$title Illustrative MPSGE model based on a social accounting matrix $ontext > I am formulating a small open economy model to tourism policy in > a small open economy. One obvious issue could be an exogenous shock > to aggregate tourism demand. How is this done? I would use a representative tourism household that demands aggregate tourism final consumption (produced by all domestic sectors) being endowed with "foreign exhange". In order to be concrete I illustrate here with a modified version of the SOE model from http://debreu.colorado.edu/lib/soe.htm. A representative tourist in the SOE model is endowed with foreign exchange -- the "global vacation budget". For concreteness, suppose that this budget denominated in US$ which may be spent at Coolangatta or Ocean City. In the base period some fraction of that budget is spent on tourist visits to the Coolangatta while the rest of the budget is spent elsewhere in the world (Ocean City). The subutility function for vacation happiness is: U(T,Z) = ( alpha T^rho + (1-alpha) Z^rho)^(1/rho) where T represents vacation trips to Coolongatta, the resort town in our SOE, and Z represents tourism visits elsewhere (Ocean City). The foreign tourist solves: max U(T,Z) s.t. Pt T + e Z = e B where B is the tourist's budget in foreign currency, and e is the "real exchange rate" (the domestic price of foreign exchange, A$/US$). Note that the price on Z remains fixed relative to the tourist budget, embodying the SOE assumption that the cost of vacations in Ocean City remain constant even with a decline in tourism expenditures. A scenario which reduces B would reduce T and Z preportionally if Pt/e were constant. However, if the small open economy suffers a deterioration in the exchange rate as a result of a decline in tourism exports, then Pt/e will decline and the foreign tourism demand will fall less than proportionally with B. The actually response depends on the elasticity of substitution between T and Z, characterized here by rho in U(T,Z) (sigma = 1/(1-rho); rho = 1 - 1/sigma) $offtext set tb Percent decline in global tourism expenditure /0*10/, sg Alternative elasticities of substitution /0*3/; set i SAM row and column indices /1*14/, s Sectors / agr Agriculture, ind Industry, ser Services /, f Primary factors / L Labor, N Land, K Capital/, h Households / rural, urban/ * Goods and sectors are identical: alias (s,g,gg), (i,j); set mapa(i,s) Mapping from SAM to activities /1.agr, 2.ind, 3.ser/, mapc(i,g) Mapping from SAM to commodities /4.agr, 5.ind, 6.ser/, mapf(i,f) Mapping from SAM to factors /7.L, 8.N, 9.K /, maph(i,h) Mapping from SAM to households / 10.rural, 11.urban/, mapg(i) Identifies government in the SAM /12/, mapi(i) Identifies the investment row /13/, mapx(i) Identifies the rest of world /14/; parameter sam(i,j) Base year social accounts; $libinclude xlimport sam sam.xls sam * Scale the social accounting matrix so that the average entry * is roughly 1: sam(i,j) = sam(i,j) / 1000; display sam; parameter chksam(i) Consistency check of social accounts; chksam(i) = sum(j, sam(i,j)-sam(j,i)); display "Consistency check before balancing:", chksam; variable obj Objective -- least squares deviation; positive variable es(i,j) Estimate of SAM entries; equations objdef Defines the deviation balance(i) SAM balance condition; scalar penalty /1e6/; objdef.. obj =e= sum((i,j), sqr(es(i,j)-sam(i,j))) + sum((i,j)$(not sam(i,j)), penalty * es(i,j)); balance(i).. sum(j, es(i,j)) =e= sum(j, es(j,i)); es.l(i,j) = sam(i,j); model sambal /all/; solve sambal using nlp minimizing obj; parameter nz(i,j) New nonzeros in the SAM; nz(i,j) = es.l(i,j)$(not sam(i,j)); display nz; sam(i,j) = es.l(i,j); chksam(i) = sum(j, sam(i,j)-sam(j,i)); display "Consistency check after balancing:", chksam; * Extract submatrices from the social accounts: parameter id0(g,s) Intermediate demand fd0(f,s) Factor demand tm0(g) Import tariff collection m0(g) Imports (cif), c0(g,h) Private consumption g0(g) Government demand i0(g) Investment demand x0(g) Exports tx0 Export taxes (total) ti0 Investment taxes (total) fe0(f,h) Factor endowments it0(h) Income taxes, s0(h) Private saving, gs0 Government saving fs0 Foreign savings tf0(f) Factor taxes tr0(h) Government transfers to households, tx(g) Export tax rate (assumed uniform) px0(g) Reference price for exports