An Estimated New Keynesian Phillips Curve for Chile

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1 An Estimated New Keynesian Phillips Curve for Chile Luis F. Céspedes Research Department Central Bank of Chile Marcelo Ochoa Research Department Central Bank of Chile September, 2005 Claudio Soto Research Department Central Bank of Chile Abstract This paper presents GMM empirical estimations of the New Keynesian Phillips curve (NKPC) for Chile. Our results tend to support the NKPC. The evidence shows that the backward-looking coefficient in the Phillips curve is about This number is slightly larger than the estimated value for the U.S. The estimated Calvo coefficient that captures the degree of price rigidity is in the range of 0.85 to 0.88, indicating that prices remain unchanged on average for about 7 to 8 quarters. Our results support the hypothesis of the existence of a structural break in the NKPC, which occurred when the inflation target converged to its long-run level (between 1999 and 2000). JEL Classification: E31 1 Introduction The New Keynesian Phillips Curve (NKPC) has attracted broad attention by academics and policy makers in recent years. Several theoretical developments have given new insights regarding the inflationary process. These new developments have influenced significantly the way many central banks around the world assess inflation dynamics. As opposed to the old tradition, the NKPC emphasizes the role played by the forward looking component of the Phillips curve, and importance of the marginal costs as the driving force behind the inflationary process. Empirical work has tended to confirm the importance of the forward looking component (see Galí and Gertler (1999), GG henceforth, and Sbordone (2002)). 1 We thanks coments by Romulo Chumacero, Pablo García, Igal Magendzo, Eric Parrado, Klaus Schmidt-Hebbel, Rodrigo Valdés and seminar participants at the Central Bank of Chile. The views expressed in this paper are our own and do not necessarily represent those of the Central Bank of Chile. lcespede@bcentral.cl mochoa@bcentral.cl csoto@bcentral.cl 1 However, the current empirical debate hinges on the extent by which rational expectation forecast of inflation can actually account for the inflation dynamics (see Rudd and Whelan (2003)) 1

2 Most of the empirical work has been devoted to estimate versions of the NKPC for OECD countries mainly for the U.S. with little empirical literature exists for developing economies. 2 Developing economies have special characteristics on their own that make them an interesting case of analysis. For example, it has been argued that low credibility regarding inflation goals by monetary authorities may have led to more persistent inflation dynamics (see Fraga, Goldfajn and Minella, 2003). This would imply a larger weight for the backward looking component in the hybrid version of the NKPC. Also, a larger dependency on imported inputs and structural transformations make potential output measures for these economies much less reliable than in their developed countries counterpart. Therefore, the emphasis of the NKPC on the role of marginal cost as the driving force behind the inflationary process may be particularly relevant to accurately estimate the Phillips curve in those economies. In this paper, we estimate a NKPC for Chile using quarterly data for the period 1990:1-2004:4. Estimating a Phillips curve for an emerging economy like Chile allow us to address and assess the relevance of some of the issues mentioned before. First, the Chilean economy has successfully gone through a disinflationary process over the 90s, converging to a stationary single digit inflation rate by the end of that decade. 3 Nevertheless, historically high inflation rates led, until recently, to widespread use of contracts with explicit indexation clauses based on previous inflation. Moreover, poor previous inflation performance affected the credibility of the monetary authority. For both reasons, we would expect an important role for the backward looking component of the Phillips curve in the Chilean case. Second, being an small open economy, external terms of trade shocks may have played an important role determining the dynamics followed by the relevant marginal cost in the economy. Therefore, the explicit use of measures of real marginal costs instead of the output gap, as suggested by the NKPC literature, may be particularly important to obtain more accurate estimations of the Phillips curve. Estimating Phillips curves is not only interesting from an academic point of view. An assessment of the existence of a relationship between inflation and some measure of economic activity, plus an adequate characterization of this relation have important implications for policy analysis. The recent trend towards monetary policy conduction based on inflation targets has increased the need of improving the understanding of the inflationary process. Therefore, Phillips curve estimations constitute a key tool for the conduction of monetary policy in an inflation targeting country like Chile. As in the New Keynesian tradition, we consider a version of the basic Calvo (1983) price setting model, were firms adjust prices according to the expected evolution of their marginal costs. We modify the basic model to allow the possibility of passive price adjustments to account for the trend in inflation observed over the 90s. We also consider the hybrid version of the NKPC where not only forward looking inflation determines the 2 One of the few exceptions is Agenor and Bayraktar (2003) who estimate Phillips curve equations for middle-income countries, including, amongst others, Chile. 3 This disinflationary process has been characterized by a declining target for the CPI inflation rate set by the monetary authority and the active use of the interest rate as the main policy instrument in the conduction of the monetary policy. 2

