I have an emergency. I've written a paper months ago as part of my PhD and I was just about to submit it to a conference, but I read through it and found a mistake in the mod file.
The problem now is that the BK conditions fail to hold and I suspect that it is because of the time subscripts. I tried to follow the dynare user guide.
The code includes both bonds and capital stock. I solve the model using 2nd order approximation so upper case letters denote levels. Capital stock enters the household budget constraint, capital accumulation function and production function as K(-1). Bonds on the other hand are specificied via predetermined_variables command. The slight complication is that the household budget constraint considers the portfolio of bonds OMEGA, whereas the demands for different types of bonds are a function of this variable.
I can't find what is wrong with it. All variables and equations are described in detail, so if you didn't mind having a quick look at it, I would very much appreciate it.
P.S. The deadline is Friday 5th of February and I still need to run loops that are time consuming in order to obtain my key results.
- Code: Select all
//-------------------------------------------------------------------------------------------------
// DECLARATION OF ENDOGENOUS VARIABLES
//-------------------------------------------------------------------------------------------------
var
//
//
%%%%%%%%%%%%%%%%%%%%%%
%%%%REAL VARIABLES%%%%
%%%%%%%%%%%%%%%%%%%%%%
//
//
Y //AGGREGATE OUTPUT
I //AGGREGATE INVESTMENT
NX //NET EXPORTS OF RETAIL GOODS
C //AGGREGATE CONSUMPTION
C_H //AGGREGATE CONSUMPTION OF DOMESTICALLY PRODUCED RETAIL GOODS
C_F //AGGREGATE CONSUMPTION OF IMPORTED RETAIL GOODS
UC //MARGINAL UTILITY OF CONSUMPTION
UC_star //FOREIGN MARGINAL UTILITY OF CONSUMPTION
W //NOMINAL WAGES
B //DOMESTICALLY HELD STOCK OF FOREIGN BONDS
D //DOMESTICALLY HELD STOCK OF DOMESTIC BONDS
OMEGA //ASSET PORTFOLIO
LAMBDA //STOCHASTIC DISCOUNT FACTOR
XI //FIRM PROFIT DIVIDEND
N //AGGREGATE LEVEL OF EMPLOYMENT
K //AGGREGATE CAPITAL STOCK
R //REAL RATE OF RETURN FROM CAPITAL STOCK
TQ //TOBINS Q
DELTA //INVESTMENT ADJUSTMENT COSTS
MC //REAL MARGINAL COSTS
PHI1 //AUXILIARY VARIABLE 1
PHI2 //AUXILIARY VARIABLE 2
A //AGGREGATE LABOUR PRODUCTIVITY
//
//
%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%NOMINAL VARIABLES%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%
//
//
CPI //CONSUMPER PRICE INDEX
PPI_H //DOMESTIC PRODUCER PRICE INDEX
PPI_H_HAT //RESET PRICE IN THE DOMESTIC ECONOMY
THETA //PRICE DISPERSION
PI_CPI //DOMESTIC CPI INFLATION
PI_PPI_H //DOMESTIC PPI INFLATION
r //NOMINAL INTEREST RATE
f //FOREIGN BOND RATE OF INTEREST
S //NOMINAL EXCHANGE RATE
Q //REAL EXCHANGE RATE
//
//
%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%FOREIGN VARIABLES%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%
//
//
C_star //FOREIGN AGGREGATE CONSUMPTION
C_H_star //DOMESTIC EXPORTS
CPI_star //FOREIGN CONSUMER PRICE INDEX
