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Article Excerpt
IT IS WELL established that a policy of an interest rate peg or, more generally, of an exogenously specified sequence of interest rates can be associated with an indeterminate price level (Patinkin 1965, Sargent and Wallace 1975). This property has been reconsidered in a number of studies with a particular focus on links between monetary and fiscal policy regimes (Leeper 1991, Woodford 1994, Sims 1994, Kocherlakota and Phelan 1999, Schmitt-Grohe and Uribe 2000, Benhabib et al. 2001). Specifically, the "fiscal theory of the price level" (FTPL) has claimed that the equilibrium under exogenous interest rates is consistent with a unique price level if fiscal policy is specified as an exogenous sequence of the primary surplus. (1) By contrast, indeterminacy of the equilibrium price level prevails if the primary surplus reacts endogenously to the level of public debt (i.e., if fiscal policy is passive) such that government solvency is guaranteed for any price level sequence.
A key assumption which ensures that this classification of equilibrium (in)determinacy relates to nominal variables and not to the real equilibrium allocation is that fiscal policy has access to lump-sum taxes. The main contribution of this paper is to reconsider this classification when taxation is distortionary. We establish two results. First, we confirm the hypothesis that the purely nominal indeterminacy of equilibria is no longer an issue if taxation is distortionary (see Woodford 1998). Fiscal policy then establishes a link between equilibrium allocations and the paths of taxes and debt and, hence, the price level. (2) This link is independent of whether the sequence of primary surpluses is exogenous or endogenous, implying that an equilibrium allocation is, in general, associated with exactly one price level sequence under distortionary taxation. (3) Second, compared with lump-sum taxation, the nonneutrality of distortionary taxation increases the scope for indeterminacy of the equilibrium allocation ("real indeterminacy"). Specifically, under a passive fiscal policy and exogenous interest rates equilibrium indeterminacy can be real under distortionary taxes, while it is purely nominal under lump-sum taxes. This finding is related to Schmitt-Grohe and Uribe's (1997) result that there might exist multiple equilibrium allocations under distortionary taxation in a nonmonetary economy. Here, we consider a monetary economy in which both fiscal (due to distortionary taxation) and monetary policies (due to a cash constraint) are nonneutral. This implies that under a passive fiscal policy real determinacy relies on further restrictions on taxes, debt, and interest rates. The main contribution of the paper is to investigate this feature for the prominent case of a balanced-budget policy (as an example of a passive fiscal policy that restricts the supply of government debt).
In particular, assuming distortionary income taxes, we show that under a balanced-budget policy the equilibrium is determinate (both in nominal and in real terms) if the central bank sets exogenously the nominal interest rate in a way consistent with long-run deflation. This finding differs from the result under a balanced-budget policy and lump-sum taxes where real equilibrium determinacy does not rely on any such restriction on interest rates, while the equilibrium will be nominally indeterminate, as shown by Schmitt-Grohe and Uribe (2000). More specifically, we show that a sequence of nominal interest rates consistent with long-run deflation leads to steady-state uniqueness and equilibrium determinacy (and the latter feature, in the special case of logarithmic utility in consumption, is shown to be even globally satisfied). Intuitively, under deflation the government tends to receive negative seigniorage revenues because of falling prices and falling nominal balances. Under the balanced-budget regime these losses need to be offset by the issuance of additional debts, leading to higher interest payments, which have to be financed by distortionary income taxes. Such tax revenues, however, cannot grow without bounds for feasible equilibrium allocations. Yet, there exists a unique initial price level (associated with uniquely defined tax sequences and equilibrium allocations) that devalues the initial nominal liabilities in a manner consistent with the (nominal and real) determinacy of the equilibrium. By contrast, this mechanism does not work under a sequence of exogenous nominal interest rates consistent with long-run inflation; i.e., such a sequence fails to establish equilibrium determinacy.