3 current evolution of inflation, but also a backward looking component plays a role. Regarding marginal costs we consider several measures, each consistent with an alternative specification for the technology utilized by firms. Our results using the Generalized Method of Moments (GMM) tend to support the NKPC. The evidence shows that the backward-looking coefficient in the NKPC is approximately This figure is larger than the corresponding one for the Euro area, as estimated by Galí, Gertler and López-Salido (2001, 2002) (GGL henceforth), Gagnon and Khan (2005) and Jondeau and Bihan (2005). It is also larger to the estimated value for the U.S. by GG. The estimated Calvo coefficient that captures the degree of price rigidity is in the range of 0.7 to 0.9, indicating that prices remain unchanged on average for about 3.5 to 11 quarters. This figures are, in general, slightly larger than in the case the U.S. and similar to the ones for the Euro Area as reported by the studies mentioned before. We also evaluate the goodness of fit of our NKPC in tracking the evolution of the actual inflation rate by computing a measure of fundamental inflation as in GG and Sbordone (2002). We find that the model with the lowest mean square error between actual and fundamental inflation is the one that compute real marginal cost using a CES function with low substitution between capital and labor. Finally, we perform a test to evaluate the joint stability of our estimated parameters following Carner and Hansen (2004). Our results support the hypothesis of the existence of a structural break in the NKPC, which occurred when the inflation target converged to its long-run level (between 1999 and 2000). Moreover, our evidence supports the idea that the inflationary process became more forward looking in recent years, which is also consistent with an increased credibility in the inflation target. The paper is organized as follows. In the next section we review the theory behind the new Phillips curve in the New Keynesian tradition. In the third section we describe different measures of marginal cost and the de-trending technics utilized to compute our measure of inflation. We also describe the correlation between marginal cost, inflation and the output gap. The four section presents the main results of the paper. The fifth section presents the stability test. Finally, the sixth section concludes. 2 Theoretical Framework 2.1 Price setting and Phillips curve We follow the standard Calvo (1983) price setting setup. A fraction 1 θ of the firms in the economy, randomly picked, adjust prices each period. Therefore, the probability that a particular firm receive a signal to update its price at time t is precisely 1 θ. Notice that this probability is independent from the history of the firm. We assume that a firm that does not receive the signal to adjust optimally its price follows a simple rule to update the price (as in Yun, 1996). In particular, if the firm does not adjust its price between t and t + i, then the price it charges in t + i is given by Γ i tp t (z), whereγ i t is a function that defines the updating rule. 4 Let R t,t+i be the 4 In this formulation a firm that does not receive a signal adjust pasivelly its price. 3

4 relevant discount factor for the firm between period t a and t + i. The maximization problem faced by a generic firm z in t is the following max P t(z) E t ix i=0 Γ θ i i R t P t (z) MC t+i (z) t,t+i Y t+i (z) P t+i subject to the demand for its good which is given by 5 Γ i Y t+i (z) = t P t (z) Y t+i. (2) P t+i The first order condition for this problem can be expressed as follows: P h i i Pt new (z) = i=0 θi R MCt+i (z) t,t+i P t+i Y t+i (z) 1 P h i i Γ i (3) i=0 θi R t t,t+i P t+i Y t+i (z) where Pt new corresponds to the optimal price that any firm receiving a signal in t would charge, and where µ = 1 corresponds to the steady-state gross mark-up.6 When prices are rigid, the optimal price depends on the expected aggregate output, aggregate prices and real marginal costs. Lets define Q t = P t new Pt. Using(3)wecan express Q t as : Q t = µ P ³ i=0 θi MC R t+i (z) Γ i t t,t+i P t+i P i=0 θi R t,t+i ³ Pt P t+i Γ i t P t+i Yt+i (1) ³ Γ i t P t+i Yt+i (4) To obtain a linear expression we utilize a first order Taylor expansion of this equation around the steady state: bq t =(1 θβ) X ix (θr) i cmc t+i + bπ t+j bγ i+1 t (5) i=0 j=1 Given that a fraction θ of the firms adjust prices passively i.e. following the simple updating rule Γ i t and the remaining 1 θ fraction set prices to Pt new, the aggregate price h index is P t = (1 θ)(pt new ) 1 + θ Γ 1 i t P t 1. We assume that the updating rule for those firms that can not optimally adjust prices consist in resetting their prices 5 This demand is obtained from a utility function where households choose optimally the composition of a consumption bundle among a continuum of varieties that are implicitly substitutes with an elasticity of substitution. 6 Under flexible prices i.e φ =0 the optimal resetting price for a firm would be Pt new flex = µmc t. In other words, under flexible prices, firms define an optimal price that is a constant markup over its marginal cost of production. 4

5 accordingtotheinflation target the authority defines for the period: 7 Γ i t = iy 1+π t+j j=1 Assuming that capital is freely mobile across firms such that its marginal productivity is the same across firms we obtain the modified version of the Phillips curve based on Calvo: bπ t = λ cmc t + βe t {bπ t+1 } (6) where bπ t = π t π t corresponds to the difference between inflation and the inflation target set by the authority for the period, cmc t represents the log-deviation of the real marginal cost from its steady-state value, and where λ = (1 θ)(1 θβ) θ. 2.2 Real marginal cost Baseline formulation The baseline formulation for the marginal cost corresponds to the case where the production function is Cobb-Douglas, with two inputs: capital and labor. The nominal marginal cost that is obtained by assuming this technology and competitive factor markets is given by: MC t = 1 W t L t (7) 1 α Y t where W t corresponds to the nominal wage, and L t to labor. The linearized version of the real marginal cost is given by cmc t+i = s t+i s (8) where s t corresponds to the logarithm of the labor share, and where s is the logarithm of its steady-state (long-run) value. Then, we can rewrite the Phillips curve as: Alternative specifications bπ t = λ (s t s)+βe t {bπ t+1 } (9) We consider three alternative specifications for the underlying technology as in Gagnon and Khan (2005). These alternative specifications define different formulations for marginal costs. 7 Notice that we are assuming that the inflation target in any period may differ from steady-state inflation. Thus, under our formulation not only we eliminate the possibility of having a non-vertical Phillips curve in the long-run but also we are able to address the non-stationarity observed in inflation for the Chilean case. 5

