The Budget Constraint Does Not Mean The Government Will Pay Off Its Debt

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by: Brian Romanchuk

Professor Brad DeLong made some assertions about Modern Monetary Theory (MMT) in this article about bond bubbles, which drew responses on the Mike Norman Economics web site (here and here). Professor DeLong's points have a lot of embedded assumptions, and I cannot deal with all of them here. But I do discuss one assumption in my upcoming eReport: Understanding Government Finance. This is the idea government 'has to pay back its debt'.

DeLong's thesis is built around theories that 'bond vigilantes' exist and are powerful. This was a dominant theory when he was at the U.S. Treasury in the early 1990s. However, this was exactly the investment thesis that lead to the humbling of the JGB bears in the 'Widowmaker Trade'.

He writes:

Why? Suppose people start to fear that the government will not raise enough in taxes to pay off its debts. They will then try to dump government liabilities for real goods and services.

This is a throw-away comment in a blog post, so I do not want to stretch the textual analysis of this too far. I think he is referring to the concept of 'fiscal sustainability', which is standard in mainstream economics. Or he may be referring to some version of the Fiscal Theory of the Price Level. But 'sustainability' has nothing to do with a common sense interpretation of the phrase 'pay of its debts'.

A government 'paying of its debts' seems to imply that the debt-to-GDP ratio will go to zero at some point. In fact, the inter-temporal governmental budget constraint, which defines 'fiscal sustainability' for the mainstream, says almost nothing useful about what will happen to the debt-to-GDP ratio. Why DeLong uses such a misleading phrasing is unknown to me.

The rest of his article revolves around whether a default can be forced by the bond market. The MMT response is no, but it is a fairly complex topic, which I do not think I can cover completely even within my upcoming report.

The rest of this article is an unedited first draft of an excerpt from my upcoming report, which has the working title: Understanding Government Finance. The estimated publication date: Before the Fed hikes rates. I will attempt to reduce the complexity of this text, possibly by moving material to other sections. (Those sections are not yet complete, so I cannot judge where is the best place for material to be relocated.)

The Governmental Budget Constraint The modern mainstream approach to macroeconomics revolves around the use of Dynamic Stochastic General Equilibrium (DSGE) models. These models are the object of controversy, and they are particularly opposed by heterodox economists, such as post-Keynesians. I am not going to discuss this wider controversy, rather I wish to discuss the concepts of the inter-temporal governmental budget constraint, which I will also refer to here as the ‘governmental budget constraint’.[1] This is tied to the notion of fiscal sustainability, in that any fiscal policy ‘rule’ is allegedly sustainable if and only if it meets the inter-temporal governmental budget constraint.

In its simplest form, the inter-temporal governmental budget constraint can be written without mathematical notation as:

(Market Value of Government Debt) = (Discounted sum of all future primary fiscal balances).

The primary fiscal balance is the fiscal balance excluding interest payments. This concept only makes sense if we assume that monetary policy (which determines interest payments) and fiscal policy can be decoupled, a stance that appears dubious.

Additionally, the formulation above ignores how ‘money’ affects government finance through ‘seigneurage revenue’. This is often ignored in DSGE models, as those models implicitly assume that nobody holds money (as that would be suboptimal behavior). I will discuss this complication later.

For simplicity, I will assume that the economy is in a steady state, in which nominal interest rates and nominal GDP growth rates are constant. Within a DSGE model, this assumption is too restrictive, but I will assert that one could replicate my analysis in a more general fashion using mathematics that would be understandable to an undergraduate mathematician or electrical engineer.[2]

For now, we will assume that the interest rate on debt is greater than the growth rate of nominal GDP. This is a fairly important assumption with regards to the governmental budget constraint. If the interest rate is lower than the growth rate of GDP, the picture is quite different, as will be discussed later.

The chart above shows how the debt-to-GDP ratio evolves for a set of scenarios. In each scenario, nominal GDP grows at 4% per year, whereas the interest rate on debt is 6%. I assume that money balances are zero. The initial value of government debt represents 60% of GDP. The topmost line shows what happens if the primary surplus is held at 0% of GDP at all times: the debt-to-GDP ratio continues to grow without bound.

The middle line is what happens if the primary surplus is 1.2% of GDP: the debt-to-GDP ratio remains constant at 60% of GDP. Please note that in this case there is a total fiscal deficit at all times, but it is only allows the debt stock to grow at 4% per year, which is below the rate of interest. This illustrates the important property that continuous deficits are needed to stabilize the debt-to-GDP ratio if the economy is growing in nominal terms. This has the implication that balanced budgets are associated with a debt-to-GDP ratio converging towards zero, which would be problematic for the operation of the financial system.

The bottom line is what happens if a surplus larger than the stabilizing 1.2% of GDP level: the debt-to-GDP ratio continuously falls, and would eventually become negative.

