### Discussion Paper

## Abstract

There have been attempts to resurrect the fiscal theory of the price level (FTPL). The original FTPL rests on a fundamental compounded fallacy: confusing the intertemporal budget constraint (IBC) of the State, holding with equality and with sovereign bonds priced at their contractual values, with a misspecified equilibrium nominal bond pricing equation, and the ‘double use’ of this IBC. This fallacy generates a number of internal inconsistencies and anomalies. The issue is not an empirical one. Neither does it concern the realism of the assumptions. It is about flawed internal logic. The issue is not just of academic interest. If fiscal policy authorities were to take the FTPL seriously, costly policy accidents, including sovereign default and hyperinflation, could be the outcome. Interpreting the FTPL as an equilibrium selection mechanism in models with multiple equilibria does not help. Attempts by Sims to extend the FTPL to models with nominal price rigidities fail. The attempted resurrection of the FTPL fails. It is time to bury it again – for the last time.

## Comments and Questions

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Referee report for Buiter and Sibert, "The Fallacy of the Fiscal Theory of the Price Level - One Last Time"

In their 48-page paper, "The Fallacy of the Fiscal Theory of the Price Level - One Last Time", the authors attack the Fiscal Theory of the Price Level (FTPL) ...[more]

... as logically inconsistent (fallacious) as an academic theory, and as providing an insufficiently realistic basis for policy advice. On the consistency of the FTPL, the authors rely on proof by assertion, and they do not correctly state the theoretical logic of the model. Meanwhile, their advice for policymakers against overreliance on the FTPL is based on known limitations of the model, and is of practical concern to those who wish to avoid a fiscal crisis. The authors then discuss a set of useful model extensions and their implications for determinacy.

The authors' policy advice and academic extensions would benefit from being split into separate, clearly-focused papers for different audiences. These papers would be improved by engaging with the existing literature to outline what is original and what is a synthesis of existing insights.

Comments:

1. The authors do not back up their assertion that the FTPL is logically inconsistent with a mathematical proof or demonstration, instead relying on repeated assertion. This is a problem because the FTPL in fact does logically show how the price level, debt stock, and future primary surpluses relate to each other in an internally consistent model, with the same number of equations as unknowns.

To use a simplified version of the model used by the authors, the standard argument for the FTPL as is based on the following discrete-time law of motion for the nominal beginning-of-period public debt B_{t} and price level P_{t}, given nominal interest rates i_{t} and real public surpluses (including seigniorage) S_{t} which equals taxes T_{t} less government purchases G{t}, and where the public debt consists of one-period bonds that are rolled over every period. Shocks are realized; bonds are traded; and prices are formed at the beginning of the period, so that:

B_{t+1} = (1+i_{t})*B_{t} - P_{t}*S_{t}.

Denoting the beginning of period real debt stock b_{t} as B_{t}/P_{t}, this equation implies:

b_{t+1}*(P_{t+1}/P_{t}) = (1+i_{t})*b_{t} - S_{t}.

Solving recursively for b_{t} implies that for every state of the world:

b_{t} = B_{t}/P_{t} = Present Value(S_{tau}: tau from t to infinity) + Z,

where Z is a bubble term.

On the household side, households receive an exogenous stream of income Y_{t} to finance a stream of consumption C_{t} and to purchase government bonds B. Under market clearing in bonds, the household budget constraint takes the form:

B_{t+1} = (1+i_{t})*B_{t} + P_{t}*[Y_{t} - C_{t} - T_{t}].

A similar recursive solution for b yields:

b_{t} = B_{t}/P_{t} = Present Value(Y_{tau} - C_{tau} - T_{tau}: tau from t to infinity) + X,

where X is a bubble term.

Under non-satiation in consumption, X is equal to zero, since households would rather consume than lend money without being paid back. This in turn implies:

b_{t} = B_{t}/P_{t} = Present Value(Y_{tau} - C_{tau} - T_{tau}: tau from t to infinity).

Substituting in the definition of the public surplus as the difference between taxes and spending yields:

b_{t} = B_{t}/P_{t} = Present Value(Y_{tau} - C_{tau} - G_{tau} + S_{tau}: tau from t to infinity).