6 Overhead labor First, we consider the inclusion of overhead labor in the production function. Let L be the (fixed) quantity of labor devoted to cover fixed cost. The production function in this case can be expressed as, Y t = K α t At Lt L 1 α (10) The nominal marginal cost is then given by the following expression: MC t = 1 W t L t Lt L (11) 1 α Y t L t Again, if capital can be freely allocated across firms, the marginal cost is independent from the scale of production it depends only on the prices of factors and, therefore, is the same for all firms. The log-deviation of real marginal costs from steady-state in this case is given by: cmc t+i = s t+i s + L b lt+i (12) L L where L > L represents the steady-state level of employment for any particular firm. Therefore, under this specification the log-deviations of marginal costs do not only depend on the deviations of the unitary labor costs from steady-state but also on the deviations of employment. Thus, if the unitary labor cost remains constant, an increase in employment leads to an increase in the marginal cost. The Phillips curve under this specification is given by: bπ t = λ (s t s)+λ L b lt + βe t {bπ t+1 } (13) L L Constant Elasticity of Substitution We also consider a more general production function where we allow for a non-unitary elasticity of substitution between inputs. In particular we consider the following CES technology: Y t = hk t σ 1 σ i +(A t L t ) σ 1 σ σ 1 σ (14) Under this specification for the technology the nominal marginal cost is given by: where γ t = K t (A t L t ) σ 1 σ σ 1 σ +(A σ 1 tl t) σ MC t = W tl t Y t γ t (15). As in the previous case, if capital is perfectly mobile across firms the marginal cost for all firms will be the same. Linearizing the marginal cost about the steady state we obtain the following expression: cmc t+i =(s t+i s)+ω c yk t+i (16) 6

7 where yk c t+i represents log-deviations of the output-capital ratio, Yt K t, with respect to its ³ 1 steady state value. Parameter ω is given by ω = 1 σ 1 σ µs,whereµ is the steady-sate gross mark-up. The Phillips curve is given by bπ t = λ (s t s)+λω c yk t+i + βe t {bπ t+1 } (17) If we consider that instead of capital, the firm utilizes an imported input in the production function (with a CES technology) then the real marginal cost can be expressed as follows cmc t+i =(s t+i s)+ϕω (bp m,t+i bw t+i ) (18) where bp m,t bw t corresponds to log-deviations of the relative price of foreign inputs with respect to the nominal wage, and where ϕ = σµs. Firm specific capital When capital is specific tofirms, changes in factors relative prices and changes in output level do not affect the amount of capital utilized in production by a particular firm. In this case, there would be a difference between specific marginal costs and the observable average marginal cost. Sbordone (2002) shows that under this circumstances it is possible to establish a relationship between firm specific marginal cost and average marginal cost. 8 If we consider a production function with a CES technology we have that real marginal cost in period t + i for firms that adjusted their prices in period t is given by: µ cmc t,t+i =(s t+i s)+ωyk c 1 t+i σ µs 1 bx t + µ ix 1 σ µ s 1 bπ t+j (19) j=1 Combining equations (17), and (19) we obtain the following expression for the Phillips curve: bπ t = Ω (s t s)+ωω c yk t+i + βe t {bπ t+1 } (20) sσ(µ 1) s(σ(µ 1) µ)+1. where Ω = λξ, andwhereξ is a scaling parameter that corresponds to ξ = Therefore, assuming that ξ =1is equivalent to collapse the model to a model with free capital mobility across firms. 3 Empirical issues 3.1 Measures of inflation and marginal cost The most common measure of inflation used in empirical studies of the Phillips curve corresponds to the change in the GDP deflator (see GG, GGL and McAdam and Willman (2003), among many others). In our case we use the Consumer Price Index (CPI) to derive the measure of inflationto beusedinthe empiricalanalysis. This approach is based 8 This assumption has helped reconciling the degree of inertia implied by the empirical estimation of the Phillips curve base on the Calvo model with the micro evidence regarding the frequency of price adjustments in the US. 7

