سیاست های رمزی در یک اقتصاد کوچک باز با قیمت ها و سرمایه مهم

This paper analyzes jointly optimal fiscal and monetary policies in a small open economy with capital and sticky prices. We allow for trade in consumption goods under perfect international risk-sharing. We consider balanced-budget fiscal policies where authorities use distortionary taxes on labor and capital together with monetary policy using the nominal interest rate. First, as long as a symmetric equilibrium is considered, the steady state in an open economy is isomorphic to that of a closed economy. Second, sticky prices’ allocations are almost indistinguishable from flexible prices allocations both in open and closed economies. Third, the open economy dimension delivers results that are qualitatively similar to those of a closed economy but with significant quantitative changes. Tax rates are both more volatile and more persistent to undo the distortions implied by terms of trade fluctuations.

It is now well known that it is optimal to use unexpected variations in prices in a flexible prices set-up to smooth taxes. However, when prices are sticky, a trade-off appears between using unexpected inflation to smooth taxes and the fact that adjusting the price level is costly (Schmitt-Grohe and Uribe, 2004). When an open economy framework is considered, new issues come into play, such as whether to stabilize exchange rate fluctuations or not, and their implications on inflation and welfare (Benigno and de Paoli, 2010). The literature of optimal taxation following Lucas and Stokey (1983) in flexible prices environments has established that distorting taxes should be very smooth over time and states of nature. Chari et al. (1991) and Chari and Kehoe (1999) present a set of seminal results in a flexible prices economy with debt, capital income and labor income taxes: (i) capital taxes should be close to zero in the long run, (ii) the ex-ante tax rate on capital should be zero in the short run, (iii) the ex-post tax rate on capital income is highly volatile and bears most of the adjustment after unexpected shocks, together with debt returns, and (iv) labor taxes should consequently be almost kept constant. Restricting the analysis to balanced-budget policies, Stockman (2001) and Klein and Rios-Rull (2003) show that most of these results are preserved, including Chamley's (1986) result that states that the capital income tax rate is zero in the long run. The major difference in a balanced-budget set-up is that the ex-ante capital income tax rate is not zero anymore, since debt may not be used as a buffer mechanism after unexpected shocks. The ex-ante rate thus fluctuates a lot, and its variance is about two third of the one of the ex-post rate. Schmitt-Grohe and Uribe (2004) find that the major results about optimal fiscal policy are mostly unchanged in a closed economy when sticky prices are introduced, even though a set-up featuring public debt induces an optimal policy leading to a unit root on debt, spreading to the policy instruments, including tax rates. However, considering an open economy induces important changes in the optimal policy. In a flexible prices environment, Benigno and de Paoli (2010) show that the open-economy dimension introduces fluctuations of terms of trade that directly affect labor supply decisions through the terms of trade spillovers identified in the monetary policy literature.1 In an open economy, due to the impact of terms of trade on the trade-off between the marginal utility of consumption and the disutility of labor, policymakers face an incentive to appreciate terms of trade. This situation increases the conditional expected consumption and reduces the conditional expectation of labor supply at the same time. The monetary policy literature shows that conditional expectations of terms of trade, labor and consumption relate to the conditional second order moments of the model, and that internalization of terms of trade spillovers by policymakers implies that fluctuations in terms of trade should be stabilized. Regarding monetary policy, the literature underlines that the optimal policy in a competitive environment with flexible prices is to keep the real interest rate constant.2 However, this rule is suboptimal when sticky prices are introduced in models where taxes are not available (see for instance Woodford, 2003). In this case, the optimal monetary policy rule should aim at stabilizing the inflation rate to minimize the distortions implied by nominal rigidities. In addition, monetary policy recommendations are affected by the assumption of trade openness, through the terms of trade spillovers and domestic price stability is generally outperformed by policies that partially stabilize terms of trade fluctuations (see for instance de Paoli, 2009 or Kollmann, 2002). About the interaction between monetary and fiscal policy, if taxes and debt are reintroduced in a closed economy framework with sticky prices, Correia et al. (2008) show that a combination of taxes can replicate flexible prices allocations, and that monetary policy is not needed in such a case. To our knowledge, little work has been done on the interaction between monetary and fiscal policies in an open-economy environment with capital.3 This may look surprising because the effectiveness and proper conduct of national macroeconomic policies should clearly depend on international linkages between national economies. In particular, previous literature omits capital as an input factor, while introducing this variable seems to be crucial for the results of optimal fiscal policy. In this paper, we extend the analysis of Benigno and de Paoli (2010) to a more general environment featuring capital accumulation and sticky prices. We study the dynamic properties of setting taxes and monetary policy optimally in a small open economy with capital and Calvo sticky prices, where households trade consumption goods and engage in complete international asset markets. The set-up is a standard new Keynesian DSGE open economy model in the spirit of Galí and Monacelli (2005), in which the government levies distortionary taxes on inputs (capital and labor) to provide individuals with an exogenously determined amount of public good and keeps the budget balanced at each point in time.4 An independent regulation authority subsidizes firms to undo the distortions introduced by imperfect competition. We adopt this solution to ease the comparison with the flexible prices competitive economy. Our approach solves the dual Ramsey problem in the context of a small open economy with capital. We study the optimal taxation system both in the steady state and around this steady state (dynamics). There are several ways in which the open dimension, combined with the presence of nominal rigidities may change some of the traditional results about optimal taxation. First, nominal rigidities may imply departures from the constant interest rate rule. Second, terms of trade spillovers on labor supply, i.e. the impact of changes in terms of trade on households' wealth and labor supply, may change the dynamics of labor taxation. Third, terms of trade fluctuations introduce a distortion in the price of capital goods relative to the price of consumption goods that may affect the dynamics of capital taxation. We contrast the results of our economy with those arising in a closed economy, and with those of an economy with flexible prices. Our results may be summarized as follows. First, the open economy does not affect the optimal steady state of the economy, as long as a symmetric steady state is considered, i.e. a steady state where per capita foreign and domestic consumptions are identical. This result does not hold when considering an asymmetric steady state. In this case, the determination of steady state allocations takes into account the terms of trade spillovers, leading to a different steady state tax system. However, dynamic results are presented around a symmetric steady state. This assumption is made to ease comparison with the closed economy case and to focus on second order moments of policy instruments only. Second, in line with Correia et al. (2008), we find that price stickiness affects the optimal policy only marginally both in closed and open economy. Tax rates differ from the flexible prices solution for two periods only, and coincide from period 3 and onwards, to minimize the distortions implied by sticky prices on labor and consumption decisions. The volatility of tax rates is thus increased while their persistence falls, due to large changes in the first periods. Price stickiness therefore delivers qualitative and quantitative properties of allocations, i.e. quantities, that are quite similar to those derived in an economy with flexible prices. While this result was shown to hold in a closed economy set-up in Correia et al. (2008), we show that it extends to the case of an open economy. Third, the open economy dimension has more dramatic implications for the design of optimal allocations. While they are qualitatively the same as those of a closed economy, they imply significant quantitative changes in the volatility and in the persistence of the policy instruments. Fluctuations in terms of trade, implied by the presence of complete international financial markets, affect allocations, i.e. the dynamics of consumption, hours and capital all together, through changes in the price of consumption goods and the CPI-based real wage. In this context, optimal tax rates are both more volatile and more persistent. This result relates to the terms of trade spillovers and their implications for terms of trade stabilization. Our qualitative results thus extend those obtained by Benigno and de Paoli (2010) in a richer framework that includes both capital accumulation and sticky prices. As in Benigno and de Paoli (2010), we find that tax rates are more volatile in an open economy. However, by allowing for both capital and labor income taxes, policymakers have more instruments at their disposal to influence the economy. For instance, using both capital and labor income tax rates helps easing the wedge between consumption and leisure. Given the delay in the use of capital, the incentives to alter capital taxes increase in order to reduce the distortions on labor supply. This is what we find: capital taxes are more volatile than labor income taxes, in all scenarios considered. The paper is structured as follows. The model and its general equilibrium conditions are presented in Section 2. Section 3 describes the parameterization used along the paper. Section 4 reports the results on optimal monetary and fiscal policy both in the steady state and dynamically. The paper concludes with Section 5.

