Volume 31, Number 1 263 Estimation of Consumption Elasticities for OECD Countries: Testing Price Asymmetry with Alternative Dynamic Panel Data Techniques Edward F. Blackburne Sam Houston State University • Huntsville, TX Donald L. Bumpass Sam Houston State University • Huntsville, TX InTrODuCTIOn In recent years, the dynamic panel data literature has begun to focus on panels in which the number of cross-sectional observations ( N ) and the number of time-se- ries observations ( T ) are both large. The availability of data with greater frequency is certainly a key contributor to this shift. Some cross-national and cross-state data sets, for example, are now large enough in T such that each nation (or state) can be estimated separately. See Blackburne and Frank, (2007) for further details. The asymptotics of large N, large T dynamic panels are quite different from the asymptotics of traditional large N, small T dynamic panels. Small T panel estima- tion usually relies on fixed or random effects estimators, or a combination of fixed effects estimators and instrumental variable estimators, such as the Arellano and Bond, (1991) GMM estimator. These methods require pooling individual groups and allowing only the intercepts to differ across the groups. One of the central findings from the large N, large T literature, however, is that the assumption of homogeneity of slope parameters is often inappropriate. This point has been made by Pesaran and Smith (1995); Im et al. (2003), Pesaran et al; (1997, 1999), Phillips and Moon, (2000)1. With the increase in time observations inherent in large N, large T dynamic panels, nonstationarity is also a concern. Recent papers by Pesaran et al. (1997, 1999) offer two important new techniques to estimate nonstationary dynamic panels in which the parameters are heterogeneous across groups: the mean-group and pooled mean-group estimators. The mean-group estimator (MG) (see Pesaran and Smith, 1995) relies on estimating N time series regressions and averaging the coefficients, while the pooled mean-group estimator (PMG) (see Pesaran et al., 1997,1999) relies on a combination of pooling and averaging of coefficients. 1 For further discussion of this literature see chapter 12 in (Baltagi, 2001). 264 Journal of Business Strategies In recent empirical research, the MG and PMG estimators have been applied in a variety of settings. Freeman, (2000), for example, uses the estimators to evaluate state-level alcohol consumption over the period 1961 to 1995. Martinez-Zarzoso and Bengochea-Morancho, (2004) employ them in an estimation of an environmental Kuznets curve in a panel of 22 OECD nations over a period 1975 to 1998. Frank, (2005) uses the MG and PMG estimators to evaluate the long-term impact of income inequality on economic growth in a panel of U.S. states over the period 1945 to 2001. This paper applies the MG and PMG estimators to a panel of OECD nations for the years 1970–2004. We present a simple dynamic model of oil consumption as a function of income and prices. As in previous studies, we allow demand to respond asymmetrically to price shocks. Specifically, this paper has three goals: • test the degree of heterogeneity in oil consumption among the OECD nations • test the asymmetric response of oil consumption with respect to price • estimate precise price and income elasticities for OECD oil consumption This paper proceeds as follows. Section 2 discusses the methods involved, including price decomposition and alternative dynamic panel estimators. Section 3 briefly describes the data. Section 4 presents the results and Section 5 concludes. METhODOlOgy Demand Asymmetries Following the recent work of Gately and Huntington, (2002), this paper al- lows for asymmetric price response in oil demand. Models that assume price sym- metry when, in fact, it does not exist introduce model misspecification and down- wardly bias income elasticity estimates. Accordingly, we decompose the world price of oil (in logs), Pt , into three components: describes the data. Section 4 presents the results and Section 5 concludes. 2 Methodology 2.1 Demand Asymmetries Following the recent work of Gately and Huntington (2002), this paper allows for asymmetric price response in oil demand. Models that assume price symmetry when, in fact, it does not exist introduce model misspecification and downwardly bias income elasticity estimates. Accordingly, we decompose the world price of oil (in logs), Pt, into three components: Pmax,t = max(Pt, Pt−1) (1) Prec,t = T∑ t=1 max(0, (Pt − Pt−1) − (Pmax,t − Pmax,t−1)) (2) Pcut,t = T∑ t=1 min(0, Pt − Pt−1) (3) Pmax,t and Prec,t are non-decreasing series while Pcut,t is non-increasing. Figure 1 presents the decomposed real oil price series for the period 1970-2004. The decomposition of price listed above is convenient since it allows for simple testing of symmetric consumption responses to price changes. At any point in time, the following identity holds: Pt = Pmax,t + Prec,t + Pcut,t (4) Given a simple demand model of the form qt = α + β1Pmax,t + β2Prec,t + β3Pcut,t + �t (5) the null hypothesis of price response symmetry is tested as β1 = β2 = β3. Under the alternative hypothesis of price asymmetry, at least one βi is statistically different. Prior research convincingly argues that |β1| > |β2| > |β3|. Our results partially confirm this. (1) describes the data. Section 4 presents the results and Section 5 concludes. 2 Methodology 2.1 Demand Asymmetries Following the recent work of Gately and Huntington (2002), this paper allows for asymmetric price response in oil demand. Models that assume price symmetry when, in fact, it does not exist introduce model misspecification and downwardly bias income elasticity estimates. Accordingly, we decompose the world price of oil (in logs), Pt, into three components: Pmax,t = max(Pt, Pt−1) (1) Prec,t = T∑ t=1 max(0, (Pt − Pt−1) − (Pmax,t − Pmax,t−1)) (2) Pcut,t = T∑ t=1 min(0, Pt − Pt−1) (3) Pmax,t and Prec,t are non-decreasing series while Pcut,t is non-increasing. Figure 1 presents the decomposed real oil price series for the period 1970-2004. The decomposition of price listed above is convenient since it allows for simple testing of symmetric consumption responses to price changes. At any point in time, the following identity holds: Pt = Pmax,t + Prec,t + Pcut,t (4) Given a simple demand model of the form qt = α + β1Pmax,t + β2Prec,t + β3Pcut,t + �t (5) the null hypothesis of price response symmetry is tested as β1 = β2 = β3. Under the alternative hypothesis of price asymmetry, at least one βi is statistically different. Prior research convincingly argues that |β1| > |β2| > |β3|. Our results partially confirm this. (2) describes the data. Section 4 presents the results and Section 5 concludes. 2 Methodology 2.1 Demand Asymmetries Following the recent work of Gately and Huntington (2002), this paper allows for asymmetric price response in oil demand. Models that assume price symmetry when, in fact, it does not exist introduce model misspecification and downwardly bias income elasticity estimates. Accordingly, we decompose the world price of oil (in logs), Pt, into three components: Pmax,t = max(Pt, Pt−1) (1) Prec,t = T∑ t=1 max(0, (Pt − Pt−1) − (Pmax,t − Pmax,t−1)) (2) Pcut,t = T∑ t=1 min(0, Pt − Pt−1) (3) Pmax,t and Prec,t are non-decreasing series while Pcut,t is non-increasing. Figure 1 presents the decomposed real oil price series for the period 1970-2004. The decomposition of price listed above is convenient since it allows for simple testing of symmetric consumption responses to price changes. At any point in time, the following identity holds: Pt = Pmax,t + Prec,t + Pcut,t (4) Given a simple demand model of the form qt = α + β1Pmax,t + β2Prec,t + β3Pcut,t + �t (5) the null hypothesis of price response symmetry is tested as β1 = β2 = β3. Under the alternative hypothesis of price asymmetry, at least one βi is statistically different. Prior research convincingly argues that |β1| > |β2| > |β3|. Our results partially confirm this. (3) Volume 31, Number 1 265 Pmax,t ,and Prec,t , are non-decreasing series while Pcut,t , is non-increasing. Figure 1 presents the decomposed real oil price series for the period 1970-2004. The decomposition of price listed above is convenient since it allows for sim- ple testing of symmetric consumption responses to price changes. At any point in time, the following identity holds: describes the data. Section 4 presents the results and Section 5 concludes. 