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In this paper I consider the role of state-contingent inflation as a fiscal shock absorber in an economy with nominal rigidities. I study the Ramsey equilibrium in a monetary model with distortionary taxation, nominal non-state-contingent debt, and sticky prices. With sticky prices, the Ramsey planner must balance the shock absorbing benefits of state-contingent inflation against the associated resource misallocation costs. For government spending processes resembling post-war experience, introducing sticky prices generates striking departures in optimal policy from the case with flexible prices. For even small degrees of price rigidity, optimal policy displays very little volatility in inflation. Tax rates display greater volatility compared to the model with flexible prices. With sticky prices, tax rates and real government debt exhibit behavior similar to a random walk. For government spending processes resembling periods of intermittent war and peace, optimal policy displays extreme inflation volatility even when the degree of price rigidity is large. As the variability in government spending increases, smoothing tax distortions across states of nature becomes increasingly important, and the shock absorber role of inflation is accentuated.

An important result of the optimal policy literature is the prescription of policies which smooth tax distortions over time and across states of nature. When governments finance stochastic government spending by taxing labor income and issuing one-period debt, state-contingent returns on that debt allow tax rates to be roughly constant (see Lucas and Stokey, 1983; Chari et al., 1991). In monetary models, this tax smoothing can be achieved even when nominal returns on debt are not state-contingent; varying the price level in response to shocks allows the government to achieve appropriate state-contingent, ex-post real returns (see Chari et al., 1991). Generating inflation in the period of a positive spending shock allows the government to decrease its real liabilities by reducing the value of its outstanding nominal claims. In this way, the government is able to attenuate the increase in taxes required to maintain present value budget balance. Similarly, a deflation in response to a negative spending shock attenuates the required fall in tax revenues. Clearly, inflation plays an important policy role when nominal returns to debt are not state-contingent, since it can generate real returns which are. and A quantitative property of these models is that when calibrated to post-war US data, optimal policy displays extreme inflation volatility (see Chari et al., 1991; Chari and Kehoe, 1999). This is due to the fact that inflation is costless in these models. The aim of this paper is to determine the optimal degree of volatility when inflation is no longer costless, but still has shock absorbing benefits. This is an important consideration since studies that consider optimal monetary policy devoid of fiscal considerations prescribe stable inflation when nominal rigidities are present (see King and Wolman, 1999; Erceg et al., 2000; Khan et al., 2000). To study this question I introduce sticky prices into the standard cash–credit good model. When some prices in the economy are set before the realization of government spending, unanticipated inflation causes relative price distortions. This distortion generates costly misallocation of real resources. Optimal policy on the part of the government must balance the tax smoothing benefits of state-contingent inflation against these misallocation costs. To see this trade-off, consider an economy with a complete set of tax instruments, as in Lucas and Stokey (1983) or Chari et al. (1991). With both sticky price and flexible price firms, this can be achieved by providing the government with an additional state-contingent tax on the output of sticky price firms. In this complete instruments case, ex-post variation in the price level generates state-contingency in the real value of government liabilities, keeping tax distortions smooth. At the same time, ex-post variation in the tax on the output of sticky price firms keeps the relative price, and hence relative production, across sticky and flexible price firms at its efficient level. In the model presented in this paper, the government does not levy independent taxes on the output of sticky and flexible price firms so that the complete instruments outcome cannot be attained. Ex-post inflation drives down the relative price of sticky price firms, leading to overproduction of sticky price goods (and underproduction of flexible price goods). Likewise, ex-post deflation leads to underproduction (overproduction) of sticky price (flexible price) goods. Hence, any variation in ex-post prices used to generate real state-contingency in nominal debt results in misallocation of resources. In examples calibrated to post-war US data, I show that introducing sticky prices has a striking impact on the optimal degree of inflation volatility. While the flexible price model displays extreme volatility, the analogous sticky price model displays essentially stable deflation at the rate of time preference. This is true even when the proportion of sticky price setters is small. For