// Dynare program for open economy model with monopolistic competition and balanced budget. // This version includes FB risk premium. var a c cons_tax dfb div divf fb g i infl int_tax inv k lab lab_tax lam lamf ls_tax n ni nx psi q qf r rh rk rx w xi y gs gsts inflh padjc st rmc ups ups_d cero tau_c divai cero1; // to params: // a = technology parameter // c = real aggregate domestic consumption // cons_tax = consumption tax -> endogenised version of (1 + tau_c) // dfb = change in real foreign bond holding // div = real dividend of production firms // divf = real dividend of foreign investment firms // fb = real foreign bond holdings // fw = total real domestic household financial wealth // g = real government expenditure // h = total real domestic household wealth // hw = total real domestic household human wealth // i = domestic nominal interest rate // infl = domestic CPI inflation // int_tax = household interest income tax -> endogenised version of (1 - tau_r) // inv = real domestic investment // k = real domestic capital stock // lab = domestic labour supply // lab_tax = labour income tax -> endogenised version of (1 - tau_l) // lam = lagrange multiplier from investment decision of actuarial firms // lamf = lagrange multiplier from foreign bond decision of foreign investment firms // ls_tax = lump-sum tax -> endogenised version of tau_ls // m = real money balances // n = real actuarial note holdings // ni = household net interest // nx = real net exports // psi = real capital adjustment costs // q = real share price of production firms // qf = real share price of foreign investment firms // r = domestic real interest rate // rh = real interest rate for domestic households // rk = real rental rate of capital // rx = real interest rate (as perceived by domestic residents) on foreign bonds // s = marginal propensity to save out of wealth // w = domestic real wage rate // x = auxilliary variable in marginal propensity to consume out of wealth // xi = real foreign bond adjustment costs // y = domestic real output // z = auxilliary variable in marginal propensity to consume out of wealth // **** gs = CPI/PPI ratio // **** gsts = foreign CPI/PPI ratio // **** inflh = domestic PPI inflation // **** padjc = production firm price adjustment costs // **** rmc = real marginal cost // **** st = terms of trade = P_f/P_h // **** ydd = domestic demand of composite good // **** ytd = total demand of composite good // tau_c = consumption tax rate varexo e ge inflf ix tau_l tau_ls tau_r ups_star; // e = technology shock // ge = domestic government spending shock // inflf = foreign producer price inflation // ix = foreign nominal interest rate // tau_l = labour income tax rate // tau_r = interest income tax // tau_ls = lump sum tax // ****ups_star = foreign demand of domestic coomposite good parameters A0 bet d chi del cp cpf G0 phi the vsig alp epsi eta nn thep real_for usta om eua eub; d = 1; // probability of still being alive next period, [0,1] A0 = 1; // steady state technology level, >0 bet = 0.97; // time discount rate, [0,1] chi = 0.3; // capital share, [0,1] cp = 0.1;//1e-8; // capital adjustment costs parameter, >= 0 cpf = 0.001; //(1-d);//1e-8; // foreign bond adjustment costs parameter, >= 0 del = 0.05; // depreciation rate of capital, [0,1] G0 = 0; //10*(1-d); // steady state government spending, >= 0 phi = 1; // utility function parameter for substitutability between (consumption and money) and leisure, [0,1], 1 = leisure not valued the = 1; // utility function parameter for curvature, >= 0, 1 = log utility vsig = 1; // utility function parameter for substitutability between consumption and money, [0,1], 1 = money not valued alp = 0.5; // **** home bias, [0,1] epsi = 0.2; // **** demand curve parameter for production firms, >= 0, 0 = perfect competition eta = 0.2; // **** elasticity of substitution parameter between domestic and foreign produced goods, >= 0, nn = 0.1; // **** relative steady state size of domestic economy, [0,1] thep = 0.001; //*(1-d);//4183; // **** price adjustment costs parameter, >= 0, 0 = flexible prices real_for = 0.05; usta = 15; //*(1-d); om = 0.001; //(1-d); // **** risk premium on foreign bonds eua = -1; eub = 0; model; //---------------------------------------------------------------------------------------------------------------------- // Household equations -> ok: 2 mrt 2009 lab = 1 - ((1-phi)/(phi) * (cons_tax/lab_tax) * (c/w)); // (5.8) //((1)/(cons_tax*c)) = bet*(1+ni(+1))*(1/(cons_tax(+1)*c(+1)*infl(+1))); // Works fine // (1/(cons_tax*c))*(((c)^phi)*((1-lab)^(1-phi)))^(1-the) = bet*(1+ni(+1))*(((c(+1))^phi)*((1-lab(+1))^(1-phi)))^(1-the)*(1/(cons_tax(+1)*c(+1)*infl(+1))); // MJDGGES error 23 // (1/cons_tax)*c^(phi-(phi*the)-1)*(1-lab)^((1-phi)*(1-the)) = bet*(1+ni(+1))*c(+1)^(phi-(phi*the)-1)*(1-lab(+1))^((1-phi)*(1-the))*(1/(cons_tax(+1)*infl(+1))); // MJDGGES error 23 // (1/cons_tax)*c^(1-the-1)*(1-lab)^((1-1)*(1-the)) = bet*(1+ni(+1))*c(+1)^(1-the-1)*(1-lab(+1))^((1-1)*(1-the))*(1/(cons_tax(+1)*infl(+1))); // Works fine // (1/cons_tax)*c^(eua)*(1-lab)^(eub) = bet*(1+ni(+1))*c(+1)^(eua)*(1-lab(+1))^(eub)*(1/(cons_tax(+1)*infl(+1))); // MJDGGES error 23 (1/cons_tax)*c^(-1)*(1-lab)^(0) = bet*(1+ni(+1))*c(+1)^(-1)*(1-lab(+1))^(0)*(1/(cons_tax(+1)*infl(+1))); // Works fine cero1 = n - (1+i(-1)*int_tax)*n(-1)/(infl) + tau_ls - lab_tax*w*lab + cons_tax*c - int_tax*divai; //---------------------------------------------------------------------------------------------------------------------- // Actuarial firms -> ok: 23 feb 2009 (1+r)*q=q(+1)+div(+1); // (9.10) (1+r)*qf=qf(+1)+divf(+1); // (9.11) lam = 1 + psi + (inv/k(-1)) * 2*cp*((inv/k(-1)) - del); // (A.12) (1+r)*lam = rk(+1)+ 2*cp*((inv(+1)/k) - del)*(inv(+1)/k)^2 + lam(+1)*(1-del); // (A.13) divai = n + div + divf - (1 + i(-1))*n(-1)/infl + rk*k(-1)-inv-psi*inv; // (9.14) 0 = n(+1) + div(+1) + divf(+1) - (1 + r)*n + rk(+1)*k-inv(+1)-psi(+1)*inv(+1); // (9.14) inv = k - (1-del)*k(-1); // (9.15) psi = cp*(inv/k(-1)-del)^2; // (9.16) //---------------------------------------------------------------------------------------------------------------------- // Foreign investment firms -> ok: 23 feb 2009 lamf = 1+2*cpf*dfb; // (9.17) (1+r)*lamf = rx - 2*om*fb(-1) + lamf(+1); // (9.18) divf = (1+ix(-1) - om*fb(-1))*fb(-1)/infl - fb - xi; // (9.19) dfb = fb - fb(-1); // (9.20) xi = cpf*(dfb)^2; // (9.21) nx = fb - (1+ix(-1) - om*fb(-1))*fb(-1)/infl; // (9.22) //---------------------------------------------------------------------------------------------------------------------- // Government -> ok: 