*I appreciate data collaboration Graham Siddorn in the Inldand Revenue and supervision by Professor John Whalley *in process of construction of this model. $TITLE reformulation of P-Tax in GAMS SET J Asset / build buildings pmlon p&m long life pmsho p&m short life vehic vehicles dwell dwellings / K Industry / agric agriculture forestry fishing 1-3 extra extraction oil and gas 5 minin mining & quarrying coal stone clay metal ores and minerals 4 14 10 chemi chemicals coke nuclear fuels organin inorganic paints 6 20-29 metal metal and mineral products iron steel alum cementconcrete 11-13 15-19 30-34 37 engin engineering machine tractor tools equipment electronic 35 35 38-52 57 foodd food drink and tobacco meat grain sugar oil fat alcohol soft drink conf 58-70 othma other manufacturing motor ship aerospce hosiery textile leather53-56 71-90 power electricity gas and water 7-9 const construction 91 distr distribution hotels etc. wholesale retail hotel distribution 92-95 trans transport storage and communication rail sea air road transprt postal 96-102 finan financial sector bank ins real estate legal comput accnt advert R&D103-114 118 pubad public administration 115 educa education health and social work recreation personaldom services 116 117 119-122 house housing services 123 / L Finance / debt debt nshr new share rtearn retained Earning / M Owner / hhs households tex tax exempt ins insurance company / ; alias (j,jj), (k, kk), (l,ll), (m,mm); parameter F1(J,K) writing down allowance F2(J,K) first year capital allowance F3(J,K) cash grants (proportion of cost of an asset) G(J,K) rate of cash grant on purchase of an asset ASS(J,K) tax depreciation rate on db basis TD(J,K) 0-db 1-sl 2-soyd 3-from db to sl 4-from db to soyd AL(J,K) rate of tax depreciation for sl or soyd basis DEP(J,K) economic depreciation rate(exponential) CAP(J,K) proportion of net capital stock own(l,m) share of ownership by owner and source of finance RM(L,M) rate of personal income tax to owners of capital ; TABLE BASE(*,*,K) Basic parameters agric extra minin chemi metal engin foodd othma F1.build 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 F1.pmlon 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 F1.pmsho 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 F1.vehic 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 F1.dwell 0 0 0 0 0 0 0 0 F2.build 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 F2.pmlon 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 F2.pmsho 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 F2.vehic 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 F2.dwell 0 0 0 0 0 0 0 0 F3.build 0 0 0 0 0 0 0 0 F3.pmlon 0 0 0 0 0 0 0 0 F3.pmsho 0 0 0 0 0 0 0 0 F3.vehic 0 0 0 0 0 0 0 0 F3.dwell 0 0 0 0 0 0 0 0 G.build 0 0 0 0 0 0 0 0 G.pmlon 0 0 