Monetary policy is a controversial

Transcription

1 Inflation Persistence: How Much Can We Exlain? PAU RABANAL AND JUAN F. RUBIO-RAMÍREZ Rabanal is an economist in the monetary and financial systems deartment at the International Monetary Fund in Washington, D.C. Rubio-Ramírez is an economist in the research deartment at the Federal Reserve Bank of Atlanta. The authors thank Tom Cunningham, Karsten Jeske, and Ellis Tallman for useful comments. Monetary olicy is a controversial toic. Economists are still divided into two factions: those who believe that monetary olicy does have real (inflation-adjusted) effects and those who are convinced that it affects only nominal variables, that is, nominal interest rates and rices. Until recently, almost any macroeconomic model in which monetary olicy has real effects was based on the assumtion that exectations are formed in an adatative way, imlying that agents do not use all available information when making a decision. Critics of these models argue that, given this assumtion, agents are not rational and as a result allow the monetary authority to trick them over and over. In resonse to this imortant critique, a whole class of models New Keynesian models has been recently roosed. These tyes of models combine old Keynesian elements (imerfect cometition and short-term nominal rigidities) with a dynamic general equilibrium environment (where rices and quantities are such that markets clear) in which agents form their exectations rationally. The idea behind this aroach is that when short-term rices are sticky or rigid that is, when they adjust only slowly to market shortages or surluses a decrease in the nominal interest rate also imlies a decrease in the real interest rate. Therefore, the consumtion and investment comonents of aggregate demand increase, imlying an increase in outut. But over time the excess aggregate demand shifts rices uward, thereby restoring the level of outut to its otential. A drawback of the simlest version of such models (in which only one tye of nominal rigidity, either sticky rices or wages, is considered) is that it does not seem to be able to reroduce the observed ersistence of inflation. The objective of this article is to determine whether adding sticky wages to a basic sticky-rice model overcomes this drawback. The analysis shows that this addition artially solves the roblem. Emirical work at the micro level suggests that the average duration of rice and wage contracts is tyically three to six quarters. Chari, Kehoe, and McGrattan (998) find that, in order to match the ersistence of outut changes to a monetary shock, their model must assume an imlausible degree (ten quarters) of rice stickiness, even when caital accumulation and adjustment costs of caital are introduced. Fuhrer and Moore (995) also show that, in a model using a reasonable length of wage contracts, it is not ossible to obtain the inflation ersistence observed in the data. As Galí and Gertler (999) oint out, these models imly an aggregate suly relationshi (the new Phillis curve) that relates current inflation with exectations of future inflation and real unit-labor costs. Hence, the ersistence of rice inflation in New Keynesian models is driven by the ersistence Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23 43

2 The Model The baseline sticky-rice model resented in this section merges Keynesian assumtions, such as imerfect cometition and nominal rigidities, with the methodological advances in modern macroeconomic theory. As in traditional Keynesian models, moneof real unit-labor costs. The roblem of models with only one tye of nominal rigidity is that, even with long-duration (sixteen quarters) rice or wage contracts, real wages are still flexible and cannot induce enough ersistence of inflation. How can the baseline sticky-rice model be modified so that the induced ersistence of inflation in resonse to a monetary shock increases under lausible degrees of rice or wage stickiness? A straightforward ath would be to introduce some kind of backward-looking behavior in the determination of inflation. However, introducing backwardlooking behavior imlies dearting from the assumtion of rational exectations, and the Lucas (976) critique alies. 