THE OUTPUT-INFLATION TRADE-OFF:

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1 THE OUTPUT-INFLATION TRADE-OFF: INTERNATIONAL PANEL DATA EVIDENCE * DIMITRIOS BAKAS Department of Economics, University of Athens, Greece, and Rimini Centre for Economic Analysis (RCEA),Italy dbakas@econ.uoa.gr and GEORGIOS CHORTAREAS* Department of Management King's College London gchortar@econ.uoa.gr May 2015 ABSTRACT This paper re-examines the output-inflation trade-off using panel data techniques, extending previous empirical studies that are restricted either to a cross-country or a country-by-country time-series approach. Our panel data analysis controls for non-stationarity of the series and dynamics in the specification form, while allows for potential cross-country heterogeneity and the presence of cross-sectional dependence. We provide empirical evidence covering a sample of 60 countries over the period The results suggest that the slope of the Phillips curve as measured by the trade-off between output and inflation is higher at lower rates of inflation. These findings corroborate the New Keynesian view of a negative association between the rate of inflation and the output-inflation trade-off. Keywords: Output Inflation Trade-off Dynamic Panel Data Parameter Heterogeneity Cross-Sectional Dependence. JEL Classification: E31 E12 C23 * (Corresponding author) Georgios Chortareas, Department of Management, King's College London, Franklin-Wilkins Building, 150 Stamford Street, London SE19NH, UK. Tel +44 (0) georgios.chortareas@kcl.ac.uk

2 1 INTRODUCTION In the aftermath of the Great Moderation and the advent of the recent economic crisis, there is a renewed interest in the trade-off between output and inflation and thus on the controversy over the real effects of nominal aggregate demand shocks both on theoretical (Alex Ho and Yetman, 2008; Benigno and Ricci, 2011; Eggertsson and Giannoni, 2013), and empirical level (Abbott and Martinez, 2008; De Veirman, 2009; Fendel and Rulke, 2012; Sun, 2014). Furthermore, a growing number of papers report that the dynamics of both the persistence (Carlstrom et al., 2009) and the volatility (Summers, 2005) of inflation have changed significantly since the early 1980s in advanced economies, and in addition, there are several works that present evidence of significant changes in the slope of the short-run Phillips curve (Mishkin, 2007; Kuttner and Robinson, 2010). These changes in the shape of the Phillips curve could also reflect time variation in the slope and can be captured by its determinants as suggested in the literature, see Ball and Mazumder (2011). Therefore, there is a need for a re-examination of inflation dynamics and a further exploration of the factors that determine the slope of the Phillips curve and their significance. The debate on the output inflation trade-off starts with the seminal paper of Lucas (1973) who supports that the trade-off was occurred due to the difficulty of producers to distinguish between changes in relative prices and the general price level. Thus, expectations of producers rely on the variability of relative prices to the general price level. Lucas (1973) model implies that there exists a negative relationship between the trade-off parameter and the variability of the inflation rate as well as the variability of the change of nominal aggregate demand. Ball et al. (1988) (hereafter BMR) offer an innovative attack on Lucas (1973) approach and propose a model where the real effects of nominal aggregate demand shocks depend on the frequency of price changes. They argued that a higher inflation rate increases the frequency of price adjustments and decreases the real effects of a nominal shock. As a result, the output inflation trade-off depends also on the mean rate of inflation. Thus, the Ball et al. (1988) approach has two testable hypotheses to be examined. The first hypothesis (common with the Neo-classical view of Lucas (1973)) asks whether there exists a negative association between the variance of nominal shocks and the output-inflation trade-off, and, the second testable hypothesis (only in the New-Keynesian view of Ball et al. (1988)) is about the examination of a negative association between the average rate of inflation and the output-inflation 1

