BK rank condition not satisfied

JamAl · May 9, 2019, 7:05pm

Hi,

I’m trying to run this standard NK model for a small open economy.

Dynare answers the BK’s rank condition is not satisfied:

"There are 23 eigenvalue(s) larger than 1 in modulus
for 25 forward-looking variable(s)

The rank condition ISN’T verified!"

Can someone help me?

parameters thetah thetaf sigma n beta alphah alphaf tauh tauf ah af phih phif eta gammahpcp gammafpcp ibar pibar ahR ahPI afR afPI delta b rhoC rhoCstar rhoS;

var Yh Yf C Cstar L Lstar Ch Chstar Cf Cfstar Q bf bfstar i istar
    ph pf phpcp phlcp pflcp pfstar phstar pfpcpstar phlcpstar pflcpstar
    pih pihpcp pihlcp pihlcpstar pifstar pifpcpstar piflcpstar piflcp w wstar pi pistar mkp
    x1pcp x2pcp x1lcp x1lcpstar x2lcp x2lcpstar x1fpcp x2fpcp x1flcp x1flcpstar x2flcp x2flcpstar
    gammaC gammaCstar gammaS EPSILONS;

varexo epsilonC epsilonCstar epsilonS gammaI gammaIstar;

n           = 0.05;
beta        = 0.99;
delta       = 0.01;
b           = 117.486685;
op          = 0.3;
ah          = 0.715; //1-(1-n)*op
af          = 0.715; //1-(1-n)*op
eta         = 2;
sigma       = 1.1;
alphah      = 0.6;
alphaf      = 0.6;
thetah      = 7;
thetaf      = 7;
tauh        = 1/(1-thetah);
tauf        = 1/(1-thetaf);
phih        = 0.75;
phif        = 0.75;
gammahpcp   = 0.4;
gammafpcp   = 0.4;
ahR         = 0.7;
ahPI        = 1.5;
afR         = 0.7;
afPI        = 1.5;
ibar        = 0.010101;
pibar       = 1;
rhoC        = 0.9;
rhoCstar    = 0.9;
rhoS        = 0.9;

initval;
Yh = 0.991727466;
Yf = 0.991727466;
C = 2.166593153;
Cstar = 0.20442523;
L = 0.991727466;
Lstar = 0.991727466;
Ch = 0.828855014;
Chstar = 0.008572234;
Cf = 8.424094644;
Cfstar = 0.548354064;
Q = 0.178824091;
bf = 656.9958472;
bfstar = -34.5787288;
i = 0.010101;
istar = 0.010101;
ph = 2.302182697;
pf = 0.030675995;
phpcp = 1;
phlcp = 1;
pflcp = 1;
pfstar = 0.171542852;
phstar = 12.87400757;
pfpcpstar = 1;
phlcpstar = 1;
pflcpstar = 1;
pi = 1;
pistar = 1;
pih = 1;
pihpcp = 1;
pihlcp = 1;
pihlcpstar = 1;
pifstar = 1;
pifpcpstar = 1;
piflcpstar = 1;
piflcp = 1;
w = 2.302182697;
wstar = 0.171542852;
x1pcp = 2.8028366;
x2pcp = 2.8028366;
x1lcp = 2.342523776;
x2lcp = 2.342523776;
x1lcpstar = 0.024226991;
x2lcpstar = 0.024226991;
x1fpcp = 2.8028366;
x2fpcp = 2.8028366;
x1flcp = 23.80831589;
x2flcp = 23.80831589;
x1flcpstar = 1.549767343;
x2flcpstar = 1.549767343;
mkp = 1;
gammaC = 1;
gammaCstar = 1;
gammaS = 1;
end;

model;

//  domestic LCP and PCP firms

x1pcp = (thetah/(thetah-1))*(C^(-sigma))*w*(phpcp^(-thetah))*(Ch+((1-n)/n)*(ph^(-thetah))*(Q^thetah)*(phstar^thetah)*Chstar)+beta*alphah*(pihpcp(+1)^thetah)*x1pcp(+1); //1
x2pcp = (1-tauh)*(C^(-sigma))*ph*(phpcp^(1-thetah))*(Ch+((1-n)/n)*(ph^(-thetah))*(Q^thetah)*(phstar^thetah)*Chstar)+beta*alphah*(pihpcp(+1)^(thetah-1))*x2pcp(+1); //2