This paper contributes to a growing literature on optimal monetary and fiscal policy. In a small open economy with sticky prices and capital, we compute the optimal Ramsey policy. We show that sticky prices have little impact on optimal allocations in the sense that optimal policies under sticky prices are designed to replicate allocations under flexible prices. On the contrary, openness matters both in the steady state and in terms of dynamics. The main results are as follows: • Taxes are the preferred policy instrument to deal with nominal rigidities in the economy, not the nominal interest rate. The assumption of sticky prices affects the optimal dynamics of tax rates during the first period after a shock, but corresponding allocations under sticky prices are almost indistinguishable from those arising in a flexible price equilibrium. Optimal policies under sticky prices thus induce more volatility in tax rates, but sharp movements in the first periods drive their persistence down. This result holds both in a closed and in an open economy, which extends the result of Correia et al. (2008) to the case of a small open economy. • The open economy has larger and more persistent effects on the optimal dynamics of tax rates. The inclusion of international trade in goods and assets induces movements in terms of trade that affect the economy through the implied disconnection between the CPI and the PPI. Consumption, capital accumulation and labor supply are affected all together, and although optimal movements in tax rates are qualitatively similar to those obtained in a closed economy set-up, significant quantitative differences arise. In particular, optimal tax rates are more volatile, which extends the result of Benigno and de Paoli (2010) to a framework with capital accumulation and sticky prices. This paper is a first attempt to characterize optimal fiscal and monetary policy in an open economy set-up with sticky prices and capital accumulation. Due to the complexity of the model, we are not able to derive analytical results, which calls for further investigations. The analysis also imposes balanced-budget restrictions and abstracts from debt issues. These may be considered as an interesting extension to provide policymakers with more accurate policy recommendations.