2 Economists are still divided into two factions: those who believe that monetary olicy does have real (inflation-adjusted) effects and those who are convinced that it affects only nominal variables. This article takes an alternative aroach, exloring whether the combination of staggered rice and wage setting, as in Erceg, Henderson, and Levin (2), can match the inflation ersistence observed in the data if reasonable durations of rice and wage contracts are assumed. In this case, the forward-looking nature of the model is reserved. When both rices and nominal wages are sticky, so is the real wage, and therefore inflation ersistence should increase. This article analyzes whether adding staggered wage settings to the baseline sticky-rice model solves the ersistence-of-inflation roblem when lausible durations of rice and wage contracts are assumed. The analysis will show that, for a given duration of rice contracts, real wage ersistence significantly increases with the duration of wage contracts. This exercise is equivalent to adding sticky rices to a model with only staggered nominal wages. The exercise resented here is chosen because models containing only sticky rices are more widely used in the literature than those containing only staggered nominal wages. Both the baseline sticky-rice and the stickyrice and sticky-wage models have three main equations: an aggregate suly relationshi (the new Phillis curve), an IS tye of equation, and a monetary olicy rule. 3 As mentioned above, the new Phillis curve relates current inflation with exectations of future inflation and real unit-labor costs. Understanding the inflation real wage link is imortant in understanding why adding staggered wages to the baseline sticky-rice model may solve the lack of ersistence of inflation in these models. The IS curve relates outut and the real rate of interest negatively, as in the undergraduate textbook version of the Keynesian model, and the IS curve includes exectations of future outut. These two relationshis manifest the forward-looking nature of the New Keynesian models, in which exectations are rational. To comlete the model, a monetary olicy rule is needed. Tyically, it is modeled as an interest rate rule in which the short-term interest rate reacts to inflation and outut gas; 4 the nominal amount of money is determined from the money demand equation. Following the literature, this article uses an interest rate rule that relates today s nominal interest rates to ast nominal interest rates through an interest rate smoothing arameter. One might interret this arameter as reflecting monetary olicymakers erceived aversion to moving the nominal rate by large stes. The analysis in this article reveals the following: First, as most of the literature has roved, when only sticky rices and lausible-duration rice contracts are considered, the model is not able to relicate the inflation ersistence observed in the data. Second, in the baseline sticky-rice model most of the ersistence is driven by the exogenous nominal interest rate smoothing arameter. Finally, when sticky wages are added to the baseline sticky-rice model, it is ossible for the inflation data autocorrelations to be reasonable aroximations closely matched by the model. The first art of the article analyzes the equations that describe a general equilibrium model with sticky rices. The discussion then shows how these equations are modified when staggered wages are added to the baseline sticky-rice model. Next, the analysis examines how different arameterizations affect rice-inflation ersistence in the baseline sticky-rice model. Finally, the study considers how those conclusions are affected when both sticky rices and wages are considered. 44 Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23

3 tary olicy affects real variables in the short run. Unlike the traditional Keynesian models, in New Keynesian models the equations come from an otimization rocess of rational agents. Two models are considered: first, a model with sticky rices but flexible wages and then a model that introduces staggered wage setting into this baseline environment. The baseline sticky-rice model. Following Blanchard and Kiyotaki (987), the model consists of a large number of identical households each sulying labor services, a large number of intermediate-good roducers roducing a secific good that is an imerfect substitute for the other goods, and a large number of identical, cometitive finalgood roducers. Households consume the final good, intermediategood roducers use labor services in their roduction rocess, and final-good roducers use the intermediate good in their roduction of the final good. The model also assumes imerfect cometition in the intermediate-good markets. Thus, each intermediate-good roducer chooses its rice, taking as given all other good rices and wages. The intermediate-good roduction sector suffers an aggregate technology shock that is common across firms. For this sector, the model assumes a linear