Computable General Equilibrium Analysis: Opening a Black Box

Transcription

1 Dscusson Paer No Comutable General Equlbrum Analss: Oenng a Black Box Chrstoh Böhrnger, Thomas F. Rutherford and Wolfgang Wegard

2 Dscusson Paer No Comutable General Equlbrum Analss: Oenng a Black Box Chrstoh Böhrnger, Thomas F. Rutherford and Wolfgang Wegard Donload ths ZEW Dscusson Paer from our ft server: ft://ft.ze.de/ub/ze-docs/d/d0356.df De Dscusson Paers denen ener möglchst schnellen Verbretung von neueren Forschungsarbeten des ZEW. De Beträge legen n allenger Verantortung der Autoren und stellen ncht notendgerese de Menung des ZEW dar. Dscusson Paers are ntended to make results of ZEW research romtl avalable to other economsts n order to encourage dscusson and suggestons for revsons. The authors are solel resonsble for the contents hch do not necessarl reresent the onon of the ZEW.

3 Non-Techncal Summar Quanttatve smulatons to evaluate alternatve olc measures la a ke role n aled economc research. Numercal models accommodate the sstematc analss of economc roblems here analtcal solutons are ether not avalable or do not rovde adequate nformaton. Comared to analtcal models, the numercal aroach facltates the analss of comlex economc nteractons and the mact assessment of structural olc changes. Among numercal methods, comutable general equlbrum (CGE) models are del emloed b varous natonal and nternatonal organzatons (EU Commsson, IMF, World Bank, OECD, etc.) for economc olc analss at the sector-level as ell as the econom-de level. CGE analss consttutes a oerful scentfc method for the comrehensve ex-ante smulaton of adjustment effects nduced b exogenous olc nterference. The man vrtue of the CGE aroach s ts comrehensve mcro-consstent reresentaton of rce-deendent market nteractons. Hoever, the barrers to enterng the feld of CGE analss for students and rofessonals are commonl erceved as rather rohbtve. Wthout detaled rogrammng knoledge, the CGE aroach s doomed to reman a black box for non-modelers. The man objectve of ths artcle s to loer the barrers to CGE analss for to target grous. The frst grou conssts of economsts that ant to actvel enter the feld of CGE analss. We la out the most recent develoments n CGE model mlementaton for ths grou: The MCP aroach, combned th the calbrated share form, rovdes a comrehensve frameork to mlement equlbrum roblems n a transarent and effcent a. The second grou ncludes economsts that ant to refran from rogrammng but are nterested n CGE analss as a tool kt. For ths grou, e resent an nteractve nterface that offers convenent access to CGE analss. Wthout techncal rogrammng sklls, the can use the ntutve and smle Wndos-based nterface to exlore the determnants of olc effects. Interactve learnng-b-dong then nvolves the secfcaton of addtonal olc smulaton, the ex-ante economc reasonng on the otental effects, and the ex-ost cross-check th the results rovded b the comuter smulatons..

4 Comutable General Equlbrum Analss: Oenng a Black Box Chrstoh Böhrnger boehrnger@ze.de ZEW Mannhem Thomas Rutherford rutherford@colorado.edu Unverst of Colorado at Boulder Wolfgang Wegard olfgang.egard@.un-regensburg.de Unverst of Regensburg ABSTRACT Comutable general equlbrum models la an mortant role n aled economc research. These models accommodate the mcro-consstent sstematc analss of comlex economc roblems here analtcal solutons are ether not avalable or do not rovde adequate nformaton. Hoever, the comutatonal aroach to economc olc analss also has severe shortcomngs of ts on. In general, scentfc ublcatons nclude a comlete lstng of nether the algebrac model underlng the numercal smulaton nor the data used to calbrate model arameters. Even f the model algebra and the data ere full lad out, relcaton of results ould stll requre secalzed rogrammng sklls. As a consequence, CGE analses are often erceved as a black box to non-exert readers. Ths artcle ams at loerng the barrers to numercal CGE analss along to lnes. Frst, e rovde a comact ntroducton to recent methods of CGE model mlementaton that ma substantall ease entr for otental modelers. Second, and equall mortant, e llustrate the non-techncal access to CGE analss b means of a user-frendl nterface that allos non-modelers to test and develo ther economc ntuton on general equlbrum nteractons thout rogrammng sklls.

