Explicitly specified trend to TFP (not labor augmenting)

General DSGE Modeling
1

Greetings!

Section 5 in Johannes Pfeifer’s guide on specifying observation equations deals with writing a stationary representation into Dynare of models with an explicitly specified trend. The focus is on labor augmenting technology growth. However, suppose instead that there is trend growth in TFP. Is there a simple example representing this? In effect, I am curious about the analogue to Listing 9.

With TFP growth, there is a different balanced growth rate for technology as for the other variables, but it should otherwise not pose any problem. (I suspect I am asking something somewhat trivial, and I apologize in advance for this.)

Warm regards.

2

The reason I focused on labor-augmenting technology is that a balanced growth path requires technology to be represented in that form. Thus, generally TFP growth can be written as labor augmenting growth (usually due to the use of a Cobb-Douglas function).
Y_t=A_t K_t^\alpha N_t^{1-\alpha}=K_t^\alpha\left(A_t^{1/(1-\alpha)} N_t\right)^{1-\alpha}=K_t^\alpha\left(\tilde A_t N_t\right)^{1-\alpha}

3

Greetings. Yes, the point about balanced growth makes sense. I only raised the issue because some papers seem to specify TFP growth directly.