مالیات مطلوب با بازارهای بدهی اندوژن و ناقص

Empirical analyses of labor tax and public debt processes provide prima facie evidence for imperfect government insurance. This paper considers a model in which the government's inability to commit to future policies or to report truthfully its spending needs renders government debt markets endogenously incomplete. A method for solving for optimal fiscal policy under these constraints is developed. Such policy is found to be intermediate between that implied by the complete insurance (Ramsey) model and a model with exogenously incomplete debt markets. In contrast to optimal Ramsey policy, optimal policy in this model is consistent with a variety of stylized fiscal policy facts such as the high persistence of labor tax rates and debt levels and the positive covariance between government spending and the value of government debt sales.

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.

The empirical properties of tax rate and debt processes contrast with the implications of the Ramsey model and are suggestive of incomplete government insurance. This paper develops techniques for analyzing optimal fiscal policy under two frictions, private government information and limited government commitment.We find that these frictions imply endogenous debt value limits, a reduced smoothing of taxes across states, and enhanced persistence in tax rates and debt levels. The government retains some ability to hedge against fiscal shocks, so that the ensuing allocations and fiscal policies in our model lie somewhere between those implied by the Ramsey model and a model with exogenously non-contingent debt. This brings our model into line with evidence reported by Marcet and Scott [23].