((1-alphah*pihpcp^(thetah-1))/(1-alphah))^(1/(1-thetah))=x1pcp/x2pcp; //3

x1lcp = (thetah/(thetah-1))*(C^(-sigma))*w*(phlcp^(-thetah))*Ch+beta*alphah*(pihlcp(+1)^thetah)*x1lcp(+1); //4
x2lcp = (1-tauh)*(C^(-sigma))*ph*(phlcp^(1-thetah))*Ch+beta*alphah*(pihlcp(+1)^(thetah-1))*x2lcp(+1); //5

((1-alphah*pihlcp^(thetah-1))/(1-alphah))^(1/(1-thetah))=x1lcp/x2lcp; //6

x1lcpstar = (thetah/(thetah-1))*(C^(-sigma))*w*(phlcpstar^(-thetah))*Chstar+beta*alphah*(pihlcpstar(+1)^thetah)*x1lcpstar(+1); //7
x2lcpstar = (1-tauh)*(C^(-sigma))*phstar*Q*(phlcpstar^(1-thetah))*Chstar+beta*alphah*(pihlcpstar(+1)^(thetah-1))*x2lcpstar(+1); //8

((1-alphah*pihlcpstar^(thetah-1))/(1-alphah))^(1/(1-thetah))=x1lcpstar/x2lcpstar; //9

//  foreign LCP and PCP firms

x1fpcp = (thetaf/(thetaf-1))*(Cstar^(-sigma))*wstar*(pfpcpstar^(-thetaf))*(Cfstar+(n/(1-n))*((Q*pfstar)^(-thetaf))*(pf^thetaf)*Cf)+beta*alphaf*(pifpcpstar(+1)^thetaf)*x1fpcp(+1); //10
x2fpcp = (1-tauf)*pfstar*(Cstar^(-sigma))*(pfpcpstar^(1-thetaf))*(Cfstar+(n/(1-n))*((Q*pfstar)^(-thetaf))*(pf^thetaf)*Cf)+beta*alphaf*(pifpcpstar(+1)^(thetaf-1))*x2fpcp(+1); //11

((1-alphaf*pifpcpstar^(thetaf-1))/(1-alphaf))^(1/(1-thetaf))=x1fpcp/x2fpcp; //12

x1flcpstar = (thetaf/(thetaf-1))*(Cstar^(-sigma))*wstar*(pflcpstar^(-thetaf))*Cfstar+beta*alphaf*(piflcpstar(+1)^thetaf)*x1flcpstar(+1); //13
x2flcpstar = (1-tauf)*(Cstar^(-sigma))*pfstar*(pflcpstar^(1-thetah))*Cfstar+beta*alphaf*(piflcpstar(+1)^(thetaf-1))*x2flcpstar(+1); //14

((1-alphaf*piflcpstar^(thetaf-1))/(1-alphaf))^(1/(1-thetaf))=x1flcpstar/x2flcpstar; //15

x1flcp = (thetaf/(thetaf-1))*(Cstar^(-sigma))*wstar*(pflcp^(-thetaf))*Cf+beta*alphaf*(piflcp(+1)^thetaf)*x1flcp(+1); //16
x2flcp = (1-tauf)*(Cstar^(-sigma))*pf*(pflcp^(1-thetaf))*Cf*Q^(-1)+beta*alphaf*(piflcp(+1)^(thetaf-1))*x2flcp(+1); //17

((1-alphaf*piflcp^(thetaf-1))/(1-alphaf))^(1/(1-thetaf))=x1flcp/x2flcp; //18

// consumption demand

Ch = ah*C*ph^(-phih); //19
Cf = (1-ah)*C*pf^(-phih); //20
Chstar = (1-af)*Cstar*phstar^(-phif); //21
Cfstar = af*Cstar*pfstar^(-phif); //22

// labor supply

(L^eta)*(C^sigma)*gammaC^(-1) = w; //23
(Lstar^eta)*(Cstar^sigma)*gammaCstar^(-1) = wstar; //24