3 trade-off. The empirical evidence on the output inflation trade-off is mixed. While early tests find support for the basic implication of the Neo-classical model (Alberro, 1981; Koskela and Viren, 1980; Jung, 1985), more recent research have questioned it (Froyen and Waud, 1985; Katsimbris, 1990a;b). The support for the Neo-classical model generally weakens as the analysis moves from cross-country to time series analysis, as concluded by Katsimbris and Miller (1996). Ball et al. (1988) using a sample of 43 countries, test the prediction of their New Keynesian model by exploring the empirical relationship between the output-inflation trade-off and the average inflation after controlling for aggregate demand variability. They employ the empirical strategy of Lucas (1973) by using a two-step procedure. In the first step, they use a standard Lucas supply curve to estimate the short-run output-inflation trade-off, where real output is regressed on its own lag, the rate of change of nominal GDP, and a time trend, as time-series regressions for each country. In the second step, they estimate a cross-section regression of the estimated output-inflation trade-off coefficients on the mean rate of inflation and the volatility of aggregate demand growth and/or the volatility of the inflation rate. Their results are supportive of the New Keynesian hypothesis, and suggest that a significant negative correlation between the short-run output-inflation trade-off and the average inflation rate exists. Akerlof et al. (1988) (hereafter ARY), however, criticize the BMR approach since they observed that the mean rate of inflation and the variability of nominal demand are highly correlated, and thus, BMR s test is inevitably a weak test of their theory against Lucas s theory. They use extended cross-country regression equations to the original version of BMR test, by employing alternative non-linear specification, and find no support for the new Keynesian hypothesis. In a related work, DeFina (1991) uses BMR s data to produce intertemporal tests of their hypotheses following a one-step procedure. For each of the 43 countries, he estimates an aggregate supply function in which the output-inflation trade-off coefficient is a function of both the average inflation rate and the variability of inflation (or aggregate demand). DeFina (1991) finds a significant effect of persistent inflation on the output-inflation trade-off coefficient in 13 of the 43 countries and concludes that his evidence confirm the cross-country results of BMR. DeFina s (1991) approach is appealing since it overcomes the two-stage cross-country methodology and allows for time-series variation of the independent variables as well as for a time-varying trade-off parameter. 1 Katsimbris and Miller (1996), subsequently, using the same data set, re-estimate BMR and ARY 2

4 regressions using both time series and pooled cross-section analysis and find nearly equal (but weak) support for the Neo-classical and the New-Keynesian models. Furthermore, Yates and Chapple (1996) using the same sample of 43 countries covered by BMR, and extending the time dimension of the series, examine the robustness of BMR findings. Their empirical investigation shows that BMR results are robust to a number of different experiments they have employed. Following a different approach, Hess and Shin (1999) explore the intranational output-inflation trade-off for the U.S. by considering states and industries as markets within the country. They conclude that the Lucas model omits New Keynesian aspects of the intranational data. Asai (1999) proposes a time-series testing procedure of the BMR approach in which he takes into account for the effects of a unit root in real/nominal output, and models time varying variance of inflation rate using ARCH models. He concludes to support the New-Keynesian hypothesis. Khan (2004) extends BMR approach and investigates a third hypothesis that trend inflation has a negative and significant effect on output persistence within countries. He finds strong support only for the BMR hypothesis that high trend inflation leads to smaller impact effect of nominal demand shocks. Recently, Abbott and Martinez (2008) use an extended dataset and examine both the BMR and Lucas hypothesis by employing the two step approach while they control for non-stationarity of the series. Their findings reinforce past evidence regarding the relationship between real responsiveness and nominal volatility but are inconclusive regarding the impact of mean inflation. De Veirman (2009) assess the empirical evidence of the two classes of models (BMR and Lucas) for Japan and result in favor of the endogenous pricing models that imply that declining trend inflation causes the Phillips curve to flatten. Fendel and Rulke (2012) provide empirical evidence on the Lucas supply function based on actual inflation surprises for 19 industrial economies. They find a negative relation between the slope parameter and the inflation variability and thus support the New-classical view. Finally, Sun (2014) evaluates four different estimation approaches that have been applied in the literature to examine the New Keynesian hypothesis, and indicates that the one-stage country by country time-series procedure is superior. Her results are in line with the New Keynesian hypothesis that nominal rigidity is an important determinant of the trade-off. While there are numerous papers that empirically examine the existence of a trade-off and its determinants across countries and over time using cross-section and time-series analysis, there is no work that exploits both - time and cross-section - dimensions into a panel framework. In this direction, 3