roduction function in labor such that the marginal roduct of labor is equal to the technology shock. On the monetary olicy side, the model assumes that the central bank sets the nominal interest rate through a Taylor rule and sulies as much money as households demand. The Taylor rule relates today s nominal interest rate to ast nominal interest rates, inflation, and outut gas. The model also assumes that monetary olicy, that is, the Taylor rule, suffers from a monetary erturbation. This erturbation reflects the difference between the information that the monetary authority has when making decisions on interest rates and the information that the researcher can observe. Intermediate-good roducers face a Calvo-tye restriction when setting rices: In any given eriod of time, each intermediate-good roducer receives a signal that allows her to change the rice. This signal arrives with robability θ and thus with robability θ that she must kee last eriod s rice. The reason the Calvo-tye assumtion has become so oular is its simlicity. Because the robability of receiving the green light signal is indeendent of the ast history of signals, the ricing decisions of firms are identical. Therefore, one does not need to kee track of each firm s ricing decision to know the aggregate rice outcome, and aggregation is simle. The intuition behind this idea is as follows: Firms face some tye of menu cost when they want to change rices, so they cannot change rices every eriod. In this environment the robability that a firm has its rice fixed for one eriod is θ, for two eriods is θ ( θ ), for three is θ 2 ( θ ), and so on. Given these robabilities, the average number of eriods that rices are going to be fixed can be calculated. Hence, this average duration of a rice contract is equal to [ θ ] + 2[θ ( θ )] + 3[θ 2 ( θ )] +... = /( θ ). It is imortant to remember the relationshi between θ and the average duration of rice contracts. This analysis will not go through the derivation of the main equations. (The reader is referred to Rabanal and Rubio-Ramírez 23.) Instead, the discussion will introduce the key relationshis and give some intuition. In all cases, the variables are exressed in logarithmic terms. Let y t denote outut; w t, the nominal wage; t, the rice level; and t, the rice inflation rate. The model is reresented by the following set of equations: () yt= ( rt Et t+ ρ β ) + Etyt+ ; σ (2) t = βe t t + κ (w t a t + µ); (3) w t = ϑ + mrs t ; (4) mrs t = (σ + γ)y t γa t, and κ [( θβ )( θ)] = ; θ. For another way of answering this critique, see Christiano and Eichenbaum (992). 2. The Lucas critique imlies that any Federal Reserve olicy change will affect consumers exectations, so the Federal Reserve cannot take consumers exectations as constant. 3. An IS equation relates outut today with outut tomorrow as a function of the nominal interest rate and inflation. 4. Even though this article does not do so, it is also ossible to model the interest rate rule as forward looking in the sense that it reacts to exected future inflation and outut gas. However, simulations suggest that our results would remain basically unchanged. Outut gas are the difference between actual and otential outut. Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23 45

4 (5) a t a t t, a = ρ a + ε where β is the discount factor, ρ β is equal to log(β), γ is the inverse of the elasticity of labor suly to real wage, σ is the inverse of the intertemoral elasticity of substitution, r t is the nominal interest rate, mrs t is the marginal rate of substitution between consumtion and worked hours, µ is the desired marku on marginal roduct, w t is the hourly wage, ϑ is the desired marku on the real wage, κ is the elasticity of inflation to the marginal cost, and a t is the aggregate roductivity shock. It is assumed that ε a t ~ iidn(, σ a ). Equation () is a log-linearized version of the Euler equation, which arises from the household s The baseline sticky-rice model merges Keynesian assumtions, such as imerfect cometition and nominal rigidities, with the methodological advances in modern macroeconomic theory. otimal saving-consumtion decision, after imosing the clearing market condition that consumtion equals outut. From equation () it is clear that the higher the nominal interest rate, r t, or the lower tomorrow s exected inflation, E t t+, the lower today s outut, y t, and the higher the savings. Equation () can also be iterated forward to yield (6) yt= Et ( rt+ τ t+ + τ ρβ). σ τ= This iteration shows that outut deends on current and exected future gas between the real interest rate and its long-run value. Thus, one