0 0 0 0 0 0 G.pmsho 0 0 0 0 0 0 0 0 G.vehic 0 0 0 0 0 0 0 0 G.dwell 0 0 0 0 0 0 0 0 TD.build 1 1 1 1 1 1 1 1 TD.pmlon 0 0 0 0 0 0 0 0 TD.pmsho 0 0 0 0 0 0 0 0 TD.vehic 0 0 0 0 0 0 0 0 TD.dwell 0 0 0 0 0 0 0 0 ASS.build 0 0 0 0 0 0 0 0 ASS.pmlon 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 ASS.pmsho 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 ASS.vehic 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 ASS.dwell 0 0 0 0 0 0 0 0 AL.build 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 AL.pmlon 0 0 0 0 0 0 0 0 AL.pmsho 0 0 0 0 0 0 0 0 AL.vehic 0 0 0 0 0 0 0 0 AL.dwell 0 0 0 0 0 0 0 0 DEP.build 0.064 0.101 0.052 0.026 0.025 0.025 0.025 0.025 DEP.pmlon 0.050 0.061 0.050 0.037 0.029 0.029 0.032 0.036 DEP.pmsho 0.153 0.181 0.131 0.079 0.072 0.083 0.078 0.090 DEP.vehic 0.159 0.2 0.2 0.2 0.2 0.2 0.2 0.214 DEP.dwell 0 0 0 0 0 0 0 0 CAP.build 0.9772 0.0031 0.0702 0.7036 0.8344 0.9756 0.8435 1.5313 CAP.pmlon 0.0000 0.1851 0.000 0.4180 0.1634 0.0464 0.0572 0.3796 CAP.pmsho 0.1866 1.2491 0.1164 1.0819 1.1701 1.1628 0.8555 2.1434 CAP.vehic 0.0700 0.0177 0.0044 0.0306 0.0436 0.0662 0.0413 0.0977 CAP.dwell 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 + power const distr trans finan pubad educa house F1.build 0.96 0.96 0.96 0.96 0.048 0.048 0.048 0.048 F1.pmlon 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 F1.pmsho 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 F1.vehic 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 F1.dwell 0 0 0 0 0 0 0 0 F2.build 0.04 0.04 0.04 0.04 0.002 0.002 0.002 0.002 F2.pmlon 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 F2.pmsho 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 F2.vehic 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 F2.dwell 0 0 0 0 0 0 0 0 F3.build 0 0 0 0 0 0 0 0 F3.pmlon 0 0 0 0 0 0 0 0 F3.pmsho 0 0 0 0 0 0 0 0 F3.vehic 0 0 0 0 0 0 0 0 F3.dwell 0 0 0 0 0 0 0 0 G.build 0 0 0 0 0 0 0 0 G.pmlon 0 0 0 0 0 0 0 0 G.pmsho 0 0 0 0 0 0 0 0 G.vehic 0 0 0 0 0 0 0 0 G.dwell 0 0 0 0 0 0 0 0 TD.build 1 1 1 1 1 1 1 1 TD.pmlon 0 0 0 0 0 0 0 0 TD.pmsho 0 0 0 0 0 0 0 0 TD.vehic 0 0 0 0 0 0 0 0 TD.dwell 0 0 0 0 0 0 0 0 ASS.build 0 0 0 0 0 0 0 0 ASS.pmlon 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 ASS.pmsho 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 ASS.vehic 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 ASS.dwell 0 0 0 0 0 0 0 0 AL.build 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 AL.pmlon 0 0 0 0 0 0 0 0 AL.pmsho 0 0 0 0 0 0 0 0 AL.vehic 0 0 0 0 0 0 0 0 AL.dwell 0 0 0 0 0 0 0 0 DEP.build 0.031 0.025 0.025 0.025 0.025 0.025 0.027 0.020 DEP.pmlon 0.042 0.050 0.040 0.066 0.040 0.040 0.04 0.020 DEP.pmsho 0.208 0.134 0.138 0.166 0.146 0.137 0.120 0.020 DEP.vehic 0.2 0.2 0.2 0.173 0.2 0.2 0.2 0.2 DEP.dwell 0 0 0 0 0 0 0 0.01 CAP.build 