SAM Multiplier Analysis

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1 SM Multiplier alsis Jea-Christophe Dumot Social accoutig matri ad multiplier aalsis Priciples The Social ccoutig Matri (SM) is a comprehesive data sstem but it is ot a model as such. To come to this poit we must specif which variables are eogeous ad edogeous ad lik them through a set of mathematical relatios. This is eactl what is doe i a proper CGE model. The easiest maer to trasform a SM i some kid of a ecoomic model is to assume that all the relatios are of liear tpe ad that prices are fied (at least i the short ru). that case the SM ca be used directl to simulate the effects of shocks o some eogeous variables or accouts. This tpe of eercise is kow as SM multiplier aalsis ad ca be see as a etesio of put-output models. Depedig of which accout are set eogeous differet implicit closure hpothesis are possible. Usuall we will cosider three accouts as potetiall eogeous : the govermet, the rest of the world ad the capital accouts. Edogeous capital accout reflects some kid of iteral fleibilit ad edogeous Rest of the World accout assumes that trade is relativel free. s Rolad-Holst ad Sacho (995) report, SMs have bee used to stud (i) growth strategies i developig ecoomies (Patt ad Roud 985, Robiso -988), (ii) icome distributio ad redistributio (Patt ad Roe 977, delma ad Robiso 978, Rolad-Holst ad Sacho 99), (iii) fiscal policies (Whalle ad Hillaire 987) ad decompositio of activit multipliers that shed light o the circular flow of icome (Stoe 98, Patt ad Roud 979, Defour ad Thorbecke 984, Robiso ad Rolad-Holst 988). order to describe the mai priciples let us first cosider a simplified Schematic Social ccoutig Matri as show i Defour & Torbecke (984) : Epeses Receipts Edogeous accout. Factors. stitutios. Productive activities 4. Eogeous accouts Total. Factors T X Y. stitutios T T X Y. Productive activities T T X Y 4. Eogeous accouts L L L LX Y 4 Total Y Y Y Y 4

2 is defie as the matri of average epediture propesities. t ca be obtaied b dividig a particular elemet i a of the edogeous accouts b the total for the colum accout i which the elemet occurs. X represets the eogeous accouts ad Y the total of each edogeous accout. With those otatios it comes : ( ) a M The multiplier matri M a ca be decomposed, as Patt ad Roud (978) suggested, ito three ecoomicall meaigful additive (or multiplicative) compoets: (i) a trasfers matri that picks up the et multiplier effects iduced o a give set of accouts b eogeous trasfers accruig to the give set; (ii) a ope-loop matri that captures the cross effects betwee differet groups; ad (iii) a closed-loop matri detailig the multiplier effects of a eogeous iflow o a edogeous accout ad retur to the origial recipiet. First of all, let us ote Â as the diagoal bloc matri etract from the matri : the it comes : ( ) ( ) ( ) ( ) ( ) Multiplig both sides b ad substitutig for o the left had side ow gives: ( )( ) ( ) ( )( ) Similarl, multiplig both sides of the iitial equatio b ields : ( )( ) ( ) ( )( ) More geerall : ( ) ( ) k k t this stage, it is worth otig that the three steps decompositio that will fiall be retaied reflects the sequece of substitutio that correspods to oe complete ccle i the circular flow of icome withi the ecoom ad thus that it is ot a arbitrar choice.

3 f we ote M a (-Â) -, M a ad M a (- ) - it comes : MaM a M a M a But we ca also re-write Ma as : Ma ( M ) ( M ) M ( Ma ) a a a itial ectio LOMON et cotributio of trasfer multiplier LOMON O et cotributio of ope loop or cross-multiplier effects M M a LOOMOOO N a et cotributio of circular or closed-loop multiplier effect Mai uderlig hpothesis Several importat hpothesis are uderlig the SM multiplier aalsis. The stress the limits of this tpe of eercises. Especiall we must recall that : Prices are supposed to remai costat i all time. This meas that we implicitl assume that there eist a ecess capacit of productio. Productio techolog ad resource edowmets are give. s a result the aalsis is ecessaril a short term oe ad o damic of a kid ca be take ito accout. Epeditures propesities of edogeous accouts remai costat. the basic aalsis icome elasticities are uitar : the prevailig average epediture propesities i are assumed to appl to a icremetal ectio (M a ca be see as the matri of average epediture propesities). more realistic alterative is to specif a matri of margial epediture propesities correspodig to the observed icome ad epediture elasticities of the differet agets (M c ). verage ad margial propesities will ot geerall be equal for household demad but would correspod for productio (as far as there is o scale effect) ad for factor pamets if the value added price is set as a costat mark-up over labor costs per uit of output. Epressed i aother wa we would geerall specif : (i,) C ad C ε. least oe of the accout must be eogeous. The priciple of the aalsis itself implies that ol accouts as a whole ca be supposed eogeous (ad ot variables or cells). Povert iferece through multiplier aalsis Priciples We reproduce here a aalsis developed b Thorbecke ad Jug (996) that permits to use the multiplier results i order to ifer the effect of shocks o povert. For this purpose let us start with the basic equatios : d d d d d d d d d d d