5 we propose a testable extension of the specification used by Ball et al. (1988) and Akerlof et al. (1988) and by incorporating the DeFina (1991) approach of a time-varying trade-off we examine the determinants of the output-inflation trade-off on a panel dataset of 60 countries over the period It is evident, in the literature, that the estimated trade-off coefficient varies across countries (Akerlof et al., 1988), as well as that it is present a significant variation in the estimated size of both inflation and its variability effects on the trade-off (DeFina, 1991). Byrne et al. (2013), likewise, emphasize on the importance of heterogeneity in inflation dynamics. Therefore the assumption of homogeneous dynamics on the impact of the trade-off determinants across countries can lead to inconsistent estimates (Pesaran and Smith, 1995). Furthermore, an important characteristic of macroeconomic variables is that they are interconnected across countries (Bailey et al., 2012), and thus, it is expected that the errors of panel data regressions using macroeconomic variables are cross-sectionally correlated. This interdependence exists due to a limited number of strong factors, associated with global and/or aggregate common shocks that have heterogeneous impact across countries, and an infinite number of weak factors, such as local spillover effects between countries or regions (Chudik et al., 2011). Ignoring cross-sectional dependence of errors, conventional panel estimators can lead to inconsistent estimates of the slope parameters and misleading inference. Hence, unlike previous empirical evidence, we exploit the panel nature of the data and focus on estimation methodologies, for the determinants of the output-inflation trade-off, that allow for cross-country heterogeneity and cross-sectional dependence to gain more precise estimates of these effects. Taking into account of all preceding issues, the present paper contributes to the literature in four ways. First, we extend the analysis of Ball et al. (1988) to recent years and a wider sample of countries. Second, we extend the one-step procedure of DeFina (1991) to a heterogeneous dynamic panel framework for the first time. 2 Third, following the concerns on the work of Asai (1999) and Abbott and Martinez (2008), we control for the issue of nonstationarity of the real and nominal output, and in accordance with the work of Asai (1999) we model the time-varying variance of inflation using GARCH models, and fourth, we take advantage of recent developments in panel data methods and employ a framework that deals with empirical issues such as nonstationarity, dynamics, heterogeneity and cross-sectional dependence in the panel, overcoming misleading estimation outcomes of previous approaches on the output inflation trade-off. 4

6 Our main findings can be summarized as follows: i) there is a strong support for the New Keynesian view of a negative association between the rate of inflation and the output-inflation trade-off, that ii) remains robust to alternative samples and specification forms, while iii) there is a fairly weak evidence of a significant effect of inflation variability on the trade-off only for OECD countries over the full sample of years. iv) The results show that the significance of the estimates is not affected by the existence of non-stationarity in real/nominal GDP. Also, v) the findings hold when we employ the variability of nominal GDP instead or in addition with the variability of inflation. vi) There is no support for a nonlinear specification on the determinants of the trade-off when accounting for heterogeneity and cross-sectional dependence in the sample. Finally, vii) The evidence is robust to the specification form of both Ball et al. (1988) and Akerlof et al. (1988), as well as, viii) on the extension of Khan (2004) of a negative and significant effect of trend inflation on output persistence. The remainder of the paper is organized as follows. Section 2 discusses the econometric model and outlines the estimation methodology. Section 3 presents the data and provides the empirical results. Finally, in Section 4, concluding remarks are provided. 2 ECONOMETRIC MODEL The two stage approach of Ball et al. (1988) starts with a time series regression of a standard Lucas aggregate supply curve by regressing real output ( y t ) onto its own lagged value, the rate of change in nominal output ( x t ), and a time trend for each country i separately, as a first step. In the second step, they employ a cross-section regression of the estimated output-inflation trade-off coefficients across countries onto the rate of inflation (π i ) and the variability of the inflation rate and/or the variability of aggregate demand (σ i ). Exploring both the time-series and cross-section dimension of the data, we formulate Ball et al. (1988) equation into a dynamic heterogeneous panel data context as follows: (1) where y i,t is the logarithm of real GDP and x i,t is the logarithm of nominal GDP for country i at time t, t is a time trend, c i stands for a set of country-specific fixed effects capturing the influence of unobserved country-specific heterogeneity and u i,t is the error term. Following the method of DeFina (1991) and assuming that the trade-off τ i is time-varying and a 5

7 function of the inflation rate (π i,t ) and its variability (σ i,t ) in each time period, we can specify: (2) and, furthermore, assuming linear relationships between the trade-off parameter and the inflation rate and its variability we can combine the two step approach into a one stage regression and re-write Equation 1 as follows: (3) Finally, taking into account the existence of non-stationarity of the real and nominal output, and being into accordance with the work of Asai (1999) and Abbott and Martinez (2008), we slightly modify the panel one-step procedure and adopt a stationary specification as follows: 3 In order to allow for cross-sectional dependence in the disturbances, u i,t, we assume that they follow a multi-factor error structure: (4) where f t is a m 1 vector of unobserved common factors that capture cross-sectional dependencies (5) across countries, and i are the country specific associated factor loadings. The idiosyncratic errors,, are assumed to be independently distributed across i and t with zero mean and constant variance. The interaction terms measure the degree to which the coefficients of nominal aggregate demand vary as a consequence of changing inflation and changing inflation variability. Both, the New- Keynesian and the Neo-classical, models suggest that an increase in inflation rate variability causes a decline in the output-inflation trade-off. That is, both models suggest that β 2,i < 0. The interaction term between nominal aggregate demand with the inflation rate will allow us to discriminate between the New-Keynesian and Neo-classical models. According to the New-Keynesian model the coefficient of this interaction term is negative, that is β 1,i < 0. In other words, examination of the sign and significance of the estimated coefficient on this interaction term will indicate whether or not the 6