3.3923 0.2466 4.7905 3.1698 6.7226 3.1152 5.7320 0.000 CAP.pmlon 2.6261 0.0176 0.3979 1.3684 0.0604 0.1109 0.0000 0.000 CAP.pmsho 0.1496 0.1589 1.4610 0.8664 1.9487 0.4689 0.6362 0.000 CAP.vehic 0.0313 0.1069 0.4021 0.9618 1.1522 0.0658 0.0590 0.000 CAP.dwell 0 0 0 0 0 0 0 44.2552 ; TABLE BASE1(L,M) ownership of funds hhs tex ins debt 0.766 0.16 0.074 nshr 0.271 0.621 0.109 rtearn 0.271 0.621 0.109 ; TABLE BASE2(L,M) tax rates on interest and divident hhs tex ins debt 0.19 0.0 0.20 nshr 0.29 0.0 0.20 rtearn 0.29 0.0 0.20 ; parameter fin(l) sources of finance /debt 0.241 nshr 0.106 rtearn 0.651/ ZS(m) Marginal capital gains tax rate /hhs 0.30 tex 0.0 ins 0.240/ WP(m) personal wealth tax rate /hhs 0.0 tex 0.0 ins 0.0/ WC(J) tax rate on corporate wealth /build 0.019 pmlon 0.006 pmsho 0.006 vehic 0.000 dwell 0.000/; F1(J,K)=BASE("F1",J,K); F2(J,K)=BASE("F2",J,K); F3(J,K)=BASE("F3",J,K); G(J,K)=BASE("G",J,K); ASS(J,K)=BASE("ASS",J,K); TD(J,K)=BASE("TD",J,K); AL(J,K)=BASE("AL",J,K); DEP(J,K)=BASE("DEP",J,K); CAP(J,K)=BASE("CAP",J,K); own(l,m) =BASE1(L,M); RM(L,M)=BASE2(L,M); PARAMETER A(L,M,J,K) present value of depreciation allowance AD(L,M,J,K) depreciation allowances P(L,M,J,K) Pre-tax rate of return PAFO(J,K) Pre-tax rate of return averaged over all finance and owner groups S(L,M) Post tax real rate of return SAFO Post tax rate of return averaged over all finance and owner groups TW(L,M,J,K) Total tax wedge TR(L,M,J,K) Total tax rate CTW(L,M,J,K) Corporate tax wedge CTR(L,M,J,K) Corporate tax rate PTW(L,M,J,K) Personal tax wedge PTR(L,M,J,K) Personal tax rate TRAFO(J,K) Total tax rate averaged over all finance and owner groups CTRAFO(J,K) Corporate tax rate averaged over all finance and owner groups PTRAFO(J,K) Personal rate averaged over all finance and owner groups I nominal rate of interest BES 1-business expansion scheme 0-otherwise PIE inflation rate RFIX real rate of interest (fixed) TAU corporate tax rate THETA opportunity cost of retained earning sigma imputation rate BETA proportion of interest payments deductible from CT base D1 deductible proportion of WC from WC base INDEXC degree of indexation of capital gains INDEXNE degree of indexation of CAP GAIN OF NEW EQUITY INDEXRE degree of indexation of CAP GAIN OF RETAINED EARNINGS INDEXD degree of indexation of depreciation allowance INDEXS degree of indexation of in increases of value of inv INDEXI index of payments and receipts VLAMDA reciprocal of mean asset holding time RHO(L,M) discount rates (opportunity cost of capital) Z(L,M) effective rate of capital gains tax ; RFIX = 0.05; PIE = 0.02; I = RFIX + PIE; BES = 0; TAU = 0.33; sigma = 0.25; THETA = 1/(1-sigma); BETA = 1; D1 = 1; INDEXC = 1; INDEXNE = 1; INDEXRE = 1; INDEXI = 0; INDEXD = 0; INDEXS = 0; VLAMDA = 1/7; RHO(L,M) = 0; Z(L,M) = 0; *Post