The New Keynesian Phillips Curve for Austria An Extension for the Open Economy

Transcription

1 The New Keynesian Phillips Curve for Austria An Extension for the Open Econoy Following the epirical breakdown of the traditional Phillips curve relationship, the baseline New Keynesian Phillips Curve (NKPC) theory was forulated in the 1990s. Unlike the traditional Phillips curve, it derives fro a theoretical odel that is based on icroeconoic principles. It expresses current inflation as a function of expected future inflation, past inflation and a easure of firs arginal cost. The NKPC serves to estiate the odel s structural paraeters that capture price-setting behavior in an econoy. This study estiates the NKPC using Austrian data. As Austria is a fairly open econoy and the NKPC was initially forulated for a closed econoy, the theoretical odel is extended to include open-econoy aspects and is then estiated in various specifications. The extended NKPC proves to explain inflation developents in Austria since 1980 quite accurately. The estiation of the structural paraeters shows that around 30% of all Austrian firs change their prices every quarter, indicating that overall, prices are constant for an average of roughly ten onths. Moreover, between 30% and 50% of all firs follow a backward-looking rule of thub in setting their prices. Copared to the other euro area countries, this price duration represents an average, whereas the degree of backwardlooking behavior in price setting is above average. However, the NKPC is not found to be as suitable for forecasting purposes as tie-series odels, as none of the inflation forecasts based on the NKPC odel was able to outperfor a naive forecast (unchanged inflation rate over the forecast horizon). Fabio Ruler JEL classification: E31, C22, E12 Keywords: New Keynesian Phillips Curve, inflation dynaics, GMM, inflation forecasting. 1 Introduction 1.1 The New Keynesian Phillips Curve Background and Derivation The New Keynesian Phillips Curve (NKPC) is currently arguably the ost coonly used inflation dynaics odel in odern acroeconoics. The NKPC is derived fro New Keynesian theory, whose ost iportant assuptions are a arket governed by onopolistic copetition and short-ter price rigidity. The baseline NKPC was developed in several contributions in the 1990s in the New-Keynesian literature 1 and represents inflation (π t ) as a function of future inflation (π t+1 ) and firs arginal cost (c t ). π γ E π κ c = ( ) + ( ) t f t t t +1 (1) For epirical applications, soe contributions ake suitable assuptions for the labor arket to proxy arginal cost with a real econoic activity variable, such as the output gap. ( ) π = γ E ( π ) + λ y y t f t t+ t t 1 (2) Hence, the only difference between the forulation of the new and the traditional Phillips curve lies in the fact that the forer relies on future, rather than past, inflation to deterine current inflation. However, the two concepts differ fundaentally, as the new Phillips curve is derived fro a theoretical odel with rational ex- 1 For an overview of the literature, see Goodfriend and King (1997). Refereed by: Johann Scharler, OeNB. Monetary Policy & the Econoy Q4/06 55

2 pectations that is based on icroeconoic principles. The epirical evaluation of the Phillips curve shown in equation (2) undertaken in the early new-keynesian literature was not very successful: Frequently, estiates of the output gap coefficient λ were only negative or not significant. In a seinal article, Galí and Gertler (1999) introduced two features into the NKCP that arkedly iproved the epirical explanatory power of the odel. The authors extended the pure forward-looking odel by adding past inflation as an explanatory variable in the Phillips curve equation (π t 1 ). Further, they used real unit labor costs rather than the output gap as an epirical proxy for the (unobservable) arginal cost. The resulting forulation is generally referred to as the hybrid NKPC, as it displays features of both the traditional and the new Phillips curve: π = γ E π γ π κ t f t ( t ) + + c + 1 b t 1 ( t ) (3) At this point, it should be noted that the paraeters of the Phillips curve equation (γγ f, γ b, к or λ) are represented in reduced for in equations (1) through (3). These paraeters are theselves cobinations of the structural paraeters resulting fro the underlying theoretical odel. The theoretical odel is based on the assuption of firs axiizing profit in a onopolistic copetition arket; they face a deand function with constant elasticity of deand. Firs price-setting behavior is assued to be subject to the restrictions forulated by Calvo (1983) on the odeling of price rigidity: Each fir is allowed to adjust its price in any given period with a certain (fixed) probability of 1 θ, which eans that θ represents the probability of a fir not adjusting its price in this period. In addition to Calvo price setting, Galí and Gertler (1999) assue that a certain fraction of firs, ω, sets prices according to a rule of thub, whereas the reainder, 1 ω, sets prices optially. Firs that use the rule of thub pursue a backward-looking approach, basing their prices on the optiu price in the last period and then updating it with past inflation. After solving the axiization proble under the given assuptions, the equation for the inflation rate ay now be written in its structural for: θβ ω π = E π + t t t π t 1 ( 1 θ) ( 1 ω) ( 1 θβ ) + ct (4) with β as the discount factor of firs future profits, and Δ=θ+ω[1 θ(1 β)]. The variables in the equation are defined as deviations fro their steady state values; in other words, the equation is specified in linearized for. The NKPC has been estiated nuerous ties for various countries both in its reduced for (equation (3)) and in a structural for, using epirical data. The paraeters estiated in equation (4) represent the structural factors of a country s price-setting process underlying the odel, with θ frequently being interpreted as the paraeter of price rigidity and ω indicating the degree of intrinsic inflation persistence. 1.2 The New Keynesian Phillips Curve for Austria The NKPC has not been estiated with Austrian data so far in the existing literature. As Austria is a fairly open econoy, the extension of the Phillips curve odel to include open- 56 Monetary Policy & the Econoy Q4/06

