Hello everyone,

This is the first time that I write in this forum.

I need to representate a transitionary steady state. This is the context:

In particular, it is a stochastic model with many exogeneus shock. But, I think that the steady state must change for economic reason. I know the steady-states values of starting and ending, I just need the command (or the way) to join.

From what I have read, I found as possible solution: histval or endval. Eventually, if someone have other ideas or paper, I would be very grateful.

Another question, in the steady-state’s stage (section 4.7 of manual) , the subsection that I have to pay attention is deterministic model or stochastic model?

Steady state transitions are usually done in perfect foresight. But without more context, it is impossible to tell. DSGE_mod/Stock_SIR_2020.mod at master · JohannesPfeifer/DSGE_mod · GitHub and DSGE_mod/Solow_SS_transition.mod at master · JohannesPfeifer/DSGE_mod · GitHub are examples of such transition studies.

Thanks professor.

Another question. How to estimate with transition steady state?. That is, how to say to Dynare considering a transition steady state with the estimation command?

Thanks

What exactly do you want to do?

Hello Professor,

Ok. I hope it is understood. I have a stochastic model (DSGE) that has a single steady state. With the model I can solve it and perform Bayesian estimation.

Now, my challenge is to do a same, but with transition steady state. That is, with the same model I must agregate transition steady state. So, Im confused, becouse I don’t know where should I make changes.

For example, I attach a simple model. How to declarate transition steady state?

//=========================================================================
// Part I: Declarate
//  I.1 - Endogenous variables
var piV xV iV piObs xObs iObs;

//  I.2 - Exogenous variables
varexo epsm epsd epsi;

//  I.3 - Name of the parameters
parameters betta iota xi h sigma phi alfa rho ipi ix sigm sigd sigi;

//      I.3.1 Initialize parameters
betta = 0.995; //household discount factor
xi    = 0.75;  //price stickiness (Calvo)
iota  = 0.75;  //price indexation
h     = 0.75;  //habit persistence
sigma = 2;     //inverse intertemporal elasticity of subst.
phi   = 2;     //inverse Frisch labor supply elast.
alfa  = 0.3;   //1-labor share
rho   = 0.75;  //interest rate smoothing
ipi   = 1.5;   //inflation coeff.
ix    = 0.125; //output gap coeff.
sigm  = 0.25;  //Std. dev. markup shock
sigd  = 0.25;  //Std. dev. demand shock
sigi  = 0.25;  //Std. dev. monetary policy shock
//=========================================================================

//=========================================================================
// Part II: Declarate Enviroment
//  II.1 - Equations
model;
piV=betta/(1+iota*betta)*piV(+1)+iota/(1+iota*betta)*piV(-1)
+(1-xi*betta)*(1-xi)/(1+iota*betta)/xi*((alfa+phi)/(1-alfa)+sigma/(1-h))*xV
-(1-xi*betta)*(1-xi)/(1+iota*betta)/xi*sigma*h/(1-h)*xV(-1)+sigm*epsm;  //Phillips curve
xV=1/(1+h)*xV(+1)+h/(1+h)*xV(-1)-(1-h)/sigma/(1+h)*(iV-piV(+1))+sigd*epsd;  //IS curve
iV=rho*iV(-1)+(1-rho)*(ipi*piV+ix*xV)+sigi*epsi;                            //Taylor rule

//  II.2 Measurement equation inflation
piObs=4*piV;    //inflation
xObs=xV;        //ouput gap
iObs=4*iV;      //interest rate

end;
//=========================================================================

//=========================================================================
// Part III: Results and Estimations
//  III.1 - Initial guesses for steady state computations
initval;
piV=0;
xV=0;
iV=0;
piObs=0;
xObs=0;
iObs=0;
end;

//  III.3 Compute eigenvalues
check;

//  III.4 Define variance of shocks
shocks;
var epsm=1;
var epsd=1;
var epsi=1;
end;

//  III.5 Solve and simulate model
stoch_simul(order=1,irf=20,nograph) piObs xObs iObs;
//=========================================================================

//=========================================================================
// IV. Empirical Estimation (Full Information Bayesian Approach)
//  IV.1 - Observed data (in usdata.m)
varobs piObs xObs iObs;

//  IV.2 - Priors of estimated parameters
// (parameter_name, start_value, lower_bound, upper_bound, distr, mean, sd)
estimated_params;
xi,,,,beta_pdf,0.75,0.1;
iota,,,,beta_pdf,0.75,0.1;
h,,,,beta_pdf,0.75,0.05;
sigma,,,,gamma_pdf,2,0.5;
rho,,,,gamma_pdf,0.75,0.05;
ipi,,1.01,,gamma_pdf,1.5,0.1;
ix,,,,gamma_pdf,0.125,0.05;
sigm,,,,inv_gamma_pdf,.25,inf;
sigd,,,,inv_gamma_pdf,.25,inf;
sigi,,,,inv_gamma_pdf,.25,inf;
end;

//  IV.3 - Options for reporting of credible sets
options_.mh_conf_sig= 0.95;
options_.prior_interval= 0.95;
options_.conf_sig= 0.95;
options_.nograph=0;

//estimate model using Bayesian Maximum Likelihood
estimation(first_obs=1,
datafile=usdata,
order=1,
lik_init=1,
mode_compute=4,
mode_check,
%mode_file=nk_fullinfo_estimation_mode,
%mode_file=nk_fullinfo_estimation_mh_mode,
mh_replic=2000,
mh_nblocks=2,
mh_init_scale=.75,
mh_jscale=.75,
mh_drop=0.25,
filtered_vars,
bayesian_irf,
moments_varendo,
forecast=4,
smoother) piObs xObs iObs;

I am still lost. If your model is Blanchard-Kahn stable, it will return to a steady state. What do you mean with transition steady state? Also note that Bayesian estimation will be based on a linear approximation around a steady state. The initial states will be estimated as well and can be away from the steady state. But how do you envision transition behavior? As a deterministic process?

Professor,

Thanks for your response. I mean that variables start in a steady-state “A” and end in another steady-state “B”. Maybe I am mistake, is it extremely necessary estimate a model with only one steady-state?.

Regarding to the another question, I only know the starting and ending point.

Thanks

Are you dealing with a model with multiple steady states? Or is there a shock moving the steady state?

Professor,

I’m dealing a model with multiples steady-states. Is it possible to estimate?

Thanks.

But what determines your convergence from one steady state to the other one? And which type of solution technique did you have in mind? Approximation around a steady state should be problematic.