8 on the fact that, in the Chilean case, the GDP deflator is measured with considerable noise. Additionally, the GDP deflator in our commodity-intensive economy, is subject to strong variations due to changes in the terms of trade. Then, a significant fraction of the changes in the GDP deflator will reflect changes in relative prices as opposed to persistent changes in the general level price. Moreover, the fact that the inflation target is set in terms of CPI inflation leads us to consider this measure as the relevant one in our Phillips curve analysis. In order to avoid including in our analysis regulated prices and prices that fluctuate significantly whose dynamics are not well represented by the Phillips curve we use in our estimations a measure of core CPI inflation that removes these items from the CPI basket. 9 Figure 1 shows the evolution of CPI inflation and core CPI inflation over the period The first characteristic of the inflationary process is that it exhibits a strong decreasing tendency over the period This trend implies that deviations of inflation from a constant long-run inflation rate is a non-stationary variable. This nonstationarity is the consequence of the disinflationary process that the monetary authority started in 1990 with the introduction of the first inflation target by the Central Bank. 10 Another relevant feature of the Chilean inflationary process is the high volatility of quarterly CPI inflation. Our strategy in this case is to decompose, using the X12-ARIMA procedure, the inflation rate in two different components: irregular and non-irregular (trend plus cycle). After removing the irregular component, quarterly core inflation resembles closely yearly moving-average inflation (figure 2). We de-trend inflation by computing the difference between the non-irregular component and the interpolated inflation target set by the authority. This de-trending procedure is consistent with our theoretical framework, in which firms update their prices using the inflation target. 11 We consider several measures of real marginal costs consistent with different specifications for the production technology presented in section 2. The first measure corresponds to the one that is obtained assuming a Cobb-Douglas production function with capital and labor as inputs. As we showed in section 2, the real marginal costs in this case are given by, MC = 1 WL 1 α PY, (21) which is proportional to the labor share in the economy, S = WL/PY. 9 In our analysis we use a measure of core inflation that removes regulated prices and the prices of fruits and vegetables. 10 There have been two clear phases in the implementation of the inflation targeting regime in Chile. In the first phase, when gaining credibility was a key issue, the Central Bank set short-term horizon CPI inflation targets, and actively managed the exchange rate. In the second phase, that started in 1999, the CentralBankmovedtoafullyflexible exchange rate system with a stationary lon-run target for inflation (see Cespedes and Soto, 2005). 11 If the path for the inflation target is independent of the business cycle, estimating Phillips curves using the inflation rate that includes the cyclical and the trend components is equivalent to estimating the Phillips curve only with the cyclical component of inflation. If the inflation target is endogenous, and depend on the state of the economy, our GMM estimation should take into account the endogeneity of the target. 8

9 Anual inflation rate Anual core inflation rate Figure 1: Evolution of CPI (continuous line) and core CPI inflation (dashed line) over 1986 and Quarterly core inflation Quarterly core inflation (trend/cycle component) Figure 2: Core inflation (continuous line) and its trend/cyclical component (dashed line) 9

10 Labor share Figure 3: Evolution of the labor share as a fraction of GDP at factor prices Therefore, as a proxy for marginal cost we utilize a measure of labor share that excludes mining, fishing, energy, agriculture, and the public sector from both employment and output. 12 The reason to remove these sectors is that they are associated to commodities, regulated or non market-determined prices. In figure 3 we present the evolution of the labor share as a fraction of GDP measured at factor prices. This is our first proxy for the real marginal costs. From this figure is clear that our measure for the marginal cost exhibits some trend with a particular break around In the previous section we showed that when the production function is a CES function with labor and capital as inputs, marginal costs must be adjusted to consider the relationship between capital and output. Thus, to capture this effect we include in the estimations a measure of the capital-output ratio. It is worth mentioning at this point that during the second part of the period under analysis this ratio exhibit a decreasing trend (see figure 4). Now, if the degree of complementarity between capital and labor is high (a low σ) then decreases in the capital-output ratio are associated with decreases in the marginal cost along the business cycle. Finally we use a measure of real marginal costs that allows the inclusion of imported inputs in the production function. In particular, we construct a measures of the price of imported inputs over wages. In the last 15 years this relative price has been falling steadily (see figure 5). Again, if the elasticity of substitution between the imported inputs and the remaining inputs in the production process is low, the fall in imported prices with respect to wages should reduce real marginal costs. Depending on the elasticity of substitution between the different factors, the previous evidence is consistent with having different measures of real marginal costs exhibiting a 12 GDP is measured at factor prices., i.e., we exclude indirect taxes. 10

11 (log) Capital-output ratio Figure 4: Evolution of the capital-to-output ratio (log) Price of imported inputs over wages Figure 5: Evolution of the price of imported inputs over wage 11

12 trend. Now, this trend is likely to be related to the opening process of the Chilean economy during the period of estimation. In this case, the trend in real marginal cost measures could reflect the increasing competition domestic firms faced from abroad and/or lower inputs prices which steadily decreased during the nineties. Additionally, and probably related to the opening process, changes in relative sizes of different sectors with different markups could explain the behavior of the real marginal costs (as in McAdam and Willman (2003)). Finally, this movements could be reflecting developments in the labor market such as permanent changes in the wage markups. Nevertheless, in order to avoid estimating relations between non-stationary variables that could be subject to the problem of spurious correlation and to be consistent with our theoretical framework, we remove the trend from our different real marginal cost measures in a consistent way to the case of inflation. 3.2 Marginal cost, output gap and inflation The new Phillips curve emphasizes that the real marginal cost is the driving variable of inflation in the short-run. Although output gap measures have been commonly used as the proxy for the inflationary pressures underlying the Phillips curve, only under certain restrictions on the technology and labor markets structure, real marginal cost are proportional to the output gap (see GG). In the case of the Chilean economy, the correlation between the output gap and the real marginal cost is in fact clearly negative. 13 In section 2 we showed that there exist an inverse relationship between the markup and marginal cost. In particular, we have that: bµ t = cmc t (22) where bµ t corresponds to the log-deviation of the effective gross markup from its steady state value. Therefore, the problem is that if in fact the real marginal cost is countercyclical, this implies that markups should be procyclical, which contradicts the main implications of the New Keynesian macroeconomics. Moreover, as in GG, we find that the contemporaneous correlation between the output gap and inflation is negative. Additionally, lags of the output gap are positively correlated with inflation (see figure 6). Form this analysis is clear that if the real marginal costs is replaced by the output gap in the new Phillips curve, as in the case of the US and the UK, the Chilean new Phillips curve will resemble the old Phillips curve. One possible explanation for the procyclicality of the markups is that output gap constructed from a de-trended GDP series, is not a good measure of the theoretical output gap. In particular, if supply-side shocks to the Chilean economy have been important, as argued by Calvo and Mendoza (1999), De Gregorio (2004) and García (2003), the theoretical output gap, i.e. deviations of the effective output from its flexible price equilibrium level, can significantly differ from the de-trended output gap measure. Consider a situation in which monetary policy response respond to the deviations of inflation from its target and to the growth rate of output. Using the GDP growth rate 13 The output gap is computed using the HP filter while the real marginal cost correspond to the labor share. 12

