# How to determine variables detrend in DSGE model?

Recnetly, I read a paper written by Smets & Wouters(2007), and I found that different variables have different trend, so when detrending variable is divided by a different denominator, i.e. the trend. My question is how to determine variables trend, i.e. denominator? for example, c_t = C_t/\gamma^t, w_t = W_t/[P_t \gamma^t], how to determine \gamma^t, P_t\gamma^t? some variable’s denominator may be just P_t, \tilde p_t = \tilde P_t /P_t.

In most models that have only one source of growth, it is the technical progress that stimulates labour, that is growing. The model’s restrictions will determine which variable will grow with what trend. See the old paper by King, Plosser and Rebelo. Also, I think the technical appendix to Smets and Wouters 2007, also shows which variable grows at what rate.

Cheers
Reuben

Thanks for your reply. Yes, I have seen the appendix, but I want to konw further(it’s not just the paper), what variable trend is related to technical progress, what variable trend is influenced by price, and what variable is determined by both? could we get the trend information from mathematical expression of each variable?

Usually, you can see from the production function and the budget constraint the growth rate of real aggregates. That allows computing the growth trends of variables derived from that. A different animal are nominal objects. Here, the trend of the price level needs to be taken into account.

OK, thank you, I got it.

Hi, I was wondering if dynare can do automatic detrending? I happened to notice that it was part of the future plan:

Automatic detrending is not yet possible. For purely backward models, you may be able to compute the BGP automatically. @stepan-a should know more.