d0(s) Domestic supply a0(s) Aggregate supply pm0(s) Reference price of imports tm(s) Import tariff rate ti Investment tax rate inv0 Total investment depr0(f) Deprecation xk0(f) Foreign factor return; loop((mapc(i,g), mapa(j,s)), id0(g,s) = sam(i,j) ); loop((mapf(i,f), mapa(j,s)), fd0(f,s) = sam(i,j) ); loop((mapc(j,g), mapg(i)), tm0(g) = sam(i,j) ); loop((mapc(j,g), mapx(i)), m0(g) = sam(i,j) ); loop((mapc(i,g), maph(j,h)), c0(g,h) = sam(i,j) ); loop((mapc(i,g), mapg(j)), g0(g) = sam(i,j)); loop((mapc(i,g), mapi(j)), i0(g) = sam(i,j)); loop((mapc(i,g), mapx(j)), x0(g) = sam(i,j)); loop((mapg(i), mapx(j)), tx0 = sam(i,j)); loop((mapg(i), mapi(j)), ti0 = sam(i,j)); loop((maph(i,h),mapf(j,f)), fe0(f,h) = sam(i,j)); loop((mapg(i), maph(j,h)), it0(h) = sam(i,j)); loop((mapi(i), maph(j,h)), s0(h) = sam(i,j)); loop((mapi(i), mapg(j)), gs0 = sam(i,j)); loop((mapi(i), mapx(j)), fs0 = sam(i,j)); loop((maph(i,h), mapg(j)), tr0(h) = sam(i,j)); loop((mapg(i), mapf(j,f)), tf0(f) = sam(i,j)); loop((mapx(i), mapf(j,f)), xk0(f) = sam(i,j)); loop((mapi(i), mapf(j,f)), depr0(f) = sam(i,j)); * Assume a uniform export tax: tx(g) = tx0 / (tx0 + sum(gg, x0(gg))); px0(g) = 1 - tx(g); * Express x0(g) as a gross of tax value: x0(g) = x0(g) / (1 - tx(g)); d0(s) = sum(g, id0(g,s)) + sum(f, fd0(f,s)) - x0(s)*px0(s); tm(g) = tm0(g) / m0(g); pm0(g) = 1 + tm(g); a0(g) = d0(g) + m0(g) * pm0(g); inv0 = ti0 + sum(g, i0(g)); ti = ti0/inv0; * Introduce tourism here: parameter t0(s) Tourism exports, ytot Total tourist expenditure, sigmay Elasticity of tourist demand, tbudget Tourism budget multiplier /1/; t0("ser") = x0("ser"); ytot = 3 * sum(s, t0(s)); x0("ser") = 0; sigmay = 0.5; $ontext $model:soe $sectors: y(s) ! Sectoral output (domestic production) a(s) ! Aggregate supply (Armington aggregate) c(h) ! Household consumption invest ! Aggregate investment $commodities: pd(s) ! Domestic output pa(s) ! Composite demand price pt(s)$t0(s) ! Tourism export price pc(h) ! Household consumption price pf(f) ! Factor prices pinv ! Investment pfx ! Price of foreign exchange $consumers: ra(h) ! Private households govt ! Government tourist ! Tourist demand $auxiliary: tau ! Consumption tax rate (for trade tax experiment) * Production for domestic market and for export: $prod:y(s) s:0 t:4 va:1 o:pfx q:x0(s) p:px0(s) a:govt t:tx(s) o:pt(s) q:t0(s) p:px0(s) a:govt t:tx(s) o:pd(s) q:d0(s) i:pa(g) q:id0(g,s) i:pf(f) q:fd0(f,s) va: $report: v:x(s) o:pfx prod:y(s) v:t(s)$t0(s) o:pt(s) prod:y(s) * Armington aggregation of domestic and imported goods: $prod:a(s) s:2 o:pa(s) q:a0(s) i:pd(s) q:d0(s) i:pfx q:m0(s) p:pm0(s) a:govt t:tm(s) $report: v:m(s) i:pfx prod:a(s) * Investment: $prod:invest o:pinv q:inv0 a:govt t:ti i:pa(g) q:i0(g) * Household consumption: $prod:c(h) s:1 o:pc(h) q:(sum(g, c0(g,h))) i:pa(g) q:c0(g,h) a:govt n:tau * Household demand (with exogenously fixed investment, * taxes and transfers): $demand:ra(h) d:pc(h) e:pinv q:(-s0(h)) e:pc(h) q:(tr0(h)-it0(h)) e:pf(f) q:fe0(f,h) $demand:tourist s:sigmay d:pt(s) q:t0(s) d:pfx q:(ytot-sum(s,t0(s))) e:pfx q:(tbudget*ytot) * Government demand: $demand:govt s:0 * Government demand for goods appears here: d:pa(g) q:g0(g) * Income tax revenue less transfers, fixed in real terms: e:pc(h) q:(it0(h)-tr0(h)) * Inestment demand -- this includes government savings, foreign * savings and depreciation: e:pinv q:(-gs0-fs0-sum(f,depr0(f))) * Factor ownership includes lump-sum taxes on factor income, * depreciation and returns to foreign factor owners: e:pf(f) q:(tf0(f)+depr0(f)+xk0(f)) * Foreign savings appear as a credit, returns paid to foriegn * factor owners is a debit: e:pfx q:(fs0-sum(f,xk0(f))) $constraint:tau govt =e= sum(g, pa(g) * g0(g)); $offtext $sysinclude mpsgeset soe * Check the benchmark: soe.iterlim = 0; $include soe.gen solve soe using mcp; soe.iterlim = 2000; tau.lo = -inf; * Examine declines in tourism expenditure between 0 * and 10%: parameter impact Impact of change in tourist expenditure; loop(tb, tbudget = 1 - 0.01 * (ord(tb)-1); impact(tb,"b") = 100 * (tbudget-1); loop(sg, sigmay = ord(sg)-1; $include soe.gen solve soe using mcp; impact(tb,sg) = 100 * (t.l("ser")/t0("ser")-1); ); ); $setglobal labels tb $setglobal domain tb $setglobal gp_opt0 "set xlabel 'Percent decline in B'" $setglobal gp_opt1 "set ylabel 'Percent change in T'" $libinclude plot impact