13 0.30 Inlfation (t), Output gap (t+k) Figure 6: Dynamic cross correlations of Inflation(t) and the Output gap (t + k). The dotted lines are the approximate two standard error bounds. instead of a measure of the theoretical output gap in the monetary policy rule is consistent with evidence for the US presented by Ireland (2004). In this case, temporary technology shocks will imply a negative "real" (theoretical) output gap and at the same time a GDP growth above the long run or trend GDP growth. Therefore, a positive technology shock will generate a positive de-trended measure for the output gap and a negative theoretical output gap. In this case, inflation will initially fall below its target and therefore, it will be negatively correlated with de-trended output gap measures. Thus, not accounting for the possibility of this type of shocks could led to a wrong conclusion regarding the validity of the new Keynesian Phillips curve for the case of Chile. Using a measure of the real marginal cost instead of the output gap will help to avoid this problem. A simple correlation analysis between our real marginal cost measures and inflation indicate that this two variables are positively and significantly correlated contemporaneously. Also important is that leads of real marginal costs are positively correlated with current inflation (see figure 7). Therefore, this preliminary evidence is consistent with our theoretical framework: current inflation is positively associated to current and future real marginal costs. 4 Estimation of the New Phillips curve 4.1 Specification We estimate two specifications for the Phillips curve. The baseline case corresponds to the standard NKPC without a backward looking component, bπ t = λξ cmc t + βe t {bπ t+1 } 13

14 0.60 Inflation (t), Labor Share (t+k) Figure 7: Dynamic cross correlations of Inflation(t) and the Labor Share (t + k). The dotted lines are the approximate two standard error bounds. where bπ t is the deviation of the inflation rate from the inflation target, cmc t is the log deviation of the average real marginal cost from its long-run value, λ = (1 θ)(1 θβ) θ and ξ is a proportionality factor. This factor is ξ =1under the assumption that capital is freely mobile across firms, and ξ 6= 1under the assumption that capital is firm specific. All estimations where made using the Generalized Method of Moments (GMM). The following alternative orthogonality conditions were used: E t ½µ bπ t ¾ (1 θ)(1 θβ) ξ cmc t βbπ t+1 z t =0 (a) θ E t {(θbπ t (1 θ)(1 θβ)ξ cmc t θβbπ t+1 ) z t } =0 (b) ½µ ¾ (1 θ)2 E t bπ t ξ cmc t bπ t+1 z t =0 (c) θ where z t is a vector of instruments. The instruments list includes four lags of: the deviation of inflation from target, the deviation of real marginal cost from trend, and the output gap (lags from t 2 to t 5); two lags of the monetary policy interest rate (from t 5 to t 6); three lags of nominal wages growth relative to trend (from t 4 to t 6); and four lags of terms of trade deviations from trend (from t 1 to t 4). Notice that specification (c) normalizes β to Results Baseline case Tables 1 to 3 present the estimated values of parameters θ, β, andλ for the baseline Phillips curve (6) under four alternatives for the marginal cost, corresponding to four 14

15 different technologies: Cobb-Douglas technology, technology with overhead labor, CES technology with capital and labor, and CES technology with an imported input and labor. For each case we report results under the three alternative normalizations (specifications (a) to (c)), and considering both the case when capital is freely mobile across firms, ξ =1, and when capital is firms specific. In this case, the proportionality factor ξ is assume to be known with certainty and computed from the sample average of the labor share and the gross markup. 14 For the cases were we assume a CES technology we consider two alternative values for the elasticity of substitution across inputs: σ =0.5 and σ =1.5. Together with the estimated values of the two structural parameters and λ we also report the implied average number of quarters prices are fixed, and the J-test for overidentified restrictions. According to this test the overidentified restrictions are satisfied for all specifications of the model. Notice firstthatcoefficient λ is statistically significant in all specifications. This implies that marginal cost is in fact relevant to explain the inflationary process, as emphasized by the NKPC formulation. In general, the estimation of parameter θ is robust to the three normalizations (a)-(b). For the case were capital is assumed to be freely mobile across firms, the estimated value for this parameter lies in the range of This implies an estimated average duration of prices in the range of 7 up to 8 quarters, approximately. Therefore, our figures imply a similar price rigidity for Chile than for the Euro area as estimated by GGL, and coincident with the price rigidity in the U.S. as estimated by those authors. When we assume that capital is firm specific the estimated value of θ decreases significantly. Under this assumption the point estimate of this parameter lies in the range , which implies durations for price stickiness in the range of 2.5 up to 5 quarters. These figures are also consistent with those for the U.S. estimated by GGL when assuming firm specific capital. The estimated discount factor β is somewhat not very precise: it lies between 0.8 and 1. Again, these results are in line with those reported by GGL for the Euro area and the U.S Hybrid model We considered an alternative specification for the Phillips curve, where inflation exhibits persistency. This alternative specification is close in spirit to the hybrid Phillips curve in GG, and it is based on the formulation by Christiano, Eichenbaun and Evans (2005). For concreteness, lets assume that the passive updating rule for those firms that can not optimally adjust prices is given by Γ i t = iy j=1 (1 + π t+j 1 ) κ 1+π 1 κ t+j 14 The proportionality factor is computed as ξ = share, and where µ is the sample average gross markup. s =0.55 and µ =1.2. sσ(µ 1) s(σ(µ 1) µ)+1,wheresisthesampleaveragelabor The value for these two magnitudes were 15