2 Methodology 2.1 Demand Asymmetries Following the recent work of Gately and Huntington (2002), this paper allows for asymmetric price response in oil demand. Models that assume price symmetry when, in fact, it does not exist introduce model misspecification and downwardly bias income elasticity estimates. Accordingly, we decompose the world price of oil (in logs), Pt, into three components: Pmax,t = max(Pt, Pt−1) (1) Prec,t = T∑ t=1 max(0, (Pt − Pt−1) − (Pmax,t − Pmax,t−1)) (2) Pcut,t = T∑ t=1 min(0, Pt − Pt−1) (3) Pmax,t and Prec,t are non-decreasing series while Pcut,t is non-increasing. Figure 1 presents the decomposed real oil price series for the period 1970-2004. The decomposition of price listed above is convenient since it allows for simple testing of symmetric consumption responses to price changes. At any point in time, the following identity holds: Pt = Pmax,t + Prec,t + Pcut,t (4) Given a simple demand model of the form qt = α + β1Pmax,t + β2Prec,t + β3Pcut,t + �t (5) the null hypothesis of price response symmetry is tested as β1 = β2 = β3. Under the alternative hypothesis of price asymmetry, at least one βi is statistically different. Prior research convincingly argues that |β1| > |β2| > |β3|. Our results partially confirm this. (4) Given a simple demand model of the form describes the data. Section 4 presents the results and Section 5 concludes. 2 Methodology 2.1 Demand Asymmetries Following the recent work of Gately and Huntington (2002), this paper allows for asymmetric price response in oil demand. Models that assume price symmetry when, in fact, it does not exist introduce model misspecification and downwardly bias income elasticity estimates. Accordingly, we decompose the world price of oil (in logs), Pt, into three components: Pmax,t = max(Pt, Pt−1) (1) Prec,t = T∑ t=1 max(0, (Pt − Pt−1) − (Pmax,t − Pmax,t−1)) (2) Pcut,t = T∑ t=1 min(0, Pt − Pt−1) (3) Pmax,t and Prec,t are non-decreasing series while Pcut,t is non-increasing. Figure 1 presents the decomposed real oil price series for the period 1970-2004. The decomposition of price listed above is convenient since it allows for simple testing of symmetric consumption responses to price changes. At any point in time, the following identity holds: Pt = Pmax,t + Prec,t + Pcut,t (4) Given a simple demand model of the form qt = α + β1Pmax,t + β2Prec,t + β3Pcut,t + �t (5) the null hypothesis of price response symmetry is tested as β1 = β2 = β3. Under the alternative hypothesis of price asymmetry, at least one βi is statistically different. Prior research convincingly argues that |β1| > |β2| > |β3|. Our results partially confirm this. (5) the null hypothesis of price response symmetry is tested as describes the data. Section 4 presents the results and Section 5 concludes. 2 Methodology 2.1 Demand Asymmetries Following the recent work of Gately and Huntington (2002), this paper allows for asymmetric price response in oil demand. Models that assume price symmetry when, in fact, it does not exist introduce model misspecification and downwardly bias income elasticity estimates. Accordingly, we decompose the world price of oil (in logs), Pt, into three components: Pmax,t = max(Pt, Pt−1) (1) Prec,t = T∑ t=1 max(0, (Pt − Pt−1) − (Pmax,t − Pmax,t−1)) (2) Pcut,t = T∑ t=1 min(0, Pt − Pt−1) (3) Pmax,t and Prec,t are non-decreasing series while Pcut,t is non-increasing. Figure 1 presents the decomposed real oil price series for the period 1970-2004. The decomposition of price listed above is convenient since it allows for simple testing of symmetric consumption responses to price changes. At any point in time, the following identity holds: Pt = Pmax,t + Prec,t + Pcut,t (4) Given a simple demand model of the form qt = α + β1Pmax,t + β2Prec,t + β3Pcut,t + �t (5) the null hypothesis of price response symmetry is tested as β1 = β2 = β3. Under the alternative hypothesis of price asymmetry, at least one βi is statistically different. Prior research convincingly argues that |β1| > |β2| > |β3|. Our results partially confirm this. Under the alternative hypothesis of price asymmetry, at least one describes the data. Section 4 presents the results and Section 5 concludes. 2 Methodology 2.1 Demand Asymmetries Following the recent work of Gately and Huntington (2002), this paper allows for asymmetric price response in oil demand. Models that assume price symmetry when, in fact, it does not exist introduce model misspecification and downwardly bias income elasticity estimates. Accordingly, we decompose the world price of oil (in logs), Pt, into three components: Pmax,t = max(Pt, Pt−1) (1) Prec,t = T∑ t=1 max(0, (Pt − Pt−1) − (Pmax,t − Pmax,t−1)) (2) Pcut,t = T∑ t=1 min(0, Pt − Pt−1) (3) Pmax,t and Prec,t are non-decreasing series while Pcut,t is non-increasing. Figure 1 presents the decomposed real oil price series for the period 1970-2004. The decomposition of price listed above is convenient since it allows for simple testing of symmetric consumption responses to price changes. At any point in time, the following identity holds: Pt = Pmax,t + Prec,t + Pcut,t (4) Given a simple demand model of the form qt = α + β1Pmax,t + β2Prec,t + β3Pcut,t + �t (5) the null hypothesis of price response symmetry is tested as β1 = β2 = β3. Under the alternative hypothesis of price asymmetry, at least one βi is statistically different. Prior research convincingly argues that |β1| > |β2| > |β3|. Our results partially confirm this. is statistically different. Prior research convincingly argues that describes the data. Section 4 presents the results and Section 5 concludes. 2 Methodology 2.1 Demand Asymmetries Following the recent work of Gately and Huntington (2002), this paper allows for asymmetric price response in oil demand. Models that assume price symmetry when, in fact, it does not exist introduce model misspecification and downwardly bias income elasticity estimates. Accordingly, we decompose the world price of oil (in logs), Pt, into three components: Pmax,t = max(Pt, Pt−1) (1) Prec,t = T∑ t=1 max(0, (Pt − Pt−1) − (Pmax,t − Pmax,t−1)) (2) Pcut,t = T∑ t=1 min(0, Pt − Pt−1) (3) Pmax,t and Prec,t are non-decreasing series while Pcut,t is non-increasing. Figure 1 presents the decomposed real oil price series for the period 1970-2004. The decomposition of price listed above is convenient since it allows for simple testing of symmetric consumption responses to price changes. At any point in time, the following identity holds: Pt = Pmax,t + Prec,t + Pcut,t (4) Given a simple demand model of the form qt = α + β1Pmax,t + β2Prec,t + β3Pcut,t + �t (5) the null hypothesis of price response symmetry is tested as β1 = β2 = β3. Under the alternative hypothesis of price asymmetry, at least one βi is statistically different. Prior research convincingly argues that |β1| > |β2| > |β3|. Our results partially confirm this. Our re- sults partially confirm this. Figure 1 Price Decomposition -1 00 -5 0 0 50 10 0 1970 1980 1990 2000 Year Real Price Oil (2006$) Maximum Cut Recovery Figure 1: Price Decomposition 266 Journal of Business Strategies OIl DEMAnD MODEl We estimate a reduced form energy demand model where per capita oil