سیاست پولی بهینه در یک اقتصاد کوچک باز با دستمزد و قیمت قراردادهای مبهم

We study optimal monetary policy for a small open economy in a model where both domestic prices and wages are sticky due to staggered contracts. The simultaneous presence of the two forms of nominal rigidities introduces an additional trade-off between domestic inflation and the output gap. We derive a second-order approximation to the average welfare losses that can be expressed in terms of the unconditional variances of the output gap, domestic price inflation, and wage inflation. As a consequence, the optimal policy seeks to minimize a weighted average of these variances. We analyze welfare implications of several alternative simple policy rules, and find that domestic price inflation targeting generates relatively large welfare losses, whereas CPI inflation targeting performs nearly as well as the optimal rule.

The new Keynesian model has become a new theoretical consensus for studying various issues in monetary policy (Goodfriend, 2007). However, some features of the new Keynesian model are deemed to be unsatisfactory. For example, the monetary policy rule that stabilizes price inflation also stabilizes output gap variability. Therefore, a simple price inflation targeting monetary policy can achieve the (Pareto) optimal welfare level that would occur in the absence of nominal frictions. This property of the new Keynesian framework is called the ‘divine coincidence’ (Blanchrad and Galí, 2007). In addition, recent empirical studies (e.g., Galí, 1992, Christiano et al., 1999 and Neely and Rapach, 2008) reveal that a staggered price mechanism by itself is incapable of generating persistent real effects of monetary shocks. Instead, it has been argued that wage stickiness may be a more important force than price stickiness for generating output persistence (e.g., Ambler et al., 2012, Chari et al., 2000 and Huang and Liu, 2002). The small open economy version of the new Keynesian model with staggered price-setting (Galí and Monacelli, 2005: Clarida et al., 2002) also lead to a striking, but controversial result. In the model, domestic goods prices are sticky but foreign goods prices are flexible. This specification of pricing behavior leads to disappearance of CPI inflation from any of the structural equations needed to compute welfare of the households. Since the model's Phillips curve contains only domestic inflation, it is then not surprising that it is optimal for the central bank to target domestic rather than CPI inflation. According to the standard new Keynesian small open economy model, therefore, CPI inflation targeting in a small open economy is misguided. But all real world inflation targeting countries are open economies, and all of them target CPI inflation, not domestic inflation (Svensson, 2000). The description of the inflation dynamics and policy implications of the standard new Keynesian small open economy model, therefore, should be modified. A number of studies have incorporated both wage and price stickiness into the new Keynesian model in a closed economy framework to help solve the issues mentioned above (Christiano et al., 2005, Erceg et al., 2000, Gali, 2011 and Sbordone, 2002). In particular, Erceg et al. formulate a model in which both the labor and product markets exhibit monopolistic competition and staggered contracts. They find that the model (with both sticky prices and sticky wages) exhibits a tradeoff between stabilizing the output gap, price inflation, and wage inflation. They also find that price inflation targeting generates a relatively large welfare loss. Most of the studies involving both nominal wage and price rigidities, however, focus on the closed-economy framework. The recent papers by Adolfson et al., 2007 and Adolfson et al., 2008 are among rare notable exceptions.2 In this paper, we employ the Calvo specification to incorporate both nominal wage and price rigidities into a small open economy new Keynesian framework. The goods market side of the model is similar in structure to the one developed in Galí and Monacelli (2005). Monopolistically competitive domestic producers set prices in staggered contracts as in Calvo (1983). Following Erceg et al. (2000), however, we modify the labor market where individual households supply differentiated labor services to domestic firms, and domestic firms combine this labor services to produce domestic goods. Monopolistically competitive households also set nominal wages in staggered fashion. These modifications lead to several distinctive features of our model. First, they necessitate the presence of the terms of trade, and thus CPI inflation, in the equation for wage inflation. Therefore, the behavior of wage inflation in this model is different from that in Erceg et al. (2000), which is a natural consequence of the small open economy framework. Second, there is a direct effect of CPI inflation on domestic price inflation, the dynamics of which, therefore, differs from that in the standard new Keynesian open economy Phillips curve of Galí and Monacelli (2005). This also has a very important policy implication (discussed below). Lastly, foreign output affects the dynamics of the real wage gap. It is through the real wage gap that shocks to foreign output affect both domestic price and