The top trajectory and the bottom both represent ‘unsustainable’ debt trajectories. If the government tried to force its debt stock to be negative (somehow), the banking system would cease to function given the lack of position-making instruments. The usual worry, however, is a debt-to-GDP ratio that becoming arbitrarily large. If this is projected to happen, bondholders would presumably be nervous about owning bonds, as they will presumably become worthless at some point. The debate however, is whether such an outcome could be achieved, and the post-Keynesian position is very simple: such an out-of-control spiral would not happen in practice, and this tells us very little about fiscal policy. Mainstream models do not specify fiscal policy correctly, and the possibility of a ‘debt spiral’ is just a degenerate[3] outcome that is the result of model misspecification. I discuss this further later. But it is true that the budget constraint relation holds (under the high interest rate assumption). The issue is how to interpret it.

Paying the Debt Back? One popular interpretation of the budget constraint is that ‘the government will have to pay back its debt’. This is a formulation which is often seen in internet discussion, which seems to imply is that the government must drive the debt-to-GDP ratio to zero. This is not true. A fiscal trajectory meets the constraint so long as any upper limit to the debt-to-GDP ratio time series exists. The ratio could drift towards 10,000%, and the trajectory is 'sustainable' on this measure.

The reason why you need a positive primary fiscal balance (a primary surplus) is that you need to apply a brake to the debt dynamics in order prevent the debt-to-GDP ratio from going to infinity. If you set the primary surplus such that the debt-to-GDP ratio is constant (that is, debt grows at the same rate as GDP), the present value of the series will equal the market value of the debt. Doing this calculation requires using some manipulations of infinite series.[4]

More generally, you could run a smaller surplus for a period, and then enter a steady state primary balance in which the debt-to-GDP ratio remains constant at a higher level. The initially smaller surpluses will be balanced by higher surpluses at later dates, since the higher debt-to-GDP ratio requires a larger primary balance to reach the steady growth condition. Despite the extra dynamics, the constraint equation still holds. In this manner, we can steer the debt-to-GDP ratio to any positive level, and remain there, and still satisfy the constraint.

The above chart shows an example of how this works. Once again, there are three scenarios, with the same parameters for the growth rate (4%) and interest rate (6%). The difference is that this time, the primary balance is set to a particular percentage of GDP for the first 10 years (years 0-9 on the chart), and then the primary balance reverts to a level that is consistent with a constant debt-to-GDP ratio. The initial primary balances for the scenarios are -5%, 1.2%, and 5% of GDP.

The chart above shows the path of primary balances. The trajectory that starts with a large primary deficit (-5% of GDP) switches over to having the largest primary balance in ‘year 10’, almost 2.5% of GDP. The scenario that starts with large surpluses (5% of GDP) drops off to the smallest primary balance, as the debt-to-GDP ratio has been crushed down and a smaller surplus is needed to stabilize the debt-to-GDP ratio.

The chart above shows the cumulative discounted values of the primary surpluses for each scenario. (For each year, we calculate the dollar value of the primary balance, and then discount it by the factor (1.06) raised to the power of the number of years in the future.) In all cases, the cumulative discounted surpluses converge towards the market value of the initial amount of debt outstanding, which is 60% of GDP in ‘year 0’. This convergence will hold for any trajectory that has the debt-to-GDP ratio stabilizing at a limit which is greater than or equal to zero.

Therefore, we cannot say the ‘debt will be paid back’, other than the trivial observation that individual bond issues are paid off as they mature, while the stock of debt is steadily increasing.

All the governmental budget constraint says is that for every dollar in debt, the government will need to run a future primary surplus which has a discounted value (present value) of $1. From the point of view of the hypothetical infinitely long-lived representative household which inhabits a DSGE model, it assumes that for every dollar in per capita debt, it will get a future tax bill that is worth $1 now.[5] This property supposedly limits the effectiveness of fiscal policy, which is one reason why the mainstream consensus switched towards an emphasis upon monetary policy versus fiscal policy in the 1990s. This topic is rather complex, so I will not address it here. I will merely assert my view that the DSGE framework is ill-posed, and does not handle fiscal policy correctly. Fiscal policy is always effective, regardless of the level of interest rates.[6]


[1] This is technically too simplistic, as there are two parts to the governmental budget constraint. The first part is the non-controversial accounting identity which describes debt dynamics (the increase in government liabilities outstanding equals the budget deficit, after controlling for market value changes). The second part is the inter-temporal component, which I describe here. Since the first component is trivial, I ignore it.

[2] Instead of assuming that growth rates are constant, we can pin down the actual trajectory between two trajectories that have growth rates that are slightly above, and slight below the ‘long-term’ growth rate. As long as nominal GDP growth rates do not become unbounded (‘tend to infinity’) this can always be done. And if the growth rate does tend to infinity, we are in the realm of an ‘unsustainable trajectory’. A hyperinflation would be such a case, as the growth rates are hyper-exponential. An economy will collapse, breaking the model assumptions, before it reaches infinite size.

[3] I am using degenerate in a formal sense that is used by mathematicians; it does not imply anything about moral standing of a model. The meaning is that the model is technically correct, but the results make no sense. Assumptions embedded in the model do not correspond to real world behaviour.

[4] This is left as an exercise to the reader.

[5] This leads to the concept of Ricardian Equivalence.

[6] After the financial crisis, there has been a move to resurrect fiscal policy within DSGE models by arguing that fiscal policy is effective (only) at the zero lower bound on interest rates.

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