(In this post, I will be using a slightly modified version of the model with the output-gap-indifferent monetary policy rule in my last post for analysis)
This first chart shows the log deviation from steady state of (left to right, top to bottom) real GDP, capital, labor, consumption, investment, real wages, the real interest rate, the nominal interest rate, and the gross rate of inflation (inflation rate plus one) in response the the fiscal stimulus outlined above. Output does increase by the full 2% reflected in the shock and, unlike before, the capital stock and consumption increased which means that the addition of cuts in "distortionary" taxes can negate some of the negative crowding out effects of stimulus.
The problem I have had with most of the papers I have read on fiscal stimulus is that taxes usually take the form of lump sum transfers to and from the government. There are no income, capital, or consumption taxes that distort the outcome. For simplicity's sake, I'm just going to look at the effects of stimulus with income taxes because they seem to be what most politicians focus on. Before I go further, a short description of how fiscal policy works in my model in order. The government receives tax revenue from lump sum taxes (which don't cause distortions) and from income taxes and spends all of its revenue While technically, there are not deficits, the lump sum transfers serve as a neutral way of allowing government spending to be less than or greater than income tax revenues.
The stimulus takes the form of a simultaneous unexpected positive shock to government spending and negative shock to the income tax rate with a persistence of $ \rho $ (which I have set to 0.9). Also, its worth stating that the central bank is still targeting inflation but is indifferent to the output gap, but will stabilize output in the long run because of the nature of New Keynesian models (namely the structure of the New Keynesian Phillips Curve). Without further adieu, here are the charts along with some brief explanations:
Figure 2 shows the fiscal effects of the stimulus where (in log deviations again) T is the lump sum transfer, g is government spending, rev is government revenue from income taxes, and t_n is the income tax rate. Everything looks pretty normal; taxes and revenue go down while spending goes up. Revenue doesn't go the full 1% down because of the increase in output from the stimulus, but, because of the way I set things up, government spending makes up for the lack of revenue reduction (that sounds like a really strange thing to say in a normal context).
I guess the point here is that even adding just one tax that distorts one thing (in this case the marginal rate of substitution between consumption and labor) can drastically increase the effects of what would otherwise be somewhat dubious policy. Of course, a central bank that ignores the output gap is a bit unrealistic, but it allows for a more raw view of the real effects of fiscal stimulus.
P. S. I did run a simulation with a normal monetary policy rule. The graphs are here.