The Debt Ceiling
It seems like the debt ceiling is going to be a hot topic for the next months. From what I read, this is a political battle with big economic consequences. I thought it was important enough to write a paper about but then realized that there was almost no literature in Economics about the debt ceiling. How can that be?
Deficits and the Debt
A useful starting point is to remember some basic relationships (essentially identities).
First there is the deficit over period t, def(t), defined by:Here G(t) measures outlays during period t. This measures government purchases (airplanes) plus transfers (say unemployment insurance) plus payment of principal and interest on the debt. Receipts in period t, denoted T(t), are largely tax revenues collected from households and corporations.
These are all flows over a period of time, normally a year. Looking at the data, the US has run a federal budget deficit for almost all of the past 50 years.
Related to the deficit is the stock of debt, measured at a point in time. Its evolution over time is given by:
where D(t) is the level of debt at the start of year t and def(t) is the deficit over year t.
So the stock of debt at the start of next year is the stock of debt at the start of this year plus the deficit over the year. This is useful to keep in mind when you hear politicians planning to reduce the deficit to zero and thus remove all the outstanding government debt.The Politics of the Debt Ceiling
These are the two key relationships in thinking about the deficit and the evolution of the debt. This is all cleanly stated without talking about a debt ceiling!
The debt ceiling is not a fundamental concept for economists. It is rather a political invention (perhaps innovation) that has found its way into budgetary policies.
It has a long history of use and abuse as a political tool. This summary from the US Treasury gives you some sense of the debate going forward. Before turning to that, a little economic context might help.
The Game of Chicken
Whenever I hear about this game, a movie scene which captures a version of the game of chicken comes to mind. If you do not know the scene, think of : (i) fast cars and (ii) a choice to avoid a crash (an accident) or not and (iii) the shame of being the one that goes to safety first.
Generally, a game of chicken has two players. In the context of the fast cars, each player simultaneously chooses one of two actions: (i) swerve (S) or (ii) not swerve (NS). The first to swerve is the chicken. In terms of payoffs, the game looks like:
For each pair of actions, the first entry is the payoff for the row player and the second is the playoff for the column player. So, for example, if row chooses to swerve (S) and column chooses not to swerve (NS), then the payoff to row is -10 and the payoff to column is 10. The numbers by themselves do not mean much. Instead, look at them relative to the outcome if both swerve. Doing so avoids a collision and yields a payoff of 0 to each player. So if row swerves and column doesn’t, then row is worse off and column better off compared to the outcome when they both swerve. Clearly the payoffs are really low when neither swerve.
What is the outcome of this game? We use the prediction of a Nash Equilibrium, a fundamental concept in game theory.
It is actually quite intuitive. A Nash Equilibrium is a pair of strategies, one for each player, that maximizes the payoff to each player given the choice of the other.Looking at the game of chicken, there are (at least) two Nash equilibria. In both, if one player chooses to swerve and the other chooses not to swerve, then these choices constitute a Nash equilibrium. For example, focus on the equilibrium in which row chooses S and column chooses NS. From the table of payoffs, if row chooses S then column’s best choice is NS. And if column does choose NS, then row will choose S. Thus these choices are self enforcing.
In another equilibrium, the roles are switched: row chooses NS and column chooses S. These two equilibria are symmetric but from row’s perspective, the second one where column chooses S is better, i.e. 10>-10! The good news is that the outcome in which neither swerves does not occur. In that sense, they are both winners.
There is another, more complicated equilibrium, that is symmetric. This involves a mixed strategy, i.e. each of the two players independently flipping coins. There is an equilibrium, called a mixed strategy equilibrium, such that both players will choose S with probability p. The idea is that if the row player selects S with probability p, then, for the right value of p, the column player will be indifferent between S and NS.
Given the symmetry, the same is true from the perspective of the row player. So the mixed strategy equilibrium is built upon the indifference of each player between actions given that the opponent is randomizing.The outcome in this case is stochastic. Among other things the outcome can be a disaster: with probability (1-p)*(1-p) both choose not to swerve and they crash. The outcome is really bad for both players but possible given their choices.
The Politics of the Economics of the Debt Ceiling
So where are we in this game? One player is the executive branch (the President) and the other is Congress (Speaker of the House). For both the strategies are a bit more nuanced than the simple game of chicken.
For the Speaker, no increase in the debt ceiling will be allowed unless there is tighter control of government spending. For the President, the preferred outcome is an increase in the debt ceiling without any restrictions on spending. Swerving by the Speaker is approving an increase in the debt ceiling without any fiscal restrictions. Swerving by the President is to allow those restrictions to be imposed.
The political game is not just about choosing to swerve or not. These two players are engaged in a preliminary of the game which is all about stating their positions. The stage is often called “cheap talk”. There is talk in the form of communications back and forth about intentions in the game. The talk is cheap though as it really has no direct consequences for the play of the game: the payoffs from the actions are given by the table and are independent of the messages sent by the players. Think of the talk back and forth between the car drivers prior to the start of the contest.
But, interestingly enough, the messages can impact the beliefs players have about the actions of the other.
This can arise because of the multiplicity of Nash equilibria so that the statements of the players can influence the selection of an equilibrium.From the perspective of the game theory, the worst outcome is when neither player swerves and so there is a crash. And as we have seen, this can happen in the mixed strategy Nash equilibrium.
Dire Consequences
If no one swerves, what are the economic consequences?
Looking at the expressions developed above, the government budget constraint must hold without issuing more debt. This means that tax revenues have to be enough to pay for all of government spending, including the payment of interest on the debt. Since the start of the fiscal year, the federal government has a deficit of about $460 billion with the expectation of a deficit for the year of $1.4 trillion.
So, without the ability to issue more debt, adjustments have to be made to fill this gap. As you can see from this letter sent by Secretary Yellen to House Speaker McCarthy, the Treasury is already suspending the issuance of some forms of new debt. This is apparently standard practice as the debt ceiling tightens but at some point there are no measures remaining.
This does not mean that the US government must default on its debt per se. The government can continue to pay its debt obligations and either find a quick raise to raise revenue or cut spending. But cutting spending is a form of default: not to external debt holders but to those, such as government workers, with an ongoing claim on government revenues.
There is an interesting issue here about the conduct of monetary policy. In some countries, there is essentially a printing press in the office of the President. So if there is a limit on the ability to sell additional debt, the government can always print more currency and use it to fund expenditures. This leads, through the resulting increase in prices, to an inflation tax on nominal wealth. This way to raise taxes is swift and perhaps subtle as no one literally sees a change in their tax form.
As far as I can tell, this is not an option in the US. As I understand it, the debt ceiling applies to the total amount of Federal debt, regardless of who is holding it.
What is the Outcome going to be?
Well we know the game theory side of it. There are multiple equilibria. Only the mixed strategy equilibrium involves default and that occurs with probability (1-p)*(1-p). The stakes are very high and this probability is very low. If history can guide (or console) us, this is not the first time we have seen this game in action. Somehow we have avoided default so far. Fingers crossed …. I can hear the sound of those engines.
For the US, the CBO is a main source of information on the current deficit, its forecast and the impact of proposed policies on the deficit and thus debt outstanding. They also published a useful primer that includes historical data. Thanks to competition within the government, there is a Department of Treasury interface as well.
Here the entire deficit, which includes the payment of interest on the debt, is financed by issuing more debt. There is no distinction here between the primary deficit and interest payments.
Here is a White House memo written by the Council of Economic Advisors explaining the debt ceiling from Oct. 2021.
For this game, p=0.9.
These is some experimental evidence of this in work I participated in.
The deficit to date comes from the US Treasury and the forecast is from the CBO.