5 INTRODUCTION Quanttatve smulatons to evaluate alternatve olc measures la a ke role n aled economc research. Numercal models accommodate the sstematc analss of economc roblems here analtcal solutons are ether not avalable or do not rovde adequate nformaton. Comared to analtcal models, the numercal aroach facltates the analss of comlex economc nteractons and the mact assessment of structural olc changes. Among numercal methods, comutable general equlbrum (CGE) models are del emloed b varous natonal and nternatonal organzatons (EU Commsson, IMF, World Bank, OECD, etc.) for economc olc analss at the sector-level as ell as the econom-de level. The man vrtue of the CGE aroach s ts mcro-consstent reresentaton of rce-deendent market nteractons. The smultaneous exlanaton of the orgn and sendng of the agents' ncome makes t ossble to address both econom-de effcenc as ell as dstrbutonal macts of olc nterference. Ths has made CGE models a standard tool for the quanttatve analss of olc nterference n man domans ncludng fscal olc, trade olc, and envronmental olc. 2 The comutatonal aroach to olc analss, hoever, has also shortcomngs of ts on. In general, scentfc ublcatons nclude a comlete lstng nether of the algebrac model underlng the numercal smulaton nor the data used to calbrate model arameters. Even f the model algebra and the data ere full lad out, relcaton of results or senstvt analss ould stll requre secalzed rogrammng sklls. 3 As a consequence, CGE analses s often erceved as a black box to non-exert readers. All the can do s to... delver summar grunts of belef or dsbelef but fnd t dffcult to artculate reasons n a dsclned a (McCloske 983,. 502). The objectve of ths ntroductor aer s to loer the barrers of entr to CGE analss for graduate students and rofessonals that are nterested n ths method for aled olc analss. We rovde a comact ntroducton to recent methods of CGE model mlementaton that hghl facltate the accessblt of CGE analss for otental modelers. Furthermore, e llustrate the non-techncal The mortance of CGE modelng n academc research s reflected b the fact, that snce 99 - the Journal of Economc Lterature has lsted a searate classfcaton number for ths te of analss (D 58: Comutable and other Aled General Equlbrum Models). 2 For surve artcles see e.g. Conrad (999, 200), Bergman (990), Gottfred et al. (990), Borges (986), Kehoe and Kehoe (994), Kleer et al. (995), Perera and Shoven (988), Shoven and Whalle (984, 992), Fehr and Wegard (996), Pggot and Whalle (985, 99), Bhattachara (996), Gunnng and Kezer (995). 3 Obvousl, errors n the numercal model secfcaton can never be ruled out. In fact, Deald, Thursb and Anderson (986) conclude from ther famous The Journal of Mone, Credt and Bankng Project that nadvertent errors n ublshed emrcal artcles are a commonlace, rather than a rare, occurrence. (. 587).

6 access to CGE analss b means of a user-frendl nterface, allong non-modelers to test and develo ther economc ntuton on general equlbrum nteractons thout rogrammng sklls. The remander of ths aer s organzed as follos. In secton 2, e brefl descrbe the basc rocedure n CGE analss. In secton 3, e la out the mlementaton of the common textbook 2x2x-model usng the mxed comlementart aroach n hch the equlbrum roblem s formulated as a sstem of eak nequaltes and comlementar slackness condtons (beteen equlbrum varables and equlbrum condtons). In secton 4, e ntroduce a generc vsual nterface for erformng quanttatve equlbrum analses thout techncal rogrammng sklls. In secton 5, e rovde olc-relevant examles of actvt analss and exlct rce restrctons as ell as quantt constrants to demonstrate the advantages of the mxed comlementart aroach n general equlbrum analss. In secton 6, e extend the stlzed 2x2x-model to a large-scale mult-regon, mult-sector model of global trade and energ use n order to nvestgate the economc macts of nternatonal clmate rotecton olces. Fnall, e conclude. 2 BASIC APPROACH CGE models buld uon general equlbrum theor that combnes behavoral assumtons on ratonal economc agents th the analss of equlbrum condtons. Analtcall, the economc mlcatons of olc nterference could be studed n a comaratve-statc frameork: One derves the total dfferentals of the market equlbrum condtons and solves ths sstem of equatons for the relatve changes n the varables of nterest. Ths s the normal rocedure emloed n the theoretcal lterature. Although theoretcal analss rovdes mortant qualtatve nsghts, ts contrbuton to actual olc analss remans lmted. Ths s because theoretcal models are hghl stlzed to kee analtcal tractablt. As soon as certan real-orld comlextes are taken nto account, e.g. a more detaled roducton structure, analtcal solutons are no longer avalable and numercal soluton methods are requred. Furthermore, analtcal models can onl be aled to margnal analss (gven non-lnear relatonshs), hereas numercal models are suted for the nvestgaton of structural changes. Fgure summarzes the fve man stes nvolved n constructng and usng CGE models. Intall, the olc ssue must be carefull studed to decde on the arorate model desgn as ell as the requred data. The second ste nvolves the use of economc theor (at best, the draft of a smle analtcal maquette model) n order to la out ke economc mechansms that drve the results n the more comlex numercal model. Data ork, model formulaton, and mlementaton then delvers the frameork for numercal olc analss. Ths ste also nvolves the set-u of alternatve olc nstruments and strateges that nduce changes vs-à-vs the reference stuaton (scenaro defnton). In determnng results of olc smulaton, the choce and arameterzaton of functonal forms are crucal. 2

