Perfect Foresight for Monopolistic Competition Model with flexible prices and wages


I am trying to run a perfect foresight simulation to see the effect of labor income taxes on household utility. Unfortunately DSGE modeling and I are not on good terms :sweat_smile: and I struggle to understand which equations I can (and should) use for my model. I ran a similar model setup with a productivity and monetary shock, but I’m not able to apply this to this fiscal shock. This is the model I am trying to set up:

Households have an instantaneous utility function that depends on C, consumption; N, hours worked; (1/theta), the intertemporal elasticity of substitution; and (1/phi), the Frisch elasticity of labor supply.

They are under the following budget constraint:
P(t)*C(t) + 1/(1+i(t)) * B(t) + T(t) = (1 - theta(t)) * W(t)*N(t) + B(t-1) + PI(m)
where i is the nominal interest rate, B are government bonds, T are lump-sum transfers and PI are the profits of m firms (as households are the owners). There is no capital in the model, but saving is somewhat implemented using the bonds.

The shock I want to simulate is a 5 % decrease in the labor income tax rate for some periods, like this:
theta(t) = theta(bar) - epsilon(theta)
where theta is the labor income tax rate (the bar denotes steady state) and epsilon is the fiscal shock.

I want the income tax reduction to be financed by debt using this government budget restriction:
where gamma is the constant share of spending on GDP, b is the real public debt share, w is the gross real wage and t is the real share of lump sum taxes on GDP.

The government reacts to this debt by adjusting the lump sum taxes according to:
t(t) = t(bar) + omega(b) * (b(t-1) - b(bar))

So this is what I would like to do: I want to plot labor income tax rate, net and gross real wage, working hours, HH utility, output, consumption, nominal and real interest rate, public debt, lump-sum taxes and inflation. Can you help me finding the formulas I can use to set this up? Sorry for such a broad question, I have tackled this several times but found myself stuck somewhere again and again…

I hope I described the setup thoroughly enough, if you would need more information, please let me know! Unfortunately I couldn’t show more formulas, like the HH Utility function or others. I hope it is still enough info.

You can use the rplot command followed by the variable name you want to plot at the end of your .mod file.

This seems like a straightforward DSGE model you would need to set up. The first step would be to derive the first order conditions for your envisioned setup. Shocking particular variable is usually straightforward once the basic model works.