%************************************************************************** % Farms, Fertiliser, and Financial Frictions: Yields from a DSGE Model * % Sébastien E.J. Walker (2014) * %************************************************************************** %----------------------------------------------------- % 0. Housekeeping %----------------------------------------------------- %This version is written for MATLAB 2013b and Dynare 4.4.2 %close all; %digits(100) %format long; %----------------------------------------------------- % 1. Define variables % Endogenous (var) and exogenous (varexo) %----------------------------------------------------- var A,a,B,Bf,Bh,C,Cf,Ch,Ch_star,e,i, k,L,Lambda,lambda_cons,Gamma,geta_g,M, m,m_star,N, omega,P,Prh,pi, r,rm,r_star,S,s,T,W,Y,Yh,z; %TEST,D,Df,Dh,Omega_f, varexo eta_A,eta_a,eta_m_star,eta_r_star; %----------------------------------------------------- % 2. Define parameters and assign parameter values %----------------------------------------------------- % ******************* % *Define parameters* % ******************* parameters % Behavioural parameters beta,epsilon, gamma,mu,mu_f,nu,phi,rho, Sigma,S_M,tau,theta,varsigma,zeta, % Constants pi_, % Fiscal and monetary parameters gamma_pi,gamma_S,gamma_y,kappa,pi_Theta,S_Theta,Y_Theta, % Initialisation values A0,a0,Cf0,e0,L0,M0,m0,m_star0,N0, P0,Prh0,pi0,W0,Y0,Yh0, % Parameters/initialisation values for the financial accelerator fail_Y,fail_Q,omega0,sigmasq_l,sigmasq,mean_n,sigma_omega,k0,Lambda0,Gamma0, geta_g0,s0,z0, % Derived Parameters alpha_L,alpha_M,B0,Bf0,Bh0,C0,Ch0,Ch_star0,delta,i0,lambda_cons0,lambda_p, Pwh0,r0,rm0,r_star0,T0,Y_star, check1, check2, C_phi, % Autoregressive parameters for structure of shocks rho_A,rho_a,rho_m_star,rho_r_star,S0 ; % ************************* % *Assign parameter values* % ************************* % Behavioural parameters beta = 0.91; % Discount factor, 0.91 from Adam et al. (2008) (discount rate = 0.1) epsilon = 1.00; % Relative-price sensitivity of foreign demand for domestic retail goods, 1 from GGN gamma = 0.75; % Share of domestic retail goods in domestic consumption, 0.8 from below (Cf =0.2) mu = 1.20; % Retailers' desired (actual in steady state) mark-up over wholesale prices, 1.2 from GGN mu_f = mu; % Foreign retailers' desired mark-up over wholesale prices, 1.2 from GGN nu = 2.00; % Inverse of intertemporal elasticity of substitution, 1/0.50 from Adam et al. (2008) rho = 0.50; % Elasticity of substitution between domestic and foreign retail goods, 0.50 from Adam et al. (2008) Sigma = 0.50; % Fertiliser/labour elasticity of substitution with 0 < Sigma < 1 [cf. agriculture] tau = 0.8; % 'Monitoring cost' paid in case of farm bankruptcy, 0.12 from GGN [certainly higher in Kenya] theta = 0.25; % Quarterly probability of price NOT changing (domestic firms), 0.75 from GGN [ANNUALISE?] zeta = 0.25; % (1-zeta)= degree of inertia in export demand, with zeta in (0,1), 0.25 from GGN % Constants pi_ = 3.14159265358979; % Pi % Fiscal and monetary policy parameters gamma_pi = 1; % Inflation weight in interest rate rule, 2.00 in GGN gamma_y = 1; % Output weight in interest rate rule, 0.75 in GGN gamma_S = -1; % Nominal exchange rate weight in interest rate rule kappa = 0.8;% Proportion of fertiliser cost NOT