de- mand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, (6) where the number of nations i=1,2, ..., N, the number of time periods t =1,2, ..., T,qit, is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL (1,1,1) dynamic panel specification of (6) is 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, (7) The error correction re-parametrization of (7) is 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, (8) where 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, . The error-correction speed of adjustment parameter, 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, , and the long-run co- efficients, 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, and 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, are of primary interest. One would expect 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, , should be negative and the long-run income elasticity, 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. ThE MEAn-grOuP AnD POOlED | MEAn-grOuP EsTIMATOrs The recent literature on dynamic heterogeneous panel estimation in which both and are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith, (1995). With this estimator, Volume 31, Number 1 267 the intercepts, slope coefficients, and error variances are all allowed to differ across groups. More recently, Pesaran et al., (1997), Pesaran et al., (1999) have proposed a pooled mean-group (PMG) estimator that combines both pooling and averaging. This intermediate estimator allows the intercept, short-run coefficients, and error variances to differ across the groups (as would the MG estimator), but constrains the long-run coefficients to be equal across groups (as would a FE estimator). Since equation (8) is nonlinear in the parameters, Pesaran et al., (1999) develop a maxi- mum likelihood (ML) method to estimate the parameters. Expressing the likelihood as the product of each cross-section’s likelihood and taking the log yields: the intercepts, slope coefficients, and error variances are all allowed to differ across groups. More recently, Pesaran et al. (1997, 1999) have proposed a pooled mean-group (PMG) estimator that combines both pooling and averaging. This intermediate esti- mator allows the intercept, short-run coefficients, and error variances to differ across the groups (as would the MG estimator), but constrains the long-run coefficients to be equal across groups (as would a FE estimator). Since equation (8) is nonlinear in the parameters, Pesaran et al. (1999) develop a maximum likelihood (ML) method to estimate the parameters. Expressing the likelihood as the product of each cross-section’s likelihood and taking the log yields: lT (θ ′ , ϕ ′ , σ ′ ) = − T 2 N∑ i=1 ln(2πσ2i ) − 1 2 N∑ i=1 1 σ2i (∆yi − φiξi(θ))′Hi(∆yi − φiξi(θ)) (9) for i = 1, . . . , N, where ξi(θ) = yi,t−1 −Xiθi, Hi = IT −Wi(W ′i Wi)Wi, IT is an identity matrix of order T , and Wi = (∆yi,t−1, . . . , ∆yi,t−p+1, ∆Xi, ∆Xi,t−1, . . . , ∆Xi,t−q+1). The parameter estimates from iterated conditional likelihood maximization are asymptotically identical to those from full-information maximum likelihood. But the estimated covariance matrix is not. However, since the distribution of the pooled mean-group parameters is known, we are able to recover the full covariance matrix for all estimated parameters. As shown in Pesaran et al. (1999), the covariance matrix can be estimated by the inverse of   ∑N i=1 φ̂2i X ′ iXi σ̂2i −φ̂1X′1ξ̂1 σ̂21 · · · −φ̂N X ′ N ξ̂N σ̂2 N −φ̂1X′1W1 σ̂21 · · · −φ̂N X ′ N WN σ̂2 N ξ̂′1ξ̂1 σ̂21 · · · 0 ξ̂ ′ 1W1 σ̂21 · · · 0 ... ... ... ... ... ξ̂′ N ξ̂N σ̂2 N 0 · · · ξ̂ ′ N WN σ̂2 N W ′1W1 σ̂21 · · · 0 ... ... W ′ N WN σ̂2 N   (10) The mean-group parameters are simply the unweighted means of the individual coefficients. For example, the mean-group estimate of the error correction coefficient, (9) for i =1, ..., N, where , the intercepts, slope coefficients, and error variances are all allowed to differ across groups. More recently, Pesaran et al. (1997, 1999) have proposed a pooled mean-group (PMG) estimator that combines both pooling and averaging. This intermediate esti- mator allows the intercept, short-run coefficients, and error variances to differ across the groups (as would the MG estimator), but constrains the long-run coefficients to be equal across groups (as would a FE estimator). Since equation (8) is nonlinear in the parameters, Pesaran et al. (1999) develop a maximum likelihood (ML) method to estimate the parameters. Expressing the likelihood as the product of each cross-section’s likelihood and taking the log yields: lT (θ ′ , ϕ ′ , σ ′ ) = − T 2 N∑ i=1 ln(2πσ2i ) − 1 2 N∑ i=1 1 σ2i (∆yi − φiξi(θ))′Hi(∆yi − φiξi(θ)) (9) for i = 1, . . . , N, where ξi(θ) = yi,t−1 −Xiθi, Hi = IT −Wi(W ′i Wi)Wi, IT is an identity matrix of order T , and Wi = (∆yi,t−1, . . . , ∆yi,t−p+1, ∆Xi, ∆Xi,t−1, . . . , ∆Xi,t−q+1). The parameter estimates from iterated conditional likelihood maximization are asymptotically identical to those from full-information maximum likelihood. But the estimated covariance matrix is not. However, since the distribution of the pooled mean-group parameters is known, we are able to recover the full covariance matrix for all estimated parameters. As shown in Pesaran et al. (1999), the covariance matrix can be estimated by the inverse of   ∑N i=1 φ̂2i X ′ iXi σ̂2i −φ̂1X′1ξ̂1 σ̂21 · · · −φ̂N X ′ N ξ̂N σ̂2 N −φ̂1X′1W1 σ̂21 · · · −φ̂N X ′ N WN σ̂2 N ξ̂′1ξ̂1 σ̂21 · · · 0 ξ̂ ′ 1W1 σ̂21 · · · 0 ... ... ... ... ... ξ̂′ N ξ̂N σ̂2 N 0 · · · ξ̂ ′ N WN σ̂2 N W ′1W1 σ̂21 · · · 0 ... ... W ′ N WN σ̂2 N   (10) The mean-group parameters are simply the unweighted means of the individual coefficients. For example, the mean-group estimate of the error correction coefficient, , is an identity matrix of order T, and the intercepts, slope coefficients, and error variances are all allowed to differ across groups. More recently, Pesaran et al. (1997, 1999) have proposed a pooled mean-group (PMG) estimator that combines both pooling and averaging. This intermediate esti- mator allows the intercept, short-run coefficients, and error variances to differ across the groups (as would the MG estimator), but constrains the long-run coefficients to be equal across groups (as would a FE estimator). Since equation (8) is nonlinear in the parameters, Pesaran et al. (1999) develop a maximum likelihood (ML) method to estimate the parameters. Expressing the likelihood as the product of each cross-section’s likelihood and taking the log yields: lT (θ ′ , ϕ ′ , σ ′ ) = − T 2 N∑ i=1 ln(2πσ2i ) − 1 2 N∑ i=1 1 σ2i (∆yi − φiξi(θ))′Hi(∆yi − φiξi(θ)) (9) for i = 1, . . . , N, where ξi(θ) = yi,t−1 −Xiθi, Hi = IT −Wi(W ′i Wi)Wi, IT is an identity matrix of order T , and Wi = (∆yi,t−1, . . . , ∆yi,t−p+1, ∆Xi, ∆Xi,t−1, . . . , ∆Xi,t−q+1). The parameter estimates from iterated conditional likelihood maximization are asymptotically identical to those from full-information maximum likelihood. But the estimated covariance matrix is not. However, since the distribution of the pooled mean-group parameters is known, we are able to recover the full covariance matrix for all estimated parameters. As shown in Pesaran et al. (1999), the covariance matrix can be estimated by the inverse of   ∑N i=1 φ̂2i X ′ iXi σ̂2i −φ̂1X′1ξ̂1 σ̂21 · · · −φ̂N X ′ N ξ̂N σ̂2 N −φ̂1X′1W1 σ̂21 · · · −φ̂N X ′ N WN σ̂2 N ξ̂′1ξ̂1 σ̂21 · · · 0 ξ̂ ′ 1W1 σ̂21 · · · 0 ... ... ... ... ... ξ̂′ N ξ̂N σ̂2 N 0 · · · ξ̂ ′ N WN σ̂2 N W ′1W1 σ̂21 · · · 0 ... ... W ′ N WN σ̂2 N   (10) The mean-group parameters are simply the unweighted means of the individual coefficients. For example, the mean-group estimate of the error correction coefficient, The parameter estimates from iterated conditional likelihood maximization are asymptotically identical to those from full-information maximum likelihood. But