7 Fgure : Stes n comutable general equlbrum analss. Issue Polc background 2. Theor Theoretcal foundaton of ke mechansms (e.g. analtcal maquette of numercal model) 3. Model formulaton Constructon of consstent Benchmark Equlbrum Data Set Formulaton and mlementaton of numercal model (ncl. choce of functonal forms); scenaro defnton Data: nut-outut tables, natonal accounts, tax data, ncome and exendture data Choce of exogenous elastctes (lterature surve) 4. Comuter smulatons Calbraton: Calculaton of arameter values from benchmark data Smulatons: Calculaton of ne olc equlbrum (counterfactual) Relcaton Check successful? Yes No Senstvt analss 5. Interretaton Reortng and economc nterretaton of results Robust results? Yes Conclusons and olc recommendatons No The rocedure most commonl used to select arameter values s knon as calbraton (see Mansur and Whalle 984). Calbraton of the free arameters of functonal forms requres a consstent one ear s data (or a sngle observaton reresented as an average over a number of ears), together th exogenous elastctes that are usuall taken from lterature surves. The calbraton s a determnstc rocedure and does not allo for a statstcal test of the model secfcaton. The one consstenc check that must necessarl hold before one can roceed th olc analss s the relcaton of the ntal benchmark: the calbrated model must be caable of generatng the base-ear (benchmark) equlbrum as a model soluton thout comutatonal ork. Wthn the olc smulatons, sngle arameters or exogenous varables are changed and a ne (counterfactual) equlbrum s comuted. Comarson of the counterfactual and the benchmark equlbrum then rovdes nformaton on the olc-nduced changes of economc varables such as emloment, roducton, consumton, relatve rces, etc. Fnall, the model results must be nterreted based on sound economc theor. Due to the relance on exogenous elastct values and a sngle base-ear observaton, comrehensve senstvt analss on ke elastctes (and ossbl 3