16 This updating rule implies that whenever firms do not receive a signal they adjust their prices by a geometric average of the inflation target set by the authority and past inflation. Parameter κ is a measure of the degree of persistency of inflationandcanbe associated to the credibility of the target set by the authority. The Phillips curve under this updating rule is given by bπ t = λξ cmc t + γ f E t bπ t+1 + γ b bπ t 1 + ζ t (23) where λ(θ, β, κ) = (1 θ)(1 θβ) θ(1+κβ),γ f (θ, β, κ) = β 1+κβ,γ b(θ, β, ω) = 1+κβ κ. The term ζ t is a function of changes in the inflation target and it is given by ζ t = τ 1 E t π t+1 + τ 2 π t, where τ 1 = βγ b, τ 2 = γ b. 15 For this case, we utilize the following orthogonality condition to estimate parameters θ, β and κ: E t {(θ (1 + κβ) bπ t (1 θ)(1 θβ) ξ cmc t θβbπ t+1 θκbπ t 1 θ (1 + κβ) ζ t ) z t } =0 (d) where z t is a vector of instruments similar to the one considered previously. However, in this case we include only three lags of the inflation deviation from target, the real marginal cost deviation from trend, and the output gap (from t 3 to t 5). Results for the estimated hybrid model are presented in Table 4. Again, we report the estimated values of parameters θ, β, and λ under four different specification for the marginal cost, and assuming alternatively that capital is freely mobile and firm specific. We also report the estimated value of parameter κ, which measures the degree at which firms index their prices to past inflation. The estimated share of the backward-looking component γ b is statistically significant in all specifications and it is about This figure is slightly smaller than the one reported by Agenor and Bayraktar (2003) for Chile in their study of the inflation dynamics in middle income countries. These authors estimate a non-structural Phillips curve that includes both a backward and a foreward-looking component, and found that the backward-looking component is about Unlike our case, Agenor and Bayraktar use several lag of the output gap (up to 3 for Chile) as the driving force for inflation. Parameter κ is consistently estimated in the range implying that within the sample period firms weighted more past inflation rather than announced inflation targets to passively adjust their prices. Not surprising, these figures imply a much stronger role for the backward looking component of inflation in the Chilean case than the estimated by GGL for the Euro area. However, they are quiet similar to the estimates of for the U.S. by GG, and GGL. The estimated values for parameter θ under the hybrid specification do not significantly change from the baseline case. The same holds true for the discount factor β which, again, is somewhat low. As in the baseline case, marginal cost specification with firm-specific capital tend to give lower values for θ implying shorter average duration 15 Notice that in steady-state ζ t =0. 16

17 of price stickiness. Finally notice that for all cases the overidentifying restrictions are satisfied. Despite the important role of the backward looking component in our estimations of the Phillips curve for Chile, our results could be biased against this component if additional lags of inflation enter directly in the true Phillips curve. 16 Therefore, we follow GG,and GGL, and perform a robustness exercises to address the importance of the backward looking component of the Phillips curve. In particular, we add additional lags of inflation to the hybrid model. Table 5 presents the results for the specification for marginal that assumes firm-specific capital (results assuming capital mobility are similar). Additional lags of inflation turn out to be non-significant. Neither is the sum of the three additional lag of inflation. Recent literature has questioned inference using GMM methods in the presence of weak instruments (e.g., Stock, Wright and Yogo, 2002). In order to check the relevance of the instrument set used in our regressions we test null hypothesis that the coefficients on all the instruments are jointly zero in the first stage of the estimation. In Table 6wereporttheF-statistic, the associated p-value and the adjusted R 2 from the first stage regressions. As can be seen, the null hypothesis that the instruments are jointly irrelevant is soundly rejected in all cases and generally the adjusted R 2 is over 0.5. Finally, it is important to notice that most studies on the Phillips curve for OECD countries use raw data on inflation and marginal cost, despite clear trends in those series (see for example Galí and López-Salido (2001) for estimations of the Spanish Phillips curve). Our results presented so far were obtained using de-trended data (inflation minus inflation target and detrended marginal costs). To analyze whether these results were driven by the de-trending methodology we re-estimate the hybrid model using undetrended data. Results do not significantly change. The new estimates for parameter λ, γ f, γ b are 0.06, 0.55 and 0.45, respectively Actual versus fundamental inflation Following GG and Sbordone (1999), we assess the goodness-of-fit of our estimations by comparing the extent to which the inflation rate and the deviation of the inflation rate from the inflation target implied by our model lines up against actual data. The model-based measure of inflation or fundamental inflation, as termed by GG, can be obtained by iterating the pricing equation (23), bπ t = δ 1 bπ t δ 2 γ f E t X µ 1 i=0 δ 2 i λξ cmct+i + τ 1 π t+1+i + τ 2 π t+i (24) where δ and δ 2 > 1 are the stable and the unstable root associated with the stationary solution to the difference equation given by (23) and π t is the inflation target. In the 16 As noted by Rudd and Whelan (2001), if the instrument set includes variables that cause inflation directly but are not included in the hybrid specification of the Phillips curve, the estimation of the model may be biased in favor of the forward looking component. 17 Structural estimate with raw data are not directly comparable with the ones obtained with de-trended data as the underlying model implies removing the inflation target from inflation. 17