To facilitate comparisons with related studies we also consider monetary policy in the form of a simple Taylor-rule; i.e., we consider interest rates that are endogenously set contingent on changes in inflation. The analysis of local equilibrium determinacy for this case shows that the results obtained for exogenous interest rates (which can be interpreted as a special case of a passive interest rate rule) are consistent with the determinacy results derived for this broader set of monetary policy specifications. In particular, we find that (nominal and real) equilibrium determinacy under distortionary taxation and a balanced budget is consistent with a passive interest rate policy and long-run deflation, while it requires an active interest rate policy under long-run inflation. However, our analysis also shows that the (in)determinacy of equilibria does not only rely on monetary policy being active or passive, but, in general, depends on further restrictions on monetary and fiscal policy. One important reason for this feature is that changes in inflation can have ambiguous budgetary effects in our model. In all cases considered, higher inflation tends to increase the costs of money holdings and distorts--via the cash constraint--the allocation in a contractionary way. This tends to lead to a decline in real tax revenues for a given tax rate. However, higher inflation, by reducing the real value of debt, affects the budget of indebted governments also in a positive manner. (4)
The question addressed in this paper is directly related to Leeper (1991), Woodford (1994), Sims (1994), Benhabib et al. (2001), and, most importantly, Schmitt-Grohe and Uribe (2000). As in these studies, it is assumed that prices are fully flexible, but we relax the common assumption of lump-sum taxes. Our findings correspond to Benassy (2000, 2005). These two papers depart from Ricardian equivalence not via taxation but instead by means of an overlapping generations structure and establish that an interest rate peg is consistent with nominal determinacy. (5) Canzoneri and Diba (2005) establish the possibility of nominal determinacy under an interest rate peg and endogenous primary surpluses if public debt is nonneutral due to transaction services of government bonds. In an overview paper, Leeper and Yun (2006) point out that the existence of asset revaluation effects induced by an exogenous primary surplus does not rely on the assumption of lump-sum taxes. (6) Finally, our local determinacy analysis relates to Schmitt-Grohe and Uribe's (1997) analysis of balanced-budget regimes in a real business cycle model where monetary policy is neglected. They show that real indeterminacy can arise when labor income tax rates take high (though empirically plausible) values, whereas in our model the monetary and the fiscal stances are decisive for real indeterminacy.
The paper is structured as follows. Section 1 presents a model with a transaction friction and distortionary taxes, implying that both monetary and fiscal policies affect the equilibrium allocation and prices in a nontrivial way. Section 2 establishes the nominal (in)determinacy of equilibria under lump-sum and distortionary taxation. Similarly, Section 3 establishes the real (in) determinacy of equilibria under lump-sum and distortionary taxation. Sections 2 and 3 consider exogenously set interest rates. In Section 4, we examine nominal and real equilibrium determinacy for endogenously set interest rates. Section 5 concludes. The Appendix contains technical parts of the analysis.
1. THE MODEL
In this section, we present a simple representative agent model with flexible prices. Money demand is introduced via a cash constraint in the goods market. Government purchases of the final good are financed by public debt, tax revenues, and seigniorage. Tax revenues are raised in a lump-sum way or by a proportional tax on labor income. Throughout the paper, small (large) letters denote real (nominal) variables.
1.1 Private Sector
There exists a continuum of infinitely lived and identical households of mass one. Their utility increases in consumption [c.sub.t] and decreases in working time [l.sub.t], the latter being bounded by some finite value [bar.l] such that [l.sub.t] [member of] (0, [bar.l]). The objective of a representative household is given by
max [[infinity].summation over (t=0)] [[beta].sup.t] [[[c.sup.1-[sigma].sub.t]/1 - [sigma]] - [[l.sup.1+v.sub.t]/ 1 + v]]], with [sigma] [greater than or equal to] 1, v [greater than or equal to] 0, [beta] [member of] (0, 1), (1)
where [beta] denotes the discount factor, [sigma] represents the inverse of the intertemporal elasticity of substitution in consumption, and v denotes the inverse of the Frisch elasticity of labor supply. The restriction [sigma] [greater than or equal to] 1 is not irrelevant for our results and will be discussed at the end of Section 3.