8 alternatve assumtons on economc ncentves) should be erformed before concrete olc recommendatons are derved. The essence of CGE economcs s the combnaton of general equlbrum theor th a consstent data set (most commonl from Natonal Accounts) n order to derve olc nsghts. 3 MODEL IMPLEMENTATION AND ANALYSIS At frst glance, the requrements of numercal equlbrum analss aear rohbtve. Shoven and Whalle, to romnent rotagonsts of the CGE aroach, bemoan the necesst for modelers to be a jack-of-all-trades: Modelers must kno general equlbrum theor so that ther models have a sound theoretcal bass; the must kno ho to solve ther models; the need to be able to rogram; the must understand the olc ssues on hch the ork; the have to kno about data sources and all ther assocated roblems; and the have to be conversant th relevant lterature, esecall that on elastctes (Shoven and Whalle 984,.047). Hoever, there has been substantal rogress durng the last to decades, artcularl n the felds of numercal soluton technques and hgher-level rogrammng languages, hch has dramatcall loered the barrers to enter numercal modelng. Comared to the old das, there s no longer a need for modelers to rogram ther on talored soluton algorthms, snce a varet of oerful commercal soluton ackages for nonlnear equaton sstems no exst (e.g. CONOPT (Drud 985), MINOS (Murtagh and Saunders 995) or PATH (Drkse and Ferrs 995). Moreover, hgher-level rogrammng languages (such as MATLAB (997), MATHEMATICA (Wolfram 996), AMPL (Fourer, Ga, and Kernghan, 987) or GAMS (Brooke, Kendrck, and Meeraus 988)) have been develoed that greatl facltate the translaton of an algebrac model formulaton nto a comuter-readable rogram. 4 The tradtonal aroach n CGE analss s to cast equlbrum condtons as a sstem of equatons here functonal forms are calbrated to benchmark data n the so-called coeffcent form. Ths aroach, hoever, mles restrctons th resect to the reresentaton of otentall mortant economc features and can be rather mess concernng the calbraton of the free arameters of functonal forms. To avod such drabacks, our aroach emlos the mxed comlementart frameork to secf an economc equlbrum and the so-called calbrated share form for functon calbraton. 4 For our comuter mlementaton e emlo GAMS (Generalzed Algebrac Modelng Sstem), hose fundamental strength les n the ease th hch mathematcall-defned models can be formulated and solved. GAMS tself does not rovde model solutons but delegates ths task to subsstems,.e. secalzed algorthms for artcular classes of mathematcal rograms. 4

9 In secton 3., e secf an economc equlbrum as a mxed comlementart roblem (MCP) here equlbrum condtons are formulated as eak nequaltes and condtons of comlementar slackness beteen varables and equlbrum condtons. Comared to the tradtonal equaton-based format, the MCP aroach easl accommodates the exlct treatment of actvt analss (.e. the ossblt of regme shfts beteen alternatve actvtes) as ell as dscrete rce and quantt constrants that ma become bndng n equlbrum or not. In secton 3.2, e resent common functonal forms n CGE analss to characterze technologes and references. Aart from the tradtonal coeffcent form, e ntroduce the equvalent calbrated share form hch substantall reduces the efforts as ell as sources of errors n the determnaton of free functon arameters. In secton 3.3, e ntroduce the standard textbook 2x2x-model and resent an llustratve olc smulaton. 3. General Equlbrum as a Mxed Comlementart Problem (MCP) An economc equlbrum can be cast as a mxed comlementart roblem. For llustraton, e consder a standard Arro-Debreu econom th n commodtes (ncl. factors), m sectors and h households (ncl. government). 5 The endogenous varables of the Arro-Debreu econom can be classfed nto 3 categores (Mathesen 985): := a non-negatve n-vector n rces for all goods and factors (I ={,...,n}), := a non-negatve m-vector for actvt levels of CRTS-roducton sectors (J={,...,M}), and M:= a non-negatve k-vector n ncomes (H ={,...,k}). In equlbrum the varables must fulfll three classes of condtons: zero roft of CRTS-roducers (exhauston-of-roduct constrant) - ( ) C ( ) R ( ) 0 j j j j here (usng Hotellng's Lemma): ( ) j the unt roft functon, j Cj( ) mn f j() the unt costs functon, and j Rj( ) max g j() the unt revenue functon. 5 The comettve settng can be easl adjusted th rce restrctons and quantt constrants to reflect market merfectons. 5

10 The functons f j and g j characterze feasble nut- and outut-combnatons of roducton n sector j. market clearance for all goods and factors: here: j ( ) j bh dh j h h b h the ntal endoment of household h th commodt, and dh(, Mh) argmax Uh ( x) x Mh the demand for good b household h maxmzng utlt. 6 budget constrants for households: h b M d h h h h h For common utlt functons (non-sataton), households are alas on ther budget lne,.e. b M d, and Walras la holds. 7 h h h h h Usng Walras la, aggregaton of market clearance condtons and zero roft condtons eld: j j( ) 0; j j( ) 0 j j and j ( ) j bh dh 0 j h h as ell as:. M ( b d ) 0 h h h h h h Thus, economc equlbrum features comlementart beteen equlbrum varables and equlbrum condtons: ostve market rces ml market clearance otherse commodtes are n excess sul and the resectve rces fall to zero. Actvtes ll be oerated as long as the break even - negatve revenues ml the shutdon of the resectve roducton actvtes. 6 U h denotes the utlt functon of household h. 7 Due to lnear-homogenet of roft functons and homogenet of demand functons of degree zero n rces, the economc equlbrum onl determnes relatve rces. 6