3 econoy aspects is especially relevant for Austria. In this contribution, the existing odel of the hybrid NKPC is extended by the introduction of international trade as well as interediate inputs. Thus, the odel also captures the effects of iport prices and the price of interediate inputs on firs arginal costs and ultiately inflation. The structural paraeters of the odel are then estiated and interpreted in various specifications, using Austrian quarterly data fro 1980 to In particular, we identify the specification with the highest explanatory power for the analyzed period and copare the estiated degree of price rigidity of the closed econoy specification with that of the open econoy specification to establish whether they differ. Moreover, the forecasting perforance of the extended NKPC for Austrian inflation fro 2003 to 2006 is exained and copared with that of a naive forecast. This study is structured as follows: Section 2 presents the extension of the NKPC odel, which accounts for open-econoy effects, and describes the epirical approach to estiating the odel. The estiation results of the odel s structural paraeters along with soe easures of fit for the individual specifications are presented and discussed in section 3. Section 4 contains an evaluation of the NKPC s forecasting perforance, and section 5 concludes. 2 Extending the New Keynesian Phillips Curve to the Open Econoy 2.1 The Model For the sake of brevity, we refrain fro deriving the extended odel step by step, but discuss only the changes in the assuptions to account for an open econoy and present the resulting Phillips curve. Ruler (2006) contains detailed inforation about the derivation of the Phillips curve for open econoies. The starting point is the hybrid NKPC known fro the literature presented in equation (4). 2 The hybrid NKPC reflects the optiality condition of firs price-setting in a general equilibriu odel, expressing current inflation as a function of expected future inflation, past inflation and a easure of firs arginal cost. In recent years, this function has been epirically tested for various countries in innuerable contributions; the epirical evidence has proved to be quite ixed. In a nuber of large industrial econoies, the hybrid NKPC which uses real unit labor cost as a proxy for arginal cost has been able to deliver a good explanation of inflation dynaics over the past two decades. 3 However, a nuber of other epirical studies have shown that especially in sall, open econoies, the standard NKPC odel is not always suited to explaining inflationary developents during the past decades. 4 2 The theoretical odel underlying the hybrid NKPC is described in detail in Galí and Gertler (1999) and in Galí et al. (2001). 3 See e.g. Galí and Gertler (1999) as well as Sbordone (2002) for the U.S.A., Galí et al. (2001) and McAda and Willan (2003) for the euro area and Jondeau and Le Bihan (2005) for the large EU countries. 4 See Balakrishnan and López-Salido (2002), Bårdsen et al. (2004), Freystätter (2003) and Søndergaard (2003). Monetary Policy & the Econoy Q4/06 57

4 One reason for the low epirical explanatory power of the NKPC for soe countries is that real unit labor costs are not sufficiently representative of firs total cost. For any firs, the cost of interediate inputs plays just as iportant a role and should therefore be taken into consideration in the proxy for arginal cost. However, it ust be noted that a large fraction of interediate inputs are iported, which eans they are subject to different often ore dynaic price developents than doestic interediate inputs. Taking these considerations into account yields an epirically ore relevant proxy for the arginal cost variable of the Phillips curve, which contains not just unit labor costs but also the prices of iported and doestically produced interediate inputs. Therefore, the NKPC odel is extended by two production factors in addition to doestic labor, naely iported as well as doestic interediate inputs. Moreover, openeconoy aspects are built into the odel by incorporating international trade both at the final deand and at the interediate input level. Thus, the odel accounts for the fact that the fir-specific deand function and the arginal cost depend also on foreign variables. 5 Maxiizing future discounted profits of a representative fir assuing Calvo pricing with the restriction that part of the price-setting firs follow a backward-looking rule of thub yields a hybrid NKPC (linearized) for this open-econoy odel. θβ ω π = E π + π + t t t+ 1 t 1 ( 1 θ ω θβ + )( 1 )( 1 ) ε ( φ 1 ) + c t, 1 (5) with θ representing the part of firs that do not adjust their prices in a given period, β the steady-state dis- count factor, ω the fraction of firs following the backward-looking rule of thub, ε the elasticity of deand and = θ+ω[1 θ(1 β)]. The ain difference between the open-econoy NKPC and the standard odel in equation (4) is the arginal-cost expression (in square brackets), which now contains a nuber of additional variables: s d + s f s f sˆ nt ( φ 1) yˆ t ( 1 ( pˆ φ) ( s d + s f ) d t pˆ f t ) 1+ ( 1 φ) ( s d + s f ) s d s d s n d ct = ( 1 ρ) + ρ wˆ ˆ t pt sn + s d + s f + s d s s s f d s f ( )( + ) n φ s f s f s n f ( 1 ρ) + ρ wˆ pˆ t t sn + s d + s f 1+ 1 φ ( )( + ) + + s s s s s d f n d f ( ) ( ) (6) 5 Siilar Phillips curve odels that take open-econoy aspects into account can be found in the contributions of Leith and Malley (2003), Batini et al. (2005), and Razin and Yuen (2002). 58 Monetary Policy & the Econoy Q4/06