Households enter a representative period t with two types of nominal assets, money balances [M.sub.t-1] and interest bearing government debt [B.sub.t-1]. The latter is issued in the form of one-period nominally risk-free bonds, earning a predetermined net interest rate [i.sub.t-1] in period t. Households pay a proportional tax on labor income [[tau].sup.d.sub.t][w.sub.t][l.sub.t] (where [[tau].sup.d.sub.t] and w t denote the distortionary tax rate on labor income and the real wage, respectively) and a lump-sum tax [[tau].sub.t]. Moreover, households face a cash constraint in the goods market
[P.sub.t][c.sub.t] [less than or equal to] [M.sub.t], (2)
where [P.sub.t] denotes the aggregate price level. The cash constraint (2) implies that households can in every period adjust their money holdings before they enter the goods market. The budget constraint of households is given by
[P.sub.t][c.sub.t] + [B.sub.t] + [M.sub.t] [less than or equal to] (1 + [i.sub.t-1])[B.sub.t-1] + [M.sub.t-1] + (1 - [[tau].sup.d.sub.t]) [P.sub.t][w.sub.t][l.sub.t] - [P.sub.t][[tau].sub.t]. (3)
Let [[pi].sub.t] = [P.sub.t]/[P.sub.t-1] and [R.sub.t-1] = 1 + [i.sub.t-1] denote the gross inflation rate and the nominal gross interest rate, respectively. In the initial period t = households are endowed with nominal money balances [M.sub.-1] > and (not necessarily positive) holdings of nominal bonds [B.sub.-1] with [R.sub.-1] > 1, satisfying [R.sub.-1][B.sub.-1] + [M.sub.-1] > 0. Given these initial conditions, maximizing (1) subject to a no-Ponzi game condition [lim.sub.t[right arrow][infinity]] ([b.sub.t] + [m.sub.t]) [[PI].sup.t.sub.i=1] [[pi].sub.i]/[R.sub.i-1] [greater than or equal to] 0, (2) and (3) leads to the first-order conditions
[2[R.sub.t] - 1/[R.sub.t]] [c.sup.[sigma].sub.t][l.sup.v.sub.t] = (1 - [[tau].sup.d.sub.t]) [w.sub.t], (4)
[beta] [[R.sub.t+1]/2{R.sub.t+1] - 1] [c.sup.-[sigma].sub.t+1] [[pi].sup.-1.sub.t+1] = [1/2[R.sub.t-1]] [c.sup.-[sigma].sub.t], (5)
[c.sub.t] [less than or equal to] [m.sub.t]. (6)
where [m.sub.t] = [M.sub.t]/[P.sub.t] and [b.sub.t] = [B.sub.t]/[P.sub.t]. The first equation summarizes the first- order conditions associated with the labor supply and consumption decisions, the second equation describes the intertemporal Euler equation, and the third equation turns into [c.sub.t] = [m.sub.t] if [R.sub.t] > 1. (7) Further, the transversality condition
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
has to be satisfied. There is a continuum of perfectly competitive firms of mass one. Firms produce the consumption good with the linear technology [y.sub.t] = [l.sub.t]; i.e., labor is the only production factor supplied by the households. Assuming a competitive labor market, profit maximization leads to zero profits and [w.sub.t] = 1. Total output [y.sub.t] consists of private sector consumption [c.sub.t] and government purchases of the consumption good [g.sub.t], i.e., [y.sub.t] = [c.sub.t] + [g.sub.t].
1.2 Public Sector
Monetary policy is specified in terms of the nominal interest rate [R.sub.t]. For the main part of the analysis, we consider the case where the central bank follows an exogenously specified path of the interest rate. In Section 4, we consider cases where the interest rate is adjusted in response to changes in endogenous variables. Throughout the analysis we assume [R.sub.t] > 1 [for all]t [greater than or equal to] 0, implying that the cash constraint is always binding....
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