А model without balanced growth

Hello! I am trying to apply a very basic model, which is described in Dynare User Guide, to an economy without balanced growth path. For example, consider an equality y_t = i_t + c_t. Statistics for my economy shows that investments decrease over time, consumption increases rapidly, and y increases slowly. So there is no balanced growth here. Do I understand correctly that there is no way to rewrite this model in such a way it has a steady state and hence there is no way to perform an analysis of impact of stochastic shock?

Best regards, Stanislav.

Are you sure you are not looking at a portion of IRF after a shock? If so, the shock is realized in the economy in its steady state.

Also, Dynare would stumble if there is not steady state in the model. I would suggest checking Dynare’s User Guide (not the manual) for a starter.

Yes, I am sure, I am looking at the official statistical data for my economy, and I see more or less stable trends described in my previous message. So my question remains: is there a way to rewrite a model or do something else so Dynare would be capable to handle it, or nothing can be done?

There are a two issues here:

  1. Do you think that the non-balanced growth is a “steady state” feature or something that happens during the transition to a balanced growth path (e.g. catch-up growth)? I do not have much experience with models of the first class, featuring things like generalized balanced growth paths. Note also that countries like the US feature some (moderate) degree of capital deepening that is very hard to model in one-sector economies, but people consider this still to be consistent with balanced growth as there is no massive trend over time.
  2. Are you thinking about a stochastic model or a perfect foresight/deterministic one? Stochastic models are linearly approximated around an approximation point whose dynamics are meaningful for the experiment under consideration. In that case, non-balanced growth may be hard to model, because there is no steady state around which to approximate.

Regarding your first question, I would like to know how to distinguish these cases. Regarding your second question, I would like to build a stochastic model, and I am aware it requires a steady state, which is a source of my trouble.

For the first issue, there is no general answer as we do not know the data-generating process. Thus, it is your decision whether you think that i) there will be balanced growth in the long run and the current behavior is just convergence to this point or ii) that non-balanced growth is a feature of the data that you need to model. Section 4 of Fernald (2014): “Productivity and Potential Output Before, During, and After the Great Recession” at frbsf.org/economic-research/files/wp2014-15.pdf might be informative to guide your thought process.