instance, when 2% of price setting firms post prices before the realization of shocks, the standard deviation of inflation falls by a factor of 8 (relative to the case with flexible prices); when 5% of firms have sticky prices, the standard deviation falls by a factor of 16. When the model displays diminishing marginal product of labor, 5% sticky prices causes the standard deviation of inflation to fall by a factor of 40. Hence, for post-war calibrations, the gains from achieving state-contingency in real debt returns are small relative to the misallocation costs induced by variable ex-post inflation. The nominal interest rate is no longer zero in the sticky price model, as prescribed by Friedman (1969), but instead fluctuates across states of nature. However, the deviation from the Friedman Rule is quantitatively small. Finally, the serial correlation properties of optimal tax rates and real government debt differ markedly in the two environments. In contrast to Barro's (1979) random walk result, Chari et al. (1991) show that with flexible prices, these variables inherit the serial correlation of the model's underlying shocks (see Lucas and Stokey, 1983, for the initial exposition of this result with state-contingent debt). Faced with sticky prices, a benevolent government finances increased spending largely through increased taxes. As high spending regimes persist, tax revenues are gradually increased and real debt is accumulated. During spells of low spending, taxes fall and accumulated debt is paid off. As a result, the autocorrelations of these objects are near unity regardless of the persistence in the shock process, partially reviving Barro's result. This finding is similar to that of Aiyagari et al. (2002) who consider optimal policy in a model with incomplete markets (i.e. real non-state-contingent debt). In fact, I show that the sequence of restrictions imposed on the set of feasible equilibria by sticky prices and market incompleteness are analytically similar. As the volatility in government spending increases, the shock absorbing benefits of state-contingent inflation come to dominate the costs of resource misallocation. For instance, when government spending is 3 times more volatile than post-war experience, optimal policy prescribes extreme volatility in inflation even with a large proportion of sticky prices. With large spending shocks, tax smoothing considerations are accentuated, and the Ramsey planner tolerates misallocation associated with volatile inflation in order to smooth tax distortions across states of nature. To shed light on this result, I analyze the nature of the benefits and costs of inflation volatility when government spending is volatile. The next section presents a cash–credit good model with price setting on the part of intermediate good firms; a subset of these firms post prices before the realization of the state of nature. Section 3 characterizes equilibrium, and develops the primal representation of equilibrium. I show that the primal representation requires consideration of two sequences of cross-state constraints not present with flexible prices. Section 4 presents the Ramsey allocation problem. The existence of the cross-state constraints makes solving this problem difficult. Section 5 provides additional analysis of the key cross-state constraint introduced by sticky prices. Section 6 discusses the characteristics of the Ramsey equilibrium that make development of a solution method feasible. I show that the solution builds upon the recursive contracts approach developed in Marcet and Marimon (1999). Section 7 presents quantitative results. Section 8 concludes.

This paper characterizes optimal fiscal and monetary policy with sticky price setting in intermediate goods markets. With sticky prices, a benevolent government must balance the shock absorbing benefits of state-contingent inflation against its resource misallocation costs. The results of this study extend those found in the literature in a number of ways. With government spending calibrated to post-war data, the Ramsey solution prescribes essentially constant deflation, even when the fraction of sticky price firms is small. Hence, responses in the real value of inherited government liabilities are largely attenuated. Instead, tax distortions can essentially be characterized as being smoothed over time. Persistent spells of high spending are accompanied by increasing tax collection and the accumulation of debt; spells of low spending by falling taxes and the reduction of debt. This imparts a high degree of persistence in tax rates and real debt holdings, regardless of the persistence in the underlying shock process. In summary, the extreme volatility in optimal inflation rates described in the optimal policy literature, at least for post-war calibrated shocks, is sensitive to small departures from the assumption of flexible price setting. However, for volatile government spending processes, inflation volatility is retained as a policy prescription despite the presence of sticky prices. Ramsey policy tolerates resource misallocation in favor of cross-state tax smoothing achieved through ex-post movements in the price level. The implications of this result for welfare experience associated with historical war episodes is still to be determined