8 coefficient vary systematically as the New-Keynesian model suggests. The time-varying measure of inflation variability, σ i,t, has been generated by estimating a generalized autoregressive conditional heteroscedasticity (GARCH (1,1)) model for π i,t. The estimated conditional variance of π i,t is a parametric proxy of the inflation variability. 4 In order to analyze the output-inflation trade-off using panel regression we need to consider the issues of non-stationarity, dynamics, heterogeneity and cross-sectional dependence that emerge from the specification form of Equation ESTIMATION METHODOLOGY The starting point for the analysis of Equation 4 stems on traditional panel estimation methods. The fixed effects (FE) estimator allows for individual heterogeneity through different intercepts across countries but restricts slopes to be homogeneous, and can be estimated using ordinary least squares. The FE estimator lacks consistency and can be severely biased when dealing with dynamics in the specification form (Nickell, 1981). Furthermore, these standard estimators will generate inconsistent estimates in the case of a dynamic panel data model when there is presence of slope heterogeneity across countries, as presented by the work of Pesaran and Smith (1995). The homogeneity assumption of the traditional panel estimators is quite restrictive in the context of our analysis, and thus the application of pooled estimation methods will lead to substantially heterogeneity bias in the estimated parameters of the panel specification of Equation 4. Pesaran and Smith (1995) introduce a procedure to yield consistent estimates in dynamic panels with considerable heterogeneity across countries. They propose the Mean Group estimators (MG), that allows for slope heterogeneity in the panel, and consists of estimating separate OLS regressions for each country and then calculating averages of the specific coefficients over groups. A second concern, in our context, is the existence of cross-sectional dependence among countries. Interdependence across cross-sections is a significant characteristic in the analysis of macro panel data models, and estimators that rely on the assumption of cross-sectional independence becomes inefficient and inconsistent (Sarafidis and Wansbeek, 2012). In this case, we extend the heterogeneous approach of the Mean Group estimator by relying on the Common Correlated Effects (CCE) procedure of Pesaran (2006) that accounts for unobserved common factors. The CCE estimator uses cross-section averages of the dependent and independent variables as proxies for the unobserved factors and can be employed by including these proxy variables in the regression as additional regressors. The CCE 7

9 estimator provides consistent estimates of the slopes and their standard errors under the general case of a multifactor error structure as well as of a spatial error correlation (Pesaran and Tosetti, 2011). Furthermore, the CCE estimator remains consistent in the case where the unobserved factors are non-stationary as well as where there is possible contemporaneous dependence of the observed regressors with the unobserved factors (Kapetanios and Pesaran, 2007; Kapetanios et al., 2011). Coakley et al. (2006) explore the small sample properties of CCE estimators and conclude that the Mean Group version of the CCE estimator perform the best. Finally, to control for the presence of the lagged dependent variable in our specification and taking into account altogether all preceding issues, we expand our empirical methodology to the recent extension of the CCEMG estimator that proposed by Chudik and Pesaran (2013) and allows for the inclusion of lagged values of the dependent variable and/or weakly exogenous regressors in the panel data model. Chudik and Pesaran (2013) investigate the estimation of heterogeneous panel data models with lagged dependent variable and show that the dynamic CCEMG (dynccemg) extension of the CCE estimator performs well and continue to be valid asymptotically when (i) there is a sufficient number of lags of cross-section averages that included in the individual equations of the panel in addition to the cross-section averages, (ii) the number of cross-section averages have to be at least as large as the number of unobserved common factors, and (iii) the time dimension have to be large enough so that the regression can be estimated for each cross-section. Therefore, to apply the dynccemg estimator we employ the augmentation of Equation 4 with the cross-section averages of the dependent and independent variables as well as their lags as additional regressors: (1) where z i,t is a vector that contains the set of regressors,, and. We perform the estimation using different number of lags of crosssection averages up to the p T, where p T is equal to the integer part of T 1/3 as suggested by Chudik and Pesaran (2013). Controlling for cross-country heterogeneity and cross-sectional dependence is of major importance in the analysis of our dynamic panel context as the impact of inflation and its variability on the trade-off varies across countries and depends on country specific factors as well as on spillover effects 8

