رشد نامحدود بدهی های عمومی و تئوری مالی سطح قیمت

The fiscal theory of the price level asserts that the price level is determined by the ratio of outstanding public nominal debt into the present value of real primary budget surpluses of the government. We here argue that price determinacy, in general, fails when at least part of the public debt takes the form of securities of infinite maturity. Indeed, price determinacy requires non-Ricardian fiscal plans and a predetermined nominal debt of the government. As no equilibrium restriction prevents the occurrence of a speculative bubble on infinite-maturity public debt, the initial nominal debt of the government is indeterminate and so is the price level under canonical specifications of non-Ricardian fiscal plans.

A non-Ricardian fiscal regime is defined by Woodford, 1994, Woodford, 1998, Woodford, 2001 and Woodford, 2003 as a policy such that government primary surpluses or revenues from inflation need not be readjusted after some initial fiscal disturbance. This policy contradicts a common understanding, exemplified by Sargent and Wallace, 1975 and Sargent and Wallace, 1981 unpleasant monetarist arithmetic, according to which a fall in money creation can only be followed by a reduction of future government deficits or a rise in future inflation. In a non-Ricardian regime, the price level is determined by the present value budget constraint of the government. In fact, treating seignorage as negligible, equilibrium requires a sort of valuation equation for government debt of the form View the MathML sourceNominal government debtPrice level=Present value of primary surpluses. Turn MathJax on Outstanding nominal debt is predeterminate and, in a non-Ricardian regime, primary public budget surpluses are set according to some given rule, independent of a public intertemporal budget constraint, so that the price level serves to fulfill the valuation equation. In addition, under an interest rate pegging and exogenously given fiscal plans, the most canonical case in the literature, public liabilities, consisting of money balances and government debt, are endogenously determined by the sequence of government budget constraints. This procedure is known as the ‘fiscal theory of the price level’. In the present note, we argue that price determinacy fails, under a non-Ricardian regime, when primary public surpluses are set exogenously and at least part of the government liabilities are in the form of infinite-maturity nominal securities, like perpetuities, whose market value is to be determined at equilibrium. In fact, we shall show that, as speculative bubbles on infinite-maturity public debt are not ruled out by any of the equilibrium restrictions, the price level is indeterminate under the non-Ricardian regime, when nominal interest is pegged by the Central Bank. 1 The reason for the indeterminacy is easy to grasp and can be understood through a simple intertemporal accounting. According to the fiscal theory, the price level is jointly determined by the present value of government future surpluses and the current value of government interest-bearing bonds. Neglecting seignorage and assuming that public debt entirely consists of perpetuities, at equilibrium, a valuation equation for government debt imposes View the MathML sourcePerpetuity price×Perpetuity stockPrice level=Present value of primary surpluses. Turn MathJax on This single restriction involves two distinct unknowns: the price level and the perpetuity price. Illegitimately, assuming that public debt were quoted at its fundamental value, Perpetuity price=Present value of perpetuity nominal dividends,Perpetuity price=Present value of perpetuity nominal dividends, Turn MathJax on the valuation equation for government debt would univocally determine the price level.2 However, there is in fact no equilibrium restriction that can be invoked in order that public debt be quoted at its fundamental value and, in fact, any price of the perpetuity, above its fundamental value, is consistent with equilibrium. Consequently, the price level is indeterminate.3 Why are speculative bubbles not ruled out by equilibrium restrictions? Are we omitting a crucial transversality condition? As a matter of fact, consolidating the private sector and the government, infinite-maturity public debt is a nominal security in zero net supply and, in general, speculative bubbles on such a sort of securities are consistent with equilibrium (e.g., Santos and Woodford, 1997, Example 4.3). In the case of real productive asset, like land, intertemporal accounting (i.e., Walras’ Law or, in the case of single representative individual, the intertemporal budget constraint evaluated at market clearing) yields Land price×Land stock=Present value of land stock dividends.Land price×Land stock=Present value of land stock dividends. Turn MathJax on It is such a condition which excludes speculative bubbles, and whose analog, in the case of infinite-maturity public debt, is the valuation equation for the government debt. Hence, there is no further restriction to establish that the perpetuity issued by the government is priced at its fundamental value. At equilibrium with a speculative bubble, the market value of the government perpetuity might grow unboundedly, but the supply of such a security declines through time. At equilibrium without a speculative bubble, instead, the supply of the perpetuity might grow unboundedly, though its market price remains stable. If there is inflation at equilibrium (that is, nominal interest exceeds real interest) and fiscal plans for real primary surpluses are set exogenously, the value of the overall intertemporal public revenue grows over time and must be balanced by an increasing value of public debt liabilities. The fiscal theory of the price level has been mostly developed and advocated by Leeper (1991), Sims (1994), Woodford, 1994, Woodford, 1995 and Woodford, 2001 and Cochrane (2005). Cochrane (2001) has extended the theory to long-term government debt and Dupor (2000) has analyzed the consequences on exchange rate determination in an open economy framework. Cochrane (1999) and Loyo (1999) have argued that the fiscal theory is useful for understanding the actual patterns of inflation in the US (during the seventies) and in Brazil (during the eighties). Namely, a failure of the policymakers to understand the role of government fiscal policy for price stabilization may explain why high inflation can arise even without high money creation and limited levels of seignorage. The theory has been also used to show that the price level is well defined even in economies without money (Cochrane, 2005; Woodford, 1995). The fiscal theory of the price level has been discussed and criticized at length. Buiter (2002) objects to the very logic of the theory by arguing that the government must necessarily commit to satisfy an intertemporal budget constraint at all prices (i.e., at equilibrium and out of equilibrium). Treating the government intertemporal budget constraint as an equilibrium restriction leaves one uncertain about the mechanisms responsible for bringing a disequilibrium price level to its equilibrium position. McCallum (2001) makes similar claims. Bassetto (2002) attempts to clarify the validity of the theory by assuming that the government is a large player and by describing the economy as a game between the government and the private sector. One of the problems with the fiscal theory highlighted by Bassetto (2002) is that, in this framework, an unconditional and pre-specified sequence of primary surpluses may not be a valid strategy if the private sector may choose not to lend to the government. Niepelt (2004) criticizes the fiscal theory on the ground that, under rational expectations, the value of the outstanding government debt at the beginning of a period cannot be given arbitrarily. Instead, this value must be derived as an equilibrium outcome for the economy in the previous (possibly) unrepresented periods. None of the above is an objection that we raise in this paper, as we take it for granted that fiscal plans need not satisfy an intertemporal budget constraint at every price sequence and the initial value of government liabilities can be set exogenously. The contribution most closely related to our paper is Dupor (2000), where the use of the fiscal theory as an effective equilibrium selection device is shown to be inadequate. In particular, Dupor finds that an indeterminate price level coexists with a non-Ricardian regime in a two-country economy where governments peg the nominal interest rates on domestic bonds. This type of indeterminacy is connected to the existence of a multiplicity of nominal exchange rates. The paper is organized as follows. In Section 2, we describe a very simple monetary economy with public debt of infinite maturity. In Section 3, we present the notion of equilibrium and, in Section 4, we show that equilibrium restrictions are consistent with any arbitrary value of speculative bubbles, thus delivering an indeterminate price level. Finally, in Section 5, we discuss the robustness of this sort of price indeterminacy to other specifications of a non-Ricardian fiscal-monetary regime.