r_star //FOREIGN NOMINAL INTEREST RATE
PPI_F //FOREIGN PRODUCER PRICE INDEX
//
//
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%DEVIATIONS FROM THE STEADY STATE%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
//
//
y //OUTPUT DEVIATION FROM THE STEADY STATE
c //CONSUMPTION DEVIATION FROM THE STEADY STATE
k //CAPITAL STOCK DEVIATION FROM THE STEADY STATE
i //INVESTMENT DEVIATION FROM THE STEADY STATE
w //NOMINAL WAGE DEVIATION FROM THE STEADY STATE
n //EMPLOYMENT DEVIATION FROM THE STEADY STATE
ppi_H //PPI DEVIATION FROM THE STEADY STATE
cpi //CPI DEVIATION FROM THE STEADY STATE
pi_cpi //CPI INFLATION DEVIATION FROM THE STEADY STATE
pi_ppi_H //PPI INFLATION DEVIATION FROM THE STEADY STATE
mc //REAL MARGINAL COST DEVIATION FROM THE STEADY STATE
ppi_H_HAT //RESET PRICE DEVIATION FROM THE STEADY STATE
s //NOMINAL EXCHANGE RATE DEVIATION FROM THE STEADY STATE
q //REAL EXCHANGE RATE DEVIATION FROM THE STEADY STATE
//
//
;
predetermined_variables OMEGA;
//
//-------------------------------------------------------------------------------------------------
// DECLARATION OF EXOGENOUS VARIABLES
//-------------------------------------------------------------------------------------------------
//
varexo
upsilon_A
upsilon_p
upsilon_star
upsilon_r
upsilon_mp;
//
//-------------------------------------------------------------------------------------------------
// DECLARATION OF PARAMETERS
//-------------------------------------------------------------------------------------------------
parameters
beta //TIME-INVARIANT DISCOUNT FACTOR
varphi //INVERSE FRISCH ELASTICITY OF LABOUR
alpha //OPENNESS TO TRADE IN GOODS AND SERVICES
eta //ELASTICITY OF SUBSTITUTION BETWEEN THE DOMESTIC AND FOREIGN GOODS
varepsilon //ELASTICITY OF SUBSTITUTION BETWEEN THE DOMESTIC VARIETIES
sigma //COEFFICIENT OF RELATIVE RISK AVERSION
pi //INDEX OF PRICE STICKINESS
chi //LABOUR SHARE OF INCOME
zeta //SIZE OF THE ADJUSTMENT COSTS OF INVESTMENT
delta //CAPITAL DEPRECIATION RATE
rho_a //PERSISTENCE OF THE LABOUR PRODUCTIVITY
rho_p //PERSISTENCE OF THE FOREIGN CPI
rho_star //PERSISTENCE OF THE FOREIGN AGGREGATE CONSUMPTION
rho_r //PERSISTENCE OF THE FOREIGN NOMINAL INTEREST RATE
phi //MONETARY POLICY RESPONSIVENESS TO INFLATION
xi //DEGREE OF IMPERFECT SUBSTITUTABILITY BETWEEN THE DOMESTIC AND FOREIGN BONDS
theta //DEGREE OF FINANCIAL OPENNESS
;
//
//
//-------------------------------------------------------------------------------------------------
// CALIBRATION OF PARAMETERS
//-------------------------------------------------------------------------------------------------
//
beta=0.99;
varphi=3;
alpha=0.4;
eta=1;
varepsilon=6;
sigma=1;
pi=0.75;
chi=0.68;
zeta=2;
delta=0.05;
rho_a=0.757;
rho_p=0.91;
rho_star=0.832;
rho_r=0.732;
phi=1.5;
xi=1;
theta=0.99;
//
//-------------------------------------------------------------------------------------------------
// NON-LINEAR MODEL EQUATIONS