5 with, s n, s d and s f representing shares of labor (n), doestic interediate inputs ( d ) and iported interediate inputs ( f ) in total doestic production, ρ denoting the elasticity of substitution between the input factors, and φ ( f ) ( d f ) ( ε = 1 ) 1 + s + s d ε s + s + s n The variables, w, p d and p f, in turn, represent the prices of the input factors labor (wages), doestic and iported interediate inputs. Hatted variables denote deviations fro the steady state, and barred variables represent steady-state values. Equation (6) shows that unlike in the standard odel, arginal cost is not just a function of real unit labor cost, s n, but also of the relative prices of the three production factors (1) doestic labor and doestic interediate inputs (real wages), w p d, (2) doestic labor and iported interediate inputs, w p f, and (3) doestic and iported interediate inputs (the ters of trade), p d p f. The weights with which the relative prices of the three production factors enter arginal cost are deterined by their steady-state shares and the elasticity of substitution between the. Hence, this general forulation of the open-econoy NKPC nests the existing forulations for closed econoies and for open econoies exclusive of doestic interediate inputs: if the share of doestic interediate inputs in production is set at s d = 0, we obtain the open-econoy Phillips curve odel of Leith and Malley (2003); if we additionally set the share of iported interediate inputs at s f = 0, the odel yields the standard closed-econoy specification of equation (4) Epirical Approach In a next step, the structural paraeters of the NKPC presented in equations (5) and (6) are estiated for Austrian data fro the first quarter of 1980 to the second quarter of Data fro the third quarter of 2003 to the second quarter of 2006 are used to evaluate the NKPC s forecasting perforance. As the estiation equation contains rational expectations (first ter on the right-hand side of equation (5)), and a correlation between the error ter and the regressors is therefore to be expected, an estiation ethod with instruental variables should be used. Consequently, we use the generalized ethod of oents (GMM) approach, which is frequently used in the literature for this type of odel (Galí et al., 2005). The odel is estiated in three different specifications SP1 for closed econoies, SP2 for open econoies without doestic interediate inputs and SP3 for the general for to allow conclusions about the estiated degree of price rigidity and inflation persistence to be drawn for the different odel assuptions of arginal costs. Using various easures of fit, we then deterine which of the three specifications can explain inflation dynaics in Austria best in the period under review. Following the procedure used by others in the literature, the rate of change of the GDP deflator at the quarterly frequency is used as the dependent variable of the inflation rate in the regressions, real unit labor cost, s n, is defined as the noinal total copensation to eployees divided by noinal GDP, and s d as well as s f are the ratios of doestically Monetary Policy & the Econoy Q4/06 59