the estimated covariance matrix is not. However, since the distribution of the pooled mean-group parameters is known, we are able to recover the full covariance matrix for all estimated parameters. As shown in Pesaran et al., (1999), the covari- ance matrix can be estimated by the inverse of the intercepts, slope coefficients, and error variances are all allowed to differ across groups. More recently, Pesaran et al. (1997, 1999) have proposed a pooled mean-group (PMG) estimator that combines both pooling and averaging. This intermediate esti- mator allows the intercept, short-run coefficients, and error variances to differ across the groups (as would the MG estimator), but constrains the long-run coefficients to be equal across groups (as would a FE estimator). Since equation (8) is nonlinear in the parameters, Pesaran et al. (1999) develop a maximum likelihood (ML) method to estimate the parameters. Expressing the likelihood as the product of each cross-section’s likelihood and taking the log yields: lT (θ ′ , ϕ ′ , σ ′ ) = − T 2 N∑ i=1 ln(2πσ2i ) − 1 2 N∑ i=1 1 σ2i (∆yi − φiξi(θ))′Hi(∆yi − φiξi(θ)) (9) for i = 1, . . . , N, where ξi(θ) = yi,t−1 −Xiθi, Hi = IT −Wi(W ′i Wi)Wi, IT is an identity matrix of order T , and Wi = (∆yi,t−1, . . . , ∆yi,t−p+1, ∆Xi, ∆Xi,t−1, . . . , ∆Xi,t−q+1). The parameter estimates from iterated conditional likelihood maximization are asymptotically identical to those from full-information maximum likelihood. But the estimated covariance matrix is not. However, since the distribution of the pooled mean-group parameters is known, we are able to recover the full covariance matrix for all estimated parameters. As shown in Pesaran et al. (1999), the covariance matrix can be estimated by the inverse of   ∑N i=1 φ̂2i X ′ iXi σ̂2i −φ̂1X′1ξ̂1 σ̂21 · · · −φ̂N X ′ N ξ̂N σ̂2 N −φ̂1X′1W1 σ̂21 · · · −φ̂N X ′ N WN σ̂2 N ξ̂′1ξ̂1 σ̂21 · · · 0 ξ̂ ′ 1W1 σ̂21 · · · 0 ... ... ... ... ... ξ̂′ N ξ̂N σ̂2 N 0 · · · ξ̂ ′ N WN σ̂2 N W ′1W1 σ̂21 · · · 0 ... ... W ′ N WN σ̂2 N   (10) The mean-group parameters are simply the unweighted means of the individual coefficients. For example, the mean-group estimate of the error correction coefficient, (10) The mean-group parameters are simply the unweighted means of the indi- vidual coefficients. For example, the mean-group estimate of the error correction 268 Journal of Business Strategies coefficient, φ, is: φ̂ = N−1 N∑ i=1 φ̂i (11) with the variance ∆̂φ̂ = 1 N(N − 1) N∑ i=1 (φ̂i − φ̂)2 (12) The mean and variance of other short-run coefficients are similarly estimated2. 3 Data We use annual aggregate data for 27 OECD nations to estimate the oil demand model in equation (8)3. These data are taken from Alan Heston and Aten (2006); IEA (2006), and encompass the years 1970 through 2004. Summary statistics for the data are listed in Table 1. Figure 2 shows oil consumption (million tonnes) and income (real GDP per capita) for the 27 OECD countries in our sample. Although we expect OECD countries, as a whole, to be a homogeneous group, our estimation procedures do not impose parameter homogeneity. At one extreme, the mean-group estimator allows for complete heterogeneity while the dynamic fixed effects estimator imposes parameter homogeneity across all countries. As a com- promise, the pooled mean-group estimator allows for country-specific short-run ad- justments while imposing common long-run elasticities4. The next section presents results of these alternative estimators. 4 Results Im et al. (2003) developed a unit root test for dynamic heterogeneous panels based on the the augmented Dickey–Fuller statistics averaged across all panels. 2All models are estimated in Stata using the xtpmg command developed by Blackburne and Frank (2007). 3Due to data sparsity, Luxembourg, Czech Republic, and Slovakia are dropped from our sample. 4Our model (8) includes income in the long-run equation which imposes the same speed of adjustment parameter on income and price. When estimated in this way, the long-run income elasticities were implausibly large. Following Gately and Huntington (2002), we reparametrized our model so that each country instantaneously adjusts to income. , is: φ, is: φ̂ = N−1 N∑ i=1 φ̂i (11) with the variance ∆̂φ̂ = 1 N(N − 1) N∑ i=1 (φ̂i − φ̂)2 (12) The mean and variance of other short-run coefficients are similarly estimated2. 3 Data We use annual aggregate data for 27 OECD nations to estimate the oil demand model in equation (8)3. These data are taken from Alan Heston and Aten (2006); IEA (2006), and encompass the years 1970 through 2004. Summary statistics for the data are listed in Table 1. Figure 2 shows oil consumption (million tonnes) and income (real GDP per capita) for the 27 OECD countries in our sample. Although we expect OECD countries, as a whole, to be a homogeneous group, our estimation procedures do not impose parameter homogeneity. At one extreme, the mean-group estimator allows for complete heterogeneity while the dynamic fixed effects estimator imposes parameter homogeneity across all countries. As a com- promise, the pooled mean-group estimator allows for country-specific short-run ad- justments while imposing common long-run elasticities4. The next section presents results of these alternative estimators. 4 Results Im et al. (2003) developed a unit root test for dynamic heterogeneous panels based on the the augmented Dickey–Fuller statistics averaged across all panels. 2All models are estimated in Stata using the xtpmg command developed by Blackburne and Frank (2007). 3Due to data sparsity, Luxembourg, Czech Republic, and Slovakia are dropped from our sample. 4Our model (8) includes income in the long-run equation which imposes the same speed of adjustment parameter on income and price. When estimated in this way, the long-run income elasticities were implausibly large. Following Gately and Huntington (2002), we reparametrized our model so that each country instantaneously adjusts to income. (11) with the variance φ, is: φ̂ = N−1 N∑ i=1 φ̂i (11) with the variance ∆̂φ̂ = 1 N(N − 1) N∑ i=1 (φ̂i − φ̂)2 (12) The mean and variance of other short-run coefficients are similarly estimated2. 3 Data We use annual aggregate data for 27 OECD nations to estimate the oil demand model in equation (8)3. These data are taken from Alan Heston and Aten (2006); IEA (2006), and encompass the years 1970 through 2004. Summary statistics for the data are listed in Table 1. Figure 2 shows oil consumption (million tonnes) and income (real GDP per capita) for the 27 OECD countries in our sample. Although we expect OECD countries, as a whole, to be a homogeneous group, our estimation procedures do not impose parameter homogeneity. At one extreme, the mean-group estimator allows for complete heterogeneity while the dynamic fixed effects estimator imposes parameter homogeneity across all countries. As a com- promise, the pooled mean-group estimator allows for country-specific short-run ad- justments while imposing common long-run elasticities4. The next section presents results of these alternative estimators. 4 Results Im et al. (2003) developed a unit root test for dynamic heterogeneous panels based on the the augmented Dickey–Fuller statistics averaged across all panels. 2All models are estimated in Stata using the xtpmg command developed by Blackburne and Frank (2007). 3Due to data sparsity, Luxembourg, Czech Republic, and Slovakia are dropped from our sample. 