سیاست های پولی و مالی مطلوب با قیمت های بااهمیت

This paper studies optimal fiscal and monetary policy under sticky product prices. The theoretical framework is a stochastic production economy. The government finances an exogenous stream of purchases by levying distortionary income taxes, printing money, and issuing nominal non-state-contingent bonds. The main findings of the paper are: First, for a miniscule degree of price stickiness (i.e., many times below available empirical estimates) the optimal volatility of inflation is near zero. Second, small deviations from full price flexibility induce near random walk behavior in government debt and tax rates. Finally, price stickiness induces deviation from the Friedman rule.

Two distinct branches of the existing literature on optimal monetary policy deliver diametrically opposed policy recommendations concerning the long-run and cyclical behavior of prices andinterest rates. One branch follows the theoretical framework laidout in Lucas and Stokey [16]. It studies the joint determination of optimal fiscal andmoneta ry policy in flexible-price environments with perfect competition inproduct and factor markets. In this group of papers, the government’s problem consists in financing an exogenous stream of public spending by choosing the least disruptive combination of inflation and distortionary income taxes. The criterion under which policies are evaluated is the welfare of the representative private agent. Calvo andGuid otti [4,5] andChar i et al. [6] characterize optimal monetary and fiscal policy in stochastic environments with nominal non-state-contingent government liabilities. A key result of these papers is that it is optimal for the government to make the inflation rate highly volatile and serially uncorrelated. Under the Ramsey policy, the government uses unanticipatedinfl ation as a lump-sum tax on financial wealth. The government is able to do this to the extend that it has nominal, non-state-contingent liabilities outstanding. Thus, price changes play the role of a shock absorber of unexpected innovations in the fiscal deficit. This ‘front-loading’ of government revenues via inflationary shocks allows the fiscal authority to keep income tax rates remarkably stable over the business cycle. On the other hand, a more recent literature focuses on characterizing optimal monetary policy in environments with nominal rigidities and imperfect competitions. 1 Besides its emphasis on the role of price rigidities and market power, this literature differs from the earlier one described above in two important ways. First, it assumes, either explicitly or implicitly, that the government has access to (endogenous) lump-sum taxes to finance its budget. An important implication of this assumption is that there is no needto use unanticipated inflation as a lump-sum tax; regular lump-sum taxes take up this role. Second, the government is assumed to be able to implement a production (or employment) subsidy so as to eliminate the distortion introduced by the presence of monopoly power in product and factor markets. A key result of this literature is that the optimal monetary policy features an inflation rate that is zero or close to zero at all dates and all states.2 The reason why price stability turns out to be optimal in environments of the type described here is straightforward: the government keeps the price level constant in order to minimize (or completely eliminate) the costs introduced by inflation under nominal rigidities. Taken together, these two strands of research on optimal monetary policy leave the monetary authority without a clear policy recommendation. Should the central bank pursue policies that imply high or low inflation volatility? The goal of this paper is to contribute to the resolution of this policy dilemma. To this end, it incorporates in a unifiedframew ork the essential elements of the two approaches to optimal policy described above. Specifically, we build a model that shares three elements with the earlier literature: (a) The only source of regular taxation availableto the government is distortionary income taxes. In particular, the fiscal authority cannot adjust lumpsum taxes endogenously in financing its outlays. (b) The government cannot implement production subsidies to undo distortions created by the presence of imperfect competition. (c) The government issues only nominal, oneperiod, non-state-contingent bonds. At the same time, our model shares two important assumptions with the more recent body of work on optimal monetary policy: (a) Product markets are not perfectly competitive. In particular, we assume that each firm in the economy is the monopolistic producer of a differentiated intermediate good. (b) Product prices are assumed to be sticky. We introduce price stickiness a` la Rotemberg [19] by assuming that firms face a convex cost of price adjustment. An assumption maintained throughout this paper that is common to all of the papers citedabove (except for Lucas and Stokey [16]) is that the government has the ability to fully commit to the implementation of announcedfiscal and monetary policies. In this environment, the government faces a tradeoff in choosing the path of inflation. On the one hand, the government would like to use unexpected inflation as a non-distorting tax on nominal wealth. In this way, the fiscal authority could minimize the needto vary distortionary income taxes over the business cycle. On the other hand, changes in the rate of inflation come at a cost, for firms face nominal rigidities.3 The main result of this paper is that under plausible calibrations of the degree of price stickiness, this trade off is overwhelmingly resolved in favor of price stability. The optimal fiscal/monetary regime features relatively low inflation volatility. Thus, the Ramsey allocation delivers an inflation process that is more in line with the predictions of the more recent body of literature on optimal monetary policy referredto above, which ignores fiscal constraints by assuming that the government can resort to lump-sum taxation. Moreover, we findthat a miniscule amount of price stickiness suffices to bring the optimal degree of inflation volatility close to zero. Specifically, our results suggest that for a degree of price stickiness that is 10 times smaller than available estimates for the US economy, price stability emerges as the central feature of optimal monetary policy. The fragility of front-loading government revenue via surprise changes in the price level reveals that the welfare gains of this way of government financing must be small. To understand why this is so, it is useful to relate price stickiness to the ability of the government to make nominally non-state-contingent debt state contingent in real terms. Under full price flexibility, the government uses unexpected variations in the price level to render the real return on nominal bonds state contingent. Under price stickiness, this practice is costly for firms are subject to price adjustment costs. It follows that as price adjustment costs become large, the Ramsey planner is less likely to use variations in the price level to create state-contingent real debt. Thus, the more sticky prices are, the more the economy will resemble one without realstate-contingent debt. Recent work by Aiyagari et al. [1] shows that the level of welfare in Ramsey economies with andwi thout real state-contingent debt is virtually the same. As a consequence, in the sticky-price model studied in this paper, the Ramsey planner is willing to give up front loading all together to avoid price adjustment costs even when such costs are fairly small.4 Indeed, in financing the budget the Ramsey planner replaces front-loading with standard debt and tax instruments. For example, in response to an unexpected increase in government spending the planner does not generate a surprise increase in the price level. Instead, he chooses to finance the increase in government purchases partly through an increase in income tax rates andpartl y through an increase in public debt. The planner minimizes the tax distortion by spreading the required tax increase over many periods. This tax-smoothing behavior induces near-random walk dynamics into the tax rate and public debt. By contrast, under full price flexibility (i.e., when the government can create real-state contingent debt) tax rates and public debt inherit the stochastic process of the underlying shocks. An important conclusion of our study is thus that the Barro [2]-Aiyagari et al. [1] result, namely, that optimal policy imposes a near random walk behavior on taxes and debt, does not require the unrealistic assumption that the government can issue only non-state-contingent real debt. This result emerges naturally in economies with nominally non-state contingent debt, clearly the case of greatest empirical relevance, anda minimum amount of price rigidity. The remainder of the paper is organized in 8 sections. Section 2 describes the economic environment andd efines a competitive equilibrium. Section 3 presents the Ramsey problem. Section 4 analyzes the business-cycle properties of Ramsey allocations. It first describes the calibration of the model. Then it presents the central result of the paper, namely, that even under very small price adjustment costs the optimal inflation volatility is near zero. Section 5 shows that when prices are sticky, public debt and tax rates are near random walk processes whereas when prices are flexible they have a strong mean reverting component. Section 6 shows that pricestickiness introduces deviations from the Friedman rule. Section 7 presents a discussion of the accuracy of the numerical solution method. Section 8 investigates whether the time series process for the nominal interest rate impliedby the Ramsey policy can be representedas a Taylor-type interest rate feedback rule. Finally, Section 9 presents concluding remarks.