6 produced and iported interediate inputs to noinal GDP. 6 γ denotes real GDP, doestic noinal wages per eployee are used for w, and the doestic GDP deflator and the iport deflator are used as proxies for p d and p f, respectively. The data ste fro the Austrian Syste of National Accounts (ESA 79 until 1988, ESA 95 fro 1988); input/output tables available for the review period were used to separate interediate inputs into doestic and iported shares. 3 Results 3.1 Estiation for Austria Table 1 suarizes the estiation results of the structural paraeters of equations (5) and (6) for odel specifications SP1, SP2 and SP3. The coluns contain the estiated coefficients for the share of firs that keep prices fixed in a given period (the Calvo probability of not changing a price), θ ˆ, ˆθ, for the firs discount factor, β, βˆ, ˆ for the share of firs that follow a backward-looking rule of thub, ωˆ, ωˆωˆ and for the elasticity of substitution between input factors, ρˆ. The standard errors of the coefficient estiators are given in parentheses. The adjustent frequency of prices, 1 θˆ,, ay be used to derive the iplicit average duration of prices using the forula 1/(1 θˆ.θ.θ) This duration, easured in onths, 7 is stated in the last colun. The Calvo probability of changing a price, θ, is frequently referred to as the NKPC s price rigidity paraeter in the literature. Under specification SP1 (closed econoy; standard NKPC), 68% of all Austrian firs leave their prices unchanged during a given quarter. This iplies an average price duration of 9.5 onths. For specification SP2 (open econoy without doestic interediate inputs), the degree of acroeconoic price rigidity is estiated at 0.45, which corresponds to an average 5.5 onth price duration. The difference between the estiated degree of acroeconoic price rigidity in each specification is thus likely to be attributable to the odeling of arginal cost: The SP2 specification includes iport prices as a key deter- Table 1 Estiation of the Structural Paraeters of Model Specifications SP1, SP2 and SP3 for the Extended New Keynesian Phillips Curve Model for Austria Dependent variable: Inflation rate of the GDP deflator quarter on quarter changes θˆ βˆ ωˆ ρˆ Iplied price duration in onths SP (0.16) 1.02 (0.12) 0.52 (0.20) x 9.5 SP (0.09) 0.95 (0.08) 0.52 (0.09) 3.83 (2.07) 5.5 SP (0.14) 0.97 (0.06) 0.32 (0.18) 4.07 (3.79) 9.7 Instruent variables: Rate of inflation lags 2 to 4, wage inflation lags 1 to 4, real unit labor cost lags 1 to 6, ratio of wages to iport prices lags 1 to 4. Source: Author s calculations. Note: The estiation ethod is GMM. Newey-West standard errors are given in parentheses. 6 Unlike the paraeters θ, β, ω and ρ, firs deand elasticity, ε, cannot be estiated epirically, as it is not explicitly included in the estiation equation. The coon practice in the literature is followed to obtain an epirical value for /o/o/o by calibrating deand elasticity with a value of 11, which iplies a steady-state arkup of 10% (Galí et al., 2001). 7 To give the duration in onths, 1/(1 θˆθ) has to be ultiplied by 3, as θ is estiated with quarterly data. 60 Monetary Policy & the Econoy Q4/06

7 inant of arginal costs in addition to real unit labor cost. As a rule, iport prices exhibit a ore volatile developent than the cost of doestic labor, possibly propting firs that use a large share of iported interediate inputs in production to adjust prices ore often. Consequently, the estiation results confir the hypothesis that the extension of the odel to include open-econoy aspects has a significant 8 influence on the estiated degree of price rigidity. Interestingly, for the general specification of the extended odel SP3 (which includes both doestic and iported interediate inputs), the price rigidity estiate of 0.69 is again slightly higher than that for SP2, but roughly of the sae order as that for the SP1 closed-econoy specification. The SP3 value ay be higher than that for SP2 because doestic firs ay have substituted doestic interediate inputs for iported interediate inputs (provided the production process allows for such a substitution) owing to fluctuations of the relative prices of the two input factors. Such a substitution would neutralize the ipact of price fluctuations of iported interediate inputs on arginal cost and would reduce the need of a fir to adjust its prices. Thus, the estiated degree of price rigidity of the Austrian econoy differs depending on the specification of the NKPC. Now, to answer the question which of these values is ost appropriate, one has to evaluate the different specifications by eans of econoetric easures of fit. 9 Copared with other euro area countries, Austria exhibits an estiated degree of price rigidity that is neither especially high nor especially low: Ruler (2006) estiated the structural paraeters of the extended NKPC for a total of nine euro area countries (euro area except Ireland, Luxebourg and Portugal). According to this study, Austria s values of θ place it fifth out of the nine countries. Gerany displayed the highest degree of price rigidity aong these countries, followed by Belgiu, whereas price rigidity was estiated to be lowest in Greece and the Netherlands. An additional coparison ay be ade using the results of a study on price-setting behavior in Austria in which the degree of price rigidity was estiated on the basis of icro CPI data (Baugartner et al., 2005). The study finds that the average duration of a price spell for all products represented in the CPI is about 11 onths. This value is roughly coparable to the estiated price duration of just under 10 onths for SP1 and SP3, but is arkedly higher than the price duration estiated for SP2. However, 8 A test of whether this difference in the paraeter estiates of SP1 (0.68) and SP2 (0.45) is also statistically significant shows only a arginally significant difference (significance level: 15%); see Ruler (2006). However, as the two paraeter values iply a difference in the average price duration of four onths, the difference is at least econoically significant. 9 The results refer to the estiation period Q to Q To verify the robustness of the results, the odel was also estiated for the period Q to Q However, the fundaental revision of Austrian national accounts data in 2004, when all series were also adjusted retroactively, akes the coparison of the results probleatic. Despite this revision, the results reain qualitatively unchanged for the longer estiation period. The results for θ ay serve as an exaple: For the longer estiation period, SP3 exhibits the highest θ at 0.66, followed by SP1 at 0.64 and SP2 at Hence, the agnitude of the coefficients and the ranks of the specifications for θ are hardly different. Overall, the additional estiation confirs that the results of table 1 are also robust for a longer estiation period and revised data. Monetary Policy & the Econoy Q4/06 61

