Problems on a model with trend

General DSGE Modeling
#1

Dear Professor Pfeifer,

I am learning the DSGE model set by LWZ(2013) in Land-Price Dynamics and Macroeconomic Fluctuations. This is the first time I handling a model with specified trend. I’ve got a few problems about it. Would you please give any tips? Thank you for your precious time.

  1. I learn the process of dealing with this kind of model in their appendix (
    SUPPLEMENT TO “LAND-PRICE DYNAMICS AND MACROECONOMIC FLUCTUATIONS”.pdf (587.1 KB)
    ). However, I am quite confused why {{\Gamma }_{t}} is defined as {{\left[ {{Z}_{t}}{{Q}_{t}}^{\left( 1-\phi \right)\alpha } \right]}^{1/\left( 1-\left( 1-\phi \right)\alpha \right)}} on page 9. What is the reason to give this definition?

  2. If I want to add trend in my model, could I just consider one type of trend?

  3. On page 53 in your guidence A Guide to Specifying Observation Equations for the Estimation of DSGE Models, Does the sentence “This section will thus be mostly concerned with using data in first differences” mean that we’d better use data in first differences rather than the data filtered by one-sided HP filter?

Thank you so much for reading this post, and sincerely looking forward to your reply.

#2
  1. With two sources of growth (investment specific and labor augmenting), this expression yields the composite growth rate of the economy on the balanced growth path.
  2. Yes, you could set one of the elements to a constant (Z_t or Q_t).
  3. For these types of models where you have unit roots with drift, it is common to use first differences.