10 across them. We, therefore, continue our analysis by estimating the dynamic output inflation trade-off relationship for our panel, exploiting the issues of nonstationarity, dynamics, heterogeneity and cross-sectional dependence, by considering alternative estimation strategies for panel data. 2.2 PANEL DATA PROPERTIES Prior to the estimation of the panel data analysis, we need to investigate the time-series and crosssection properties of our panel data set using formal tests. Specifically, we need to check for the order of integration of the series (panel unit root tests), the assumption of cross-sectional independence among countries (cross-sectional dependence tests), and the issue of potential slopes heterogeneity across countries (poolability tests) PANEL UNIT ROOT TESTS To check for the order of integration, we use the IPS test of Im et al. (2003) as well as the CIPS test of Pesaran (2007) that accounts for cross-sectional dependence among countries. The IPS test is an extension of the univariate ADF regression as follows: (2) where y i,t stands for each series under consideration for country i at time t. The null hypothesis is that all series contains a unit root, φ i = 0 for all i (with i = 1, 2,..., N ), while the alternative hypothesis assumes that some of the N panel units are stationary with individual specific autoregressive coefficients. Im et al. (2003) propose a test based on the average of the ADF statistics computed for each individual in the panel. Specifically, the IPS statistic is defined as: (3) This statistic is normally distributed under cross-sectional independence. The IPS test is based on the restrictive assumption that series are independent across countries i, and thus, suffers from serious size distortion and restricted power in the presence of cross-sectional 9

11 dependence (O Connell, 1998). To overcome this, Pesaran (2007) explores a simple approach to deal 1

12 with the problem of cross-sectional dependence. He considers a one-factor model with heterogeneous factor loadings for residuals and suggests augmenting the standard ADF regression with the cross- section averages of lagged levels and first-differences of the individual series. The regression used for the i th cross-section unit is defined as: where and.t he CIPS test is based on the average of individual cross-sectionally augmented ADF statistics (CADF) as follows: t j (4) The critical values for the CIPS test are given in Pesaran (2007). (5) CROSS-SECTIONAL DEPENDENCE TESTS To determine the existence of cross-sectional dependence across countries, we employ the simple tests suggested by Pesaran (2004). The Cross-Sectional Dependence (CD) test statistics are based on the average of pair-wise correlation coefficients (ρˆi j ) of the OLS residuals, obtained from the individual ADF regressions. The C D P test is given by: The C D P statistic, under the null of cross-independence, is distributed as a two-tailed standard normal distribution, i.e. C D P ~ N (0, 1) for T i j > 3 and sufficient large N. (6) POOLABILITY TESTS The assumption of homogeneity of the slope coefficients across countries is a crucial issue for the estimation of panel data models. Pesaran and Yamagata (2008) proposed a standardized version of 10

13 Swamy s (1970) statistic in order to test for slope homogeneity in large panels. The standardized Delta test statistic ( ) can be defined by (7) and the bias adjusted version of the Delta test statistic is where and, and S is the modified version of Swamy s (1970) statistic that based on the dispersion of individual slope estimates from a weighted Fixed Effects pooled estimator. The Delta test and its bias adjusted version have an asymptotic standard normal distribution under homogeneity null and as (N, T ) with. (8) 3 DATA AND EMPIRICAL RESULTS 3.1 DATA For the empirical analysis we use annual data over the period for a sample of 60 countries on real GDP ( y i,t ), nominal GDP (x i,t ) and GDP price deflator (p i,t ), all measured in U.S. dollars. Table 1 presents the countries, and their abbreviations, studied in our analysis. The data were obtained from United Nations National Accounts Main Aggregates Database in order to assure a comparable and balanced data set. All series transformed in logarithms and the inflation rate was calculated using the GDP price deflator as. A time varying measure for the variability of inflation (σ i,t ) is obtained through a GARCH (1,1) modeling of inflation. In order to assess BMR and ARY empirical evidence, we examine also the sub-sample of 42 countries originally explored in Ball et al. (1988) and Akerlof et al. (1988) work. 5 Table 2 presents descriptive statistics for the full sample. 12