18 pure forward looking specification, the lagged term in (24) disappears, thus, fundamental inflation reduces to a discounted stream of expected future real marginal costs. As argued by GG, we do not observe future marginal costs nor variations in the inflation target. However, under certain assumptions we can construct an estimate of the right-hand side as follows. Let, X t =[cmc t, cmc t 1,..., cmc t+1 q ] for some finite value of q. We can use an unrestricted autoregressive process of order q to forecast future inflation using the fact that, E t { cmc t+i } = A i X t where A is the companion matrix of the AR(1) representation of X t. Analogously to marginal costs, expected future values of the inflation target can be obtained by estimating a first-order autoregressive process, E t π t+i π ª = φ i (π t π ) where π corresponds to the steady-state (long run) inflation target. Accordingly, we can re-write (24) as, π t = π t + δ 1 bπ t 1 + λξ δ 2 γ f I δ 1 2 A 1 Xt τ 2 δ 2 γ f π t + τ 1 + δ 1 2 τ 2 (1 φ) δ2 (δ 2 φ) δ 2 γ f (π t π ) (25) Figures 8 to 11 depict the actual inflation and our measure of fundamental inflation together with the observed difference between inflation and the inflation target versus the deviations of inflation from the target implied by our estimated model. Overall, under all specifications, our measure of fundamental inflation tracks actual inflation and its deviations from the inflation target quite well. The lowest mean square error between actual and fundamental inflation is obtain when assuming a CES technology with a low degree of substitution between capital and labor. 5 Stability of the hybrid Phillips Curve One issue that has not been formally analyzed in the literature is the temporal stability of the hybrid Phillips curve estimated parameters. 18 This concern is particularly important in an emerging country like Chile that has experienced a significant decrease of the inflation rate accompanied with an increase in the credibility of the inflation targeting regime over the last fifteen years (Céspedes and Soto, 2005). The lower inflation rate might have been reflected in a decrease in the average length between price adjustments (a lower value of D) while the gain of credibility by the monetary authority could have translated in an increased number of firms updating their prices according to the inflation target (lower values of κ). 18 The paper of Jondeau and Le Gihan (2005) test the stability of their Phillips curve estimates but examine only the reduced (linear) form parameters and use Wald-type tests which have some important drawbacks as they point out. 18

19 In order to examine the stability of the parameters and the occurrence of a break point, we consider a predictive test for structural change with unknown breakpoint developed in the papers of Ghysels and Hall (1990), Ghysels et. al. (1997) and Guay (2003). This test consists on estimating the parameter vector for the first subsample and then evaluating the moment conditions for the second subsample at these parameter values. 19 In our particular case, this approach has several advantages over alternative approaches like the Wald-type tests proposed in the work of Andrews (1993) and Andrews and Ploberger (1994). Firstly, we only use first subsample estimates of the parameters which allow us to test the presence of a break even when the second subsample contains a few observations and parameter estimates are not feasible. Indeed, it is a common drawback of Wald-type tests that they cannot be applied to detect structural instability at the end of the sample. Secondly, we do not set a priori orthogonality conditions equal to zero in the second subsample thus, weavoidrejectingstabilitywheninfact the parameters were stable but there was certain type of mis-specification (e.g., omitted variables). Table 7 presents the estimated predictive tests (supremum sup PR,average avgp R and exponential exp PR) along with the date for which the largest PR test is obtained. The PR-type tests can be divided into a test of structural change for the vector of parameters and a test of the stability of the overidentifying restrictions (Sovell, 1996). We report the PR 1 -type statistics that tests both parameter and overidentifying restrictions stability and, the PR 2 -type tests for parameter variations only. The results show that for the four specifications of marginal costs, we cannot reject the existence of a breakpoint. Furthermore, the PR 1 and the PR 2 tests estimate consistently the date of the breakpoint around the first quarters of 2001 which is close to the date that the inflation target reached its stationary annual value of 3%. We also report the estimated values of the parameter κ and the duration of price stickiness before the breakpoint date. It is noteworthy that in most cases the first subsample value of κ is larger than the estimated parameter using the whole sample suggesting that there are more firms updating their prices according to the inflation target. In regard of price stickiness, we find that the estimated duration of price stickiness is smaller before the breakpoint as expected. 6 Conclusion and directions for further work In this paper we estimate a NKPC for Chile, using quarterly data for the period 1990:1-2004:4. Our results using the Generalized Method of Moments (GMM) tend to support the NKPC.The evidence shows that the backward-looking coefficient in a hybrid specification of the Phillips curve is about This figure is larger than the corresponding one for the Euro area and the U.S. as estimated by GG and GGL. In general, different specifications for the marginal costs lead to similar estimates. The estimated Calvo coefficient that captures the degree of price rigidity lies, in the baseline case, in the range of 0.85 to 0.88 indicating that prices remain unchanged on average for about 7 to 8 quarters. When firm specific capital is considered then the Calvo coefficient falls to a 19 A brief description of the test can be found in Appendix A. 19