4Our model (8) includes income in the long-run equation which imposes the same speed of adjustment parameter on income and price. When estimated in this way, the long-run income elasticities were implausibly large. Following Gately and Huntington (2002), we reparametrized our model so that each country instantaneously adjusts to income. (12) The mean and variance of other short-run coefficients are similarly estimat- ed2. DATA We use annual aggregate data for 27 OECD nations to estimate the oil de- mand model in equation (8)3. These data are taken from Alan Heston and Aten, (2006), IEA, (2006), and encompass the years 1970 through 2004. Summary sta- tistics for the data are listed in Table 0. Figure 2 shows oil consumption (million tonnes) and income (real GDP per capita) for the 27 OECD countries in our sample. Although we expect OECD countries, as a whole, to be a homogeneous group, our estimation procedures do not impose parameter homogeneity. At one extreme, the mean-group estimator allows for complete heterogeneity while the dynamic fixed effects estimator imposes parameter homogeneity across all countries. As a compromise, the pooled mean-group estimator allows for country-specific short-run adjustments while imposing common long-run elasticities4. The next section pres- ents results of these alternative estimators. rEsulTs Im et al., (2003) developed a unit root test for dynamic heterogeneous panels based on the the augmented Dickey–Fuller statistics averaged across all panels. 2 All models are estimated in Stata using the xtpmg command developed by Blackburne and Frank, (2007). 3 Due to data sparsity, Luxembourg, Czech Republic, and Slovakia are dropped from our sample. 4 Our model (8) includes income in the long-run equation which imposes the same speed of adjustment parameter on income and price. When estimated in this way, the long-run income elasticities were implausibly large. Following [Gately and Huntington, 2002], we reparametrized our model so that each country instantaneously adjusts to income. Volume 31, Number 1 269 Figure 2 OECD Per Capita Oil Consumption and Income] 1970 1980 1990 2000 Year Australia 1970 1980 1990 2000 Year Austria 1970 1980 1990 2000 Year Belgium 1970 1980 1990 2000 Year Canada 1970 1980 1990 2000 Year Denmark 1970 1980 1990 2000 Year Finland 1970 1980 1990 2000 Year France 1970 1980 1990 2000 Year Germany 1970 1980 1990 2000 Year Greece 1970 1980 1990 2000 Year Hungary 1970 1980 1990 2000 Year Iceland 1970 1980 1990 2000 Year Ireland 1970 1980 1990 2000 Year Italy 1970 1980 1990 2000 Year Japan 1970 1980 1990 2000 Year Korea, South 1970 1980 1990 2000 Year Mexico 1970 1980 1990 2000 Year Netherlands 1970 1980 1990 2000 Year New Zealand 1970 1980 1990 2000 Year Norway 1970 1980 1990 2000 Year Poland 1970 1980 1990 2000 Year Portugal 1970 1980 1990 2000 Year Spain 1970 1980 1990 2000 Year Sweden 1970 1980 1990 2000 Year Switzerland 1970 1980 1990 2000 Year Turkey 1970 1980 1990 2000 Year United Kingdom 1970 1980 1990 2000 Year United States Figure 2: OECD Per Capita Oil Consumption and IncomeMEAn-grOuP EsTIMATIOn The mean-group estimator is the least restrictive of all estimations we consid- er. Model (8) is estimated independently for each country via ordinary least squares. The country-specific regression estimates for the mean-group model are listed in Table 5. The estimated (instantaneous) income elasticity of .636 is quite plausible. Further, the long-run adjustment parameter, 2.2 Oil Demand Model We estimate a reduced form energy demand model where per capita oil demand is a log-linear function of the real price of oil (which is common across all countries) and real per capita GDP. Assume the long-run demand function qit = θ0i + θ1ipt + θ2iyit + µi + �it (6) where the number of nations i = 1, 2, . . . , N, the number of time periods t = 1, 2, . . . , T , qit is the log of per capita oil consumption (million tonnes), pt is the log of real price of oil (2006$ per barrel), and yit is the log of real per capita income. If the variables are I(1) and cointegrated, then the error term is I(0) for all i. The ARDL(1,1,1) dynamic panel specification of (6) is qit = δ10ipt + δ11ipt−1 + δ20iyit + δ21iyi,t−1 + λiqi,t−1µi + �it (7) The error correction re-parametrization of (7) is ∆qit = φi (qi,t−1 − θ0i − θ1ipt − θ2iyit) + δ11i∆pt + δ21i∆yit + �it (8) where φi = −(1 − λi), θ0i = µi1−λi , θit = δ10i+δ11i 1−λi , and θ2i = δ20i+δ21i 1−λi . The error-correction speed of adjustment parameter, φi, and the long-run coef- ficients, θ1i and θ2i are of primary interest. One would expect φi to be negative if the variables exhibit a return to long-run equilibrium. Economic theory indicates the long-run price elasticity, θ1i, should be negative and the long-run income elasticity, θ2i to be positive. Further, to allow for price asymmetries, we substitute the price decomposition from equation (1) above. 2.3 The Mean-Group and Pooled Mean-Group Estimators The recent literature on dynamic heterogeneous panel estimation in which both N and T are large suggests several approaches to the estimation of equation (8). On one extreme, a fixed effects (FE) estimation approach could be utilized in which the time series data for each group is pooled and only the intercepts are allowed to differ across groups. If the slope coefficients are in fact not identical, however, then the FE approach produces inconsistent and potentially misleading results. On the other extreme, the model could be estimated separately for each individual group, and a simple arithmetic average of the coefficients could be calculated. This is the mean- group (MG) estimator proposed by Pesaran and Smith (1995). With this estimator, =-.23, indicates oil demand moves toward long-run equilibrium at a rate of 23% per year. Note the estimated price elas- ticities are not statistically different from zero. In fact, since the price coefficients are so imprecisely estimated, the hypothesis of price symmetry is not rejected5. These results exemplify the reason researchers pool data, if possible: there is not enough intra-country data variation for precise parameter estimates. 5 The test yields a Table 2: Augmented Dickey–Fuller Unit Root Tests Variable Z(t) p-value Pmax,t -3.664 0.0047 Prec,t 2.305 0.9990 Pcut,t 0.092 0.9655 critical values 1%: -3.689, 5%: -2.975, 10%: -2.619 Table 3: Im, Pesaran, and Shin Panel Unit Root Tests Variable Wtbar p-value yt -1.0459 0.1478 oilt -.5601 0.2877 demeaned, trend included lag lengths chosen via AIC 4.1 Mean-Group Estimation The mean-group estimator is the least restrictive of all estimations we consider. Model (8) is estimated independently for each country via ordinary least squares. The summary results of the mean-group estimates are presented in Table ??. The country- specific regression estimates for the mean-group model are listed in Table 5. The estimated (instantaneous) income elasticity of .636 is quite plausible. Further, the long-run adjustment parameter, φ=-.23, indicates oil demand moves toward long- run equilibrium at a rate of 23% per year. Note the estimated price elasticities are not statistically different from zero. In fact, since the price coefficients are so imprecisely estimated, the hypothesis of price symmetry is not rejected5. These results exemplify the reason researchers pool data, if possible: there is not enough intra-country data variation for precise parameter estimates. 5The test yields a χ22 statistic of 1.02. The corresponding p-value is .600. statistic of 1.02. The corresponding p-value is .600. 