subsidised, so (1-kappa)=subsidy rate pi_Theta = 0; % Inflation target S_Theta = 1; % Nominal exchange rate target % Initialisation values Cf0 = 0.20; % SS consumption of foreign retail goods, [0.20 from Lozev - cf. Kenya data] e0 = 1; % Real exchange rate normalisation L0 = 1/3; % SS labour used M0 = 2/3; % SS fertiliser used m0 = 1; % Normalisation of domestic real fertiliser price m_star0 = 1; % Normalisation of foreign real fertiliser price pi0 = pi_Theta; % SS inflation = inflation target r_star0 = 0.04; % SS foreign real interest rate, 0.04 from Buffie et al. (2012) S0 = S_Theta; % SS nominal exchange rate = exchange rate target Y0 = 1; % SS domestic real wholesale output Yh0 = 1; % SS domestic real retail output C0 = 0.8*Y0; % SS consumption 80% of initial real wholesale output [80% of GDP from data.worldbank.org] Y_Theta = Y0; % Output target, [SS output in Lozev, but GGN target flex-price output - equivalent?] %Parameters/initialisation values for the financial accelerator %[I still need to check where some of these come from] %fail_Y = 0.086427384216111; % Annual 'failure' rate [= NPL close to 8.6?] fail_Y = 0.144; % Annual 'failure' rate (Kenya NPL 4.4% in 2011, WB website (higher before)) fail_Q = 1-(1-fail_Y)^(1/4); % Quarterly 'failure' rate [NOT NECESSARY IF PERIODS ARE YEARS] = normcdf(z0) %sigmasq_l = 0.42432634083021^2; % [Lozev trying to calibrate this close to 0.39? (Bulg. thesis p. 28)] sigmasq_l = 2.9^2; sigmasq = log(sigmasq_l+1); mean_n = -0.5*sigmasq; sigma_omega = sqrt(sigmasq); omega0 = logninv(fail_Q,mean_n,sigma_omega); z0 = (log(omega0)+0.5*sigma_omega^2)/sigma_omega; geta_g0 = (1-tau)*normcdf(z0-sigma_omega)+omega0*(1-normcdf(z0)); Gamma0 = normcdf(z0-sigma_omega)+omega0*(1-normcdf(z0)); Lambda0 = 1/(1-tau*omega0*lognpdf(omega0,mean_n,sigma_omega)/(1-fail_Q)); s0 = Lambda0/(1-Gamma0+Lambda0*geta_g0); k0 = 1 + Lambda0*geta_g0/(1-Gamma0); % Derived Parameters Pwh0 = S0; Prh0 = mu*Pwh0; % SS ... (desired mark-up achieved) P0 = (gamma*Prh0^(1-rho)+(1-gamma)*(mu_f*S0)^(1-rho))^(1/(1-rho)); % SS domestic CPI lambda_p = (1-theta)*(1-beta*theta)/theta; % Sensitivity of price of domestic retail goods to MC of production r0 = 1/beta - 1; % SS domestic real interest rate i0 = (1+pi0)/beta - 1; % SS domestic nominal interest rate delta = (Sigma-1)/Sigma; % Parameter related to fertiliser/labour elasticity of substitution rm0 = (1+i0)/(1+pi0)*s0 - 1; % SS `return on fertiliser' syms x y; [x, y] = solve(x*((Y0/M0)^delta) == ((1/(kappa*m0))*(Pwh0/P0)*((y)^Sigma)*((Y0/M0)^(1/Sigma))/(1+rm0))^(-1), y == Y0/((x*((Y0/M0)^delta)*(M0^delta)+(1-x)*((Y0/L0)^delta)*(L0^delta))^(1/delta)) , x, y,'Real',true); S_M = x; % Fertiliser share of national income A0 = y; % SS TFP alpha_M = S_M*((Y0/M0)^delta); % Fertiliser distribution parameter alpha_L = (1-S_M)*((Y0/L0)^delta); % Labour distribution parameter W0 = alpha_L*Pwh0*(A0^Sigma)*(Y0^(1/Sigma))*(L0^(-1/Sigma)); % SS real wage varsigma = ((1/C0)*(W0/P0))/((1/(1-L0)+(1/C0)*(W0/P0))); % Preference for leisure vs. consumption lambda_cons0 = (1-varsigma)*((C0^((nu-1)*(varsigma-1)-1)))*((1-L0)^(varsigma*(1-nu))); % Lagrange mult.: HH BC N0 = (kappa*m0*M0)/k0; % SS farm net worth B0 = (kappa*m0*M0-N0)*P0; % SS farmers' nominal borrowings/`bonds' sold Bh0 = 0.5*B0; % SS farmers' nominal