wage inflation. Within this model, we discuss how the economy responds to a contractionary monetary policy shock when both domestic prices and wages are sticky. In order to disentangle the role played by nominal wage rigidity, we examine four different assumptions on domestic price and wage stickiness. We consider an economy in which (i) both domestic prices and wages are flexible, (ii) only domestic prices are flexible, (iii) only wages are flexible, and (iv) both domestic prices and wages are sticky. We find that the existence of staggered wage setting influences the economy's equilibrium response to a monetary policy shock regardless of the presence of sticky domestic prices. This exercise also implies that wage stickiness is more important than price stickiness for generating persistent real effects of monetary shocks in a small open economy. In order to find the optimal monetary policy we derive a second-order approximation to the average welfare losses experienced by households in the economy with both wage and price stickiness around a steady state with zero inflation. The resulting welfare function can be expressed in terms of the unconditional variances of the output gap, domestic price inflation, and wage inflation, and the optimal policy seeks to minimize a weighted average of these variances. For the standard new Keynesian small open economy model as in Galí and Monacelli (2005), the optimal monetary policy requires full stabilization of domestic price inflation. Then the output gap is also stabilized under that optimal policy. As a result, a fully stabilizing domestic price inflation, which is optimal for the standard new Keynesian small open economy model, is no longer an optimal policy. Instead, the central bank should stabilize both domestic inflation and wage inflation in addition to the output gap. We also employ our framework to analyze welfare implications of alternative policy rules. In addition to the optimal rule, we study four different simple policy rules whereby the domestic nominal interest rate responds to inflation and the output gap. The first rule requires that the domestic interest rate respond systematically to domestic inflation whereas the second assumes that the domestic interest rate responds to CPI inflation. They are referred to as the domestic inflation-based Taylor rule and the CPI inflation-based Taylor rule respectively. We consider an analogous rule for wage inflation (the wage inflation-based Taylor rule). The last rule considered seeks to stabilize a weighted average of domestic price and wage inflation and is referred to as the composite inflation-based Taylor rule. We use the derived approximation to the welfare function to evaluate the performance of alternative policy rules. The welfare level under the optimal monetary policy rules provides a benchmark. We rank these alternative policy rules in terms of their implied volatility for domestic inflation, wage inflation, and the output gap. From this exercise, we find that the domestic price inflation-based Taylor rule generates relatively large welfare losses due to excessive variation in wage inflation and the output gap. This finding is consistent with Erceg et al. (2000) where price inflation targeting induces substantial welfare costs. The CPI inflation-based Taylor rule, however, performs nearly as well as the optimal rule, leads to relatively small variation in inflation and output gap. There is a direct effect of CPI inflation on the dynamics of domestic price and wage inflation. Therefore, stabilizing CPI inflation is important for reducing volatility of domestic price and wage inflation. Less volatile domestic price inflation induces relatively small variance of the output gap under the CPI inflation-based Taylor rule. This result stands in sharp contrast with the policy implication of the standard new Keynesian model without staggered wage-settings (Clarida et al., 2002 and Galí and Monacelli, 2005). The plan of this paper is as follows. We describe the basic model in Section 2 and present the equilibrium conditions and dynamics of the model in Section 3. The implications and performance of each targeting regime are discusses in Section 4. And in Section 5 we draw the main conclusions.

In this paper, we study several monetary policy rules for a small open economy within a framework where both domestic prices and wages are sticky due to staggered contracts. This study delivers three messages regarding the issue of monetary policy design in a small open economy. First, the optimal policy is to seek to minimize a weighted average of the variances of domestic price inflation, wage inflation, and the output gap. Second, the policy that exclusively targets domestic price inflation is suboptimal. Last, the policy that responds to CPI inflation is almost as good as the optimal policy. To bring our work in line with growing empirical evidence that fluctuations in exchange rates result in less than proportional changes in prices of traded goods and that prices respond with some delay (Engel, 1999 and Parsley and Wei, 2001), we plan to extend this research to the case of incomplete and delayed exchange rate pass-through. We also intend to explore the relative performance of various composite inflation-based Taylor rules in these environments.