# DSGE growth model and detrending

Dear users,

Do I have to detrend all my variables (variables expressed in labor efficiency units) to simulate a growth model? Or can I just express them in per capita?

Data and the model should be detrended in the same way, right?

You need eleborate. What exactly are you trying to do? Estimation? Or just a simulation? If the latter, do you do a stochastic simulation or perfect foresight?

I am trying to do stochastic simulations of my model (and some forecasting). I also have some parameters to estimate from some observable variables.

Best regards

For stochastic simulations, your model needs to have a well-defined steady state. So you cannot have growth trends in the model, i.e. you need to write down a model with well-defined BGP and add the trend back later, e.g. by relying on first differences. The same applies for estimation, where you need to use a stationary transformation of the data.

That’s what I thought: detrending the model and the data.

So if I want nice graphs exhibiting growth trends, I have to do a deterministic simulation of my model ?

Have a nice weekend

No, you need to work with the detrended model and later add the trend back. That is straightforward.

OK thank you very much.

Do you know a textbook for derivating the BGP with nested-production functions in an economy? I am having a hard time doing it and cannot find anything on the net.

Best

Unfortunately, I am not aware of such a reference.

Thank you.

One last question: if I simulate my model from 2017 to 2035, will my steady state represent year 2035 (or 2017?), since it is the long-run state of my economy? I calibrate the values of my parameters on year 2017 representing a near to zero output gap.

“long-run” in this context (a linear model) means not a particular year, but rather the long-run average over time or where the economy is if there are no shocks happening.

Good evening,

I am finally working on a perfect-foresight model. In that case the model does not have to be stationary, right? So I can put my model without detrending. In that case, do I still need to specify growth trends (I have two of them)?

What about bayesian estimation? Do I have to transform the data?

Thanks

1. No, perfect foresight models need not be stationary. See e.g. https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Solow_model/Solow_nonstationary.mod
2. For Bayesian estimation, you cannot use perfect foresight. Both model and data need to be stationary.

Oops… So how do I estimate my elasticities of substitution if I cannot use bayesian estimation?

Thanks

Without context that is hard to tell. Why can’t you detrend your model?

I have two different technical progress, so my model won’t be stationary in Uzawa’s sense. I’m gonna try to shut down one technical progress, so I only have labor-augmenting technical progress and can stationnarise the model. I think it’s best.

Can I use perfect foresight with a stationary model and perform a Bayesian estimation? Or does it have to be in a stochastic environnement necessarily?

Thank you

Bayesian estimation requires a stochastic model.

Damn…

Well. I’m going to try to simplify my model as much as I can then.

Thank you.

Have a nice WE

Is it the same for maximum likelihood estimation? Does it require the model in stationary form?

Thank you

Yes. As soon as you want to construct a likelihood function, you need a stochastic model.