Two Agents Model and Steady State

General DSGE Modeling
1

Dear all,

when solving the two agent RBC model below(Tank.mod), I run into problems with the steady state.

In preparation for a model with heterogeneous human capital I started out with the most basic two agent(Tank) model, to get fast first results and an idea for basic dynamics. Now I am stuck for quite a while with issues on the steady state.

My basic Tank model just features static high and low productivity in workers (hh,hl), both groups are just half of total population.

When solving the model with dynare I encounter the following problems:

  • Not all solve_algos find a steady state. (Following problems base on solve_algo = 1)
  • Steady state values found depend on initial values. This comes unexpected to me.
  • When running IRFs assets and consumption (ah,al,ch,cl) do not return to zero but persistently deviate from the steady state previously found by dynare (as in oo_.steady_state)
  • Values in oo_.steady_state differ from what I expected from my calculations.

Mod files are added below as Rank.mod and Tank.mod. Added the simple representative agent version, to check that basic equations are fine and the problem appears when expanding to two agents. Rank version is running fine.

Did I miss anything in my equations or is there eventually an indeterminacy issues with assets between the two agents? I have tried around for quite a while and could not find any solution to the deviating IRFs or steady state issues. Unreasonable initvals can lead to proper IRFS. But I expect this kind of workaround to be improper and to fail when adding accumulation of human capital or heterogeneous agents.

Thanks in advance for any suggestion

Best Sven

Rank.mod (842 Bytes)
Tank.mod (1.4 KB)

2

Your model features a unit root, which explains both the permanent IRFs and the fact that there are multiple steady states.

3

Dear Prof. Pfeifer,

thank you very much for your answer, this gave me a lead how to continue, while it took quite a bit until I returned to this project.
I solved my model with nonlinear methods, policy function iteration. That attempt yielded unique policy functions and a unique steady state.

I am still wondering, why the linear model runs into problems with multiple steady states. Could it be the problem that it is not determined, which of the two households owns how many assets, due to the linearity of the policy function? (While the curvature of the nonlinear policy functions apparently solves this issue.) Linear policy functions c_low(a_low,a_high), c_high(a_low,a_high), determine the ratio between assets a and consumption c, but not the ratio between a_low & a_high?

It would be great to know if that interpretation is correct and if there could be some simple workaround to repair the linear model?

4

I don’t know your model, but what you describe sounds sensible. In linear models, asset allocations are often indeterminate.