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Hello there,
I am getting a little desperate with the current code I am working on.
It deals with two new-keynesian countries trading with each other and constituting a monetary union.
I do not have tricky features in it (no fiscal sector, no nontradables, no sticky wages) and until recently I did not see an issue with the model.
In order to analyse second-order moments I added price dispersion to the model equations.
At a first-order approximation this should not change anything but unfortunately suddenly dynare tells me that I have indeterminacy due to rank failure.
This seems extremely odd to me and I wonder whether there is a simple explanation for this (see code below.

Thanks in advance for any hints/comments!

Code: Select all

close all; clc;
var %Home country variables
    C %consumption
    Pie %CPI inflation
    w %real wage
    mc %real marginal costs
    Y %output
    x1 x2 %auxiliary variablers (Schmitt-Grohé and Uribe)
    pop %optimal price relative to actual price level
    Pie_H %Home inflation
    b %real debt
    d %price dispersion
    N %labour
    %Foreign country variables
    C_star
    Pie_star
    w_star
    mc_star
    Y_star
    x1_star
    x2_star
    pop_star
    Pie_F
    b_star
    N_star 
    d_star
    %'global' variables
    ToT %terms of trade
    R %nom. interest rate
    err % monetary policy shock
     ;
varexo e; 

parameters beta sigma kappa epsilon theta phi varphi omegaH omegaF n;

beta = 0.99; %discount factor
sigma = 3; %risk aversion
kappa = 3; %Frisch elasticity
epsilon = 11; %elast. of subs. btw. diff. goods
theta = 0.5; %Calvo
phi = 3; %strength of MP
varphi = 11; %elasticity of subs. btw. H- and F-goods
omegaH = 0.5; %hh steady state import share
omegaF = 0.5; %hh steady state import share in country F
n = 0.5; %size of foreign country


model;
%%%%%%%% HOME/FOREIGN ECONOMY %%%%%%%%%%
C^(-sigma) = beta*((R-0.001*b)/Pie(+1))*C(+1)^(-sigma); %Euler equation
C_star^(-sigma) = beta*((R-0.001*b_star)/Pie_star(+1))*C_star(+1)^(-sigma);

N^(kappa)*C^(sigma) = w; %labour supply
N_star^(kappa)*C_star^(sigma) = w_star;

Y = N/d;
Y_star = N_star/d_star;

d = (1-theta)*pop^(-epsilon) + (theta*Pie_H^(epsilon))*d(-1); %law of motion for price dispersion
d_star = (1-theta)*pop_star^(-epsilon) + (theta*Pie_F^(epsilon))*d_star(-1);

mc = w*((1-omegaH) + omegaH*(ToT^(1-varphi)))^(1/(1-varphi)); %real marginal costs (linear prod. fct) with A=1 (mc=w/A)
mc_star = w_star*((1-omegaF) + omegaF*(ToT^(varphi-1)))^(1/(1-varphi));

x1 = (epsilon/(epsilon-1))*x2; %auxiliary Schmitt-Grohe and Uribe/FOC of firms
x1_star = (epsilon/(epsilon-1))*x2_star;

x1 = Y*(pop^(1-epsilon)) + ((Pie_H(+1)*(pop(+1)/pop))^(epsilon-1))*theta*beta*(1/Pie(+1))*((C(+1)/C)^(-sigma))*x1(+1);
x1_star = Y_star*(pop_star^(1-epsilon)) + ((Pie_F(+1)*(pop_star(+1)/pop_star))^(epsilon-1))*theta*beta*(1/Pie_star(+1))*((C_star(+1)/C_star)^(-sigma))*x1_star(+1);

x2 = Y*(pop^(-epsilon))*mc + ((Pie_H(+1)*(pop(+1)/pop))^(epsilon))*theta*beta*(1/Pie(+1))*((C(+1)/C)^(-sigma))*x2(+1);
x2_star = Y_star*(pop_star^(-epsilon))*mc_star+ ((Pie_F(+1)*(pop_star(+1)/pop_star))^(epsilon))*theta*beta*(1/Pie_star(+1))*((C_star(+1)/C_star)^(-sigma))*x2_star(+1);

1 = theta*Pie_H^(1-epsilon) + (1-theta)*pop^(1-epsilon); %law of motion of inflation
1 = theta*Pie_F^(1-epsilon) + (1-theta)*pop_star^(1-epsilon);

Y = (1-omegaH)*(((1-omegaH) + omegaH*(ToT^(1-varphi)))^(varphi/(1-varphi)))*C + omegaF*(n/(1-n))*(((1-omegaF)*(ToT^(1-varphi)) + omegaF)^(varphi/(1-varphi)))*C_star ; %market clearing
Y_star = omegaH*((1-n)/n)*(((1-omegaH)*(ToT^(varphi-1)) + omegaH)^(varphi/(1-varphi)))*C + (1-omegaF)*(((1-omegaF) + omegaF*(ToT^(varphi-1)))^(varphi/(1-varphi)))*C_star;

Pie = Pie_H*(((1-omegaH) + omegaH*(ToT^(1-varphi)))/((1-omegaH) + omegaH*(ToT(-1)^(1-varphi))))^(1/(1-varphi)); %CPI inflation
Pie_star = Pie_F*(((1-omegaF) + omegaF*(ToT^(varphi-1)))/((1-omegaF) + omegaF*(ToT(-1)^(varphi-1))))^(1/(1-varphi));

ToT/ToT(-1) = Pie_F/Pie_H; %terms of trade definition (ToT=P_F/P_H)

R = (1/beta)*((1-n)*Pie + n*Pie_star)^(phi)+err; %Taylor rule

b + C = ((R-0.001*b)/Pie)*b(-1)+ Y*((1-omegaH) + omegaH*ToT^(1-varphi))^(1/(varphi-1));
(1-n)*b = -n*b_star;

err = 0.7*err(-1) + e;
end;

shocks;
var e=0.01;
end;

initval;
C=((epsilon-1)/epsilon)^(1/(kappa+sigma)); 
mc = (epsilon-1)/epsilon;
w = mc;
Pie = 1;
R = 1/beta;
ToT = 1;
x2 = C*w;
pop = 1;
Pie_H = 1;
x1 = (epsilon/(epsilon-1))* x2;
Y = C;
N=Y;
C_star=((epsilon-1)/epsilon)^(1/(kappa+sigma)); 
mc_star = (epsilon-1)/epsilon;
w_star = mc_star;
x2_star = C_star*w_star;
x1_star = (epsilon/(epsilon-1))* x2_star;
pop_star = 1; 
Pie_F = 1;
Pie_star = 1;
Y_star = C_star;
N_star = Y_star;
b =0;
b_star = 0;
d = 1;
d_star = 1;
end;

steady;
check;
steady(solve_algo=4);
stoch_simul(periods=200,irf=50,order=1);% pruning, replic=1000); 


Then you should check the equations you introduced, particularly things like timing and exponents. The message you obtain refers to all variables of the model jointly. Even if you add an indepent subsystem of three equations in three unknowns, if these three equations are rank-deficient, you will get the error message.

Hey Johannes,
a million thanks for the hint to check the exponents.
Found the mistake!
Cheers!