4 thus d d d d d ( ) d ( ) ( ) d ( ) d d f we ote Ma the block i the matri Ma that liks households icome ad productive activities i order to test the effect of sectoral growth o povert (but the part to be cosidered depeds clearl of the questio addressed), the it come that Ma RD : R Now followig Kakwai (99) we have ( ) ( ) ( ) ( ) D ( ) P dp d l k P dθ k θ The distributioal effect of the eogeous shock is suppose to be egligible, so that the precedig formula simplifies to the first term. This meas that the distributio itra group is supposed to be costat. The elasticit of povert to mea icome (η) ca be computed as follow: PF(z) the povert head cout ratio (for other povert measuremet see Kakwai -99) z the povert lie f(.) the probabilit desit fuctio of icome L(.) the Loretz curve of the tpe : L()-a α (-) β Thus, assumig that the Loretz curve does ot shifts : P z L ( P) But we kow that L ( P) z f ( z) Because L ( P) z ad fiall P zf ( z) η P P The elasticit of povert to mea icome depeds positivel of the distace betwee the mea icome ad the povert lie. s a matter of fact wealthier group will have a higher elasticit. Followig the stadard result of the SM multiplier aalsis it comes that: k

5 thus d m i d dp d η m P Usig a additive decomposable aggregated povert measure (as the FGT idicator) it comes after few calculatios (see Thorbecke ad Jug 996) that : dp m d m s η m r s d q i i P i i with s i the povert share of household group i out of total povert q the sesitivit of the povert measure to the chage i icome (povert sesitivit effect) d the elemet (i,) of the matri D ad (i,) r m /d

6 Refereces delma ad Robiso (978), come distributio Polic i Developig coutries : a case stud of Korea, Oford Uiversit Press Defour ad Thorbecke (984), Structural path aalsis ad multiplier decompositio withi a social accoutig matri framework, The Ecoomic Joural, 94, pp. -6. Kakwai (99), Povert ad ecoomic growth with applicatio to Cote d voire, Review of come ad Wealth 9, pp. -9. Patt ad Roe (977), SM approach to modellig, Joural of polic modelig, pp. -7. Patt ad Roud (979), ccoutig ad fied price multiplier i a social accoutig matri, Ecoomic Joural 89, pp Patt ad Roud (985), Social accoutig : a basis for plaig., World Bak ad Oford Uiversit Press. Robiso (988), Multisectoral models of developig coutries :a surve., i H cheer ad T.N. Sriivasa Had book of developmet Ecoomics, North Hollad. Robiso ad Rolad-Holst (988), Macroecoomic Structure ad Computable Geeral Equilibrium Models, Joural of Polic Modelig, pp Rolad-Holst ad Sacho (99), Relative icome determiatio i the US: a Social ccoutig perspective, Review of come ad Wealth 8, pp.-7. Rolad-Holst ad Sacho (995), Modelig price i a SM Structure, The review of Ecoomics ad Statistics, pp Stoe (98), spects of ecoomic ad Social Modellig, 6, Librairie Druz, Geeva. Thorbecke ad Jug (996), multiplier decompositio method to aalse povert alleviatio, Joural of Developmet Ecoomics 48, pp Whalle ad Hillaire (987), microcosistet data set for Caada for use i regioal Geeral Equilibrium polic aalsis,, pp. 7-4.

Monopoly vs. Competition in Light of Extraction Norms. Abstract

Monopoly vs. Competition in Light of Extraction Norms. Abstract Moopoly vs. Competitio i Light of Extractio Norms By Arkadi Koziashvili, Shmuel Nitza ad Yossef Tobol Abstract This ote demostrates that whether the market is competitive or moopolistic eed ot be the result