In this post, a longer version of the fiscal-policy-model simulation from last time. My eventual aim is to consider some effects of a tax cut on income from wealth. My next move was to check that no big surprises lurk just around the corner in my “20-year” simulation of last time—surprises that might suggest correctable flaws in my analysis.

Before, in this previous post, three variables seemed to be stabilized by work of a countercyclical fiscal policy function, while a fourth—government debt divided by capital–appeared to have an upward trend as well as ongoing fluctuations. These indicated that government deficits as defined in the model changed but were positive on average.

Here again, I simulate multiple times using the program PHASER, and four variables are shown in my output: public spending divided by capital; output divided by capital, which I will call capacity utilization; government debt divided by capital; and net investment divided by capital, which is equivalent to the growth rate of the stock of goods used to produce goods—the “capital stock.” I have not run many simulations of larger versions of our model (described on this site’s fiscal policy model page) with the PHASER software package.

The model is not calibrated with serious numbers, but rather off-the-top-of-the-head guesses that make economic sense. An example would be target capacity utilization average values observed in the U.S. in recent years. The growth rate of the capital stock; public spending & employment; and capacity utilization are stabilized at nearly steady levels fairly quickly. In considering a simulation of such lengthy duration, I am in essence checking to see if a simple version of our model seems to come up with results that are consistent with the economic theory that I am using. I claim that the model is at least consistent with Modern Monetary Theory and some principles of “stock-flow consistent” economics.

This time, I run the model for 200 years instead of 20. Again, government debt divided rises steadily at first, but it clearly levels off this time, reaching a “cruising altitude” that is discernible in the longer figure. Also, the other 3 variables converge more completely. This exercise is designed to test properties of the model that are not important for analysis of the economy, which undergoes structural changes repeatedly at such a long interval—changes of expectations, institutions, political frameworks, etc. and in which numerous variables matter. My intention is not to model a long run in which the business cycle somehow ends—an impractical idea. A “long run” exercise merely teases out properties of the model, which reflect an effort to capture theory and existing economic institutions.

All pathways in the figure show stabilization. Some are even selected at later starting points; despite varied starting points, pathways for each variable all seem to approach a steady state.

The explanation for longer-run convergence lies in rising interest income from Treasury bills. These short-run government securities generate rising interest payments; these payments gradually replace net issuance of liabilities to the wealthy sector. The bills constitute a steady source of income and hence demand for consumption and investment goods—in contrast to labor income, which is cyclical—at least at first. This debt-accumulation effect occurs alongside the work of countercyclical fiscal policy to pull the public spending and capacity utilization toward a steady state.

I have assumed that wealthy households (a separate group in the model, for simplicity) put a fixed percentage of their (new) assets into the interest-bearing form and that the government keeps the real (inflation-adjusted) interest rate steady using open-market operations. A policy that holds the real rate constant is perhaps weak compared to the mainstream “Taylor rule,” if a comparison can be suggested. A Taylor rule for the nominal interest rate—oft-advocated—tries to more than offset changes in inflation.

In this model, in contrast, fiscal policy does the stabilizing work. In this model, government wage payments—and increasingly, interest payments–stabilize demand for private-sector output. Once government net liabilities to the private sector reach a sufficient quantity, steady interest payments on existing debt make up such a large part of income that the demand for goods is nearly constant. Government interest-bearing liabilities grow at a rate close to the rate of growth of the capital stock, resulting in a flattening trajectory toward the top of the diagram that wipes out the need for stabilizing fiscal policy.

Now try a cut in taxes for for the wealth-holding group of only of 5 percentage points of income, so that they now pay 15 percent while the workers pay 20 percent, the same rate as in the original model. Here is the revised output.

There does not appear to be much of an effect in the broad patterns of convergence, but b converges to a lower level, with lower tax payments in our new scenario allowing for lower interest payments in equilibrium.

Here I show the effects of a tax cut for the wealthy in a scenario based on parameter values that generate fairly steady, frequent fluctuations over a 200-year simulation period. Baseline and tax-cut scenarios are pictured in the same figure:

Again, a tax cut substitutes for interest income, resulting in a lower path for government debt b.

I have not assumed that consumption depends on assets—an effect found to be weak empirically. But the stock-flow-consistent features of the model matter throughout the simulation, causing a gradual leveling-off of the trend in b throughout the simulation period in all of the 200-year runs.

I would expect a tax cut for the workers in the model to have a different effect, as they do not collect interest income and consume a higher percentage of their disposable income.