bonds held by foreign investors (arbitrary assumption) Bf0 = 0.5*B0; % SS farmers' nominal bonds held by domestic investors (arbitrary assumption) phi = ((1+i0)/(1+pi0))/(1+r_star0)*(P0/Bf0)*Yh0; % Domestic country risk premium parameter Ch0 = (P0*C0-(mu_f*S0)*Cf0)/Prh0; % SS domestic consumption of domestic retail goods %a0 =(e0*m_star0*M0+i0*Bf0/P0-Yh0+Ch0+Cf0)/e0; % SS real net budgetary aid in foreign currency a0=0.05; T0 = (1-kappa)*e0*m_star0*M0 - e0*a0; % Constant real lump-sum taxes Ch_star0 = Yh0-Ch0-tau*normcdf(z0-sigma_omega)*(1+rm0)*m0*M0; % Foreign demand: dom. retail goods Y_star = Ch_star0; % SS real foreign output check1 = (kappa*m0*M0)/k0; check2 = (1+rm0)*kappa*m0*M0-(1+i0)*B0/P0-tau*normcdf(z0-sigma_omega)*(1+rm0)*kappa*m0*M0; C_phi = check1-check2; % Balancing term (farmers' consumption) % Autoregressive parameters for structure of shocks rho_A = 0.95; % Persistence of total factor productivity (weather), 0.95 from Lozev [cf. lit.] rho_a = 0.95; % Persitence of real net budgetary aid in foreign currency, [cf. lit.] rho_m_star = 0.95; % Persistence of foreign real fertiliser price, [cf. lit.] rho_r_star = 0.95; % Persistence of foreign real interest rate, [cf. lit.] %----------------------------------------------------- % 3. Defining the model %----------------------------------------------------- model; % Demand side Yh = Y; %(1) Output: retail = wholesale Yh = Ch+Ch_star+tau*normcdf(z-sigma_omega)*(1+rm)*m(-1)*M(-1); %(2) Domestic resource constraint lambda_cons= (1-varsigma)*((C^((nu-1)*(varsigma-1)-1)))*((1-L)^(varsigma*(1-nu))); %(3) Lagrange mult. on HH BC lambda_cons= beta*lambda_cons(+1)*(1+i)*P/P(+1); %(4) Euler equation C = ((gamma*Ch^(rho-1))^(1/rho)+((1-gamma)*Cf^(rho-1))^(1/rho))^(rho/(rho-1));%(5) Domestic consumption index Ch/Cf = (gamma/(1-gamma))*((Prh/(mu_f*S))^(-rho)); %(6) FOC dom. goods vs. imports P = (gamma*Prh^(1-rho)+(1-gamma)*(mu_f*S)^(1-rho))^(1/(1-rho)); %(7) Domestic price level Ch_star = (((((Prh/S)/mu_f)^(-epsilon)*Y_star))^zeta)*(((Ch_star(-1))^(1-zeta))); %(8) Foreign demand: dom. retail goods L = (((alpha_L*S)/W)^Sigma)*(A^(Sigma^2))*Y; %(9) Labour demand (1+rm(+1))=(1/(kappa*m))*(S(+1)/P(+1))*alpha_M*(A(+1)^Sigma)*((Y(+1)/M)^(1/Sigma)); %(10)Fertiliser demand %(1+rm) = (1/(kappa*m(-1)))*(S/P)*alpha_M*(A^Sigma)*((Y/M(-1))^(1/Sigma)); % Supply side Y = A*((alpha_M*((M(-1))^delta)+alpha_L*(L^delta))^(1/delta));%(11) Production function (1-varsigma)*(1/C)*(W/P) = varsigma*(1/(1-L)); %(12) FOC labour supply (1+rm(+1)) = s*(1+i)*P/P(+1); %(13) Supply: external finance %(1+rm) = s(-1)*(1+i(-1))*P(-1)/P; % Pricing, interest rates, and exchange rates Prh/Prh(-1) = ((mu*S/Prh)^lambda_p)*((Prh(+1)/Prh)^beta); %(14) Domestic retail goods 'inflation' e = S*mu_f/Prh; %(15) Real exchange rate (increase = domestic depreciation) % Budget constraints and other identities B/P = kappa*m*M-N; %(16) Farmers' real borrowing N = (1+rm)*kappa*m(-1)*M(-1)-(1+i(-1))*B(-1)/P-tau*normcdf(z-sigma_omega)*(1+rm)*kappa*m(-1)*M(-1)+C_phi; %(17) Farm net worth B = Bh+Bf; %(18) Nominal farm 'bonds' %1+pi = P/P(-1); %(19) Definition: inflation 1+pi(+1)= P(+1)/P; m = e*m_star; %(20) Domestic real fertiliser price 1+r = (1+i(-1))*P(-1)/P; %(21) Definition: real interest rate %1+r(+1) = (1+i)*P/P(+1); % Interest rate premium z = (log(omega)+0.5*sigma_omega^2)/sigma_omega; %(22) `Standardised' idiosyncratic shock threshold Lambda = 1/(1-tau*((exp((-(log(omega)-mean_n)^2)/(2*sigma_omega^2))/sqrt(2*pi_*sigma_omega^2))/(1-normcdf(z)))); %(23) Lagrange mult. on lenders' constraint: expected return = opportunity cost Gamma = normcdf(z-sigma_omega)+omega*(1-normcdf(z)); %(24) Gross share of profits to lender [Lozev's `geta'] geta_g = (1-tau)*normcdf(z-sigma_omega)+omega*(1-normcdf(z)); %(25) Net share of profits to lender [Gamma-tau*G in GGN] s = Lambda/(1-Gamma+Lambda*geta_g); %(26) External finance premium %s=s0; k = 1+Lambda*geta_g/(1-Gamma); %(27) Fertiliser expenditure per unit net worth [GGN'S k(omega bar), Lozev's psi] k = (kappa*m*M)/N; %(28) Fertiliser expenditure per unit net worth [GGN'S k(omega bar), Lozev's psi] % Government budget constraint (1-kappa)*e*m_star*M = T+e*a; %(29) % Interest parity condition (1+i)*P/P(+1)= (1+r_star(+1))*((e(+1)/e)^(gamma))*phi*((Bf(-1)/P)/Yh); %(30) % Shocks log(1+A)-log(1+A0) = rho_A*(log(1+A(-1))-log(1+A0))-eta_A; %(31) TFP (weather) log(1+a)-log(1+a0) = rho_a*(log(1+a(-1))-log(1+a0))+eta_a; %(32) Real net budgetary aid, foreign currency log(1+m_star)-log(1+m_star0)= rho_m_star*(log(1+m_star(-1))-log(1+m_star0))+eta_m_star;%(33) Foreign real fertiliser price log(1+r_star)-log(1+r_star0)= rho_r_star*(log(1+r_star(-1))-log(1+r_star0))+eta_r_star;%(34) Foreign real interest rate % Policy rules 1+i = ((1+i0)/(1+pi0))*(((1+pi)/(1+pi_Theta))^gamma_pi)*((Yh/Y_Theta)^gamma_y)*((S/S_Theta)^gamma_S);%(35) 'Taylor' rule end; %kappa = ...; % Fertiliser subsidy rule (if endog.) %----------------------------------------------------- % 4. Initialisation of endogenous variables % - steady - allows approximate values to be included %----------------------------------------------------- initval; A = A0; a = a0; B = B0; Bf = Bf0; Bh = Bh0; C = C0; Cf = Cf0; Ch = Ch0; Ch_star = Ch_star0; e = e0; i = i0; k = k0; L = L0; Lambda = Lambda0; lambda_cons = lambda_cons0; Gamma = Gamma0; geta_g = geta_g0; M = M0; m = m0; m_star = m_star0; N = N0; omega = omega0; P = P0; Prh = Prh0; pi = pi0; r = r0; rm = rm0; r_star = r_star0; S = S0; s = s0; T = T0; W = W0; Y = Y0; Yh = Yh0; z = z0; end; resid(1); steady; check; %check(qz_zero_threshold =1e-15); model_diagnostics; %----------------------------------------------------- % 5. Calibration of Shocks %----------------------------------------------------- shocks; %var eta_A; stderr 0.000000001; %[Autocorrelated shock = drought? Trend = climate change?] var eta_A; stderr 0.01; var eta_a; stderr 0.000000001; %var eta_a; stderr 0.01; var eta_m_star; stderr 0.000000001; %var eta_m_star; stderr 0.01; var eta_r_star; stderr 0.000000001; %var eta_r_star; stderr 0.01; end; %----------------------------------------------------- % 6. Simulation % For stoch_simul:... %----------------------------------------------------- %resid(2); set_dynare_seed(500); stoch_simul(periods=1000, order=1,irf=16) A Y pi P Prh S e m_star m M L k N B Bf i r rm s r_star %a lambda_cons geta_g T Yh z Bh omega W C Lambda Gamma omega ; %stoch_simul(periods=1000, order=1,irf=16) %A a B Bf Bh C Cf Ch Ch_star e i %k L Lambda lambda_cons Gamma geta_g M %m m_star N %omega P Prh pi %r rm r_star S s T W Y Yh z; %close all; //dynasave results_oibg2;