11 The MCP (Cottle and Pang 992, Rutherford 995): n Gven : f : R R Fnd : z R T st..: f( z) 0, z0, z f( z) 0 n n (MCP) corresonds to the roblem of fndng an economc equlbrum for z = [,, M] and f(z) = [ ( ), ( b d ) j, equlbrum condtons. ], thereb statng comlementart beteen varables and h h h h In ths context, the term mxed comlementart roblem (MCP) s straghtforard: mxed ndcates that the mathematcal rogram ncludes equaltes as ell as nequaltes; comlementart refers to comlementar slackness beteen sstem varables and sstem condtons. The above formulaton of an economc equlbrum s ver comact: Varables such as consumton and factor demand or commodt sules are treated mlctl, hch reduces comutaton tme sgnfcantl for hgher-dmensonal models. 3.2 Functonal Forms n Calbrated Share Form Numercal calculaton of an economc equlbrum requres the choce of concrete functonal forms for roducton ossbltes and references. In aled modelng, combnatons of Leontef-, Cobb- Douglas-, or constant-elastct-of-substtuton (CES) functons are most common. Such functons have certan mathematcal roertes (regulart) that ease the numercal analss consderabl, but are stll flexble enough to allo for an arorate reresentaton of economc behavor. Tables and 2 rovde an overve of standard functonal forms n conventonal coeffcent form and (less common) calbrated share form. The follong notatons are adoted th resect to functonal forms characterzng roducton: dstrbuton arameter for nut, scale arameter, substtuton arameter, substtuton elastct ( : ), x benchmark demand for nut, benchmark rce for nut, 7

12 f x, benchmark outut level C c benchmark outut rce, benchmark cost, benchmark unt cost, and x benchmark value share of nut. Equvalent notatons for functonal forms characterzng fnal demand nclude: d benchmark consumton demand for good, benchmark consumer rce for good,, U benchmark utlt level U gd E e M benchmark exendture, benchmark unt exendture, benchmark ncome, and d benchmark value share of consumton demand. M The so-called calbrated share form eases the calculaton of free arameters of functonal forms, because there s no need to nvert demand functons (as oosed to the coeffcent form aroach). Equvalence of the coeffcent form and the calbrated share form s straghtforard. For examle, let us consder CES roducton functons. Usng the nverted factor demand functons n coeffcent form e obtan: / / x, / / x. Substtutng ths exresson thn the coeffcent forms for roducton, cost and demand functons, e can derve the equvalent calbrated share forms: for the CES roducton functon: / / x = x x x =, x / 8

13 9 Table : Functonal forms n roducton Coeffcent Form Calbrated Share Form Leontef mn x = mn x = x CD = x x = x Producton functon CES / = x / x = x Leontef C C C CD C C C Cost functon CES / C / C C Leontef x x x CD x c x x c Demand functon CES x c x x c

14 0 Table 2: Functonal forms n consumton Coeffcent Form Calbrated Share Form Leontef mn d U mn d U=U d CD U d d U U d Utlt functon CES / / U d / d U=U d Leontef E U U E E U CD E U U E E U Exendture functon CES / E U / U E E U Leontef M d j j j j j j M d d M CD M d M d d M Demand functon CES M e d e M e d d M e

15 for the CES cost functon: / / C x / / C and for the CES demand functon: / x x C C C C x x C 3.3 Numercal Analss for the 2x2x-Model We ant to nvestgate the mlcatons of changes n the factor endoments for a stlzed equlbrum model th to factors of roducton, to goods (or lkese roducton sectors), and one household (see e.g. Boada and Wldasn 984 for a comrehensve analtcal treatment). Ths smle textbook 2x2x-model features the basc structure for all hgher dmensonal, more comlex models that are tcall used n CGE analss of olc nterference. For numercal analss, e must frst calbrate the model to a gven reference stuaton (the benchmark equlbrum),.e. the economc stuaton before the varaton of the factor endoment. The calbraton of functonal forms requres benchmark data that coml to general equlbrum condtons. As to our smle comettve 2x2x-Arro-Debreu econom, ths means that () sul equals demand of goods and factors, () no sector earns a ostve roft, and () the reresentatve household satsfes hs budget constrant. Table 3 rovdes stlzed data for our benchmark equlbrum n terms of a socal accountng matrx (Kng 985). The uer secton resents the benchmark rces, the loer secton reorts the benchmark quanttes. In general, data consstenc of a socal accountng matrx requres that the sums of each of the ros and columns equal zero. Whereas market equlbrum condtons are assocated th the ros, the columns cature the zero-roft condton for roducton sectors as ell as the

