Explaining the Fiscal Theory of the Price Level

Many traditional macroeconomic models do not have determinate predictions for the path of inflation: even for a given specification of money supplies, many paths of inflation are consistent with equilibrium. According to the fiscal theory of the price level, fiscal policy can be used to select which of these many paths actually occur. This article explains the fiscal theory of the price level and discusses its empirical and policy implications. The article argues that the theory is equivalent to giving the government an ability to choose among equilibria. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. How can governments influence inflation rates? Economists’ standard answer is that the central bank controls the inflation rate through its ability to control the money supply. In particular, if output grows at γ percent per year and the money supply grows at μ percent per year, then, at least over sufficiently long periods of time, prices will grow at (μ−γ) percent per year. Simply put, the inflation rate is determined by the change in the relative scarcities of money and goods. Unfortunately, there is a large hole in this simple, static reasoning. How much money a household wants to hold today depends crucially on that household’s beliefs about future inflation. As it turns out, this dependence of current money demand on beliefs about future inflation creates the possibility of a large number of equilibrium paths of inflation rates, besides the one in which prices grow at (μ−γ) percent. (See Obstfeld and Rogoff 1983, for example.) Thus, control of the money supply alone is not sufficient to pin down the time path of the inflation rate. This analysis suggests the following important question: Can the government use some other policy instrument, such as taxes or debt policy, in conjunction with monetary policy to determine the time path of the inflation rate? In an important recent paper, Woodford (1995) proposes a new theory of price determination, the fiscal theory of the price level. He argues that the government’s choice of how to finance its debt plays a crucial role in the determination of the time path of the inflation rate. In this article, we explain this theory. We make three main points. First, we show that according to Woodford’s (1995) theory, fiscal policy affects inflation rates if and only if the government can behave in a fundamentally different way from households. Households must satisfy intertemporal budget constraints, no matter what price paths they face. Woodford (1995) argues that the government does not face this same requirement; the government can follow non-Ricardian fiscal policies under which the intertemporal budget constraint is satisfied for some, but not all, price paths. Following Woodford (1995), we show that fiscal policy can affect inflation rates if and only if the government can use non-Ricardian policies. Why can the government influence inflation rates when it uses non-Ricardian policies? We show that if the government’s intertemporal budget constraint is not satisfied for a price path, then that price path cannot be an equilibrium (because such a path is inconsistent with market-clearing and household optimality). Hence, the government can reject any price path as an equilibrium by guaranteeing that its intertemporal budget constraint is not satisfied along that price path. Our second point concerns a natural question: Can the government implement non-Ricardian policies, even though households cannot? We argue that this question cannot be answered using data. Whether a fiscal policy is non-Ricardian concerns the government’s behavior at unobserved price paths; therefore, such a determination is nontestable. Fundamentally, then, whether the government can follow a non-Ricardian policy is a religious, not a scientific, question. Finally, we demonstrate that the predictions of a specific popular non-Ricardian fiscal policy for inflation are highly counterintuitive. In particular, we show that under this non-Ricardian policy, one-time decreases in the money supply can lead to hyperinflations. This is in stark contrast to the usual monetarist intuition under which onetime decreases in the money supply have no effect on long-run inflation rates. We proceed in three parts. First, we show that standard monetary models have an infinite number of predictions for the time path of inflation rates. Our analysis closely follows that of Obstfeld and Rogoff (1983). Next, we demonstrate how the fiscal theory of the price level serves to shrink the set of predictions by allowing the government to use non-Ricardian policies. Finally, we argue that the fiscal theory is not falsifiable, and we consider its implications for the consequences of a once-andfor-all decrease in the money supply. On the Indeterminacy of Monetary Equilibria In this section, we present an example economy, originally due to Obstfeld and Rogoff (1983), that shows how standard monetary models have a continuum of equilibrium time paths for the inflation rate. In our example economy, time is discrete and infinite. There is a continuum of identical households. The households are initially endowed with M−1 dollars and with a constant stream of y perishable consumption goods. In our example, we assume that the money supply does not change over time. In each period, households exchange money, nominal bonds, and consumption in a competitive market. In this market, households face a sequence of flow budget constraints (for all t ≥ 0) of the following form: (1) Ptct + Mt + Bt ≤ Mt−1 + Rt−1Bt−1 + Pty with ct and Mt ≥ 0, B−1 = 0, and M−1 given. In this market, ct is the amount of consumption goods consumed by the household in period t, Mt is the amount of dollars held by the household at the end of period t, Bt is the amount of the nominal bonds held by the household at the end of period t, Rt is the number of dollars a bond pays in period t + 1, and Pt is the price of consumption in terms of dollars in period t. (Here and throughout the article, uppercase letters refer to nominal variables, and lowercase letters to real variables.) Households also face a borrowing condition that for all t ≥ 0, (2) Mt−1 + Rt−1Bt−1 + ∞ j=0 Pt+jy/∏ j s=0Rt+s ≥ 0. In words, this condition requires that the household’s wealth at the end of period t, including the present value of its income stream, be nonnegative. This condition eliminates Ponzi schemes (or financing unlimited consumption by running Bt to negative infinity). If Pt > 0 for all t, then the price of a period t dollar in terms of period 0 dollars is 1/∏ s=0Rs. Given this, the formulation above of a household’s budget set as a sequence of flow budget constraints (1) and a borrowing condition (2) is equivalent to the perhaps more familiar formulation of a consumer’s budget set as one in which the value of expenditures in terms of some numeraire good equals the value of resources in terms of that same numeraire. That is, constraint (1) and condition (2) define the same set of feasible consumption and money sequences as the present-value budget condition (3) ∞ t=0 [(1−1/Rt)Mt + Ptct]/∏ s=0Rs ≤ ∞ t=0 (Pty/∏ s=0Rs) + R−1B−1 + M−1. Here, the left side is the value of the household’s net purchases of money and the household’s consumption, while the right side is the value (in terms of period 0 money) of the household’s endowment stream. Each household has the same preferences over streams of consumption and real balances: (4) ∞ t=0 β[u(ct) + v(Mt/Pt)]. Here, 0 < β < 1. Also, the utility functions over consumption and real balances, u and v, are assumed twice differentiable, strictly increasing, and strictly concave, with u′(0) = ∞. The household seeks to maximize this objective function, subject to equations (1) and (2). If the borrowing condition (2) ever binds, the household must have ct = 0 in all future periods; therefore, the assumption that u′(0) = ∞ ensures that (2) never binds. An equilibrium is a sequence {Pt,Rt} ∞ t=0 of nominal prices and interest rates such that, given this sequence, households find it optimal to choose to hold the supply M−1 of dollars and eat y of the consumption goods in each period (and thus set Bt = 0 each period). Examination of the first-order conditions delivers that any positive sequence {Pt,Rt} ∞ t=0 is an equilibrium if and only if condition (3) holds with equality and for all t ≥ 0, (5) v′(M−1/Pt) = u′(y)[1−1/Rt] (6) Rt = (1/β)(Pt+1/Pt). The present-value budget condition (3) holding with equality is equivalent to the flow budget constraint (1) holding with equality and the limiting condition (7) limT→∞(MT−1 + RT−1BT−1)/∏s=0Rs = 0. In this economy, output does not grow and money does not grow. Hence, the standard, static thinking about inflation would say that nominal prices should not grow. There is indeed an equilibrium of this form. In this equilibrium, for all t,