concludes that outut is at its steady-state value only when real interest rates differ by the log of the discount factor and are exected to do so. In other words, when the real interest rate is high, savings are high and consumtion (and, hence, outut) is low; when the real interest rate is low, savings are low and consumtion is high. Equation (2) is called the New Keynesian Phillis curve, and it is obtained from the aggregation of rice-otimal decisions of firms. Price inflation deends on tomorrow s exected rice inflation, E t t+, and the ercentage deviation of real wage, w t, from the desired marku over the marginal roduct of labor, a t µ, where µ is the desired marku on the marginal roduct and deends on the elasticity of substitution between different tyes of intermediate goods used to roduce the final good. This equation is the most imortant iece of the New Keynesian models. As mentioned above, until the introduction of these models, almost any setu able to generate short-term real effects of monetary olicy was based on backward-looking behavior. As equation (2) shows, this situation is no longer true: In this environment, inflation has a forward-looking root, and monetary olicy affects outut through its effects on future real interest rates and real wages. If equation (2) is solved forward, the resulting equation is (7) = κ E ( w a + µ ). t t t+ τ t+ τ t+ τ τ= It reveals that rice inflation deends on current and exected future gas between real wages and the desired marku over the marginal roduct of labor. Thus, one concludes that rice inflation is at its steady-state value only when real wages and the marginal roduct of labor differ by the desired marku and are exected to do so. If firms do not exect wages to increase over the marginal roduct of labor more than the desired marku, they will not increase rices, and inflation will be at its steady-state value. Equation (3) relates the real wage, w t, the marginal rate of substitution between consumtion and worked hours, mrs t, and the desired real-wage marku, ϑ, that deends on the elasticity of substitution between different tyes of labor used to roduce each intermediate good. Equation (4) relates the marginal rate of substitution between consumtion and worked hours, mrs t, with outut, y t, and the aggregate roductivity shock, a t. This exression is obtained by imosing the clearing market condition that consumtion equals total roduction and by using the roduction function that relates hours worked with outut and the roductivity shock. Equation (5) shows how the aggregate roductivity shock, a t, (or technology shock) evolves over time. A monetary olicy rule is needed to comlete the general equilibrium model. This analysis will consider a Taylor-tye rule with the following formulation: (8) r t = ρr t + ( ρ)(γ π t + γ x y t ) + ε t, where γ π and γ x are the elasticities of the nominal interest rate to current rice inflation and outut ga. ε t is the monetary shock, and it is indeendent and identically distributed normally with zero mean and standard deviation σ r. 46 Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23

5 Equation (8) relates today s nominal interest rate, r t, to yesterday s nominal interest rate, r t, rice inflation, t, and outut ga, y t. It is assumed that ρ is between and, γ π >, and γ x >. The interest rate smoothing coefficient is included in the Taylor rule mainly for emirical reasons (see the aer by Clarida, Galí, and Gertler 2). In addition, Woodford (22) rovides some theoretical background about why the central bank might be interested in smoothing interest rates. In this way, the nominal interest rate will have some exogenously driven ersistence. This model imoses the condition γ π > : The monetary authority increases the nominal interest rate more than one to one with resect to inflation to induce a unique, stationary solution to the system (see Woodford 22). In the baseline sticky-rice model, and in the sticky-rice and -wage model resented in the next section, two sources of uncertainty exist: one is technological, ε ta, and the other is monetary, ε t. Two key arameters drive inflation ersistence in the baseline sticky-rice model: First, θ modifies the sloe in equation (2). Hence, the larger θ, the longer the duration of rice contracts and the higher the generated ersistence of inflation. The second, ρ, is the interest rate smoothing coefficient. A higher ρ increases the ersistence of both monetary shocks and outut gas, also making inflation more ersistent. Given the imortance of these two arameters, the next section demonstrates how different calibration choices for