SFC Models And Introductory MMT-Style Fiscal Analysis

The usefulness of Stock-Flow Consistent (SFC) models is that they allow us to illustrate concepts in economics without relying solely on verbal descriptions. In this article, I will discuss my interpretation of some of the ideas floating around in Modern Monetary Theory (MMT). I will note that these are my interpretations of statements made by others, illustrated by an extremely simple model. The key is that even simple models can be used to clarify our thinking.

This article is only a partial response to an article by Gerard MacDonell. He is unhappy about some of the writings of Professor Bill Mitchell, one of the leading MMT economists. I am not going to argue on Mitchell's behalf, rather I just want to offer some analysis that touches on some of the technical issues Gerard made. He noted that Federal taxation and spending are roughly similar, so how does that square with MMT pronouncements about the independence of taxation and spending? This outcome is not surprising, as it is exactly the sort of thing that is predicted by SFC models -- and MMT mathematical analysis of the economy uses SFC models.

For those if you who are not fully up-to-date on post-Keynesian factionalism, please note that SFC models were meant to be a mathematical lingua franca for post-Keynesian economics. In other words, MMT economists use SFC models, but they are not exclusive to MMT.

Since I want to work with my Python modelling framework here, and it currently cannot support full business cycle analysis (extensions will be added later), I cannot do complete justice to Functional Finance. Therefore, I have to just focus on a couple of more basic ideas about fiscal polict:

1. there is little relationship between taxes and spending; and
2. governments cannot control the budget deficit.

I will address these here in turn.

Taxes and Spending

One basic reason to question the relationship between taxes and spending is that they are not in the same units,

• Taxes are mainly imposed as a percentage of incomes (or activity, such as tariffs or sales taxes). There are some user fees that are fixed, but these are typically a small part of total revenue for the central government.
• Spending is set in dollar amounts, or dollar amounts based on rules. (For example, welfare recipients receive benefits based on some fixed scale).

When we talk about taxes, we are talking about percentages; when we talk about government spending, we are talking about dollars (or whatever the local currency is). Very serious budget analysts will discuss changes to taxes in terms of dollar amounts, but those dollar amounts are based on crippled economic models that very few other people take seriously. (For example, see the latest debate on "dynamic scoring" in the United States,)

Take the simplest possible SFC model of an economy with a government - model SIM. (From Chapter 3 of Monetary economics, my implementation is described in this article.)

Fiscal policy is set by two parameters:

• A tax rate, which is a flat percentage of household income.
• Spending, which is expressed as an annual dollar amount. (Note that there is no explicit modelling of prices here.)

We assume that the tax rate is 20%, and we are in a steady state with spending at $15/year. We then look at two scenarios, where we ramp up spending to:

• Scenario 1: $20/year.
• Scenario 2: $25/year.

Note that we decided to ramp up spending purely based on feeling good (or bad) after some Stanley Cup playoff games; we did not care what the boring government debt nags have to say. We make no adjustments to our tax rates whatsoever to compensate for increased spending.

Figure: GDP in the two scenarios

Since this is a red-blooded Keynesian model, we see that increased government spending resulted in greater activity. The more we spend, the more the economy grows.

Figure: Fiscal Deficit

Oh noes, the deficits! As can be seen above, we have a larger deficit when we ramp up spending. But in both cases, we end up in balance. I will return to this later,

Figure: Debt-to-GDP Ratio

What about the dreaded debt-to-GDP ratio? It must be explosive, with all the increased spending and no tax hikes? Whoops. As seen above, it actually fell, and then it reverts to the initial level. (The difference that is visible was the result of rounding issues, which I will look into.*)

Even though we adjusted spending without any reference to raising the tax rate, we still ended up with the same debt-to-GDP ratio. If one reads Monetary Economics, there is a long discussion of steady states, and this outcome is exactly the sort of thing we are supposed to expect. The steady state debt ratio is a function of the tax rate and private sector behaviour.

