 # Non-explosive debt in a Perfect Foresight setup

Good afternoon everyone,

I would like to know how one fixes the reaction parameters of passive fiscal instrument to the deviation of debt. I have three instruments: taxes, which are exogenous (active policies), and public spendings and social transfers, which are the passive policies. My issue is with gamma(g) and gamma (tr). I cannot find any literature on these. Is there a simple way to define passive policies? I would rather take a different approach that consists in separating the fiscal stance (i.e. the size of the public deficit) from the instruments of that policy (the tax rates and public spending).

You would have a single γ parameter appearing in the equation determining the fiscal deficit. For a eurozone country, there’s a natural value for this parameter, given by the debt criterion of the Stability and Growth Pact. It is equal to 1/20 (in annual frequency), assuming the steady state debt is 60% of GDP (in reality, the criterion states that it’s the 3-year moving average of debt-to-GDP that should be diminished by 1/20th of its distance to the 60% target).

Then you need to decide how to implement that policy. There are many options. One is to have all instruments constants, save one which will bear all the adjustment. Another option is to have the share of all taxes constant in the total tax revenue (and probably keep spending constant).

Best,

It is always hard to transplant fiscal rules from other papers, because specifications often differ. One reference that always shows up in this context is Leeper/Plante/Traum (2010)

Thanks for the ref. However, the authors work in a stochastic set up.

Best

Working in a stochastic setup should not alter the strength of fiscal feedback

Is that form okay? With taxes and transfers being constant and public spendings doing the adjustment What if I want to perform a permanent shock on labor taxation? Can I still write down tau(l) as being a constant or time-subscripted tau(l)?
Thanks

The equations looks good to me.

Of course, if you want to introduce a permanent shock on τₗ, you have to declare that variable as an exogenous (I’m assuming you’re doing a perfect foresight simulation).

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Good afternoon,

I’m getting back at that topic. I just would like to know, when computing my BGP variables for my initial block, should I fix my public spendings (from the long run ratio to output) to compute debt at BGP?

Transfers and taxes are constant here, only government spending do the adjustment. SO my first hint is that I should be able to compute the BGP value of public spendings G and debt. But when doing so, I can’t manage to do. I have three hints:
a) Find BGP debt from the household’s budget constraint, and then compute public spendings BGP from the government equations
b) Find public spendings at BGP from the resource constraint and find debt BGP value from the government equations.
c) Fix the debt value at BGP (long run debt/gdp ratio) and find public spendings at GDP from government equations
Thank you.

Best regards