them modify the ersistence of inflation that this model can generate. The sticky-rice and -wage model. As the next section of the article will show, with only sticky rices it is not enough to relicate the ersistence of inflation that is observed in the data. Therefore, this section resents a version of the model with staggered rices and wages, as in Erceg, Henderson, and Levin (2). The inclusion of nominal wage rigidities will increase the real wage and, one hoes, inflation inertia. The model setu is similar to the one resented in the last subsection. As before, the model consists of a continuum of households each sulying a secific labor service that is an imerfect substitute for the other labor services, a continuum of intermediategood roducers roducing a secific good that is an imerfect substitute for the other goods, and a continuum of identical cometitive final-good roducers. As in the baseline sticky-rice model, households consume the final good, intermediate-good roducers use labor services in their roduction rocess, and final-good roducers use the intermediate good in their roduction of the final good. The model also assumes imerfect cometition on the intermediategood markets. Thus, each intermediate-good roducer chooses its rice, taking as given all other good rices and wages. The intermediate-good roduction sector suffers an aggregate technology shock that is common across firms. For this sector, a linear roduction function in labor is assumed, so the marginal roduct of labor is equal to the technology shock. Finally, the central bank also sets the nominal interest rate, through a Taylor rule, and sulies as much money as households demand. Also, as in the revious model, it is assumed that the Taylor rule suffers from a monetary erturbation. Just as in the baseline sticky-rice model, roducers of intermediate goods face a Calvo-tye restriction when setting rices, as described earlier. In this new model, households face an additional Calvo-tye restriction when setting their wages. In this environment the robability that a household has its wage fixed for one eriod is θ w. Therefore, the average duration of a wage contract is equal to /( θ w ). The model can be reresented by the following set of equations: (9) yt= ( rt Et t+ ρ β ) + Etyt+ ; σ t = βe t t+ + κ (w t a t + µ); () w t = βe t w t+ + κ w (mrs t (w t ) + ϑ); where With only sticky rices it is not enough to relicate the ersistence of inflation that is observed in the data. w t = w t + w t t; mrs t = (σ + γ)y t γa t; κ κ w [( θβ )( θ)] = ; θ [( θwβ)( θw)] =. θ ( + γϕ) w Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23 47

6 FIGURE The Autocorrelation Function of the GDP Deflator for the Nonfarm Business Sector between 96: and 2: Again, a monetary olicy rule is needed to comlete the model. As before, a Taylor-tye rule with the following structure is considered: r t = ρr t + ( ρ)(γ π t + γ x y t ) + ε t. If the equations that describe the baseline stickyrice model are carefully comared with those that describe the sticky-rice and sticky-wage model, two differences should be aarent. First, the inclusion of sticky wages does not modify the structure of the New Keynesian Phillis curve (equations [2] and [9] are identical). Second, mrs t is no longer equal to a marku over real wages. Instead of equation (3), equation () now relates wage inflation to exected wage inflation and the ercentage deviation of real wages, mrs t, from the desired marku over the real wage of labor, (w t ) ϑ, in the same way the New Keynesian Phillis curve does. Comarison of the two models. Although in the baseline sticky-rice model θ and ρ drive inflation, in the sticky-rice and -wage model a bigger θ w imlies a longer duration of wage contracts and, hence, a more ersistent real wage. The New Keynesian Phillis curve (equation [9]) imlied by this new version of the model relates rice inflation ersistence to real wage ersistence; hence, a larger θ w imlies higher inflation ersistence. In the next section, the analysis exlores how different calibration choices for these three arameters modify the ersistence of inflation that this model can generate. Notably, because the New Keynesian Phillis curve remains unaltered, then in either model ersistence in rice inflation after a monetary shock hits the economy is driven by κ and the ersistence of the real wage, w t. The inclusion of nominal wage rigidities does not modify κ. Hence, the addition of nominal wage rigidities only increases the rice-inflation ersistence if it increases the ersistence of real wages. Inflation Persistence Analysis To study the ersistence of rice