tax real rate of return S(L,M) = I*(1-RM("DEBT",M))-PIE-WP(M)+RM("DEBT",M)*PIE*INDEXI; *Effective rate of capital gains tax Z(L,M) = (ZS(M)*VLAMDA)/(VLAMDA+S(L,M)+PIE); *DISCOUNT RATES *debt RHO("DEBT",M) = I*(1-BETA*TAU) + BETA*TAU*PIE*INDEXI; *new equity RHO("NSHR",M) = ((1-RM("NSHR",M)*BES)/(THETA*(1-RM("NSHR",M))) *(I*(1-RM("NSHR",M))+PIE*(RM("NSHR",M)*INDEXI -(Z("NSHR",M)*INDEXNE)/(1-(RM("NSHR",M)*BES))))); *retained earnings RHO("RTEARN",M) = ((1-RM("RTEARN",M)*BES)/(1-Z("RTEARN",M))) *(I*(1-RM("RTEARN",M))+PIE*(RM("RTEARN",M)*INDEXI -(Z("RTEARN",M)*INDEXRE)/(1-(RM("RTEARN",M)*BES)))); *depreciation allowances *a) declining balance method AD(L,M,J,K)$(TD(J,K) EQ 0) =(TAU*ASS(J,K))/(ASS(J,K)+RHO(L,M)-PIE*INDEXD); *b) straight line method AD(L,M,J,K)$(TD(J,K) EQ 1) = (TAU*AL(J,K)*(1-EXP(-(RHO(L,M)-PIE*INDEXD)*(F1(J,K)/AL(J,K))))) /(F1(J,k)*(rho(l,m)-pie*INDEXD)); *c) sum of the years digit method set h /1*25/; parameter n(j,k), nn(h),f(j,k), ff(h); f(j,k) = 0; n(j,k)$al(j,k) = 1/al(j,k); ff(h) = 0; loop(h, f(j,k)$(f(j,k) gt 0) = n(j,k) -1; ff(h+1) = ff(h)+1 ); AD(L,M,J,K)$(TD(J,K) EQ 2) = (tau/(al(j,k)*25*(rho(l,m)-pie*indexd))) *(1-exp(-0.5*(rho(l,m)-pie*indexd))+sum(h$(card(h) le 25), (exp(-(ord(h)-0.5)*(rho(l,m)-pie*indexd)) - exp(-(ord(h)+0.5)*(rho(l,m)-pie*indexd))) *(1-al(j,k)*(ord(h)-0.5)))); A(L,M,J,K) = F1(J,K)*AD(L,M,J,K)+F2(J,K)*TAU +F3(J,K)*G(J,K); *pre-tax rate of return P(L,M,J,K) = (((1-A(L,M,J,K))*(rho(l,m)+dep(j,k)-pie) + (1-d1*tau)*wc(j)) / (1-tau)) - dep(j,k); *total tax wedge TW(L,M,J,K) = P(L,M,J,K) - S(L,M); *total tax rate TR(L,M,J,K) = TW(L,M,J,K)/P(L,M,J,K); *corporate tax wedge, for debt CTW("DEBT",M,J,K) = P("DEBT",M,J,K) - RFIX; *corporate tax wedge, for new equity CTW("NSHR",M,J,K) = P("NSHR",M,J,K) - (RHO("NSHR",M)*THETA - PIE); *corporate tax wedge, for retained earnings CTW("RTEARN",M,J,K) = P("RTEARN",M,J,K) - (RHO("RTEARN",M) - PIE); *personal tax wedge PTW(L,M,J,K) = TW(L,M,J,K) - CTW(L,M,J,K); *corporate tax rate CTR(L,M,J,K) = CTW(L,M,J,K)/P(L,M,J,K); *personal tax rate PTR(L,M,J,K) = PTW(L,M,J,K)/(P(L,M,J,K)-CTW(L,M,J,K)); *total tax rate averaged over all finance/owner groups TRAFO(J,K) = SUM(L, SUM(M, TR(L,M,J,K) * OWN(L,M) * FIN(L))); *corporate tax rate averaged over all finance/owner groups CTRAFO(J,K) = SUM(L, SUM(M, CTR(L,M,J,K) * OWN(L,M) * FIN(L))); *personal tax rate averaged over all finance/owner groups PTRAFO(J,K) = SUM(L, SUM(M, PTR(L,M,J,K) * OWN(L,M) * FIN(L))); *pre tax rate of return personal averaged over all finance/owner groups PAFO(J,K) = SUM(L, SUM(M, P(L,M,J,K) * OWN(L,M) * FIN(L))); *post tax rate of return averaged over all finance/owner groups SAFO = SUM(L, SUM(M, S(L,M) * OWN(L,M) * FIN(L))); *Set housing tax rates equal to zero TRAFO(J,"HOUSE")=0; Trafo ("dwell",k)=0; DISPLAY TRAFO;