// composition Euler equations

beta*((gammaC(+1)*C(+1)^(-sigma))/(gammaC*C^(-sigma)))*((1+i)/pi(+1))=1; //25
beta*((gammaC(+1)*C(+1)^(-sigma))/(gammaC*C^(-sigma)))*((1+istar)/pistar(+1))*(Q(+1)/Q) = gammaS/(1-delta*(Q*bf - b)); //26  
beta*((gammaCstar(+1)*Cstar(+1)^(-sigma))/(gammaCstar*Cstar^(-sigma)))*((1+istar)/pistar(+1))=1; //27

pi = ph(-1)*pih/ph; //28
pistar = pfstar(-1)*pifstar/pfstar; //29
mkp = pf/(Q*wstar); //30

// price indices

1 = ah*ph^(1-phih)+(1-ah)*pf^(1-phih); //31
1 = af*pfstar^(1-phif)+(1-af)*phstar^(1-phif); //32
1 = gammahpcp*phpcp^(1-thetah)+(1-gammahpcp)*phlcp^(1-thetah); //33
1 = gammahpcp*(phpcp*ph*(Q^(-1))*phstar^(-1))^(1-thetah)+(1-gammahpcp)*phlcpstar^(1-thetah); //34
1 = gammafpcp*pfpcpstar^(1-thetaf)+(1-gammafpcp)*pflcpstar^(1-thetaf); //35
1 = gammafpcp*(pfpcpstar*(pfstar*Q/pf))^(1-thetaf)+(1-gammafpcp)*pflcp^(1-thetaf); //36

// inflation rates

pihpcp = phpcp*pih/phpcp(-1); //37
pifpcpstar = pfpcpstar*pifstar/pfpcpstar(-1); //38
pihlcp = phlcp*pih/phlcp(-1); //39
pihlcpstar = (phlcpstar*phstar*pfstar(-1)*pifstar)/(phlcpstar(-1)*phstar(-1)*pfstar); //40
piflcpstar = pflcpstar*pifstar/pflcpstar(-1); //41
piflcp = (pflcp*pf*ph(-1)*pih)/(pflcp(-1)*pf(-1)*ph); //42

// production functions

Yh = L; //43
Yf = Lstar; //44

// resource constraints

C+Q*bf/((1+istar)*(1-delta*(Q*bf - b))) = Yh+(Q*bf(-1)/pistar); // //45
n*bf+(1-n)*bfstar = 0; //46

// monetary policy rules

log(i/ibar) = ahR*log(i(-1)/ibar)+ahPI*log(pi/pibar)+gammaI;
log(istar/ibar) = afR*log(istar(-1)/ibar)+afPI*log(pistar/pibar)+gammaIstar;

EPSILONS = -epsilonS;

// good markets equilibrium

Yh = ah*(ph^(-phih))*C+((1-n)/n)*(1-af)*(ph^(-phih))*(Q^phih)*Cstar; //49
Yf = (n/(1-n))*(1-ah)*(pfstar^(-phif))*(Q^(-phif))*C+af*(pfstar^(-phif))*Cstar; //50

// other shocks

gammaC = 1-rhoC+rhoC*gammaC(-1)+epsilonC; //51
gammaCstar = 1-rhoCstar+rhoCstar*gammaCstar(-1)+epsilonCstar; //52
gammaS = 1-rhoS+rhoS*gammaS(-1)+EPSILONS; //53

end;

model_diagnostics;
resid;

steady;
check;
shocks;
var epsilonC = 1;
var epsilonCstar = 1;
var gammaI = 1;
var gammaIstar = 1;
var epsilonS = 1;
end;

stoch_simul(order=1,irf = 100,nograph,periods=50000);

JamAl · May 10, 2019, 5:13pm

This model replicates the standard NK DSGE model for a small open economy presented in Forbes, Hjortsoe and Nenova (2015): “The shocks matter: improving our estimates of exchange rate pass-through.”

Someone could help me?

jpfeifer · May 11, 2019, 6:26pm

This is usually a timing error. Recheck all equations with a particular focus on predetermined states. Also keep an eye open with respect to problems arising with stocks and a sectoral structure.

JamAl · May 13, 2019, 11:58am

OK, thank you for the response.

My difficulty is with finding what variables are predetermined in the model.
Could it be inflation? Or relative prices? I guess not…

The most straightforward is the internationally traded bonds, but this variable is already lagged.
Also, this model has no capital stock.