inflation imlied by the two models, this analysis first reorts the observed autocorrelations of rice inflation and then erforms some numerical exercises to study the autocorrelation functions of rice inflation imlied by the basic sticky-rice model when only a monetary shock is considered. Finally, the analysis does the same for the sticky-rice and sticky-wage model. To understand how much ersistence in rice inflation these models can generate given a lausible degree of rice and wage stickiness, one could modify the arameters of the model (in articular, θ and θ w ) until κ or real-wage stickiness is such that rice inflation matches observed inflation. As 48 Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23

7 FIGURE 2 The Elasticity of Inflation to Marginal Cost (κ ) As a Function of the Probability of Price Change (θ ) in the Sticky-Price Model κ θ mentioned, the roblem with this aroach is that access to additional emirical evidence, such as surveys or data anels, rovides us reasonable bounds for most of the arameters of the model. Thus, a lausible degree of rice and wage stickiness means that the wage and rice contract length imlied by θ and θ w are inside these bounds. The autocorrelation function of rice inflation. Figure shows the autocorrelation function of the gross domestic roduct (GDP) deflator for the nonfarm business sector between 96: and 2:4. First, the autocorrelation function imlied by the GDP deflator reorted here is similar to the one imlied by either the consumer rice index (CPI) or the ersonal consumtion exenditures index (PCE). Second, even after five eriods the autocorrelation is.5. The following analysis shows that New Keynesian models with only sticky rices have a number of roblems relicating this slow decay of the autocorrelogram. Persistence in the sticky-rice model. The effects of θ on rice inflation are twofold. First, it affects the sloe of the New Keynesian Phillis curve: κ [( θβ )( θ)] = ; θ Second, θ affects the ersistence of the ercentage deviation of the real wage (w t ) with resect to the marginal roduct of labor (a t ). Before studying the relationshi between θ and real wage ersistence, the analysis will first concentrate on understanding how the rice contract duration, /( θ ), affects κ. Notice the following relationshi: κ θ σ = + γ 2 ( θβ ) <. 2 θ This derivative imlies that the higher θ (that is, the higher the rice contract duration), the lower κ. One can observe this relationshi in Figure 2, which lots κ as a function of θ. Under the limitation θ, that is, when rices are fixed forever, κ and π t = forever, imlying the highest ersistence ossible. As mentioned before, the issue is that, as Figure 3 shows, the higher θ, the higher the average duration of rice contracts, /( θ ). As many authors have reorted (see, for examle, Dutta, Berger, and Levy 997; Blinder et al. 998), observed average rice change is not much longer than one year. This observation imlies that analysis should be restricted to values of θ that imly durations no longer than five quarters, that is, θ 4 /5. Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23 49

8 FIGURE 3 Duration As a Function of the Probability of Price Change (θ ) in the Sticky-Price Model 25 2 Duration (number of quarters) θ TABLE Calibration for the Sticky-Price Model Variable Value σ γ β.99 µ.2 ϑ.2 ρ.8 ρ a.8 σ r σ a γ π.5 γ x.5 θ 3 /4 The analysis has shown that increasing ersistence by letting θ (κ ) is not consistent with the evidence on rice contract duration. The following numerical simulations study the effects of different arameter values of θ (different rice contract durations) on rice inflation ersistence, examining the real-wage and rice-inflation autocorrelation functions that the baseline sticky-rice model generates under these conditions. The baseline calibration used in the following analysis is shown in Table. The inverse intertemoral rate of substitution and the elasticity of labor suly, σ and γ, are set to. Because quarterly data are used, β being set to.99 imlies a 4. ercent annualized real interest rate. The calibration of µ and ϑ at.2 imlies a 2 ercent marku over marginal costs and real wages, resectively. Both ρ and ρ a are set to.8, and σ r and σ a are set to. Taylor s rule elasticities, γ π and γ x, are set to Taylor s original guesses. θ is set to 3 /4, which imlies an average duration of rice contracts of four eriods. Figures 4 and 5 illustrate the autocorrelation functions of rice inflation and real wages when only a monetary shock is considered for different average durations of rice contracts. The longer the duration, the higher rice inflation ersistence. The intuition for this result is that when rices are sticky, a ositive (negative) monetary shock will increase (decrease) demand and real outut. The longer the average rice contract lasts, the more ersistent is the effect on outut. As equations (3) and (4) show, real wages are linked to outut, so the higher the outut ersistence, the higher the real wage ersistence. Because no technology shock is involved, the marginal roduct of labor is constant, and the real wage and its deviation from the marginal roduct of labor exhibit the same auto- 5 Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23