270 Journal of Business Strategies Table 1 OECD Country Mean Statistics Country Oil Consumption Real GDP (2006$) Population Australia 31.62 20,230.15 16,316,271.49 Austria 11.34 20,564.82 7,765,886.91 Belgium 27.86 19,128.36 9,973,123.17 Canada 81.78 20,777.17 26,935,737.46 Denmark 12.23 21,876.40 5,164,047.06 Finland 11.21 17,669.87 4,929,411.46 France 98.27 19,723.86 57,294,371.77 Germany 136.82 19,797.17 79,676,279.66 Greece 14.18 11,992.03 9,905,299.89 Hungary 8.65 9,318.39 10,419,609.57 Iceland 0.68 20,032.92 247,243.20 Ireland 5.70 14,418.69 3,487,859.20 Italy 93.74 17,764.94 56,570,715.43 Japan 241.96 18,751.73 119,837,178.57 Korea, South 51.47 8,755.94 41,245,183.86 Mexico 58.44 6,874.63 79,701,564.94 Netherlands 37.16 20,271.80 14,718,023.54 New Zealand 4.94 17,551.91 3,377,838.74 Norway 9.13 23,651.83 4,215,137.60 Poland 16.00 6,506.01 36,741,996.60 Portugal 10.47 12,248.06 9,850,355.97 Spain 51.66 14,486.69 38,186,561.03 Sweden 20.20 20,303.75 8,526,435.06 Switzerland 12.63 25,252.59 6,769,738.29 Turkey 20.82 4,424.15 52,663,862.60 United Kingdom 85.84 18,683.08 57,450,871.43 United States 806.49 25,780.08 246,064,078.23 Overall 72.64 16,919.89 37,334,617.88 Volume 31, Number 1 271 Table 2 Augmented Dickey–Fuller Unit Root Tests Variable Z(t) p-value Pmax,t -3.664 0.0047 Prec,t 2.305 0.9990 Pcut,t 0.092 0.9655 critical values 1%: -3.689, 5%: -2.975, 10%: -2.619 Table 3 Im, Pesaran, and Shin Panel Unit Root Tests Variable Wtbar p-value y1 -1.0459 0.1478 oilt -.5601 0.2877 demeaned, trend included lag lengths chosen via AIC 272 Journal of Business Strategies Table 4 Estimation Results Dynamic Fixed Effects Mean Group Pooled Mean Group EC1 -0.0467*** -0.230*** -0.0770*** (0.00801) (0.0366) (0.00761) ΔPmax,t -0.0254*** -0.00556 -0.0153* (0.00815) (0.00866) (0.00852) ΔPrec,t 0.0158 -0.00316 -0.00041 (0.0198) (0.0116) (0.0162) ΔPcut,t 0.00142 0.00298 0.000864 (0.0154) (0.0208) (0.015) Δyt 0.524*** 0.636*** 0.661*** (0.0613) (0.0958) (0.095) Pmax,t -0.779*** -0.471 -0.464*** (0.16) (0.352) (0.0766) ΔPrec,t -0.556*** -0.182 -0.223** (0.214) (0.137) (0.0882) Pcut,t -0.532*** -0.273 -0.267*** (0.147) (0.198) (0.0668) constant -0.493*** -2.974*** -0.897*** (0.109) (0.489) (0.0875) Observations 918 918 918 R-squared 0.26 Number of groups 27 Volume 31, Number 1 273 Table 5 Mean-Group Model Estimates C ou nt ry E C t P m ax ,t P re c, t P cu t,t ∆P m ax ,t ∆P pr ec ,t ∆P cu t,t ∆G D P t c on st an t Au st ra lia - 0. 08 74 - 0. 34 3 - 0. 42 4 - 0. 35 3 0. 04 56 * 0 .0 41 7 0 .0 07 09 0 .2 52 - 1. 05 1 (0 .1 09 ) (0 .4 61 ) (0 .7 92 ) (0 .6 05 ) (0 .0 27 5) (0 .0 61 8) (0 .0 49 2) (0 .3 58 ) (1 .4 34 ) Au st ria - 0. 28 9* - 0. 13 1 0 .2 67 * 0 .0 72 3 - 0. 04 49 - 0. 08 - 0. 06 59 0 .3 97 - 3. 74 3* (0 .1 61 ) (0 .1 25 ) (0 .1 39 ) (0 .0 81 1) (0 .0 41 3) (0 .0 97 5) (0 .0 70 7) (0 .4 59 ) (2 .2 11 ) B el gi um - 0. 16 3 - 0. 35 2* 0 .3 11 - 0. 04 64 - 0. 06 12 0 .0 88 4 - 0. 11 9* 0 .7 95 * - 1. 90 9 (.1 12 ) (0 .2 03 ) (0 .2 28 ) (0 .1 66 ) (0 .0 42 2) (0 .0 89 2) (0 .0 67 7) (0 .4 37 ) (1 .3 98 ) C an ad a 0. 01 41 1 .6 61 0 .8 3 1 .9 2 0. 03 13 - 0. 01 81 0 .0 38 8 0 .8 53 ** * 0 .2 32 (. 09 93 ) (1 1. 7) (4 .6 14 ) (1 2. 13 ) (0 .0 24 6) (0 .0 58 9) (0 .0 46 5) (0 .2 42 ) (1 .2 5) D en m ar k - 0. 09 36 - 0. 40 1 - 0. 53 2 - 0. 32 6 - 0. 01 71 - 0. 03 57 0 .0 96 0 .9 32 ** - 1. 09 4 (. 09 03 ) (0 .2 9) (0 .8 22 ) (0 .6 1) (0 .0 44 7) (0 .1 ) (0 .0 79 1) (0 .4 11 ) (1 .0 87 ) Fi nl an d - 0. 33 5* - 0. 11 1 0 .0 69 5 0 .1 16 - 0. 04 82 0 .0 70 8 - 0. 05 01 0 .2 13 - 4. 16 5 (0 .1 97 ) (0 .1 03 ) (0 .1 29 ) (0 .0 81 4) (0 .0 43 7) (0 .0 96 9) (0 .0 77 4) (0 .2 44 ) (2 .5 64 ) Fr an ce - 0. 11 2 - 0. 57 2 - 0. 16 2 - 0. 18 7 - 5. 09 E- 05 0 .0 02 34 - 0. 00 01 5 1 .1 43 ** - 1. 26 3 (0 .0 84 8) (0 .4 42 ) (0 .3 68 ) (0 .3 29 ) (0 .0 31 2) (0 .0 75 ) (0 .0 54 1) (0 .4 46 ) (1 .1 11 ) G er m an y - 0. 17 2 - 0. 17 5 0 .0 31 1 - 0. 00 48 6 - 0. 00 73 5 - 0. 07 88 - 0. 04 59 1 .4 82 ** * - 2. 18 8 (0 .1 05 ) (0 .1 27 ) (0 .1 64 ) (0 .1 03 ) (0 .0 29 6) (0 .0 69 9) (0 .0 51 8) (0 .3 59 ) (1 .3 88 ) G re ec e - 0. 11 3 - 0. 12 5 - 0. 43 4 - 0. 34 3 - 0. 00 27 7 0 .1 64 ** * 0 .0 66 8 0 .7 04 ** * - 1. 48 3 (0 .0 96 7) (0 .2 84 ) (0 .5 53 ) (0 .2 57 ) (0 .0 29 4) (0 .0 62 2) (0 .0 47 1) (0 .2 31 ) (1 .3 94 ) H un ga ry - 0. 31 0* * 0 .0 72 1 - 0. 14 1 0 .1 38 - 0. 03 57 0 .0 43 6 0 .0 59 0 .1 84 - 4. 34 9* (0 .1 49 ) (0 .1 15 ) (0 .1 51 ) (0 .0 88 1) (0 .0 45 6) (0 .1 08 ) (0 .0 84 2) (0 .2 81 ) (2 .2 2) Ic el an d - 0. 37 8* * - 0. 20 5* - 0. 06 17 - 0. 19 6 - 0. 00 11 3 0 .0 16 4 0 .1 96 - 0. 30 8 -4 .5 73 ** (0 .1 59 ) (0 .1 07 ) (0 .2 25 ) (0 .1 45 ) (0 .0 81 6) (0 .1 81 ) (0 .1 4) (0 .4 34 ) (2 .0 15 ) Ire la nd - 0. 18 8* * -0 .3 37 0 .8 10 ** 0 .2 72 0 .0 87 6 - 0. 02 51 -0 .3 88 ** * 1 .6 69 ** * -2 .3 50 ** (0 .0 86 8) (0 .2 13 ) (0 .3 19 ) (0 .2 14 ) (0 .0 54 6) (0 .1 35 ) (0 .1 1) (0 .5 08 ) (1 .1 77 ) Ita ly - 0. 22 0* * - 0. 17 7* * - 0. 16 2 - 0. 12 5 - 0. 00 14 6 0 .0 03 64 0 .0 27 8 0 .7 37 ** * -2 .7 92 ** (0 .0 99 2) (0 .0 86 7) (0 .1 26 ) (0 .0 90 4) (0 .0 21 7) (0 .0 45 5) (0 .0 35 5) (0 .2 22 ) (1 .3 16 ) 274 Journal of Business Strategies Ja pa n - 0. 13 6* - 0. 41 8* - 0. 49 5 - 0. 44 6 0 .0 45 4 - 0. 00 53 1 0. 07 56 0 .8 63 ** - 1. 6 (0 .0 79 4) (0 .2 51 ) (0 .3 91 ) (0 .3 13 ) (0 .0 33 1) (0 .0 74 8) (0 .0 57 ) (0 .3 43 ) (1 .0 3) K or ea , S ou th - 0. 02 71 - 0. 68 - 2. 84 7 - 2. 21 6 - 0. 03 9 - 0. 13 7 0 .1 52 1. 14 4* ** - 0. 31 3 (0 .0 68 5) (2 .5 73 ) (7 .5 93 ) (4 .3 89 ) (0 .0 52 1) (0 .1 36 ) (0 .1 09 ) (0 .3 11 ) (1 .0 77 ) M ex ic o - 0. 35 4* ** 0. 28 2* ** - 0. 06 87 -0 .0 69 2* * -0 .0 46 7* * -0 .0 04 42 - 0. 00 39 5 0 .7 89 ** * -5 .4 52 ** * (0 .0 78 8) (0 .0 21 7) (0 .0 50 5) (0 .0 30 9) (0 .0 22 9) (0 .0 41 7) (0 .0 33 1) (0 .1 14 ) (1 .2 18 ) N et he rla nd s - 0. 19 8 - 0. 24 0 .3 25 0 .0 82 3 - 0. 05 07 0 .0 14 6 - 0. 07 76 0 .9 16 - 2. 38 4 (0 .1 45 ) (0 .1 67 ) (0 .2 85 ) (0 .1 67 ) (0 .0 53 ) (0 .1 23 ) (0 .0 88 ) (0 .7 04 ) (1 .8 24 ) N ew Z ea la nd -0 .3 25 ** -0 .2 01 ** * - 0. 03 25 - 0. 18 8* * - 0. 03 04 - 0. 02 11 0 .0 58 7 - 0. 54 6 - 4. 14 6* * (0 .1 28 ) (0 .0 71 2) (0 .1 31 ) (0 .0 89 7) (0 .0 43 7) (0 .0 92 1) (0 .0 74 1) (0 .3 49 ) (1 .7 02 ) N or w ay -0 .4 04 ** - 0. 00 32 3 - 0. 09 28 - 0. 04 76 -0 .0 74 7* * 0 .0 28 6 0 .0 49 3 0 .7 44 * -5 .2 83 ** (0 .1 6) (0 .0 37 9) (0 .0 89 ) (0 .0 52 9) (0 .0 35 5) (0 .0 84 ) (0 .0 64 9) (0 .4 34 ) (2 .0 92 ) Po la nd 0. 04 35 0. 21 3 - 0. 25 5 - 0. 38 2 - 0. 00 55 2 0 .0 13 2 - 0. 02 62 0 .9 10 ** * 0. 68 8 (0 .0 95 8) (0 .4 36 ) (1 .4 53 ) (1 .3 14 ) (0 .0 34 9) (0 .0 86 4) (0 .0 69 1) (0 .1 82 ) (1 .4 87 ) Po rtu ga l - 0. 47 3* ** 0 .0 75 0 .0 73 7 - 0. 19 0* * 0 .0 10 1 - 0. 09 99 0 .0 14 3 0 .0 64 6 -6 .7 85 ** * (0 .1 73 ) (0 .0 64 5) (0 .1 32 ) (0 .0 79 6) (0 .0 56 9) (0 .1 43 ) (0 .1 07 ) (0 .4 03 ) (2 .5 41 ) Sp ai n -0 .0 51 7 - 0. 63 0 .0 58 4 - 0. 4 0 .0 36 1 - 0. 03 74 0 .0 60 8 0 .5 64 - 0. 57 6 (0 .1 24 ) (1 .9 27 ) (1 .2 26 ) (1 .3 93 ) (0 .0 39 6) (0 .1 02 ) (0 .0 71 8) (0 .5 28 ) (1 .7 68 ) Sw ed en - 0. 22 5 - 0. 20 4 0 .0 55 9 0 .1 58 - 0. 00 31 7 - 0. 04 33 0 .0 15 0 .2 99 - 2. 70 6 (0 .1 56 ) (0 .1 29 ) (0 .2 42 ) (0 .1 69 ) (0 .0 55 5) (0 .1 32 ) (0 .0 98 5) (0 .5 64 ) (1 .9 21 ) Sw itz er la nd - 0. 61 8* ** -0 .0 83 3* ** -0 .0 05 06 0 .0 43 6 - 0. 02 18 - 0. 00 36 3 - 0. 13 7* * 0 .4 27 -7 .9 10 ** * (0 .1 73 ) (0 .0 29 5) (0 .0 55 6) (0 .0 33 5) (0 .0 39 4) (0 .0 81 1) (0 .0 63 1) (0 .2 68 ) (2 .2 63 ) Tu rk ey -0 .2 31 ** - 0. 12 3 - 0. 15 8 - 0. 21 3* - 0. 03 17 0 .0 27 1 0 .0 39 6 0 .6 75 ** * - 3. 33 3* (0 .1 11 ) (0 .1 51 ) (0 .1 93 ) (0 .1 17 ) (0 .0 40 1) (0 .0 97 9) (0 .0 77 9) (0 .2 12 ) (1 .7 19 ) U ni te d K in g- do m - 0. 76 8* ** -0 .1 50 ** * - 0. 05 71 - 0. 01 38 0. 12 4* * - 0. 03 36 0 .0 74 6 0 .2 11 -9 .8 23 ** * (0 .1 65 ) (0 .0 26 8) (0 .0 57 1) (0 .0 35 2) (0 .0 50 7) (0 .1 03 ) (0 .0 81 ) (0 .5 12 ) (2 .1 18 ) U ni te d St at es - 0. 00 35 8 - 9. 37 1 - 1. 82 2 - 4. 42 8 - 0. 00 62 7 0 .0 23 1 - 0. 03 72 1 .0 58 ** * 0 .0 51 5 (0 .0 69 6) (1 82 .2 ) (3 7. 87 ) (8 8. 3) (0 .0 18 3) (0 .0 40 5) (0 .0 31 3) (0 .1 75 ) (0 .8 73 ) St an da rd e rr or s ar e lis te d in p ar en th es es . ** * < p 0. 01 , * * < p 0. 05 , * < p 0. 