20 range 0.6 to 0.8, implying average price durations in the range of 2.5 up to 5 quarters. These results do not significantly change when considering the hybrid specification for the Phillips curve. Regarding parameter stability, our results support the hypothesis of the existence of a structural break in the NKPC, which occurred when the inflation target converged to its long-run level (between 1999 and 2000). Moreover, our evidence supports the idea that the inflationary process became more forward looking in recent years, which is also consistent with an increased credibility in the inflation target. There are still several issues that need to be address. First, it its necessary to analyze more in detail how robust are our estimates to weak identification. As it has been put forward by Ma (2002), Kurmann (2004) and Nason and Smith (2005), GMM estimation of the structural parameters of the NKPC may be inaccurate because of weak instruments. Therefore, it is necessary to test whether our instruments are not only valid but also relevant. Another important issue are possible misspecification problems associated with structural breaks. The Chilean economy has gone through different monetary policy frameworks over the last years, that may have affected the way prices are set. This could have change some of the structural parameters of the model. Third it is necessary to perform more research on the determinant of the evolution marginal cost. We showed that labor unit cost and marginal cost in Chile have exhibit a clear trend over the 90s. Factors behind that trend may include changes in the optimal markups by firms, composition effects associated to changes in the relative share of different sectors in the economy, and changes in wages markups. As emphasized by the NKPC, understanding the dynamics of marginal costs is key to understand the dynamics of inflation. 20

21 A Appendix: Variable definitions Inflation rate: Cyclical component of the quarterly variation of the core CPI (IPCX1), π t = Pt P t 1 1. Output gap: Log-deviation of output from its long-run value, by t = 100 (y t ȳ t ). The long-run value of output, ȳ t, is approximated by using a quadratic trend. Inflation target: Quarterly linear interpolation of the annual inflation targets, bπ t. Labor share: Ratio of the nominal labor compensation and the nominal output, S t = W tl t P ty t. The log-deviation of the labor share is: bs t = 100 (s t s t ) where s t =logs t, and where the long run value of this variable, s t, is approximated by using a quadratic trend. Nominal output is computed by using real GDP and the core CPI index used to compute inflation. Output-Capital ratio: We compute the log-deviation of the output-capital ratio from its long-run trend by using quarterly data on capital stock and GDP. The longrun value for this ratio is computed by using a polynomial trend of four degrees Relative price of imports: We utilize an imports price index (IVUM) that is computed by the Central Bank, and a nominal wages index by INE (Instituto Nacional de Estadísticas). 21

22 B Predictive tests for structural change This appendix briefly describes the predictive tests for structural change with unknown breakpoint presented in the papers of Ghysels and Hall (1990), Ghysels et. al. (1997) and Guay (2003). Recall that the GMM estimator is based on a set of moment conditions, E [f (x t,θ)] = 0 where f( ) is a q 1 vector of continuous differentiable functions of a vector of data (x t ) and, the model parameters (θ). When this moment conditions do not hold throughout the whole sample (t =1,...,T), the model is said to be structurally unstable. If we presume that there is a break at some date [πt] for π (0, 1), Ghyselsand Hall (1990) propose to estimate the model parameters θ using the observations in the first subsample T 1 (π) ={1, 2,...,[πT]} and then, evaluate the moment conditions for the observations in the second subsample, T 2 (π) ={[πt]+1,...,t}, at these parameter values. The idea behind the predictive tests is to examine whether parameter estimates of one subsample can be used to predict over the other subsample. Particularly, they propose to test whether these estimated moment conditions are approximately zero (i.e., H 0 : E [f (x t,θ 1 )] = 0 for T 1 (π) and T 2 (π) while H 1 : E [f (x t,θ 1 )] = 0 for T 1 (π) but E [f (x t,θ 1 )] 6= 0for T 2 (π)). The predictive tests used in this paper are based on the following statistics, PR 1 (π) = PR 2 (π) = (T [πt]) 1 2 π T π TX t=[πt]+1 TX t=[πt]+1 f (x t,θ 1 ) f (x t,θ 1 ) (π) (T [πt]) 1 2 V 1 S 1 2 T P 2 (π) S 1 2 T T 1 2 TX t=[πt]+1 TX t=[πt]+1 f (x t,θ 1 ) f (x t,θ 1 ) where V 2 (π)=s 2 (π)+ 1 π π F 2 (π) F 1 (π) 0 S1 1 (π) F 1 (π) 1 F2 (π) 0 and P 2 (π) =S F 2 (π) F 1 (π) 0 S1 1 (π) F 1 (π) F 2 (π) 0 S with S 1 (π) being the covariance estimator involving data from the first subsample and, S 2 (π) the estimator using the second subsample data, while the matrices F 1 and F 2 denote the jacobian of the moment conditions evaluatedinthefirst and second subsample, respectively. Sovell (1996) shows that the test PR 1 (π) is divided into a test of structural change for the vector of parameters and a test of stability of the overidentifying restrictions. The statistic PR 2 (π) accounts for the test for parameter variation. Statistics for optimal predictive tests with unknown breakpoint can be obtained by computing the average supremum, average and exponential form, 22