9 FIGURE 4 The Autocorrelation Function of Price Inflation When Only a Monetary Shock Is Considered in the Sticky-Price Model quarters duration 4 quarters duration quarters duration FIGURE 5 The Autocorrelation Function of Real Wages When Only a Monetary Shock Is Considered in the Sticky-Price Model quarters duration 4 quarters duration quarters duration Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23 5

10 FIGURE 6 The Autocorrelation Function of Price Inflation When Only a Monetary Shock Is Considered for Different Values of ρ in the Sticky-Price Model TABLE 2 Calibration for the Sticky-Price and Sticky-Wage Model Variable Value σ γ β.99 µ.2 ϑ.2 ρ.8 ρ a.8 σ r σ a γ π.5 γ x.5 θ 3 /4 θ w 4 /5 correlation function. Thus, one can conclude that the longer the average contract, the more ersistent is the effect on real wages and rice inflation. It is imortant to understand what the source of this ersistence is. The following analysis considers how the source of exogenous nominal interest rate ersistence, ρ, affects the ersistence of inflation that this simle model is able to generate. Figure 6 shows the autocorrelation function of rice inflation for different values of ρ (the exogenous ersistence arameter of the nominal interest rate) when only a monetary shock is considered. For low values of ρ, inflation ersistence is very low. The intuition is as follows. Nominal interest rate ersistence deends on ρ. As equation (6) shows, the higher (lower) the nominal interest rate ersistence, the higher (lower) the outut ersistence. Because only a monetary shock is considered, real wages and outut share the same autocorrelation function, so the higher (lower) the nominal interest rate ersistence, the higher (lower) the real wage and rice inflation ersistence. Under these conditions, inflation ersistence greatly deends on ρ, the nominal interest rate exogenous ersistence. Indeed, Figure 6 shows that a model with only sticky rices does not amlify the inflation ersistence of a monetary shock beyond that induced by ρ. From this analysis one can conclude that the model with only sticky rices is not able to generate endogenous ersistence beyond that obtained through the coefficient ρ. This conclusion raises the following questions: Is it ossible to generate inflation ersistence in this model? Is inflation ersistence highly linked to ρ? Is there an obvious mechanism generating it? From the observations in Figure 6, it seems that the correct answer is that the inflation 52 Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23

11 FIGURE 7 The Autocorrelation Function of Price Inflation When Only a Monetary Shock Is Considered in the Sticky-Price and Sticky-Wage Model.8 2 quarters duration 4 quarters duration quarters duration ersistence is highly related to ρ and that there is no other mechanism that can generate it. These results indicate that the baseline stickyrice model is not able to generate enough endogenous inflation ersistence, so the analysis next considers whether the sticky-rice and sticky-wage model can do it. Persistence in the sticky-rice and stickywage model. As mentioned earlier, the inclusion of wage rigidities does not modify κ. Thus, the imact of wage rigidities on rice inflation ersistence should come through their effect on the ersistence of the real wage. Table 2 lists the basic calibration used in this model. The arameters are set to the same values used in the baseline sticky-rice model. θ w is set to 4 /5, imlying an average wage contract duration of five quarters. Figures 7 and 8 show the autocorrelation function of rice inflation and real wage for a given average duration of the rice contract of four quarters (θ = 3 /4) when different values of θ w and just a monetary shock are considered. The inclusion of wage rigidities increases the ersistence of both real wages and rice inflation. In the sticky-rice model, nominal wages move freely, making real wages not ersistent. When both wages and rices are sticky, real wages dislay more ersistence. As