8 three iportant differences between the two studies ipair the coparison: the period reviewed (1996 to 2003 in the icro CPI survey versus 1980 to 2003 in this study), the data base (icro CPI data versus acro tie series of the GDP deflator) and the ethod (price duration easured directly fro price data versus GMM estiates fro a structural odel). According to the NKCP theory, the discount factor, β, which corresponds to the reciprocal value of the steady-state real interest rate, should exhibit a value of close to but below The estiates for SP2 and SP3 are in line with this theory. However, as the coefficients were estiated with uncertainty, values arginally higher than 1 like for SP1 do not represent a proble either, as long as they are not significantly higher than 1. The paraeter ω, which gives the fraction of firs that follow the backward-looking rule of thub in setting prices, is directly linked to inflation persistence: The higher ω is, the higher is inflation persistence as easured by the GDP deflator. The estiation results show that the share of backward-looking firs in Austria coes to 30% to 50%, iplying that the degree of inflation persistence in Austria is fairly high. This result is broadly confired in a cross-country coparison, as well as in other studies that exaine inflation persistence in Austria epirically (Ruler, 2006; Cecchetti and Debelle, 2005; Gadzinski and Orlandi, 2004). Moreover, we found that the specification of a closed versus an open econoy of the NKPC has no ipact on ω, as the estiation values of SP1 and SP2 are nearly the sae. Only for SP3 did the estiates result in a soewhat lower ω, which nevertheless reains high in an international coparison. The elasticity of substitution between the input factors of the production function, ρ, cannot be estiated for SP1, as this specification contains only one variable production factor (labor). In the case of SP2, ρ denotes the elasticity of substitution between labor and iported interediate inputs. This elasticity is fairly high, posting an estiated value of 3.8, and is also statistically significant. 11 A negative elasticity of substitution between the production factors albeit not statistically significant is estiated for SP3. This result could reflect the fact that a constant elasticity of substitution between the three production factors is hard to estiate with the available data, because the actual substitution is possibly not the sae between all production factors. 3.2 Identifying the Specification with the Highest Explanatory Power An evaluation of the inflation rates iplied by SP1, SP2 or SP3 ay help deterine which of the three specifications is best suited to characterize the Austrian inflation dynaics during the period observed. The idea of using this iplied inflation rate also called fundaental rate of inflation to evaluate the explanatory power of the NKPC goes back to Galí and Gertler (1999). The fundaental rate of inflation is derived fro the pres- 10 An estiated value of 0.99 for β would, for instance, correspond to an average real interest rate of around 1% per β quarter during the estiation period. 11 A value of 1 would iply a Cobb-Douglas production function. 62 Monetary Policy & the Econoy Q4/06

9 Coparison between Fundaental Rates of Inflation of SP1, SP2 and SP3 and the Actual Inflation Rate Quarterly change in % Chart 1 FUNDINF SP1 Actual inflation rate FUNDINF SP2 Actual inflation rate FUNDINF SP3 Actual inflation rate Source: Author s calculations. Measures of Fit of the Iplied Fundaental Rate of Inflation Derived fro SP1, SP2 and SP3 and the Actual Developent of Inflation Table 2 StDev(л * t ) t StDev(л t ) Corr (л * t,л t ) RMsD (л * t,л t ) Rank SP SP SP Source: Author s calculations. Monetary Policy & the Econoy Q4/06 63