//-------------------------------------------------------------------------------------------------
model;
//
//
Y=C+I+NX; //(1) AGGREGATE RESOURCE CONSTRAINT
Y=C_H+C_H_star+I; //(2) AGGREGATE DEMAND FOR THE DOMESTIC VARIETIES
NX=C_H_star-C_F; //(3) NET EXPORTS IDENTITY
C_H=(1-alpha)*((PPI_H/CPI)^(-eta))*C; //(4) DOMESTIC AGGREGATE DEMAND FOR THE DOMESTIC VARIETIES
C_F=alpha*((PPI_F/CPI)^(-eta))*C; //(5) DOMESTIC AGGREGATE DEMAND FOR THE FOREIGN VARIETIES
C_H_star=alpha*((PPI_H/(S*CPI_star))^(-eta))*C_star; //(6) FOREIGN AGGREGATE DEMAND FOR THE DOMESTIC VARIETIES
//
//
B=theta*(OMEGA)/S; //(7) DOMESTIC DEMAND FOR THE FOREIGN BONDS
D=(1-theta)*OMEGA; //(8) DOMESTIC DEMAND FOR THE DOMESTIC BONDS
OMEGA(+1)=(1/(PI_CPI(+1)*LAMBDA(+1)))*(OMEGA/CPI+(W/CPI)*N+(R(-1)/CPI)*K(-1)+(XI/CPI)-C-I); //(9) HOUSEHOLD BUDGET CONSTRAINT
XI=PPI_H*Y-W*N-R(-1)*K(-1); //(10) DOMESTIC FIRM PROFITS
f=r_star+xi*(exp(S*B)-1); //(11) FOREIGN BOND RATE OF INTEREST
W=CPI*(N^varphi)*(C^sigma); //(12) INVERSE LABOUR SUPPLY SCHEDULE
PI_CPI(+1)=beta*(UC(+1)/UC)*(1/LAMBDA); //(13) EULER EQUATION
UC=1/(C^sigma); //(14) MARGINAL UTILITY OF CONSUMPTION
LAMBDA=(1-theta)*exp(-r)+theta*((exp(-f)*S)/S(+1)); //(15) STOCHASTIC DISCOUNT FACTOR
//
//
Y=(((A*N)^chi)*(K(-1))^(1-chi))/THETA; //(16) AGGREGATE PRODUCTION FUNCTION
MC=((varepsilon-1)/varepsilon)*((W*N)/(CPI*Y))*(STEADY_STATE(Y)/STEADY_STATE(N)); //(17) REAL MARGINAL COSTS
PPI_H_HAT=CPI*(PHI1/PHI2); //(18) RESET PRICE IDENTITY
PHI1=(varepsilon/(varepsilon-1))*(Y*UC)*MC+pi*beta*(PI_CPI(+1)^varepsilon)*PHI1(+1); //(19) AUXILIARY VARIABLE 1
PHI2=(Y*UC)+pi*beta*(PI_CPI(+1)^(varepsilon-1))*PHI2(+1); //(20) AUXILIARY VARIABLE 2
THETA=pi*(PI_PPI_H^varepsilon)*THETA(-1)+(1-pi)*(PHI1/PHI2)^(-varepsilon); //(21) PRICE DISPERSION
//
//
K=(1-delta)*K(-1)+(1-DELTA)*I; //(22) CAPITAL ACCUMULATION FUNCTION
DELTA=(zeta/2)*((I/I(-1))-1)^2; //(23) INVESTMENT ADJUSTMENT COSTS
K(-1)=(((1-chi)*W)/(chi*R(-1)))*N; //(24) COST-MINIMISING CAPITAL LABOUR RATIO
TQ=beta*((UC(+1)/UC)*((R/CPI(+1))+TQ(+1)*(1-delta))); //(25) REAL RATE OF RETURN
1=TQ*(1-DELTA-zeta*((I/I(-1))-1)*(I/I(-1)))-beta*TQ(+1)*(UC(+1)/UC)*zeta*((I(+1)/I)-1)*((I(+1)/I)^2); //(26) TOBIN'S Q
//
//
PI_CPI=CPI/CPI(-1); //(27) CPI INFLATION IDENTITY
PPI_H=((1-pi)*PPI_H_HAT^(1-varepsilon)+pi*PPI_H(-1))^(1/(1-varepsilon)); //(28) PPI IDENTITY
PI_PPI_H=PPI_H/PPI_H(-1); //(29) PPI INFLATION IDENTITY
S=CPI*Q/CPI_star; //(30) REAL EXCHANGE RATE IDENTITY
Q=UC_star/UC; //(31) CONSUMPTION RISK SHARING EQUATION
UC_star=1/(C_star^sigma); //(32) FOREIGN MARGINAL UTILITY OF CONSUMPTION
PPI_F=(CPI_star*(S/PPI_H)^alpha)^(1/(1-alpha)); //(33) FOREIGN PPI
//
//
r=-log(beta)+phi*log(CPI/CPI(-1))+upsilon_mp; //(34) CIT
//r=-log(beta)+phi*log(PPI_H/PPI_H(-1))+upsilon_mp; //(34) DIT
//exp(-r)=(S/S(+1))*((1-theta)*exp(-r_star)+theta*exp(-f))+upsilon_mp; //(34) ERP (1)
//S=S(-1)^(1-theta); //(34) ERP (2)
//
//
log(A)=rho_a*log(A(-1))+upsilon_A; //(35) LABOUR PRODUCTIVITY SHOCK
