The Lesser of Two Evils: Choosing Optimal Methods of 'Distortionary' Taxation

The ideal method of taxation comes up frequently in political debate. Governments often tweak the levels of financing they receive from a wide gamut of taxes. Of course, most of the debate over government policy remains uninformed by the members of academia so the various recommendations for ideal methods of taxation have little basis in economic theory.

Here, I won't pretend to be any kind of expert on fiscal policy, or even computing (Ramsey) optimal policy in general, but I will compare welfare under a "High Income Tax - Low Consumption Tax" regime and a "Low Income Tax - High Consumption Tax" regime in an attempt to add some model-based input.

I ran two different simulations. The first one determines which regime is better for consumer welfare when there is a 1% shock to the government spending to GDP ratio and the second one looks at which regimes provides more welfare and/or more tax revenue in the long run (steady state). As it turns out, the results to each test are slightly different.

In test #1, the high income tax regime (with a 10% flat consumption tax and a 50% flat income tax) edges out the high consumption tax regime (50% consumption, 10% income). When the government increases spending, the household's objective function (welfare) is higher throughout due mainly to less of an increase in output and subsequently less of an increase in labor as well as a smaller reduction in consumption.

 (click here for the rest of the comparisons)

In the long run, however, the consumption-tax-dominant regime is superior for welfare in the long run and output in the short run. Steady state welfare is much higher in this regime, pointing to the long run advantages of having higher consumption taxes and lower income taxes.

The disadvantage of consumption-tax-dominance is that tax revenues are lower in the steady state. Lower revenues either mean a lower level of government spending in the long run (which also means less output which is socially optimal, but maybe not optimal from a policy perspective) or higher deficits.

Consumption taxes turn out to be optimal in most economic situations as they are less 'distortionary' than income taxes and they increase consumer welfare in the long run (basically consumption per unit of labor). The only case for keeping an income-tax-dominant regime (assuming both taxes are flat), is if government spending is extremely volatile. In all other cases, cutting income taxes and raising consumption taxes is more optimal. Of course, if government spending had the ability to increase welfare in my model, then the results could be very different indeed.

Fiscal Stimulus Take Two

(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)

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:

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. 

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.