14 3.2 EMPIRICAL RESULTS DATA PROPERTIES Prior to the estimation of Equation 4 we conduct various initial tests to exploit the properties of our data. We explore the level of integration of the series in Table 3, the assumption of cross-sectional dependence in Table 4, and the poolability (slopes homogeneity) hypothesis of our specification in Table 5. The Im et al. s (2003) IPS as well as the Pesaran s (2007) CIPS panel unit root test results, reported in Table 3, indicate that real and nominal GDP series are integrated of order one, I (1), while inflation and inflation variability series are found to be stationary, I (0). 6 The issue of cross-sectional dependence is examined by applying the C D p test of Pesaran (2004) (Table 4). The null hypothesis of no cross-sectional correlation among the countries in our panel is strongly rejected at the 5% level 13

15 of significance, indicating that our data are subject to considerable cross-section dependence. Finally, the assumption of homogeneous slope parameters in our panel is tested by the Delta test of Pesaran and Yamagata (2008). The results from Table 5 clearly indicate that the hypothesis of common slopes is strongly rejected, and thus heterogeneity among countries is notable ESTIMATION RESULTS We proceed by exploring the determinants of output-inflation trade-off using panel estimation of the one step dynamic regression of Equation 4. Table 6 presents our main results based on alternative estimation approaches. Column 1 reports the estimates from the (homogeneous) Fixed Effects estimator while Column 2 presents the (heterogeneous) Mean Group estimates. 7 Columns 3-5 report the results from the heterogeneous estimators that account for cross-sectional dependence, in its standard version (CCEMG) as well as its extension suggested by Chudik and Pesaran (2013) (dynccemg). 8 All five estimates yield a statistically significant and positive coefficient on the direct impact of nominal demand on real output, confirming the conventional understanding of the short-run Phillips curve. However, there is a considerably larger value of the coefficient when we move to heterogeneous estimation approaches compared to that of the FE pooled estimates. Turning our attention to the interaction terms, that measure the impact of the determinants of real responsiveness to nominal changes, there is a strong agreement of all alternative estimates concerning the source of the response. All estimates show a negative and significant coefficient of the interaction term between the rate of inflation and the nominal aggregate demand, while reveal an insignificant (though negative) coefficient of the interaction term between inflation variability and nominal demand. 9 The value of the coefficient on the impact of inflation is substantially smaller in the homogeneous approach than those obtained from heterogeneous approaches. Specifically, the estimate using the Fixed Effects method is and becomes in the case of the Mean Group estimator. However, when we take control of cross-sectional correlation across countries (Columns 3-5) the magnitude of the interaction term is mitigated ( to ). These results, clearly, stress the importance of the rate of inflation as the main explanatory factor that influence the effectiveness of nominal demand, and thus, are supportive of the New Keynesian hypothesis. 10 This evidence corroborates previous studies such as Ball et al. (1988); DeFina (1991); Khan (2004), while calls into question more recent evidence (Abbott and Martinez, 2008; Fendel and Rulke, 2012). Hence, our findings highlight the limitations of all previous time-series and pooled cross-sectional analyses and 14

16 support the necessity to account for heterogeneity and cross sectional dependence in the estimation of alternative specifications of the Phillips curves, see Byrne et al. (2013) for a similar outcome. To ensure that the results are not affected by the stationary specification of Equation 4, we employ the panel analysis using the one stage specification of Equation 3 (using y i,t instead of y i,t ). 11 Columns 6-10 repeat the five estimation approaches (FE, MG and the CCEMG in static and dynamic form) with y i,t as the dependent variable. We can observe that the results are not affected by the non-stationary treatment of real GDP, confirming the conclusion of Abbott and Martinez (2008). The impact of nominal growth in real GDP is weaker but with the correct sign (except in Column 10 where it is found to be insignificant). In turn, the sign of the coefficients of the interaction terms is consistent with the stationary specification. Hence, our main conclusions of a significant negative relation of the rate of inflation (and not of its variability) and the output-inflation trade-off remains. The only difference is that the coefficient on the interaction term of the mean inflation and nominal GDP is smaller in absolute terms than those of the stationary specification (using the DynCCEMG estimator) ROBUSTNESS CHECK Table 7 documents the robustness of our previous findings, by reporting the dynamic CCEMG estimates under alternative time periods and country samples. We examine the robustness of the results over the entire period (Columns 70 10), the period after the early 80 until the recent crisis of 07, consisting the period of the Great Moderation (Columns 80 07). 12 Finally, we examine the whole period excluding the recent years of the crisis (Columns 70 07). 13 With respect to the grouping of countries we employ three different sample sets. The full sample of countries (Columns FULL), the reduced sample of the 42 countries that originally explored by Ball et al. (1988) (Columns BMR) and the sub-sample of 24 OECD countries (Columns OECD). Therefore, Table 7 consists of nine sub-samples, combining the partitions of the full sample over alternative time periods and country grouping. Regarding the estimated parameters of primary interest, we observe that the coefficients of the interaction terms, of the level of inflation as well as its volatility with the nominal aggregate demand, are of the correct sign and are consistent with those reported in Table 6. However, there is a substantial variation on their significance, depending on the alternative sub-sample we employ the analysis. The results from the entire time period (Columns 1, 4 and 7) over the alternative grouping 15