1 Volume 31, Number 1 275 POOlED-MEAn grOuP EsTIMATIOn Table 4 lists results of the pooled mean-group estimator for model (8). In this context, the PMG estimator allows for heterogeneous short-run dynamics and com- mon long-run price elasticities. The first equation presents the normalized cointe- grating vector6. The country-specific estimates are listed in Table 6. Referring to Table 4, the pooled mean-group estimated precisely. The long- run price elasticities are significantly negative. The estimated long-run price effect is asymmetric. The test of price symmetry is 4.2 Pooled-Mean Group Estimation Table 4 lists results of the pooled mean-group estimator for model (8). In this context, the PMG estimator allows for heterogeneous short-run dynamics and common long- run price elasticities. The first equation presents the normalized cointegrating vector6. The country-specific estimates are listed in Table 6. Referring to Table 4, the pooled mean-group estimated precisely. The long-run price elasticities are significantly negative. The estimated long-run price effect is asymmetric. The test of price symmetry is χ22 = 17.91, with p-value<0.001. Results indicate demand responds equally to price recoveries and price cuts, but is twice as responsive to a new historical maximum price (comparing -.223, -.267, and -464, respectively). The average long-run income elasticity (0.661) is significant, correctly signed, and in line with previous studies. A serious potential problem exists, however, with the pooled mean-group estima- tion. Since the model includes a lagged-dependent variable, there is a possibility of endogeneity bias in the parameter estimates. The existence of such an endogeneity problem is tested via the familiar Hausman test. In this context the mean-group estimator is consistent under both the null and alternative hypotheses. The pooled mean-group estimator is efficient under the null, but is inconsistent under the alter- native. The Hausman test statistic is 1.62 with a p-value of 0.6552 which rejects the presence of endogeneity bias at the traditional levels of significance. This was to be expected since, in fact, the parameter estimates did not change much between procedures but the precision increased dramatically. 4.3 Dynamic Fixed Effects We can further restrict the parameters by imposing complete parameter homogeneity. Recall the pooled mean-group estimator restricted long-run price responses and speed of adjustment to be equal across countries yet allowed for country-specific income responses and short-run adjustments. Under dynamic fixed effects all parameters are assumed equal across all countries. If dynamic fixed effects does not result in model misspecification, there are two advantages in such a specification. Firstly, dynamic fixed effects results in a parsimonious model, which is always preferred. Secondly, if we expect OECD countries to be a homogeneous group modelling as such is aligned with our prior. 6The vector has been normalized such that the coefficient on the first term in the cointegrating vector is 1. Accordingly, the normalized term is omitted from the estimation output. , with p-value <0.001. Results indicate demand responds equally to price recoveries and price cuts, but is twice as responsive to a new historical maximum price (comparing -.223, -.267, and -464, respectively). The average long-run income elasticity (0.661) is significant, correctly signed, and in line with previous studies. A serious potential problem exists, however, with the pooled mean-group es- timation. Since the model includes a lagged-dependent variable, there is a possibility of endogeneity bias in the parameter estimates. The existence of such an endogene- ity problem is tested via the familiar Hausman test. In this context the mean-group estimator is consistent under both the null and alternative hypotheses. The pooled mean-group estimator is efficient under the null, but is inconsistent under the alter- native. The Hausman test statistic is 1.62 with a p-value of 0.6552 which rejects the presence of endogeneity bias at the traditional levels of significance. This was to be expected since, in fact, the parameter estimates did not change much between proce- dures but the precision increased dramatically. DynAMIC FIxED EFFECTs We can further restrict the parameters by imposing complete parameter homo- geneity. Recall the pooled mean-group estimator restricted long-run price responses and speed of adjustment to be equal across countries yet allowed for country-specific income responses and short-run adjustments. Under dynamic fixed effects all param- eters are assumed equal across all countries. If dynamic fixed effects does not result in model misspecification, there are two advantages in such a specification. Firstly, dynamic fixed effects results in a parsimonious model, which is always preferred. Secondly, if we expect OECD countries to be a homogeneous group modelling as such is aligned with our prior. 276 Journal of Business Strategies Table 6 Pooled Mean-Group Estimates C ou nt ry E C t P m ax ,t P re c, t P cu t,t ∆P m ax ,t ∆P pr ec ,t ∆P cu t,t ∆G D P t c on st an t Au st ra lia - 0. 07 05 ** * - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 42 3* 0 .0 47 2 - 0. 02 07 0 .3 16 - 0. 81 8* ** (0 .0 22 5) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 23 ) (0 .0 46 7) (0 .0 36 3) (0 .2 99 ) (0 .2 66 ) Au st ria - 0. 10 6* ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 05 13 - 0. 02 2 - 0. 02 31 0 .2 81 - 1. 23 7* ** (0 .0 33 4) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 36 3) (0 .0 74 5) (0 .0 56 2) (0 .4 08 ) (0 .4 04 ) B el gi um - 0. 08 95 ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 08 45 ** 0 .1 74 ** - 0. 10 00 * 0 .7 13 * - 1. 01 1* * (0 .0 39 7) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 34 3) (0 .0 71 9) (0 .0 54 9) (0 .4 07 ) (0 .4 47 ) C an ad a - 0. 05 68 ** * - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 27 4 0 .0 25 7 0 .0 31 5 0 .7 58 ** * - 0. 64 1* ** (0 .0 20 3) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 21 1) (0 .0 45 ) (0 .0 35 6) (0 .2 11 ) (0 .2 28 ) D en m ar k - 0. 07 31 ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 01 84 - 0. 06 87 0 .0 76 9 1 .0 01 ** * - 0. 84 9* * (0 .0 29 9) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 37 2) (0 .0 77 3) (0 .0 59 4) (0 .3 46 ) (0 .3 39 ) Fi nl an d - 0. 08 15 ** * - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 04 52 - 0. 02 38 0 .0 18 2 0 .2 03 - 0. 91 9* * (0 .0 31 6) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 37 8) (0 .0 77 8) (0 .0 60 3) (0 .2 28 ) (0 .3 64 ) Fr an ce - 0. 11 2* ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 08 13 - 0. 05 43 0 .0 35 9 1 .4 31 ** * - 1. 31 6* ** (0 .0 25 4) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 25 8) (0 .0 55 2) (0 .0 41 6) (0 .3 59 ) (0 .3 1) G er m an y - 0. 06 84 ** * - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 01 6 - 0. 07 08 - 0. 03 6 1 .4 80 ** * - 0. 81 8* ** (0 .0 24 ) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 23 2) (0 .0 50 1) (0 .0 38 7) (0 .2 86 ) (0 .2 85 ) G re ec e - 0. 07 55 ** * - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 02 28 0 .1 59 ** * 0 .0 31 2 0 .4 76 ** * - 0. 87 5* ** (0 .0 17 2) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 24 4) (0 .0 47 3) (0 .0 36 ) (0 .1 73 ) (0 .2 1) H un ga ry - 0. 05 90 ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 23 - 0. 17 1* 0 .1 53 ** 0 .3 52 - 0. 70 9* * (0 .0 26 7) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 43 8) (0 .0 93 5) (0 .0 73 8) (0 .2 79 ) (0 .3 31 ) Ic el an d - 0. 18 2* ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 05 71 0 .1 51 0 .0 98 3 - 0. 64 8* - 1. 99 2* * (0 .0 69 2) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 68 ) (0 .1 43 ) (0 .1 06 ) (0 .3 52 ) (0 .7 89 ) Ire la nd - 0. 09 52 ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 78 4 0 .0 61 6 - 0. 27 2* ** 1 .4 11 ** * - 1. 17 8* ** (0 .0 37 7) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 48 7) (0 .1 15 ) (0 .0 83 8) (0 .3 78 ) (0 .4 43 ) Ita ly - 0. 