10 ent value forulation of the NKPC, which presents the inflation rate as the su of present and all expected future arginal costs. 12 For the evaluation, the following three coon easures of fit are used to copare the fundaental rate of inflation, π * t, for each specification with the actual developent of inflation, π t (1) the ratio of the standard deviation of the fundaental and the actual rate of inflation, StDev(π * t )/ StDev(π t ), (2) the correlation coefficient between the fundaental and the actual rate of inflation, Corr(π * t, π t ), and (3) the root ean squared deviation of the fundaental rate of inflation fro the actual inflation rate, RMSD(π * t, π t ). Chart 1 copares fundaental inflation as derived fro SP1, SP2 and SP3 and actual inflation developents (quarter on quarter) fro 1980 to Overall, chart 1 shows that all three specifications of the NKPC explain inflation developents in Austria during the observation period fairly well. The deviations fro the actual developents were soewhat ore pronounced only in the first third of the observation period (until about 1987), when inflationary developents were generally slightly ore volatile. Moreover, specification SP1 is found to trace actual developents best. A siple eyeball inspection of the iddle (SP2) and lower (SP3) panels in chart 1 does not induce a clear preference for one or the other specification. Hence, the coparison should be based on the easures of fit defined above. Table 2 shows the three easures of fit of the fundaental inflation rate with actual inflation and ranks the specifications perforance resulting fro the total of all three easures. The data confir the graphic analysis that specification SP1 displays the highest explanatory power for Austrian inflation developents during the observation period: The ratio of standard deviations in the first two rows is close to the optiu value of 1, the correlation is highest with a value of just under 0.5, and the root ean squared deviation of the fundaental fro the actual inflation rate is lowest aong the three specifications. According to the easures of fit, specification SP3 has the secondhighest explanatory power, as both the deviation fro the optiu value of the ratio of standard deviations and the root ean squared deviation are saller than in the case of SP2, and the correlation coefficient for SP3 is larger than that for SP2. Thus, the closed-econoy specification of the NKPC, SP1, exhibits the highest explanatory power for Austrian inflation developents in the period fro 1980 to 2003, followed by the general open-econoy specification, SP3, and the specification with only iported interediate inputs as an additional production factor, SP2. For the estiated degree of price rigidity (table 1), this eans that the value for θ estiated at just under 0.7 for both SP1 and SP3 is likely to be ore accurate than the lower price rigidity estiate of 0.45 for SP2. Moreover, the average price duration of just under 10 onths derived fro the higher value also corresponds better to the price duration of 11 onths derived fro the icro CPI data. However, this result SP1 12 For ore detailed inforation on the derivation and calculation of the fundaental inflation rate, see Ruler (2006). 64 Monetary Policy & the Econoy Q4/06

11 exhibiting the highest explanatory power does not ean that the extension of the NKPC for Austria is irrelevant. On the one hand, the perforance of SP1 proves to be only arginally better than that of SP3, and on the other hand, there is another iportant criterion for the perforance of the NKPC, and this criterion has not yet been taken into account: the plausibility of the estiates of the reduced for odel. In particular, it is relevant whether the respective arginal cost ter is significant, as a proble with the identification of the structural paraeters arises if it is not (Guay and Pelgrin, 2004). According to this criterion, SP3 should be preferred over SP1 and SP2, as SP3 is the only specification in which arginal cost provides a significant contribution to explaining inflation developents (Ruler, 2006). Hence, based on these considerations, one ay infer that only SP2 was isspecified for Austria, and thus the relatively low price rigidity estiate of this specification is likely to be inappropriate. 4 Inflation Forecasting Using the New Keynesian Phillips Curve The NKPC is used as a structural odel above all to explain past inflation developents, but is not generally used to forecast inflation. 13 In this section, an attept is ade to eploy the NKPC odel for forecasting purposes. The starting point is the concept of the fundaental inflation rate, which is adapted to produce an inflation forecast, reporting current inflation as the su of current and expected discounted future arginal costs. To construct a easure of fundaental inflation, a forecast of future arginal cost ust be ade on the basis of an econoetric odel. Galí and Gertler (1999) propose a bivariate vector autoregressive (VAR) odel with the variables inflation and arginal cost for this purpose. If the forecast of future arginal cost is lagged by one period, so that a forecast of current and expected future arginal cost is provided fro the perspective of the last period, this forecast ay be used to construct the current fundaental inflation rate. This fundaental rate of inflation expected fro the perspective of the past period is interpreted as the inflation forecast, i.e. based on inforation fro period t a forecast of the in- flation rate iplied by the odel is calculated for t+1, and iteratively for t+2, t+3 etc. To evaluate the predictive power of the NKPC, out-of-saple forecasts were ade for each of the three specifications for the period ranging fro the third quarter of 2003 (end of the estiation period) up to the second quarter of 2006 (end of the saple period). Chart 2 shows these inflation forecasts and the actual inflation developents for this period, with a forecasting horizon of one quarter (left panel) and four quarters (right panel). Thus, the colored lines in the chart represent the stacked forecast values over the respective forecasting horizons. Chart 2 shows that pronounced forecasting errors are concentrated in the first half of the evaluation period for both forecasting horizons; forecasts converge and hence display saller forecasting errors in the second half of the period. Forecasting errors are naturally saller for the 13 In the literature no contribution was found that uses the NKPC for inflation forecasting. Monetary Policy & the Econoy Q4/06 65

