This paper considers the optimal design of fiscal policy under two sets of restrictions.
The first set is exogenous; it describes the technology by which the government can extract
resources from agents. We follow the conventional Ramsey approach and suppose that
resources can be obtained by levying linear taxes or selling state contingent debt. We also
assume that the government cannot lend. The second set of restrictions stem from incentive
problems on the side of the government which we assume can neither commit to repaying
its debt nor to truthfully revealing private information about its spending needs. These
frictions impede the government’s ability to use asset markets to hedge fiscal shocks. They
endogenously restrict the set of asset trades the government can make and this, in turn, has
implications for the optimal setting of taxes. To analyze fiscal policy design in such settings,
we embed the government’s policy problem into a repeated game.We provide an equilibrium
concept that extends Chari and Kehoe’s [15,16] sustainable equilibrium to environments
with private government information.We then give necessary and sufficient conditions for
an allocation to be an equilibrium outcome of this game. These conditions are recursive and
we obtain a dynamic programming method for finding optimal equilibrium allocations that
exploits this recursivity.We back out the supporting fiscal policies from these allocations and
analyse optimal fiscal policy in this limited commitment-private information environment.
Our immediate motivation is a contrast between the benchmark Ramsey model of fiscal
policy (as developed by Lucas and Stokey [22]) and the data. The former implies that fiscal
policy variables should depend only upon the current realization of the shocks perturbing the
economy and, consequently, should inherit their stochastic properties from these shocks. In
contrast, empirical evidence on labor tax rates and the public debt suggest that these variables
exhibit considerable persistence, much more than that for government spending and other
candidate shock processes. 1 To paraphrase Aiyagari, Marcet, Sargent and Seppälä (AMSS)
[2], the empirical labor tax rate process is smooth in the sense of being highly persistent,
rather than smooth in the sense of having a small variance.
The data are suggestive of considerable intertemporal, but limited interstate smoothing
of taxes. Thus, they provide prima facie evidence for incomplete government insurance.
The papers of AMSS, Marcet and Scott [23] and Scott [27], which assume exogenously
incomplete government debt markets, corroborate this viewand suggest that a limited ability
to hedge against fiscal shocks may have significant implications for the design and conduct
of fiscal policy. Given this, it becomes important to understand why this ability is limited
and in what circumstances it might be more or less restricted.
Many commentators have informally suggested that moral hazard problems of one sort
or another might underpin incomplete government insurance (e.g. [9,10,25]). The private
information and limited commitment frictions that we incorporate into our model formalize
these ideas. Both are linked to familiar time consistency considerations. The repayment of
debt requires the levying of distortionary taxes. Ex post the government, and all households,
would be better off if the debt were cancelled, but if such cancellation is anticipated ex ante,the government will be unable to sell any debt in the first place. Our model gives the
government two channels via which it can avoid making debt repayments. The first is an
outright repudiation of the debt. The second is more subtle; the government may exploit
the private information it has over its spending needs and the state contingency of debt
repayments to obtain a reduction in the latter. If, in order to smooth taxes, it has sold more
claims against low relative to high spending needs states, the government can reduce its
debt repayment by claiming its spending needs are high when they are really low. 2
We call allocations that can be supported as equilibrium outcomes of our game “sustainable
incentive-compatible competitive allocations” (SICCA’s). Our main focus is upon
SICCA’s that are optimal from the government’s point of view. We show that optimal
SICCA’s are recursive in the value of the government’s debt. The limited commitment constraint
translates into an upper bound on equilibrium debt values. Above this upper bound,
the government cannot be given incentives to repay its debt. It is the fiscal policy analogue
of the endogenous solvency constraints that Alvarez and Jermann [3] find in a model of
households who are unable to commit ex ante to making debt repayments. There is also a
lower debt value limit that stems from our assumption that the government cannot lend. In
making this last assumption, we follow Chari and Kehoe [15].We elaborate on its role and
its justification in Section 3.