log(CPI_star)=rho_p*log(CPI_star(-1))+upsilon_p; //(36) FOREIGN CPI SHOCK
log(C_star)=(1-rho_star)*log(STEADY_STATE(C))+rho_star*log(C_star(-1))+upsilon_star; //(37) FOREIGN AGGREGATE CONSUMPTION SHOCK
r_star=(rho_r-1)*log(beta)+rho_r*r_star(-1)+upsilon_r; //(38) FOREIGN NOMINAL INTEREST RATE SHOCK
//
//DEVIATIONS FROM THE STEADY STATE
//
y=(Y-STEADY_STATE(Y))/STEADY_STATE(Y);
c=(C-STEADY_STATE(C))/STEADY_STATE(C);
k=(K-(STEADY_STATE(K)))/(STEADY_STATE(K));
i=(I-(STEADY_STATE(I)))/(STEADY_STATE(I));
w=(W-(STEADY_STATE(W)))/(STEADY_STATE(W));
n=(N-STEADY_STATE(N))/STEADY_STATE(N);
pi_cpi=(PI_CPI-STEADY_STATE(PI_CPI))/STEADY_STATE(PI_CPI);
pi_ppi_H=(PI_PPI_H-STEADY_STATE(PI_PPI_H))/STEADY_STATE(PI_PPI_H);
s=(S-STEADY_STATE(S))/STEADY_STATE(S);
q=(Q-STEADY_STATE(Q))/STEADY_STATE(Q);
mc=(MC-STEADY_STATE(MC))/STEADY_STATE(MC);
ppi_H_HAT=(PPI_H_HAT-STEADY_STATE(PPI_H_HAT))/STEADY_STATE(PPI_H_HAT);
ppi_H=(PPI_H-STEADY_STATE(PPI_H))/STEADY_STATE(PPI_H);
cpi=(CPI-STEADY_STATE(CPI))/STEADY_STATE(CPI);
//
end;
//-------------------------------------------------------------------------------------------------
// INITIAL VALUE DECLARATION
//-------------------------------------------------------------------------------------------------
steady_state_model;
//
//
R=(1-beta*(1-delta))/beta;
N=(1/(((1-chi)/(chi*R))^(1-chi)-delta*((1-chi)/(chi*R))))^(sigma/(varphi+sigma));
C=(1/N)^(varphi/sigma);
K=((1-chi)/(chi*R))*N;
I=delta*K;
Y=(N^chi)*K^(1-chi);
TQ=1;
//
//
LAMBDA=beta;
OMEGA=0;
B=0;
D=0;
XI=Y-N-R*K;
//
//
NX=0;
C_H=(1-alpha)*C;
C_F=alpha*C;
C_H_star=alpha*C;
UC_star=C^(-sigma);
UC=C^(-sigma);
//
//
W=1;
MC=((varepsilon-1)/varepsilon);
PPI_H_HAT=1;
PHI1=(Y*UC)/(1-pi*beta);
PHI2=(Y*UC)/(1-pi*beta);
THETA=1;
PPI_H=1;
PI_PPI_H=1;
CPI=1;
PI_CPI=1;
PPI_F=1;
//
//
S=1;
Q=1;
//
//
r=-log(beta);
f=-log(beta);
//
//
A=1;
C_star=C;
CPI_star=1;
r_star=-log(beta);
//
//
y=0;
c=0;
k=0;
i=0;
w=0;
n=0;
pi_cpi=0;
pi_ppi_H=0;
s=0;
q=0;
mc=0;
ppi_H_HAT=0;
ppi_H=0;
cpi=0;
//
//
end;
steady;
//
//-------------------------------------------------------------------------------------------------
// SPECIFICATION OF SHOCKS
//-------------------------------------------------------------------------------------------------
//
shocks;
//
//
var upsilon_A; stderr 0.017849756;
var upsilon_star; stderr 0.017607805;
var upsilon_p; stderr 0.019746341;
var upsilon_mp; stderr 0.619270244;
var upsilon_r; stderr 1;
var upsilon_A, upsilon_star = 0.000181107;
var upsilon_A, upsilon_p = -0.00010589;
var upsilon_A, upsilon_mp = 0.003279128;
var upsilon_A, upsilon_r = 0.005925295;
var upsilon_star, upsilon_p= 6.30558E-05;
var upsilon_star, upsilon_mp= 0.008338872;
var upsilon_star, upsilon_r= 0.012283231;
var upsilon_p, upsilon_mp = 0.003338938;
var upsilon_p, upsilon_r = 0.003023887;
var upsilon_mp, upsilon_r = 0.402146342;
//
//
end;
//
//
stoch_simul(order=2,pruning,irf=24,ar=10)
y
c
k
i
NX
n
w
mc
ppi_H_HAT
r
f
B
D
TQ
OMEGA
LAMBDA
s
q
ppi_H
cpi
pi_cpi
pi_ppi_H;