The behaviour of the deficit is unusual when compared to real world behaviour: it reverts to zero. This is because this is a no-growth economy that heads to a steady state. If we are in a steady state, all stock variables when scaled by GDP are constant, which implies zero flows. Therefore, the net creation of government debt has to be zero. If the steady state featured a positive growth rate, we would revert to a deficit that allows debt levels to grow in line with nominal GDP, as seen below.

Figure: Deficit for country growing at 2%/year.

The chart above shows the result of a different scenario, where the economy grows at 2% per year in the "steady state."  The country did not start out at steady state, so the deficit as a percentage of GDP starts out at a higher level, then declines towards a constant value.

Figure: Debt/GDP ratio for country growing at 2%/year

The chart above shows that the debt-to-GDP ratio has reached a "steady state" by the end of the simulation. With the parameter values otherwise unchanged, the debt-to-GDP ratio stabilises at a level slightly below the no-growth steady state ratio of 80%. (The higher the nominal growth rate, the lower the debt-to-GDP ratio. This accords with the experience of the post-war era. It is possible to change the household sector behaviour to target the same wealth-to-income ratio regardless of growth rate.)

There are a spectacular number of simplifications embedded in this model. A key issue is that the private sector is not a source of growth. However, the basic principles will be roughly the same. The key point is that the deficit will take care of itself eventually, the only issue is to avoid politically unsustainable inflation (whatever that is) in the meantime. (The prospects for inflation is why we normally would not have a government ramp up spending by a huge amount in a short period of time. That said, it has been done; the latest example being World War II. Note that governments implemented rationing to make room for the increase in military production, which is a step that would be hard to justify in peace time.)

The Budget Deficit is not Controllable**

Figure: Government consumption (G) and the the deficit in the scenario.

In this example, we are looking at a country that is facing ever-increasing debt. (The source of the problem is business sector hoarding, as described in this article.) The government was running continuous deficits, and some fiscal conservatives got elected. At time period 24, the government was running a deficit of (about) $2.44, and the government decided to cut spending by $3 in time period 25, so that the budget would go back to balance.

This did not work. There was a temporary improvement in the budget balance, but it fell short of a surplus as a result of multiplier effects. (Note that a larger cut back would result in a small surplus in time period 25, that is, a surplus is possible to achieve.) This is an example of a failure of "static" budget analysis -- cutting spending by $1 does not improve the realised deficit by $1, even if the so-called budget wonks say it will. Furthermore, the improvement was only partial; the budget deficit reverted back to a similar level of deficit in response to lower output.

Examination of what was causing the deficits -- hoarding behaviour in the business sector -- tells us that any attempt to use fiscal policy to correct the budget deficit was doomed. Unless there was a policy to force the business sector to run down its financial asset holdings, the government budget would always return to deficit.

In other words, the budget balance will reflect decisions made in the private sector, and the government only has an illusion of control over the deficit. In the real world, it only looks like budgets are under control during expansions because budget assumptions systematically underestimate growth, and hence tax revenues. ("The deficit is less than projected due to our brilliant management of the economy!" is a standard press release.) Furthermore, a great deal of cookie jar accounting is used by governments to make it look like they hit budget targets.

When we look at the various stockpiles of financial assets that are building up in pension funds, tax havens, and on corporate balance sheets, we should be able to extend the logic of this example to see why we should not be surprise by "high" government debt levels.

Once again, this example is highly simplified. If we added in various welfare state programs, the budget deficit moves further and further from the control of government.

Concluding Remarks

Even simple SFC models can be used to demonstrate that we cannot think of government budgets purely in dollar amounts under the control of the government.

Appendix: Code

The code that generated these examples is on the GitHub repository. Unfortunately, the file names are only temporary placeholders, currently: intro_X_XX_sim_fiscal.py, intro_X_XX_sim_multiplier.py. They will be used in my user manual, and the "X"'s will be replaced with the chapter/section number.


Footnotes:

* This is due to have too large an error tolerance for terminating iterations. I guess I will set the parameter default to be less tolerant of errors.

** I am not using controllable in the technical sense used by control engineers, in case anyone is wondering.

(c) Brian Romanchuk 2017