# DSGE detrending

Hello everyone,

I’m new on Dynare and DSGE modeling in general. I’m currently building a DSGE model with a final output sector, three intermediate inputs, and households and government sector. The three intermediate inputs are used to produce final output.

Two of the intermediate sectors use only capital, labor, and Total Factor Productivity (TFP), while the third one uses capital, labor, TFP, and capital organizational inputs (representing technical change). I want to interpret my results as deviations around the steady-state level.

I noticed in some papers that when innovation affects all intermediate inputs, variables such as Y (output), C (consumption), I (investment), and G (government spending) are divided by the technical change variable. Otherwise, the interpretation will be a deviation around the growth rate of the steady state.

So, my question is: if my technical change variable affects only one of my three intermediate sectors, do I need to detrend aggregate variables?

Thank you.

Which type of simulation do you have in mind? Stochastic or perfect foresight? And does your model feature a balanced growth path?

Hi,

It is not possible to run stochastic simulations with `stoch_simul` (perturbation) if your model does not have a well-defined BGP, because we need to approximate the model around a steady state. You have to provide a detrended version of the model, which is not possible if your model does not have a BGP.

The absence of a BGP is also a problem for deterministic simulations because perfect foresight models require a terminal condition.

So unless your model is backward looking (no expectations) it is not possible to simulate a model without BGP.

Best,
Stéphane.

I got it, thank you.
But how to identify the variables that exhibit long-term trends in the DSGE model ? Why in many papers the detrending takes the form of Y_t / A_t, C_t / A_t, I_t / A_t …? (I know that in Solow model the change in growth is only caused by the change in TFP, is that the reason ? ) The detrending can be done with another variable ?

Theory roughly tells us that for a balanced growth path to exist, you need labor augmenting technology growth. Aggregates will then mostly inherit that trend. These theoretical results guide the detrending.

It depends on the model and the variables. You may have more than one trend (population, price, …) and some of the variables in the model may be stationary (e.g. the unemploymen rate). When you build a model you must be able to associate each variable to trends (if the variable is non stationary).

Best,
Stéphane.

Great thanks…
do you have a reference to suggest explaining the subject ?

Best