lambda percent on financia! assets. In order to trigger a change in total financia] assets and total flexible funds one has to change the amount of savings, it does not work the other way around.. Figure 12: Values of the Original Equilibrium and Results from the Experiments in Billion Euros Variable DAX Perf. R in o/o. Orii:;inal Eguilibirum 28,55% 100. Exp. 1 -28,55%. Exp. 2. 0%. 100. 100. Exp. 3. Exp.4. 18,55%. 38,55%. 100. 100. Exp.5 100%. 100. TFA. 62 558. 62,558. 62,558. 62,558. 62,558. 62,558. TFF. 43,386. 43,386. 43,386. 43,386. 43,386. 43,386. Sh (H). 18,19. 10,11. 14,15. 16,775. 19,605. 28,3. Sh(G). 32.64. 18,142. 25,391. 30,101. 35,179. 50,782. Sh (NFE). 48,78. 27,113. 37,946. 44,985. 52,575. 75,893. Sh (FE). 25,15. 13,979. 19,564. 23,194. 27, 106. 39, 129. De(ID. 49,86. 57,94. 53,9. 51 ,275. 48,445. 39,75. De(G). -3,65. 10,844. 3,595. -1 ,115. -6, 193. -21,796. De (NFE). 24,84. 46,507. 35,674. 28,635. 21,045. -2,273. De (FE). - 114,03 -102,859 -108,444 -112,073 -1 15,986 -128,009 Source:Own CGE Model in AX3. Second, the value of R which is the price for capital does not change either, even though in real life it probably would and initiate a whole chain of events affecting the product prices of the different sectors altering the consumption behavior of the household and the government. This is also dueto the savings equation which does not allow any reverse effects.. Third, the insights the model reveals are the ones which can be expected: When the DAX' performance diminishes, ali institutions buy less shares and deposit more funds into bank accounts and when the DAX' performance flourishes the effect is vice versa. What is interesting, though, is the magnitude of the effect. Whereas at a DAX increase of ten percent households raise their investment in shares by 1.42 billion Euro, financia] enterprises raise share acquisition by 1.96 billion Euro, the government by 2.54 billion Euro and non-financia) enterprises in fact by 3.8 billion Euro. Basically, this can be tracked back to each institutional parameter theta, which represents the influence the DAX has on their investment behavior in shares. So at any given change in the German Share Index, the households (altogether) are the ones who are the least and the non-financia) enterprises the ones who are the most affected. 36.

(45) 1 ina Ih. .. a11othcr outcomc o 1· th i:-, moLk I j:-, that \\ hL'n in t he -\ car 2009 thc German Sharc Indc:x. [);\ X \\ ou Id ha\ e liad a di lh:rent pcrl"ormancc. thc outcomc ami handling or thc !inane ia I and. cconomic crisis could havc bccn quite dillcrcnt. \'1aybc thc banking system would no! havc bccn that alTcctcd. or might hmc bccn alTcctcd earlier ami nen worse. This \vould be sub_jecl to l"urther imcstigation then taking into account the Di\X. inlluence on the banking system·s linancial stability.. 6. Résumé ami Conclusion. Taking into account the dcvclopmcnl or this paper and its content. FSAMs represen! an importan! analysis tool helping lo conduct complc:x economic investigations. Being ablc to include the cssential financia! par! or the economy is indispensable in nowadays· econorrnc anal\'ses.. Even though the constnrction of 1-'S;\Ms is quite an undertaking. thcy represen! ali importan! füms oran economy in an easy-to-rcad li.rnnat \Vhich takes into considcration the circular flow of funds. Once crcated. thcy can be used to easily compare different economies \vhich use the same matri:x presenlation. This could be a useful ovcrview for cconomic policy makers within the European Union or also worldwide making it a lot easier lo compare the clitkrenl econornies rapidly. Finally. FS;\Ms can be uscd to construcl CGEs which enable the analyst lo research about e:xogenous shocks ami the economy·s rcaction towards that shocks. In perspective lo the recen! and possibly t'uture (linancial) criscs those represen! an indispensable tool to investig.atc about the Euro ;\rea·s cconornic stability. In addition. CGEs can give sorne indication l"or future linancial strategics and strategic behavior for anv economy and especially for the Euro ;\rea.. Ohviously. the rnacroeconom1c model utilized in this paper still has a great potential to bccorne something more sophisticated. The equations can be elaborated in a way that takes into consideration more aspects. or the. real economy and more logical relations like the. reverse intluence the Di\X has on savings behavior. Ali institutions· savings could be reprcscnted by maximizing the institutions' utility taking into account future profits, ancl the sacrifice of current consumption. More precisely, expectations about the future could be included. In addition. any of the e:xogenous variables could be modeled to be endogenous to be ablc to analyse thcir behavior. More laxes could also be added. maybe an ecological ta:x for. 37.

(46) the seeondary sector ami its inllucnee. Elastieities eould he investigatecl and integrated to he ahlc to represen! even more equations through CES funetions including more elastieities. Maybe the institutions· spending of their savings eould also be a CFS IÍ.lnetion including the elastieity of substitution bet,veen shmes ami cleposits. Furthermore. there is probably a more accurate way or e:,;pressing the DAX · influence. too. l lence. there is a ,, orld or im estigat ion possibilities taking this FSAM ancl this CGE modelas basis.. In the eml. taking ali aspccts into consideration. 1 come to the conclusion that FSAMs and CCiLs represent an ingenious tool which shoulcl not be set aside. but used to eonduct im¡JOrtant ami indispensable economic equilibrium analyses. especially for (ierman) ami the Luropean Union. In an ultimate step there coulcl be constructed a large C(il·: taking into account ali economies of the Euro Arca revealing precise information about impaired equilibria in the Euro Area and possible advisable strategic behavior. This infonnation ,,oulcl be most valuable for economic policy makers. whether in the European Central Bank or in politics.. 38.