Abstract
We study a model in which policy aims at aggregate price stability. A fiscal imbalance materializes that, if uncorrected, must cause inflation, but the imbalance may get corrected in the future with some probability. By maintaining price stability in the near term, monetary policy can buy time for a correction to take place. The policy gamble may succeed, preserving price and fiscal stability, or fail, leading to a delayed, possibly large jump in the price level. The resulting dynamics resemble the models of a currency crisis following Krugman (J Money Credit Bank 11:311–325, 1979) and Obstfeld (Am Econ Rev 76: 72–81, 1986). Like in Obstfeld’s work, multiple equilibria arise naturally: whether or not price stability is preserved may depend on private agents’ expectations. The model can be reinterpreted as a model of partial default on public debt, in which case it is reminiscent of Calvo (Am Econ Rev 78:647–661, 1988).
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Notes
In Sect. 6, we also study a version of the model with default on public debt instead of inflation.
This series of papers had a profound influence on the policy debate about the Exchange Rate Mechanism of the European Monetary System.
An FTPL approach is inessential for modeling delayed inflation (to give an example, Burnside et al. (2001) do not use this approach) but we think that it is helpful.
We consider default on public debt in Sect. 6.
We also assume that \(\Delta <S/\left( 1-\beta \right)\).
Even in an economy where all public debt is short-term, there may be government expenditure commitments such as pensions that are imperfectly indexed to the price level. Their real value can be reduced via inflation even when inflation is anticipated.
See Corsetti and Maćkowiak (2006) for the case in which starting in period T monetary policy makes the nominal interest rate react less than one-for-one to the inflation rate, which in equilibrium produces both a price level jump at T and some subsequent growth in the price level.
See Corsetti and Maćkowiak (2006), Section 3.3.
See also Corsetti and Maćkowiak (2006), in particular Sects. 3.3–3.4, for a more thorough comparison with the Krugman model. Like Krugman, Sargent and Wallace (1981) assume that inflation is fiscally beneficial because growth in the non-interest-paying monetary base produces seigniorage revenue. Fixing a path for the budget deficit and a T, they famously show that tighter monetary policy before T, and thus lower inflation before T, implies higher inflation after T. Uribe (2020) points out that if smoothing inflation over time is socially beneficial, then the optimal inflation path in the Sargent-Wallace economy involves a constant, strictly positive inflation rate. In the Sargent-Wallace model, like in the Krugman model, inflation is unavoidable and there is a unique equilibrium.
Another interpretation is that the policy configuration is always “active fiscal policy” and “passive monetary policy,” but in the initial steady state the active fiscal policy happens to be consistent with price stability, whereas from period 0 the active fiscal policy is no longer consistent with price stability.
With a time-invariant \(\psi >0\), the probability that a correction takes place in period \(T\ge 2\) or sooner equals \(1-\left( 1-\psi \right) ^{T}\), which approaches 1 as T goes to infinity.
A subset of the literature (e.g., Davig et al. 2010) analyzes the consequences of “a fiscal limit,” an assumption similar to the upper bound on the fiscal correction here.
While in this section we generically find multiple equilibria, in Sect. 4 we always find a unique equilibrium. In Sect. 4, a hypothetical shift in private agents’ expectations could be expected to change bond prices and thus debt issuance, but the probability of a correction would remain unaffected—a feature which turns out to be critical for equilibrium determinacy in this model, according to our numerical results.
The error function appearing in the formula is the same as the cumulative distribution function of a truncated normal random variable, so that \(\psi _{t}\left( \omega _{t}\right) =1\) for \(\omega _{t}=\Delta\) and \(\psi _{t}\left( \omega _{t}\right)\) decreases smoothly to 0 as \(\omega _{t}\) rises away from \(\Delta\).
We solve for equilibrium assuming that in period 0 private agents form a belief about T and thereafter stick to that belief. We conjecture that we would find additional equilibria if after period 0 we allowed private agents to change their belief about T.
One can ask if an equilibrium is “stable” in the following sense: if initial debt \(B_{-1}\) is lowered, do debt \(B_{t}\) and the bond yield \(1/Q_{t}+\rho\) fall in every subsequent period \(t=0,\ldots ,T-1\)? It turns out that the answer is “yes” for the “optimistic” equilibrium with \(T=10\) and for the “pessimistic” equilibrium with \(T=2\), and “no” for the intermediate equilibrium with \(T=4\).
One could think of the sovereign borrower as deciding how long to wait for a correction, or one could think of the central bank which can “backstop” the sovereign borrower as deciding how long to provide the backstop.
Calvo (1988), Section II, studies a model of inflation with multiple equilibria, and therefore one may argue that Sect. 5 of our model with inflation is in the spirit of Obstfeld (1986) and Calvo (1988), Section II. See Corsetti and Dedola (2016) on the role of the cost of inflation in that section of Calvo’s paper.
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This paper was written for the 2022 IMF Jacques Polak Annual Research Conference honoring Maurice Obstfeld. The paper was also presented at the 2023 Conference in Honor of Guillermo Calvo at Columbia University. We thank for comments the participants in both conferences, Andrei Levchenko (the editor), anonymous referees, Javier Bianchi, John Cochrane, Luisa Lambertini, Iván Werning, Martin Wolf, and other audiences in front of which we presented the paper. The views expressed in this paper are solely those of the authors, and do not necessarily reflect the views of the ECB.
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