Under market clearing in the goods market, Y_{t} = C_{t} + T_{t}, so that:

B_{t}/P_{t} = Present Value(S_{tau}: tau from t to infinity),

which implies that the bubble term Z from above is equal to zero. Furthermore, under linear utility, expected real interest rates are constant.

This is the intertemporal budget constraint (IBC) to which the authors refer. As the authors state, "This IBC holds with equality when household consumption and money demand are derived from the optimizing behavior of forward-looking households with rational expectations, when there is non-satiation in real money balances and/or consumption."

This equation implies, economically, that to ensure government solvency, either the current price level P or the present value of future surpluses S has to adjust to cover the current debt level B. Furthermore, when assets are priced according to the Fisher equation (as under linear utility with a constant expected real interest rate), this closes off interest rate fluctuations as an avenue for adjustment.

Put another way, when Y, G, T (and hence S), expected real interest rates, and B are given under fiscal leadership, then market clearing in goods determines C; optimal consumption plans determine X = 0; market clearing in bonds determines Z = 0; and these objects all jointly via the law of motion for government debt determine P. Contrary to what the authors assert, this logic does not require "us[ing] the same equilibrium condition more than once".

In summary, the authors assert that it is a fallacy to assert that Z = 0, even though this is implied by the logic of the model. As such, the authors' argument merely represents proof by assertion, which it itself a logical fallacy.

2. The authors make an additional assertion, which is that this equation forms an inadequate basis for policy discussions in the real world. These assertions are well-grounded, and they reflect well-known features of the FTPL framework. However, the authors do not make clear which of these assertions are original and which of these assertions reflect the past literature.

It is important to note that this is not a discussion about the internal consistency of this class of models, but instead about the realism of those models' assumptions. This moves the paper out of the academic literature and into the policy literature. This would be a good topic for a blog post or a longer "explainer" piece.

These policy discussions focus on monetary-fiscal interactions, as in the recent case of Abenomics. The idea behind Abenomics (and some policy proposals following the Great Recession) has been to adjust the present value of S to support a higher price level or price path P. The risks and benefits of this approach depend on how well the IBC as modeled within this literature captures the real world, and on the coordination of monetary and fiscal policies to ensure that this price path represents a unique stable equilibrium which exists.

The problem arises when monetary authorities seek to independently control P while fiscal authorities seek to independently control the present value of S, in a manner that does not respect the IBC in all states of the world. In the FTPL class of models, this is the policy constellation where no stable (or sustainable) equilibrium exists. This is a known result which is a general feature of this class of models. In addition, the fiscal-dominance equilibrium falls apart with B near 0 or when B and PV(S) are of different signs. This is also well-known.

In practice, if something is unsustainable it will not be sustained. Historically, unsustainable public finances are unsustained through the risk of default, which is not a possibility included in the IBC within the toy version of the FTPL. The authors discuss onee way to fix this, which would be to put an additional "net of default" term D_{t}, into the IBC:

B_{t}/P_{t}*D_{t} = Present Value(S_{tau}: tau from t to infinity).

This setup reformulates the fiscal-monetary coordination problem into one with three policy levers: inflation/deflation, fiscal adjustment, and default/revaluation, which then affect economic activity through standard New Keynesian, old Kenesian, supply-side, and financial-accelerator channels. Since this involves adding variables to the model, it would also be necessary to add equations, for instance, a default policy function.

The authors also point out how changes to the law of motion for government debt (e.g. indexing, also duration) alter the conclusions of the FTPL. This is already well known in the literature, and the authors should cite the existing literature on these topics.

3. The paper is long and verbose, and it veers toward additional points (including nominal indeterminacy) beyond these two main points. This is painful for the reader and this mixes audiences.

It would make sense to split up this paper into at least three separate papers:

a. A paper on the logic of the FTPL, which is then thrown away because it mischaracterizes the logic underlying the FTPL.

b. A concise policy paper on the limitations of the FTPL, which would be useful for policymakers struggling to turn this academic concept into practice without provoking a fiscal crisis.

c. A scientific paper exploring the implications of the extended model with D_{t} in it, taking care to engage the actual literature beyond Investopedia, and beyond Sims (2011, 2016).

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