16 ncome balance for the aggregate household sector. Table 3: Prces and quanttes n the benchmark equlbrum Prces = 2 = r = = Socal Accountng Matrx Y Y2 Household Y Y K L Benchmark data are tcall delvered n value terms,.e. the are roducts of rces and quanttes. In order to obtan searate rce and quantt observatons, the common rocedure s to choose unts for goods and factors so that the have a rce of unt (net of all taxes and subsdes) n the benchmark equlbrum. Then, the value terms sml corresond to the hscal quanttes. Benchmark rces and quanttes, together th exogenous (substtuton) elastctes, determne the free arameters of the functonal forms lad out n Tables and 2. For our llustratve 2x2x-model, e assume Cobb-Douglas functons n roducton and consumton for hch the elastct of substtuton s equal to one b defnton. We are the no able to rte don the equlbrum condtons as lsted n Table 4. For our smle examle, one can easl do a relcaton check of the benchmark equlbrum condtons b nsertng the ntal rces and quanttes. Next, e nvestgate the mlcatons of a varaton n factor endoments. We assume that the ntal labor endoment s ncreased b L 5 from L 30 to L 35. In man cases, the transarent nterretaton of general equlbrum effects s romoted b a decomoston nto artal equlbrum effects. Here, e make use of a smle decomoston to exlan the outcome of the factor varaton. In a frst ste, e kee commodt rces constant and nvestgate ho consumton and roducton decsons of frms change n resonse to the ncreased factor endoment. The artal equlbrum rce assumton nvolves goods markets that are no longer n equlbrum. We can then derve the changes n (relatve) rces of goods and factors that are necessar to assure market clearance. For constant good rces, the Rbcznsk theorem (Rbcznsk 955) exlans the adjustment on the roducton sde 2

17 of the econom: If relatve commodt rces are constant and f both commodtes contnue to be roduced, an ncrease n the sul of a factor ll lead to an ncrease n the outut of the commodt usng that factor ntensvel and a decrease n the outut of the other commodt (Markusen et al. 995,. 9). In our concrete numercal examle, roducton of good s labor ntensve and, thus, e can redct an ncrease n the roducton of good for ncreased labor sul, hereas roducton of good 2 should decrease. In the artal equlbrum settng, e observe an excess demand on the market for good 2 and an excess sul on the market for good. For general equlbrum market clearance, relatve rces / 2 must to reduce roducton of good and ncrease roducton of good 2. The assocated sectoral shft n factor use leads to an excess sul of labor and an excess demand of catal. Consequentl, the factor rce rato / r declnes as comared to the benchmark equlbrum. Table 4: MCP formulaton of the 2x2x-econom n calbrated share form Equlbrum condtons Varables Comlementart condtons Zero roft Actvt varable r r r Market clearance Prce varables M 0 M r 2 r 2 2 Budget constrant 0 r M M r r 0 r r Income varable 30 50r M 0 M 30 50r M M 0 Table 5 summarzes the concrete numercal results for the benchmark equlbrum (column: Benchmark), the artal equlbrum calculaton th ncreased labor endoment holdng goods rces constant at the benchmark level (column: RYBCZINSKI), and the general equlbrum counterfactual (column: Counterfactual) th flexble rces. In fact, the numercal results confrm the basc theoretcal reasonng. 3