23 feb 2009 g = G0 + ge; // (9.23) tau_ls = (g - tau_r*i(-1)*n(-1)/infl -tau_l*w*lab - tau_c*c ); // (9.24) //---------------------------------------------------------------------------------------------------------------------- // Aggregators block st/st(-1) = inflf/inflh; // (9.25) gs = ((1-(1-nn)*alp)+(1-nn)*alp*st^((eta-1)/eta))^(eta/(eta-1)); //(9.26) gsts= ((1-nn*alp)+nn*alp*st^((1-eta)/eta))^(eta/(eta-1)); //(9.27) nx = (1/gs)*nn*alp*((gsts*st)^(1/eta))*ups_star - (1-nn)*alp*((gs/st)^((1-eta)/eta))*ups; // (9.28) infl = gs/gs(-1)*inflh; // (9.29) //---------------------------------------------------------------------------------------------------------------------- // Production firms -> ok: 23 feb 2009 y = a*(k(-1)^(chi))*lab^(1-chi); // (9.30) gs*w = rmc*(1-chi)*a*(k(-1)/lab)^chi; // (9.31) gs*rk = rmc*chi*a*(k(-1)/lab)^(chi-1); // (9.32) div = y/gs - w*lab - rk*k(-1)-padjc/gs; // (9.33) padjc = thep/2*(inflh-1)^2; // (9.34) epsi*thep*inflh*(inflh-1) = (ups_d/nn)*(rmc-(1-epsi))+epsi*thep/(1+r)*gs/gs(+1)*inflh(+1)*(inflh(+1)-1); // (9.35) ups_d = (1-(1-nn)*alp)*gs^(1/eta)*ups + nn*alp*(gsts*st)^(1/eta)*ups_star + padjc; // (9.42) ups = c+inv+g + psi*inv + xi; // (9.43) //---------------------------------------------------------------------------------------------------------------------- // Technology and definitions -> ok: 23 feb 2009 a = A0 + e ; // (9.36) y = gs*(ups + nx) + padjc; // (9.37) ni = int_tax*i(-1); // (9.38) 1+rh= (1+ni(+1))/(infl(+1)*d); // (9.39) 1+r = (1+i)/infl(+1); // (9.40) 1+rx= (1+ix)/infl(+1); // (9.41) cero = y - ups_d; //---------------------------------------------------------------------------------------------------------------------- // Within Dynare definitions int_tax = 1-tau_r; lab_tax = 1-tau_l; cons_tax = 1 + tau_c; ls_tax=tau_ls; end; load last_steady8b; initval; //endogenous variables a = last_steady8b(1); c = last_steady8b(2); cons_tax = last_steady8b(3); dfb = last_steady8b(4); div = last_steady8b(5); divf = last_steady8b(6); fb = last_steady8b(7); // fw = last_steady6(8); g = last_steady8b(8); // h = last_steady6(10); // hw = last_steady6(11); i = last_steady8b(9); infl = last_steady8b(10); int_tax = last_steady8b(11); inv = last_steady8b(12); k = last_steady8b(13); lab = last_steady8b(14); lab_tax = last_steady8b(15); lam = last_steady8b(16); lamf = last_steady8b(17); ls_tax = last_steady8b(18); // m = last_steady6(22); n = last_steady8b(19); ni = last_steady8b(20); nx = last_steady8b(21); psi = last_steady8b(22); q = last_steady8b(23); qf = last_steady8b(24); r = last_steady8b(25); rh = last_steady8b(26); rk = last_steady8b(27); rx = last_steady8b(28); // s = last_steady6(33); w = last_steady8b(29); // x = last_steady6(35); xi = last_steady8b(30); y = last_steady8b(31); // z = last_steady6(38) ; gs = 0.95 ; gsts = 1 ; inflh = 1 ; padjc = 0 ; rmc = 0.9 ; st = 0.9 ; ups = c+inv+g + xi + psi*inv; ups_d = ups; cero = 0; divai = 0; cero1 = 0; //exogenous variables e = 0; ge = 0; inflf = 1; ix = inflf-1+real_for; // (1-bet*d) tau_c = 0; tau_ls = 0; tau_r = 0; tau_l = 0; ups_star = usta; // **** end; steady; check; write_latex_dynamic_model; endval; ups_star = usta+1; end; steady; check; // shocks; // var ups_star; // periods 1:19; // values usta; // end; simlength = 1000; simul(periods=1000);