Best,

jpfeifer · May 13, 2019, 7:35pm

I know that this is the frustrating part, but as nobody else knows the model, you seem to be on your own here.

JamAl · May 13, 2019, 7:48pm

I’ve lagged the labor stock, and it’s worked.
Thanks!

JamAl · May 20, 2019, 1:55pm

Sorry, I thought I had resolved my problem, but the model isn’t running properly. The IRFs produce bizarre responses (positive output and inflation responses to monetary policy shocks and negative inflation responses to demand shocks, e.g.).

Dynare indicates 23 eigenvalues > 1 in modulus for 25 forward-looking variables.
The usual tip is to lag stocks as predetermined variables. The model has no capital, and thus I lagged the labor stock. But in this case they don’t appear in the current period.

I tried to lag relative prices or inflation rates, but the problems persist.

What should I do?

Thank you.

-------------------------//-------------------------//-------------------------

// model file, Hjortsoe et al model

parameters thetah thetaf sigma n beta alphah alphaf tauh tauf ah af phih phif kappa eta gammahpcp gammafpcp ibar pibar ahR ahPI afR afPI delta b rhoC rhoCstar rhoS;

var Yh Yf C Cstar L Lstar Ch Chstar Cf Cfstar Q bf i istar
ph pf phpcp phlcp pflcp pfstar phstar pfpcpstar phlcpstar pflcpstar
pih pihpcp pihlcp pihlcpstar pifstar pifpcpstar piflcpstar piflcp w wstar pi pistar
x1pcp x2pcp x1lcp x1lcpstar x2lcp x2lcpstar x1fpcp x2fpcp x1flcp x1flcpstar x2flcp x2flcpstar
gammaC gammaCstar gammaS;

predetermined_variables L Lstar;

varexo epsilonC epsilonCstar epsilonS gammaI gammaIstar;

n = 0.05;
beta = 0.99;
delta = 0.01;
b = -11.65447755;
op = 0.3;
ah = 0.715; //1-(1-n)*op
af = 0.715; //1-(1-n)*op
kappa = 1;
eta = 2;
sigma = 1.1;
alphah = 0.6;
alphaf = 0.6;
thetah = 7;
thetaf = 7;
tauh = 1/(1-thetah);
tauf = 1/(1-thetaf);
phih = 0.75;
phif = 0.75;
gammahpcp = 0.4;
gammafpcp = 0.4;
ahR = 0.7;
ahPI = 1.5;
afR = 0.7;
afPI = 1.5;
ibar = 0.010101;
pibar = 1;
rhoC = 0.9;
rhoCstar = 0.9;
rhoS = 0.9;

initval;
Yh = 0.991727466;
Yf = 0.991727466;
C = 2.166593153;
Cstar = 0.20442523;
L = 0.991727466;
Lstar = 0.991727466;
Ch = 0.828855014;
Chstar = 0.008572234;
Cf = 8.424094644;
Cfstar = 0.548354064;
Q = 0.178824091;
bf = -65.17286065;
i = 0.010101;
istar = 0.010101;
ph = 2.302182697;
pf = 0.030675995;
phpcp = 1;
phlcp = 1;
pflcp = 1;
pfstar = 0.171542852;
phstar = 12.87400757;
pfpcpstar = 1;
phlcpstar = 1;
pflcpstar = 1;
pi = 1;
pistar = 1;
pih = 1;
pihpcp = 1;
pihlcp = 1;
pihlcpstar = 1;
pifstar = 1;
pifpcpstar = 1;
piflcpstar = 1;
piflcp = 1;
w = 2.302182697;
wstar = 0.171542852;
x1pcp = 2.8028366;
x2pcp = 2.8028366;
x1lcp = 2.342523776;
x2lcp = 2.342523776;
x1lcpstar = 0.024226991;
x2lcpstar = 0.024226991;
x1fpcp = 2.8028366;
x2fpcp = 2.8028366;
x1flcp = 23.80831589;
x2flcp = 23.80831589;
x1flcpstar = 1.549767343;
x2flcpstar = 1.549767343;
gammaC = 1;
gammaCstar = 1;
gammaS = 1;
end;

model;