17 classification, reveal a significant negative impact of the level of inflation on the trade-off, which remains significant when we exclude the recent years of the financial crisis (Columns 3, 6 and 9), but losses its significance when we concentrate on the period of the Great Moderation (Columns 2, 5 and 8), and especially when we dealing with the OECD countries sample. Consequently, this result reaffirms previous evidence on the Great Moderation period (Summers, 2005; Davis and Kahn, 2008), that inflation becomes less sensitive to demand shocks, and thus, this reduced sensitivity leads to the non-significance of the interaction term (Columns 5 and 8). When we move to the examination of the effect of the country grouping on our sample, we can observe that the FULL sample (Columns 1, 2 and 3), including all 60 countries of our dataset, as well as the reduced BMR sample of Ball et al. (1988) (Columns 4, 5 and 6) convey similar results, complying with those reported in Table 6. In contrast, when we examine the OECD sub-sample over the full years of data (Columns 7 and 9), we are facing different evidence. We observe a consistent negative impact of the level of inflation on the trade-off, while in addition to this effect, we observe a significant and strong negative impact of inflation volatility of the trade-off. This result is mainly driven by the inclusion of the 1970s years where there is evident of high and volatile inflation rates for the OECD countries (Summers, 2005). Thus, for OECD countries, the result shows a significant effect of inflation dynamics (both in level and volatility) on the output-inflation trade-off. As a further check over the robustness of the results, we continue by employing alternative specifications proposed in the literature to investigate the determinants of output-inflation trade-off. Table 8 presents the results of the dynamic CCEMG estimator on various extensions and alternatives of a generalized form of Equation 4 as follows: (9) where the functional form of the trade-off on the two determinants, inflation rate and inflation variability, specified as τ i,t = f (π i,t, σ i,t ), is allowed to be a non-linear specification, either by employing a quadratic representation as determined in the functional form of Ball et al. (1988) or by using the inverse of the trade-off parameter as determined in the functional form of Akerlof et al. (1988). Furthermore, we allow to include additional explanatory variables (vector X i,t ) as regressors, that proposed in the literature (DeFina, 1991; Khan, 2004). Using this general form of Equation 14 we can explore various research questions raised in the 16

18 literature, using the dynamic CCEMG estimation method. Column 1 in Table 8, shows the results of the specification including only the rate of inflation as the trade-off determinant, while model in Column 2 contains only the variability of inflation as determinant. Column 3 repeats the specification with both determinants, πi,t and σi,t, as provided in Column 4 at Table 6. We can observe that our results, employing panel approaches accounting for heterogeneity and cross-sectional dependence, are not affected by collinearity problem among the two factors (Ball and Mazumder, 2011), and suggests that the main determinant of the output-inflation trade-off is the rate of inflation. Column 4 present the results of the quadratic specification of Ball et al. (1988), while Columns 5 and 6 reports the Akerlof et al. (1988) specification in linear and quadratic form, respectively. We can see that these estimations reaffirm the significance of only inflation rate s coefficient and reveal that there is no evidence of a non-linear specification when allowing for heterogeneous slopes and cross-sectional correlation. Columns 7 to 10 extend the analysis on the output-inflation trade-off by including as a determinant the variability of nominal demand, σ x i,t. By including this variable, we explore various alternatives on the specification form we employ. We can observe that, when we replace the variability of inflation, σ i,t, with the one of nominal demand, σ x, our main findings holds, with only exception, the case in Column 9 where we include both inflation and demand variability and we found also a significant effect of inflation s volatility on the trade-off. Next, in Column 11, we employ the extended specification, as previous suggested by DeFina (1991), of including a supply shock. Therefore, by counting the growth rate of oil price as a supply shock, we estimate Equation 14 and the results lead to support the impact of inflation rate as the only determinant for the trade-off. Finally, the last two Columns, 12 and 13, examine the hypothesis of Khan (2004), to exploit the impact of the level of inflation on the output persistence. Using Khan s 2004 specification, we continue to support the significant impact of inflation on the output-inflation trade-off, while we also found evidence to re-affirming Khan (2004), of a significant negative effect of inflation on the persistence of output. As a sum-up, there are some key findings emerging from our analysis. First and foremost, there is evidence of a significant negative impact of the rate of inflation on the output-inflation trade-off, estimated by a panel one-step procedure (for the first time in this setting), remained robust to alternative samples and specifications. This outcome corroborates with the New Keynesian results of Ball et al. (1988); DeFina (1991); Khan (2004). Second, there is a (weak) evidence of a significant i,t 17