18 Table 5: Effects of ncreased labor endoment ( L 5) Varable Benchmark RYBCZINSKI Counterfactual Prces r Quanttes L L L M For more comlex hgher-dmensonal settngs, hoever, there s n man cases no clear theoretcal exlanaton. Wthout numercal smulatons, t ould not be ossble to obtan (ossbl rather general) nsghts. On the other hand, numercal results must alas be nterreted on the bass of sound theor. In ths context, the reader should be aare of some fundamental restrctons th resect to numercal olc analss. One never knos f the concrete results are correct. It must be assumed, of course, that the numercal soluton algorthm orks roerl, but a rong model -.e. rongl secfed th resect to the underlng economcs - ma have been solved. A small rogrammng error that can easl cree n s enough to cause such a dlemma. One ma relax ths roblem, hoever, n the follong a: as an ntal consstenc check, those olc measures should be smulated frst, here the qualtatve results - based on rgorous theoretcal analss - are alread knon (see e.g. RYBCZINSKI scenaro). If the smulaton model roduces dfferent results, one must assume that t s mssecfed. Otherse, one can roceed th the analss of olc measures, here results are oen n theor. Yet, one can stll not be sure that the numercal solutons are correct. Therefore, t s alas mortant that numercal results are convncngl exlaned n economc terms. 4 USER INTERFACE Deste the rogress on the felds of commercal soluton methods and hgher-level rogrammng language, CGE analss stll requres substantal rogrammng sklls to erform adequate quanttatve 4

19 economc research. Thus, economsts ho are not llng to send (suffcent) tme on rogrammng technques ma stll reject CGE analss as a black box. More recentl, hoever, several softare ackages have been develoed that allo modelers to set u vsual nterfaces qute easl n order to communcate results to non-modelers. In our ve, such nterfaces can greatl enhance the accessblt of CGE analss snce t ermts ersons ho are unfamlar th rogrammng to erform scenaro analss, roduce tables and fgures, and transfer model results nto sreadsheets and reorts. For demonstraton uroses, e make use of the ublc doman GAMSsm tool (Rutherford 200), hch rovdes an ntutve and smle Wndos-based nterface to economc models (or other mathematcal rograms) mlemented th GAMS. 8 The reader can donload the talor-made nterface from ft://ft.ze.de/ub/ze-docs/dv/m2x2x.exe to reroduce results and stud addtonal olc scenaros for the basc 2x2x-econom and ts varants (descrbed n secton 6). The executon of M2x2x.exe nstalls these models n a drector of choce on the comuter. When startng GAMSsm for the frst tme (from Wndos/Start/Programs/... or va a Wndos-Icon), a scenaro-fle (*.scn) must be loaded va the menu tem FILE OPEN (here M2x2x.scn ). Fgure 2: Loadng of scenaro fle Uon nvocaton of the.scn-fle, the nut and outut arameters that have been re-secfed b the modeler aear on the screen. In our case, the nut otons nclude the assgnment of ntal factor endoments to labour and catal as ell as the choce beteen the artal equlbrum settng (for 8 Detaled nstructon on GAMSsm can donloaded from htt://debreu.colorado.edu. 5

20 erformng the Rbcznsk calculaton) and the general equlbrum settng (to obtan the fnal market equlbrum); the outut s condensed n an aggregate summar reort of rces and quanttes. 9 Fgure 3: Defntons of nut and outut arameters A mouse-clck on OK oens the scenaro-fle shong an ndex of revousl solved cases. In addton to the case dentfers, the Case Index table reorts the resectve scenaro values of the nut varables and the soluton status of the case ( Solved, Unsolved, or Arox. ). In our alcaton, the Benchmark scenaro, hch has alread been re-calculated to assure the relcaton check, s lsted th ts nut secfcaton. 0 Fgure 4: Case Index th re-solved scenaros 9 The user can recall the model defntons of nut and outut arameters va VIEW DEFINITIONS at an tme. 0 A default scenaro hch reflects the modeler s default arameterzaton ll alas be generated. 6

21 Va CASE NEW, ne scenaros can be defned. Ths requres a case dentfer and the selecton of case-secfc nut values. For concreteness, f e ant to add the case RYBCZINSKI, e ma frst adot the ntal nut arameterzaton from the Benchmark scenaro. Fgure 5: Defnton of ne case (scenaro) After confrmng th OK, e can then select the nut arameters to be changed. For the RYBCZINSKI case, e set the ntal labor endoment (LBAR) to 35 and choose the artal equlbrum settng th fxed outut rces (MODUS PEM ). Fgure 6: Secfcaton of nut otons 7