12 Inflation Forecasts Based on SP1, SP2 and SP3 and Actual Inflation Developents One quarter out-of-saple forecasts Four quarters out-of-saple forecasts Quarterly change in % Quarterly change in % Chart Forecast SP1 Forecast SP2 Forecast SP3 Actual inflation rate Source: Author s calculations. Root Mean Square Forecasting Error (RMSE) for Inflation Forecasts based on SP1, SP2 and SP3 and the Naive Forecast by Forecasting Horizon Table 3 RMSE One quarter out-of-saple forecasts RMSE Four quarters out-of-saple forecasts SP SP SP Naive Source: Author s calculations. shorter horizon (left panel) than for the four-quarter horizon (right panel). Interestingly, the three specifications perfor quite differently for the different forecasting horizons. According to the chart, specification SP1 appears to perfor best for the short forecasting horizon, whereas specification SP3 sees to deliver the best forecast for the longer forecasting horizon. Table 3 confirs the ipression gained by the visual inspection of chart 2 that the specifications display differences in the relative forecasting perforance for both forecasting horizons. We use a coon easure to evaluate forecasting perforance, naely the root ean square forecasting error (RMSE) for each forecasting horizon. The last line of the table provides naive forecast (rando walk forecast) figures as a benchark to gauge the forecasting accuracy. The naive forecast assues a flat forecasting profile of the inflation rate over the respective forecasting horizon (with the forecast equaling the last period s actual value). The naive forecast is frequently used as a benchark in the epirical literature, as it has proved to be hard to outperfor in the ediu to long ter for any acroeconoic variables, aong the also inflation. 66 Monetary Policy & the Econoy Q4/06

13 For the forecasting horizon of one quarter, specification SP1 has the lowest RMSE at 0.14, followed by SP2 and SP3. However, the naive forecast still perfors best, with an RMSE of 0.13 for the one-quarter horizon, and it perfors best for the four-quarter forecasting horizon at 0.21, copared with 0.25 for SP3 and uch higher results for SP1 and SP2. Thus, the evaluation of the forecasting quality of the NKPC deonstrates a fairly poor perforance for the Phillips curve odel it cannot beat a naive forecast, neither over a short- nor over a longer-ter forecasting horizon. One reason could be the relatively coplex construction of the inflation forecast, which is based on a forecast of future arginal cost using a bivariate VAR odel. Thus, the quality of the inflation forecast depends directly on the quality of the forecast of future arginal cost. The arginal cost forecast, in turn, is based on a very siple ethod whose quality cannot be verified, as the discounted su of all future arginal costs is not observable. Given these results, NKPC odels are not suited as an alternative to econoetric tie-series odels for inflation forecasts, especially because in the short ter (up to one year), tie-series odels usually clearly outperfor the naive forecast (Benalal et al., 2004). Hence, it ay be noted that the NKPC is better suited to explain inflation developents ex post and to estiate the structural paraeters of the price-setting process than to inflation forecasting. 5 Conclusions The NKPC is a structural odel to explain inflation dynaics. The odel is helpful in estiating the structural paraeters of the pricesetting process in an econoy. The resulting paraeter values in the estiation largely depend on the odel specification used. As the NKPC was originally conceived for a closedeconoy setting, it should be adapted accordingly if it is estiated for an open econoy such as Austria. The NKPC odel presented in this study is extended to account for open-econoy effects and is additionally extended by interediate inputs; it thus nests the standard closed-econoy odel as a special case. The estiates for the paraeter representing structural price rigidity differ depending on the odel specification: they are higher for the closed-econoy specification and for the general forulation of the extended NKPC (with both doestic and iported interediate inputs) than for the specification that contains only iported interediate inputs. One reason could be ore frequent price adjustents by firs that do not have the option of substituting doestic interediate inputs (with less volatile prices) for iported interediate inputs (that are subject to stronger price fluctuations resulting e.g. fro exchange rate fluctuations or volatile coodity prices). However, on evaluating the different specifications using econoetric easures of fit, we deterined that SP2, which results in a lower degree of price rigidity, is likely to be isspecified. According to the easures of fit, the general forulation of the extended NKPC odel and the standard closed-econoy odel are about equally well suited to explaining inflation developents in Austria since The estiated degree of price rigidity is also roughly equal in both specifications: They both show Monetary Policy & the Econoy Q4/06 67