noted before, the ersistence of the real wage deviation from the marginal roduct of labor drives rice inflation ersistence. In Figures 7 and 8, which consider only a money shock, the marginal roduct of labor does not move, and rice inflation ersistence also increases. One can conclude that the addition of nominal wage stickiness makes the reaction of rice inflation to money shocks more ersistent. Figure 9 reorts the autocorrelation function of rice inflation for different values of ρ when only a monetary shock is considered. In the basic stickyrice model, the rice inflation ersistence deends greatly on ρ. Figure 9 shows that when both rices and wages are sticky, the ersistence of inflation the model generates as a resonse to a monetary shock does not deend on ρ. The addition of sticky wages to the baseline sticky rice model increases real wage ersistence in such a way that, even with very low ρ, the model is able to generate a ersistent inflation resonse. In addition, the introduction of staggered wage contracts to the sticky rice model in a ure forward-looking model hels increase inflation ersistence. Conclusion This article analyzes the ability of a model with both sticky rices and wages to solve one of the most imortant shortcomings of the baseline stickyrice model: the lack of ersistence of inflation when Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23 53

12 FIGURE 8 The Autocorrelation Function of Real Wages When Only a Monetary Shock Is Considered in the Sticky-Price and Sticky-Wage Model. 2 quarters duration 4 quarters duration quarters duration FIGURE 9 The Autocorrelation Function of Price Inflation When Only a Monetary Shock Is Considered for Different Values of ρ in the Sticky-Price and Sticky-Wage Model Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23

13 only a monetary shock is considered. The findings show that, while the baseline sticky-rice model cannot relicate the inflation ersistence observed in the data unless an imlausible degree of either rice stickiness or exogenous nominal interest rate ersistence is assumed, a model with both sticky rices and sticky wages can relicate more closely the autocorrelation function of inflation, even with accetable levels of both rice and wage stickiness. This result is imortant because some notable studies, such as Fuhrer and Moore (995) and Chari, Kehoe, and McGrattan (998), have criticized the incaability of this kind of model with nominal rigidities to match inflation ersistence. REFERENCES Blanchard, Olivier Jean, and Nobuhiro Kiyotaki Monoolistic cometition and the effects of aggregate demand. American Economic Review 77 (Setember): Blinder, Alan, Edie D. Canetti, David E. Lebow, and Jeremy B. Rudd Asking about rices: A new aroach to understanding rice stickiness. New York: Russell Sage Foundation. Chari, Varadarajan V., Patrick J. Kehoe, and Ellen R. McGrattan Sticky rice models of the business cycle: Can the contract multilier solve the ersistence roblem? Federal Reserve Bank of Minneaolis Staff Reort 27, May. Christiano, Lawrence J., and Martin Eichenbaum Liquidity effects and the monetary transmission mechanism. American Economic Review 82 (May, Paers and Proceedings of the Hundred and Fourth Annual Meeting of the American Economic Association): Clarida, Richard, Jordi Galí, and Mark Gertler. 2. Monetary olicy rules and macroeconomic stability: Evidence and some theory. Quarterly Journal of Economics 5 (February): Dutta, Shantanu, Mark Berger, and Daniel Levy Price flexibility in channels of distribution: Evidence from scanner data. Emory University, hotocoy. Erceg, Christoher J., Dale W. Henderson, and Andrew T. Levin. 2. Otimal monetary olicy with staggered wage and rice contracts. Journal of Monetary Economics 46, no. 2: Fuhrer, Jeffrey C., and George R. Moore Forwardlooking behavior and the stability of a conventional monetary olicy rule. Journal of Money, Credit, and Banking 27, no. 4, art :6 7. Galí, Jordi, and Mark Gertler Inflation dynamics: A structural econometric analysis. Journal of Monetary Economics 44, no. 2: Lucas, Robert E Econometric olicy evaluation: A critique. In The Phillis curve and the labor markets, edited by Karl Brunner and Allan H. Meltzer. Sulementary series to the Journal of Monetary Economics. Amsterdam: North-Holland. Rabanal, Pau, and Juan F. Rubio-Ramírez. 23. Comaring New Keynesian models of the business cycle: A Bayesian aroach. Federal Reserve of Atlanta Working Paer 2-22a, revised February 23. Woodford, Michael. 22. Interest and rices. Princeton University, hotocoy. Federal Reserve Bank of Atlanta ECONOMIC REVIEW Second Quarter 23 55