I have a model with two stochastic trends. I have coded it successfully with standard preferences and now am trying to use Jaimovich-Rebelo preferences. In this case I get the “trends not compatible with balanced growth path” error. The only differences are in the four equations that involve the J-R preferences. As far as I can tell, growth should still be balanced, with labor constant. I have attached the code for both cases: Standard preferences (Model_fttb1S3.mod) and J-R preferences (Model_fttb1s3GHH). The second includes the equation X_t = X_{t-1}^{1-\psi} c_t^\psi and assumes \psi=0.25. Otherwise the only differences are the equation for “chi” (line 59) from the FOC for consumption, and the two FOCs for labor (lines 66-67 that substitute for the commented-out lines 64-65). In both models I provide the steady state (that I solved for numerically) in an initval block. I know the balanced growth test can be sensitive so the values in the initval block have lots of decimal places.
I think I have figured out the problem. My initval values were very slightly off from the steady state, and the balanced growth test, as I have learned from Professor Pfeifer, can be very sensitive to being even a very small distance from the steady state.
Actually, I am still having an issue with this. I am trying to use the Jaimovich-Rebelo assumption of \psi=0.001 (very close to GHH preferences). I have been able to get as close as \psi=0.0015, but only if I put the steady state for \psi=0.002 in the initval block (fttb1S3JR2.mod). When I use the steady state for \psi=0.0015 (fttb1S3JR1.mod) I get the balanced growth error again. I don’t know why the first trick works, as the steady states are very far apart, and I haven’t been able to find a similar trick to solve the model for \psi=0.001.
In case this isn’t clear, the issue is that using actual steady state in the initval block for very small values of \psi results in “trends not compatible with balanced growth error.” Using the steady state for a different value of the \psi parameter (sometimes) works.
I have commented out the simulation and estimation portions in the mod files, so they run (or don’t) in milliseconds. Appreciate any help you can provide, thanks. fttb1S3JR2.mod (7.3 KB) fttb1S3JR1.mod (7.3 KB)
Thanks, yes, that makes sense.The steady state is very sensitive to \psi when \psi is small. It’s just odd that for these small values of \psi I get the error if I start at the actual steady state, but sometimes not if I set initval at the steady state from a larger value. But I can live with that work-around.
The residual tolerance is an absolute measure in the check, not a relative one. If you use a “wrong” steady state for the initial values, it may shift the residual to a different equation where it may reduce the equation residual although the relative mistake for for each variable may be bigger.