Discount rate in DSGE

Dear all,

I wondered if having a discount rate between 0.97 and 0.98 was low or not. I compute this discount rate to reach a specific rental rate of capital that is 0.12 yearly, I also have capital taxation of 0.3 and depreciation rate of 0.07. But I see a lot of studies fixing it to 0.99. I do not fix it as I need to reach a specific r that I computed from (operating surplus + consumption of fixed capital) / net capital stock.

Thank you

You can look at whether the studies you mention consider monthly, quarterly, or yearly models.

You did not really tell us the frequency of the numbers. But if you have a dedicated calibration target, then your approach and your number should be fine.

@jpfeifer the frequency is annually and yes beta is calibrated as to reach a specific rental rate target that I find to be quite high (11.5%) when I compute it from (operating surplus + consumption of fixed capital) / net capital stock. But it’s the only way for me in my model to have the exact VA of the economy.

Thank you

As I wrote, this should be fine.

Dear @jpfeifer ,

In a perfect foresight set up, when having detrended completely the model, in some accumulation equations the gross rate appears such as in the capital accumulation equation. However, when I run the model, Results, if not rescaled, show the evolution of variables in a world with no growth, correct ? I was just wondering if the magnitude of values I put for the economic growth rate in the detrended model were crucial.

Thank you

That question cannot be generally answered. If the net growth rate is close to 0, then it will not matter at all. If it becomes bigger, then the value will of course affect the solution.

Thank you @jpfeifer . Thats what I want as results: growth rate being equal to 0. However when I set it up to 0 I have problems with simulations with Nan or Inf in the jacobian, because some variables become 0 and their exponent is below 0. That’s why I was wondering if it where possible to just put a positive growth rate in the detrended model, and just not rescale the variables so the results coincide with an economy at SS with no growth.

That suggests that, for some reason, the zero growth rate is not numerically nested in your model due to an asymptote. Moving closer to that asymptote instead of computing the particular case you have in mind is often not a good idea.

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