The focus of this paper is the study of the implications of price stickiness for the optimal degree of price volatility. The economic environment considered features a government that does not have access to lump-sum taxation and can only issue nominally risk-free debt. The central finding is that for plausible calibrations of the degree of nominal rigidity the volatility of inflation associated with the Ramsey allocation is near zero. Indeed, a very small amount of price stickiness suffices to make the optimal inflation volatility many times lower than that arising under full price flexibility. Our results show that when prices are sticky, the social planner abandons the use of price surprises as a shock absorber of unexpectedinno vations in the fiscal budget. Insteadthe government chooses to rely more heavily on changes in income tax rates. The benevolent government minimizes the distortions introduced by these tax changes by spreading them over time. The resulting tax smoothing behavior induces a near random walk property in tax rates and public debt. This characteristic of the Ramsey real allocation under sticky prices resembles that of economies where thegovernment can issue only real non-state-contingent debt, like the ones studied by Barro [2] andAiyagari et al. [1]. Our results suggest that the fragility of the use of the price level as a shock absorber is not limited to the introduction of small degrees of nominal rigidities. Any friction that causes changes in the equilibrium real allocation in response to innovations in the price level is likely to induce the Ramsey planner to refrain from using the price level as an instrument to front-loadtaxat ion. Examples of such frictions couldbe informational rigidities as in [14,17] andcosts of adjusting the composition of financial portfolios, as in limitedparticipat ion models [11,15]. We plan to explore these ideas further in future research. If this conjecture is correct, our sticky-price model is simply a metaphor to illustrate a deeper mechanism at work in the macroeconomy that leads central banks all over the world to favor price stability above any other goal of monetary policy.