# Model with a balanced growth path

Hi,

I am not sure how appropriate this is for this forum but I thought I’d try.

I am trying to do a similar exercise to this paper. What the paper does is essentially:

In particular I am trying to replicate the numbers from the figure given on page 25 (i.e. optimal capital tax rate vs Frisch elasticity). I am unable to get the same numbers for the optimal tax as the figure does and I am wondering if everything I am doing is kosher.

i) I ran the detrended model through dynare using an order = 3
ii) I used simult_ to simlulate a series (with no shocks) which starts at initial values equivalent to the steady state at tau_k = 0 (as given on page 23)
iii) Until the series converges to BGP, I make a series for Q (TFP essentially), and calculate per period utility according to equation 21. Once the series gets close enough to the steady state, I use equation 41, given in the footnotes of page 18, not forgetting to rescale c
iv) Calculate total welfare by ading up welfare from non-ss path and the welfare from the ss path
v) Loop over this using different values of tau_k.

This seems like the same process the authors use to get to an optimal capital tax rate but unfortunately I dont get the same values for a given Frisch Elasticity. For example, for an elasticity of 1/0.5, I get an optimal tax of 0.17, while they get a negative tax (a subsidy essentially). For an elasticity of 1/2.5 i get an optimal tax of 0.47. The numbers aren’t supposed to exactly match those of the paper’s because of the different value taken for G_0, but it should be in the same range. But the direction of the relationship between Frisch elasticity and the optimal tax rate seems to be teh exact opposite of what it should be!

I am not entirely sure what I am doing wrong, and I hope someone with the patience can enlighten me on where to look.

Thank you. I am attaching the .mod and .m files I use for reference. “AA_runmodel.m” runs the exercise from start to finish for a given set of parameter values.

caplabtax_paper.zip (3.1 KB)

I currently don’t have the time to look into other people’s replication attempts in detail. For now, I can only recommend to follow the original paper in every aspect to preclude other changes causing the difference. If that does not help, you may be able to ask the authors for their code.