Growth Model Using Detrending Commands

[diego.gomes]

Hi all!

I want to implement a standard deterministic neoclassical growth model in Dynare. However, I would like to left the detrending process to Dynare, using the commands: trend_var, growth_factor, and deflator. As usual, this kind of model has two exogenous sources of growth: population growth and technological growth. In this case, the variables should be detrended by these two sources of growth. I couldn't figure it out how to apply the above commands to detrend each variable using both sources of growth.

The example below by Johannes Pfeifer detrends each variable by only one source of growth.

https://github.com/DynareTeam/dynare/bl ... ionary.mod

I hope to hearing from you guys!

Best to all!

[diego.gomes]

Can anybody confirm if the statements below are correct in this case?

Code: Select all

var gN gA;
trend_var(growth_factor=gN) N;
trend_var(growth_factor=gA) A;
var(deflator=N*A) k c y;


Thanks!

[diego.gomes]

The following link solved the above question:

http://www.dynare.org/DynareWiki/RemovingTrends

However, in the link, the growth factors are endogenous. In my model, the growth factors are exogenous, taken from data. What is the solution for my case? I'm having trouble solving it.

Best to all!

[jpfeifer]

What do you mean with:

Code: Select all

growth factors are exogenous, taken from data

? Are you trying to do estimation? Or why are the data relevant for your modeling? Following the approach at the link, you could within the model simply define

Code: Select all

g=0.02;

if g is constant at 2 percent.

[diego.gomes]

Thanks jpfeifer!

In fact, I want to compute the the transition from a point in time (e.g. 1970) to the future (e.g. 2015 or SS) in order to evaluate the performance of the model in replicating the data. Hence, from 1970 to 2015, for example, I want to take as given the TFP and the population data, and check if the endogenous variables become close to data. After 2015, I will consider steady state (constant) growth rates for both variables. I don't know to do this in Dynare.

Attached is a sketch of my code. I know it is not complete, but just for you to see how I am using the detrending commands.

Best!

[jpfeifer]

You need to think more about the structure of the exercise you want to conduct. Is it perfect foresight or are innovations to TFP and population growth stochastic and agents react to these surprises? If the latter, the setup is simular to the one conducted via the simult_-function in https://github.com/JohannesPfeifer/DSGE_mod/tree/master/RBC_news_shock_model, where you could feed in a shock sequence for the bivariate shock process

[diego.gomes]

Hi jpfeifer!

As mentioned in the first post, I am using a standard deterministic neoclassical growth model, very simple. Hence, it is perfect foresight, no shocks. Below is the Dynare code for the detrended model (I detrended by hand).

So, two things are still not clear:

1) Writing a non-detrended model and use the Dynare detrend commands to solve the model.

2) Considering the historical values of the exogenous variables (TFP and pop growth rates) in the transition computation. I want to use these historical values until a certain date (e.g. 2015) and after that I consider constant values for these growth rates.

Thanks!

[jpfeifer]

If you are using perfect forsight, there is no reason to detrend the model. Essentially, you just need to provide the exogenous state variable to the solver. That is done via initval, endval, and shocks. Alternatively, you can use an initval file or just manipulate the oo_.exo_var matrix before calling the solver.

[diego.gomes]

Hi jpfeifer,

But if I don't detrend my model, there will be no steady state, right? I think I do need to detrend the model.

[jpfeifer]

A steady state is always conditional on the values of the exogenous variables. In a growth model, the BGP is a sequence of steady states. For deterministic simulations you do not necessarily need to transform this sequence of steady steady states into one fixed steady state, because you can easily compute the terminal condition.