## Modelling non stationary stochastic proceses in an RBC model

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### Modelling non stationary stochastic proceses in an RBC model

Dear All,

I would like to know if there is a way DYNARE can solve an RBC model where the error structure is stationary on first difference (ie: y(t)=x(t)-x(t-1) and y(t)=rho*y(t-1)+epsilon(t))(I am particularlly interested in solving using Dynare Mary Finn's (1995 Jornal of Economic Dynamics and Control) RBC model with variable depreciation, variable capital utilization and were the error structure is non stationary). I can transform the model to stationarity but I am interested on the moments and the dynamics of the nonstationary model.

Thanks,

Luis
luis

Posts: 2
Joined: Mon Jan 16, 2006 3:09 pm

### RE: nonstationary models

Dear Luis,

in short, you must stationarize your model before linearizing and solving it.

Because your model is nonstationary, it can wander very far from the point around which you would linearize it and the linear approximation could be very bad. So it is much better to stationarize first and linearize second.

Furthermore, you wouldn't learn much directly from a nonstationary model. Its second moments of the nonstationary variables are infinite and, if there is a deterministic trend in your model, there is no constant mean either.

With Dynare, the best strategy is to solve the stationarized model with stoch_simul, simulate the stationary variables and reconstruct ex-post the nonstationary simulated variables.

Best

Michel
MichelJuillard

Posts: 680
Joined: Thu Nov 18, 2004 10:51 am

### Re: RE: nonstationary models

Thanks a lot Michel for taking the time to answer,

In order to calculate the moments of the non-stationary model ex-post, I would have to do the folowing (for any non-stationary variable):

var(y)=E((ybar*z)^2)-(E(ybar*z))^2

were ybar=y/z is the stationary counterpart of the non-stationary variable y and z is the non stionary stochastic shock

The second term of the right hand side of this equation can be deduced using dynare but I don't have a way to compute the first term. Do you have any suggestions?

Sincerely,

Luis

MichelJuillard wrote:Dear Luis,

in short, you must stationarize your model before linearizing and solving it.

Because your model is nonstationary, it can wander very far from the point around which you would linearize it and the linear approximation could be very bad. So it is much better to stationarize first and linearize second.

Furthermore, you wouldn't learn much directly from a nonstationary model. Its second moments of the nonstationary variables are infinite and, if there is a deterministic trend in your model, there is no constant mean either.

With Dynare, the best strategy is to solve the stationarized model with stoch_simul, simulate the stationary variables and reconstruct ex-post the nonstationary simulated variables.

Best

Michel
luis

Posts: 2
Joined: Mon Jan 16, 2006 3:09 pm

### Re: RE: nonstationary models

luis wrote:var(y)=E((ybar*z)^2)-(E(ybar*z))^2

were ybar=y/z is the stationary counterpart of the non-stationary variable y and z is the non stionary stochastic shock

I'm sorry but if z is nonstationary, var(y) is infinite...

Michel
MichelJuillard

Posts: 680
Joined: Thu Nov 18, 2004 10:51 am

### Re: RE: nonstationary models

I was aware of the infinite variance of a non stationary stochastic process. However I was confused because, M.G. Finn, in the 1995 article: "Variance Properties of the Solow Productivity Residuals and their Cyclical Implications", Journal of Economic Dynamics and Control reports the variances of the non stationary variables. I will take a more carefull look at the article.

Luis

MichelJuillard wrote:
luis wrote:var(y)=E((ybar*z)^2)-(E(ybar*z))^2

were ybar=y/z is the stationary counterpart of the non-stationary variable y and z is the non stionary stochastic shock

I'm sorry but if z is nonstationary, var(y) is infinite...

Michel
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