Our elementary analysis shows that, if the Central Bank pegs nominal interest, the price level is indeterminate when at least part of public liabilities consists of infinite-maturity securities, even under a non-Ricardian policy regime. We shall here briefly discuss robustness of this sort of price indeterminacy. As the equilibrium without speculative bubble is locally isolated, it could be selected on this ground.6 However, it is to be noticed that any other equilibrium with positive speculative bubble is also locally isolated and, thus, that selection criterion is perhaps inadequate. Indeed, in our simplified economy, comparing two distinct equilibria, the distance between equilibrium prices of the perpetuity becomes arbitrarily large in the long-period, as View the MathML source|qta-qtb|=(1+r)t|γa-γb|. Turn MathJax on Woodford (2001) proposes a slightly different formulation of the fiscal theory of the price level. When considering the case of an infinite-maturity public debt, he assumes that the government is able to carry out a security price support policy, so in fact pegging the price of the security over time, consistently with a given path of nominal rates of interest. This would, indeed, deliver a full determinacy of the price level. Contrasting Woodford (2001) with Woodford (1998), which we faithfully reproduce in our analysis, it is to be noticed that a security price support is not a heuristic hypothesis for simplifying the analysis, but a precise claim on the conduct of monetary policy in order to obtain price determinacy. Statements on the determinacy of the price level needs be qualified, in particular, when public debt consists of various securities of infinite maturity and nominal interest is pegged by some mechanical Taylor rule. Finally, other non-Ricardian specifications of fiscal plans could deliver a determinate price level. This requires that fiscal surpluses be increased proportionally with the speculative bubble, so as to neutralize the effect on the price level. In our simplified economy,7 an example of such bubble-neutralizing fiscal plans would be given by View the MathML sourcest=s+γ(d0/p0)ift=0,sift>0. Turn MathJax on Substituting this rule into the intertemporal public budget constraint would yield restriction (19), so pegging a unique price level. Notice, however, that these fiscal plans do not prevent the occurrence of speculative bubbles on infinite-maturity public debt, so that there is still a continuum of equilibria. Also, with heterogeneous individuals, speculative bubbles will, in general, result in a redistribution of initial nominal claims among individuals, so bearing effects of allocative relevance, unless the tax burden is distributed across individuals proportionally with their initial holdings of the infinite-maturity public debt. Furthermore, even with a representative individual, under uncertainty, fiscal plans should be very sophisticated in order to neutralize the effects on the variability of inflation rates across states of nature.