// domestic LCP and PCP firms

x1pcp = (thetah/(thetah-1))(C^(-sigma))w(phpcp^(-thetah))(Ch+((1-n)/n)(ph^(-thetah))(Q^thetah)(phstar^thetah)Chstar)+betaalphah(pihpcp(+1)^thetah)x1pcp(+1); //1
x2pcp = (1-tauh)(C^(-sigma))ph(phpcp^(1-thetah))(Ch+((1-n)/n)(ph^(-thetah))(Q^thetah)(phstar^thetah)Chstar)+betaalphah*(pihpcp(+1)^(thetah-1))*x2pcp(+1); //2

((1-alphah*pihpcp^(thetah-1))/(1-alphah))^(1/(1-thetah))=x1pcp/x2pcp; //3

x1lcp = (thetah/(thetah-1))(C^(-sigma))w(phlcp^(-thetah))Ch+betaalphah(pihlcp(+1)^thetah)x1lcp(+1); //4
x2lcp = (1-tauh)(C^(-sigma))ph(phlcp^(1-thetah))Ch+betaalphah*(pihlcp(+1)^(thetah-1))*x2lcp(+1); //5

((1-alphah*pihlcp^(thetah-1))/(1-alphah))^(1/(1-thetah))=x1lcp/x2lcp; //6

x1lcpstar = (thetah/(thetah-1))(C^(-sigma))w(phlcpstar^(-thetah))Chstar+betaalphah(pihlcpstar(+1)^thetah)x1lcpstar(+1); //7
x2lcpstar = (1-tauh)(C^(-sigma))phstarQ*(phlcpstar^(1-thetah))Chstar+betaalphah*(pihlcpstar(+1)^(thetah-1))*x2lcpstar(+1); //8

((1-alphah*pihlcpstar^(thetah-1))/(1-alphah))^(1/(1-thetah))=x1lcpstar/x2lcpstar; //9

// foreign LCP and PCP firms

x1fpcp = (thetaf/(thetaf-1))(Cstar^(-sigma))wstar(pfpcpstar^(-thetaf))(Cfstar+(n/(1-n))((Qpfstar)^(-thetaf))(pf^thetaf)Cf)+betaalphaf(pifpcpstar(+1)^thetaf)x1fpcp(+1); //10
x2fpcp = (1-tauf)(Cstar^(-sigma))pfstar(pfpcpstar^(1-thetaf))(Cfstar+(n/(1-n))((Qpfstar)^(-thetaf))(pf^thetaf)Cf)+betaalphaf*(pifpcpstar(+1)^(thetaf-1))*x2fpcp(+1); //11

((1-alphaf*pifpcpstar^(thetaf-1))/(1-alphaf))^(1/(1-thetaf))=x1fpcp/x2fpcp; //12

x1flcpstar = (thetaf/(thetaf-1))(Cstar^(-sigma))wstar(pflcpstar^(-thetaf))Cfstar+betaalphaf(piflcpstar(+1)^thetaf)x1flcpstar(+1); //13
x2flcpstar = (1-tauf)(Cstar^(-sigma))pfstar(pflcpstar^(1-thetah))Cfstar+betaalphaf*(piflcpstar(+1)^(thetaf-1))*x2flcpstar(+1); //14

((1-alphaf*piflcpstar^(thetaf-1))/(1-alphaf))^(1/(1-thetaf))=x1flcpstar/x2flcpstar; //15

x1flcp = (thetaf/(thetaf-1))(Cstar^(-sigma))wstar(pflcp^(-thetaf))Cf+betaalphaf(piflcp(+1)^thetaf)x1flcp(+1); //16
x2flcp = (1-tauf)(Cstar^(-sigma))pf(pflcp^(1-thetaf))CfQ^(-1)+betaalphaf(piflcp(+1)^(thetaf-1))*x2flcp(+1); //17

((1-alphaf*piflcp^(thetaf-1))/(1-alphaf))^(1/(1-thetaf))=x1flcp/x2flcp; //18

// consumption demand

Ch = ahCph^(-phih); //19
Cf = (1-ah)Cpf^(-phih); //20
Chstar = (1-af)Cstarphstar^(-phif); //21
Cfstar = afCstarpfstar^(-phif); //22