14 that soewhat ore than 30% of all firs adjust their prices in a given quarter, which eans that a single fir s prices reain unchanged for an average of just under ten onths. This value is neither very high nor very low by coparison to other euro area countries, and it roughly atches the average price duration derived fro Austrian icro CPI data. The estiation of the structural paraeters shows that depending on the specification, 30% to 50% of all Austrian firs follow a backwardlooking rule of thub in updating their prices. This iplies a fairly high degree of inflation persistence, also by international standards, which is generally confired by other ulticountry studies on this topic. A high degree of inflation persistence has iplications for econoic policyaking, as pertinent studies show that it dapens the transission of specific types of acroeconoic shocks on the inflation rate. For instance, the ipact of an oil price shock on inflation is ore subdued but lasts longer if inflation persistence is high. At the sae tie, though, a high degree of inflation persistence triggers a stronger output reaction to an oil price shock, which eans that in the case of a supply shock, the inflation-output variability trade-off shifts in favor of inflation and to the disadvantage of output (Altissio et al., 2006). The result of an exaination of the NKPC s suitability as an inflation forecasting tool for Austria was rather disappointing. The results obtained using the NKPC fell short of those obtained with the naive forecast (the forecast equals the last period s actual value) both over the one-quarter and the four-quarter forecasting horizons. Thus, the NKPC does not appear to be useful as a forecasting alternative to the established tie-series odels, which perfor far better over a shortter forecasting horizon of up to one year. However, it ay by all eans copleent tie-series odels as a structural odel in which firs pricing is deterined by their expectations of the developent of their future arginal costs. Inflation forecasting using the NKPC is an indirect approach, as it is based on a forecast of future arginal cost developents. Depending on the specification, this approach indirectly accounts for labor cost developents and the price developents of doestic and iported interediate inputs. However, this ethod has the disadvantage that a forecast based on such a two-stage construction does not lend itself very well to econoic interpretation. References Altissio, F., M. Ehrann and F. Sets Inflation Persistence and Price-setting Behaviour in the Euro Area A Suary of the IPN Evidence. ECB Occasional Paper 46. Balakrishnan, J. and J. D. López-Salido Understanding UK Inflation: The Role of Openness. Bank of England. Working Paper 164. Bårdsen, G., E. S. Jansen and R. Nyoen Econoetric Evaluation of the New Keynesian Phillips Curve. In: Oxford Bulletin of Econoics and Statistics 66(S1) Batini, N., B. Jackson and S. Nickell An Open-Econoy New Keynesian Phillips Curve for the U.K. In: Journal of Monetary Econoics Monetary Policy & the Econoy Q4/06

15 Baugartner, J., E. Glatzer, F. Ruler and A. Stiglbauer How Frequently Do Consuer Prices Change in Austria? Evidence fro Micro CPI Data. ECB Working Paper 523. Benalal, N., J. L. Diaz del Hoyo, B. Landau, M. Roa and F. Skudelny To Aggregate or Not to Aggregate? Euro Area Inflation Forecasting. ECB Working Paper 374. Calvo, G Staggered Prices in a Utility-Maxiizing Fraework. In: Journal of Monetary Econoics 12(3) Freystätter, H Price Setting Behavior in an Open Econoy and the Deterination of Finnish Foreign Trade Prices. Bank of Finland Studies in Econoics and Finance E25. Gadzinski, G. and F. Orlandi Inflation Persistence in the European Union, the Euro Area, and the United States. ECB Working Paper 414. Cecchetti, S. G. and G. Debelle Has the Inflation Process Changed? BIS Working Paper 185. Galí, J. and M. Gertler Inflation Dynaics: A Structural Econoetric Analysis. In: Journal of Monetary Econoics Galí, J., M. Gertler and J. D. López-Salido European Inflation Dynaics. In: European Econoic Review Galí, J., M. Gertler and J. D. López-Salido Robustness of the Estiates of the Hybrid New Keynesian Phillips Curve. In: Journal of Monetary Econoics Goodfriend, M. and R. King The New Neo-Classical Synthesis and the Role of Monetary Policy. NBER Macroeconoics Manual Guay, A. and F. Pelgrin The U.S. New Keynesian Phillips Curve: An Epirical Assessent. Bank of Canada Working Paper Jondeau, E. and H. Le Bihan Testing for the New Keynesian Phillips Curve. Additional International Evidence. In: Econoic Modelling 22(3) Leith, C. and J. Malley Estiated Open Econoy New Keynesian Phillips Curves for the G7. CESifo Working Paper 834. McAda, P. and A. Willan New Keynesian Phillips Curves: A Reassessent Using Euro Area Data. ECB Working Paper 265. Razin, A. and C. W. Yuen The New Keynesian Phillips Curve: Closed Econoy versus Open Econoy. In: Econoic Letters 75(1) Ruler, F Estiates of the Open Econoy New Keynesian Phillips Curve for Euro Area Countries. In: Open Econoies Review. Forthcoing. Sbordone, A. M Prices and Unit Labor Costs: A New Test of Price Stickiness. In: Journal of Monetary Econoics Søndergaard, L Inflation Dynaics in the Traded Sectors of France, Italy and Spain. Essays on Inflation Dynaics. Doctoral thesis at Georgetown University (Washington D.C.), Econoics Departent. Monetary Policy & the Econoy Q4/06 69