Our recursive method allows us to jointly solve for the debt value limits and for the
government’s optimal equilibrium payoff as a function of its current debt value. The method
is related to the approach of Abreu, Pearce and Stacchetti (APS) [1] and to the recent
extensions of this approach to macroeconomic policy games provided by Chang [12], Phelan
and Stacchetti [26] and Sleet [28].We show that the government’s value function satisfies a
Bellman equation on the set of debt values that lie between the limits. The policy functions
from this dynamic programming problem can be used to recursively construct optimal
allocations and, hence, optimal fiscal policy. This policy has the following characteristics.
Away from the debt value limits, it exhibits considerable intertemporal tax smoothing, a
moderate degree of state contingency in debt returns and considerable persistence in both
taxes and debt. These features are consistent with the empirical analyses of Bizer and Durlauf
[8], Huang and Lin [20] and Kingston [21] (on taxes) and Marcet and Scott [23] (on debt).
Close to the limits, there is much more volatility in tax rates.
The limited commitment, no lending and incentive compatibility frictions interact in
interesting ways. In a model with only the incentive compatibility friction, tax rates and
the excess burden of taxation tend to drift upwards over time. Sleet [29] shows that, under
certain assumptions on preferences, this drift continues until the government is maximally
indebted. At this point, it maximizes and uses all of its tax revenues to service debt. The
severity of this outcome raises natural questions about the government’s ability to commit
to implementing it ex ante. The endogenous upper debt value limit that stems from the
commitment friction arrests the drift before this severe outcome is attained. Moreover, both
the limited commitment and no lending frictions aggravate the incentive problem, especially
when the government’s debt value is close to the debt value limits. This contributes to the
greater tax rate volatility in these regions.In a model with only the no lending and commitment frictions, such as that of Chari
and Kehoe [15], debt value limits are also present. As Chari and Kehoe show, there is
a reduced scope for fiscal hedging and a motive for intertemporal smoothing of taxes in
the neighborhood of these limits. The addition of the incentive constraints further restricts
the government’s ability to hedge fiscal shocks and creates a motive for intertemporal tax
smoothing across the whole debt value domain. Overall, numerical calculations indicate that
the three frictions result in a constrained optimal fiscal policy with properties somewhere
between those implied by the Ramsey model and a model with non-contingent debt and
exogenously set debt limits. Corroborative evidence reported by Marcet and Scott [23]
suggests that empirical fiscal policies are also somewhere between these benchmarks.
Our model is related to two recent contributions, Athey, Atkeson and Kehoe (AAK)
[5] and Sleet [28], that have considered optimal monetary policy under private government
information. InAAK’s model the private information concerns the government’s preferences
for inflation and the government implements policy contingent on the history of reports that
it has made concerning its attitude towards inflation. A key result of AAK is that optimal
monetary policy is in fact static and does not respond to past reports. Although our model
shares some of the same structure as AAK’s, we find that optimal fiscal policy is not static.
Finally, Angeletos [4] presents an alternative decentralization of benchmark Ramsey
allocations that relies upon non-contingent debt of varied maturities and a state contingent
fiscal policy. It is important to emphasize that even though explicitly state contingent debt
is absent from this model, the decentralization proposed by Angeletos does not immunize
the government from the frictions analyzed in this paper. In particular, if a government
is privately informed about its spending needs, implementation of the Ramsey allocation
under this alternative arrangement would still require it to condition its policies on this
information. This would create an opportunity and an incentive for such a government to
misrepresent its spending needs in order to justify alternative policy actions.
The outline for the remainder of the paper is as follows. Section 2, describes the benchmark
environment with full commitment and without private information. Section 3, then
introduces the incentive compatibility, limited commitment and no lending frictions and
reformulates the model in game-theoretic terms. The next section provides a recursive formulation of the optimal SICCA that is amenable to computation. In particular, this section
shows how limited commitment constraints can be recast as debt value limits. Section 5,gives a partial theoretical characterization of optimal SICCA’s, while Section 6 provides illustrative numerical calculations.