//Ch/Cf = (ah/(1-ah))(ph/pf)^(-phih); //19
//Cfstar/Chstar = (af/(1-af))(pfstar/phstar)^(-phif); //20
//C = ((ah^(1/phih))*Ch^((phih-1)/phih)+((1-ah)^(1/phih))*Cf^((phih-1)/phih))^(phih/(phih-1));
//Cstar = ((af^(1/phif))*Cfstar^((phif-1)/phif)+((1-af)^(1/phif))*Chstar^((phif-1)/phif))^(phif/(phif-1));

// labor supply

kappaYh^eta = wgammaCC^(-sigma); //23
kappaYf^eta = wstargammaCstarCstar^(-sigma); //24

// composition Euler equations

beta*(1+i)gammaC(+1)C(+1)^(-sigma) = pi(+1)gammaCC^(-sigma); //25
beta(1+istar)(1-delta*(Q*bf - b))Q(+1)gammaC(+1)C(+1)^(-sigma) = gammaSpistar(+1)QgammaCC^(-sigma); //26
beta(1+istar)*gammaCstar(+1)*Cstar(+1)^(-sigma) = pistar(+1)gammaCstarCstar^(-sigma); //27

pi = ph(-1)*pih/ph; //28
pistar = pfstar(-1)*pifstar/pfstar; //29

// price indices

1 = ahph^(1-phih)+(1-ah)pf^(1-phih); //30
1 = afpfstar^(1-phif)+(1-af)phstar^(1-phif); //31
1 = gammahpcpphpcp^(1-thetah)+(1-gammahpcp)phlcp^(1-thetah); //32
1 = gammahpcp(phpcpph*(Qphstar)^(-1))^(1-thetah)+(1-gammahpcp)phlcpstar^(1-thetah); //33
1 = gammafpcppfpcpstar^(1-thetaf)+(1-gammafpcp)pflcpstar^(1-thetaf); //34
1 = gammafpcp(pfpcpstarpfstarQpf^(-1))^(1-thetaf)+(1-gammafpcp)*pflcp^(1-thetaf); //35

// inflation rates

pihpcp = phpcppih/phpcp(-1); //36
pifpcpstar = pfpcpstarpifstar/pfpcpstar(-1); //37
pihlcp = phlcppih/phlcp(-1); //38
pihlcpstar = (phlcpstarphstar*pfstar(-1)pifstar)/(phlcpstar(-1)phstar(-1)pfstar); //39
piflcpstar = pflcpstarpifstar/pflcpstar(-1); //40
piflcp = (pflcppfph(-1)*pih)/(pflcp(-1)*pf(-1)*ph); //41

// production functions

Yh = L; //42
Yf = Lstar; //43

// resource constraints

C+Qbf/((1+istar)(1-delta*(Qbf - b))) = phYh+(Q*bf(-1)/pistar); //45

// monetary policy rules

log(i/ibar) = ahRlog(i(-1)/ibar)+ahPIlog(pi/pibar)+gammaI; //46
log(istar/ibar) = ahRlog(istar(-1)/ibar)+afPIlog(pistar/pibar)+gammaIstar; //47

// good markets equilibrium

Yh = ah*(ph^(-phih))C+((1-n)/n)(1-af)(phstar^(1-phif))(ph^(-1))QCstar; //48
Yf = (n/(1-n))(1-ah)(pf^(1-phih))((pfstarQ)^(-1))C+af(pfstar^(-phif))*Cstar; //49

// other shocks

gammaC = 1-rhoC+rhoCgammaC(-1)+epsilonC; //50
gammaCstar = 1-rhoCstar+rhoCstargammaCstar(-1)+epsilonCstar; //51
gammaS = 1-rhoS+rhoS*gammaS(-1)+epsilonS; //52

end;

model_diagnostics;
resid;

steady;
check;

shocks;
var epsilonC = 0.0193875;
var epsilonCstar = 0.1;
var gammaI = 2.2045;
var gammaIstar = 0.1;
var epsilonS = 0.017313;
end;

stoch_simul(order=1,irf = 100,nograph,periods=50000);

jpfeifer · May 21, 2019, 8:12pm

There must be a mistake somewhere. I can only give you the standard advice: try to simplify the model to see what causes the problem.