19 impact of inflation volatility on the trade-off, when considering the OECD sub-sample, suggesting the attention to both the level and the volatility of inflation as important factors causing changes on the slope of the Phillips curve for the OECD countries (Ball and Mazumder, 2011). Finally, given the vast empirical evidence of considerable heterogeneity on the dynamics of inflation (Byrne et al., 2013) and an essential variation of the trade-off parameter across countries (Akerlof et al., 1988; DeFina, 1991), as well as, of the existence of cross-sectional correlation across countries (Byrne et al., 2013), we stress the importance of employing panel data approaches that control for typical features of macroeconomic panel datasets such as cross-country heterogeneity and cross-sectional dependence, when exploiting the determinants of the slope of the Phillips curve. 4 CONCLUSIONS The purpose of this paper is to re-examine empirically the determinants of the output-inflation trade-off using an international panel of 60 countries over the period We modeled the output-inflation trade-off as one stage dynamic panel data regression, and explored the impact of the determinants on trade-off within a framework that takes into account non-stationarity, dynamics, parameter heterogeneity and cross-sectional dependence. Our findings offer a strong evidence of a negative association between the rate of inflation and the output-inflation trade-off. In contrast, we find only limited support for the hypothesis that inflation variability causes a decline in the tradeoff. The results are robust to alternative samples and specification forms that have been exploited previously in the literature. These findings corroborate the New Keynesian view that high levels of inflation will cause a decline in the responsiveness of real output to nominal shocks. 18

20 NOTES 1. Akerlof et al. (1988) points out a number of shortcomings with the two step approach. 2. To our knowledge, only Yates and Chapple (1996) consider, alongside to the two-step approach, a panel extension of the one step procedure to explore the output-inflation trade-off, but their approach was not been explicitly discussed, while the work of Loungani et al. (2001), lying in an open-economy setting, examines the impact of capital controls on the trade-off by employing, besides to the traditional cross-sectional approach, a one step panel analysis. However, both approaches were betimes and certainly are not evolved in the context of our analysis. 3. Abbott and Martinez (2008) show that the interpretation of the trade-off coefficients in this (stationary) specification is equivalent to its interpretation in previous studies (employing non-stationary specification). 4. Asai (1999) follows a similar approach to measure inflation variability on a time-series context. 5. We exclude Zaire from original BMR dataset due to data unavailability. 6. The only exception is for nominal GDP when using the IPS test the results are in favor to reject the unit root hypothesis. However, the IPS test relies on the restrictive assumption of cross-sectional independence and can be seriously misleading. 7. We include these estimators as benchmark cases for the panel analysis. 8. The dynamic CCEMG estimator of Chudik and Pesaran (2013) is performed using two alternative versions, the first augmented with one lag and the second with three lags as additional cross-section averages. 9. The joint significance of the two interaction terms is high (p < 0.05) when employing the heterogeneous panel data approaches, indicating that the Phillips curve slope is determined by inflation dynamics (π i,t and σ i,t ), see Ball and Mazumder (2011). 10. Akerlof et al. (1988) argue that one cannot discriminate the effect on the steepness of the Phillips curve that is due to the volatility from the effect that results from the level of inflation, due to the high correlation among the two variables. Using the proposed time varying measure for the variability of inflation we can observe that this is not true for our data, since the correlation among π i,t and σ i,t is very low and equals Abbott and Martinez (2008) present evidence that all previous studies employing the non-stationary specification did not yield misleading results. 12. During the Great Moderation it is evident of a substantial reduction in both the level and the volatility of inflation for most of the OECD countries, see among others Summers (2005); Davis and Kahn (2008). 13. A recent literature has identified that the recent economic crisis have caused changes in inflation dynamics, see Sim et al. (2013). 19

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