Fiscal Sustainability in a New Keynesian Model

Campbell Leith,Simon J.Q Wren-Lewis

doi:10.2139/ssrn.941120

Abstract

There has been a wealth of recent work deriving optimal monetary policy utilising New Neo-Classical Synthesis (NNCS) models based on nominal inertia. Such models typically abstract from the impact of monetary policy on the government's finances, by assuming that consumers are infinitely-lived and taxes are lump-sum such that Ricardian Equivalence holds. In this paper, in the context of a sticky-price NNCS model, we assume that the government must adjust spending and/or distortionary taxation to satisfy its intertemporal budget constraint. We then consider optimal monetary and fiscal policies under discretion and commitment in the face of technology, preference and cost-push shocks. We find that the optimal precommitment policy implies a random walk in the steady-state level of debt, generalising earlier results that involved only a single fiscal instrument. In the case of negative fiscal shocks this implies permanently higher taxation and lower output and government spending to support the new steady-state debt shock, but the optimal combination of these variables will ensure a zero rate of inflation under commitment. We also find that the time-inconsistency in the optimal precommitment policy is such that governemnts are tempted, given inflationary expectations, to raise taxation to reduce the ultimate debt burden they need to service. Since taxation is a distortionary labour income tax, this aggresive raising of taxation raises firms' marginal costs and fuels inflation. We show that this temptation is only eliminated if following shocks, the new steady-state debt is equal to the original, first-best, debt level. This implies that under discretionary policy the random walk result is over-turned: debt will always be returned to this initial steady-state even although there is no explicit debt target in the government's objective function. In a series of numerical simulations we show that the welfare consequences of introducing debt are negligible for precommitment policies, but can be significant for discretionary policy.

Highlights

IN STICKY-PRICE NEW KEYNESIAN models where social welfare is derived from consumers’ utility, Benigno and Woodford (2003) and SchmittGrohe and Uribe (2004) show that optimal steady-state debt follows a random walk when policymakers can commit to a time-inconsistent monetary and fiscal policy
In this paper we focus on the time-consistency of policies where the costs of inflation arise from nominal inertia rather than monetary transaction frictions
We show analytically and in simulation that under discretionary policy, debt will always be returned to its initial steady state to eliminate this temptation, and debt no longer follows a random walk

Summary

THE MODEL

Our model is a standard New Keynesian model, but augmented to include the government’s budget constraint where government spending is financed by distortionary taxation and/or borrowing. In order to do so, for most of the paper, we set aside the usual inflationary bias caused by an inefficiently low level of steady-state output due to imperfect competition and distortionary taxes This is achieved through a steady-state subsidy (financed by lump-sum taxation), which renders our steady state efficient and implies that the policymaker has no incentive to increase output above its steady-state level.. This is achieved through a steady-state subsidy (financed by lump-sum taxation), which renders our steady state efficient and implies that the policymaker has no incentive to increase output above its steady-state level.3 We utilize this steady-state subsidy as it enables us to formulate a valid linearquadratic (LQ) approximation to the underlying policy problem The richness of our sticky-price economy (which would contain government debt, price dispersion and the shock processes as state variables) would make such an approach prohibitively complex, given our goal of contrasting the discretionary, commitment, and quasicommitment solutions.

Households

POLICY OBJECTIVES

The Social Planner’s Problem

Social Welfare Appendix A derives the quadratic approximation to utility

Gap Variables

PRECOMMITMENT POLICY

The Time-Inconsistent Response

DISCRETIONARY POLICY

OPTIMAL POLICY SIMULATIONS

Debt under Commitment and Discretion

Controlling Debt under Discretion

ROBUSTNESS