08 80 ** * - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 01 64 - 0. 00 38 2 0 .0 00 77 2 0 .8 57 ** * - 1. 03 5* ** (0 .0 21 ) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 17 6) (0 .0 35 6) (0 .0 27 7) (0 .1 91 ) (0 .2 6) Ja pa n - 0. 13 4* ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 3 0 .0 17 0 .0 29 7 0 .7 49 ** * - 1. 54 3* ** (0 .0 31 9) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 26 2) (0 .0 55 4) (0 .0 44 2) (0 .2 55 ) (0 .3 87 ) Volume 31, Number 1 277 K or ea , S ou th - 0. 01 37 - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 05 35 - 0. 14 4 0 .0 82 1 .2 40 ** * - 0. 15 8 (0 .0 14 9) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 45 9) (0 .1 1) (0 .0 76 7) (0 .2 51 ) (0 .1 82 ) M ex ic o - 0. 01 48 - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 34 6 - 0. 06 32 - 0. 01 11 0 .9 27 ** * - 0. 17 3 (0 .0 13 1) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 22 4) (0 .0 49 1) (0 .0 39 1) (0 .1 45 ) (0 .1 64 ) N et he rla nd s - 0. 09 28 * - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 06 02 0 .0 83 9 - 0. 05 11 0 .6 24 - 1. 05 0* (0 .0 48 6) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 41 8) (0 .0 90 6) (0 .0 67 2) (0 .5 9) (0 .5 49 ) N ew Z ea la nd - 0. 10 5* ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 08 84 ** 0 .0 84 5 - 0. 02 64 - 0. 36 - 1. 21 8* * (0 .0 39 4) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 34 7) (0 .0 74 7) (0 .0 57 1) (0 .3 07 ) (0 .4 75 ) N or w ay - 0. 02 08 - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 09 35 ** * - 0. 02 93 0 .0 43 3 0 .9 45 ** - 0. 25 (0 .0 30 7) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 31 7) (0 .0 69 6) (0 .0 53 5) (0 .4 03 ) (0 .3 48 ) Po la nd - 0. 00 02 6 - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 09 02 - 0. 02 24 0 .0 06 65 0 .8 61 ** * - 0. 00 42 5 (0 .0 24 1) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 29 ) (0 .0 65 7) (0 .0 49 9) (0 .1 61 ) (0 .3 11 ) Po rtu ga l - 0. 05 78 - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 17 4 - 0. 04 27 - 0. 05 24 0 .2 71 - 0. 67 7 (0 .0 36 1) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 52 3) (0 .1 29 ) (0 .0 91 1) (0 .3 68 ) (0 .4 39 ) Sp ai n - 0. 04 28 - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 20 2 0 .0 05 39 0 .0 59 8 0 .7 41 * - 0. 49 5 (0 .0 28 4) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 32 7) (0 .0 83 4) (0 .0 55 9) (0 .4 5) (0 .3 34 ) Sw ed en - 0. 06 22 ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 01 46 - 0. 08 05 0 .0 50 3 0 .3 3 - 0. 71 6* * (0 .0 31 6) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 46 4) (0 .1 04 ) (0 .0 73 4) (0 .4 92 ) (0 .3 56 ) Sw itz er la nd - 0. 08 23 ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 06 29 * - 0. 07 81 - 0. 08 82 0 .4 81 * - 0. 95 1* * (0 .0 36 2) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 35 4) (0 .0 75 ) (0 .0 58 2) (0 .2 88 ) (0 .4 24 ) Tu rk ey - 0. 11 0* ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 03 56 0 .0 39 3 0 .0 00 12 2 0 .7 27 ** * - 1. 42 6* ** (0 .0 25 8) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 33 8) (0 .0 77 ) (0 .0 57 7) (0 .1 82 ) (0 .3 52 ) U ni te d K in gd om - 0. 12 0* * - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 14 6 - 0. 00 57 3 0 .0 05 76 0 .6 4 - 1. 42 7* * (0 .0 59 8) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 46 7) (0 .0 97 6) (0 .0 75 9) (0 .5 35 ) (0 .7 06 ) U ni te d St at es - 0. 06 52 ** * - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** 0 .0 02 78 0 .0 20 8 - 0. 01 84 1 .0 44 ** * - 0. 73 6* ** (0 .0 16 8) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 14 6) (0 .0 30 9) (0 .0 24 2) (0 .1 5) (0 .1 93 ) - 0. 06 22 ** - 0. 46 4* ** - 0. 22 3* * - 0. 26 7* ** - 0. 01 46 - 0. 08 05 0 .0 50 3 0 .3 3 - 0. 71 6* * (0 .0 31 6) (0 .0 76 6) (0 .0 88 2) (0 .0 66 8) (0 .0 46 4) (0 .1 04 ) (0 .0 73 4) (0 .4 92 ) (0 .3 56 ) 278 Journal of Business Strategies Table 4 lists results from dynamic fixed effects. Note all parameters of in- terest are correctly signed and significantly different from zero. The long-run price elasticities have increased in magnitude while the income elasticity has decreased in magnitude. Unlike the previous models, the hypothesis of price symmetry is not rejected at the 5% level7. The Hausman test statistic is 16.51 which a p-value of 0.0009. The test of parameter homogeneity across countries is rejected. The associated p-value of 0.0009 for the Hausman specification test indicates the dynamic fixed effects model suffers from endogeneity bias. The bias is a result of the constraint that all OECD countries respond identically to income changes8. In other words, the Hausman test leads us to the conclusion that the assumption that OECD nations share the same short-run dynamics and long-run income elasticity is incorrect. Based on this, the dynamic fixed effects model is biased and the results should be discarded. COnClusIOn Using recently developed dynamic panel data techniques we estimated a non-structural demand model for OECD nations. According to our analysis, oil demand responds asymmetrically to price shocks. Specifically, we observed the demand is quite sensitive to new historical maximum prices yet only moderately sensitive to price recoveries and cuts. Unlike previous studies, we fail to reject that demand responds equally to price recoveries and price cuts. Our results indicate the long-run price elasticity for a price maximum is nearly twice as great (-.464) as for other price movements (approx. -0.25). Original models we estimated, but not reported here, imposed the same speed of adjustment of oil demand to income shocks as to the price shocks. Doing so re- sulted in implausibly large income elasticities9. Following Gately and Huntington (2002), the results presented in this paper allow oil demand to adjust immediately to income shocks. The resulting estimated income elasticity is 0.66 For OECD nations over the period 1970–2004, we conclude all countries share a common long-run price elasticity and speed of adjustment to equilibrium. With respect to income, each nation responds immediately. Further, we reject the hypothesis of income elasticity homogeneity within our sample. 7 The corresponding p-value is 0.0516. 8 Recall Figure 2 to see why, in fact, that is unlikely. 9 By implausible we mean greater than unity. We expect income elasticities for OECD countries to be bound between 0 and 1. Volume 31, Number 1 279 rEFErEnCEs Alan Heston, R. S. and Aten, B. (2006). Penn World Table Version 6.2. Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania. Arellano, M. and Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Eco- nomic Studies, 58:227–297. Baltagi, B. H. (2001). Econometric Analysis of Panel Data. Wiley, England, second edition. Blackburne, E. F. and Frank, M. W. (2007). Estimation of nonstationary heteroge- neous panels. Stata Journal, 7(2):197–208. Frank, M. W. (2005). Income inequality and economic growth in the US: A panel cointegration approach. Sam Houston State University Working Paper 05-03. Freeman, D. G. (2000). Alternative panel estimates of alcohol demand, taxation, and the business cycle. Southern Economic Journal, 67(2):325–344. Gately and Huntington, (2002) The asymmetric effects of changes in price and in- come on energy and oil demand. The Energy Journal, 23(1):19–55. IEA, (2006). World Energy Outlook 2006. Paris: IEA,OECD. Im, K. S., Pesaran, M. H., and Shin, Y. (2003). Testing for unit roots in heteroge- neous panels. Journal of Econometrics, 115(1):53–74. Martinez-Zarzoso, I. and Bengochea-Morancho, A. (2004). Pooled mean group estimation of an environmental kuznets curve for 2co . Economics Letters, 82(1):121–126. Pesaran, M. H., Shin, Y., and Smith, R. P. (1997). Estimating long-run relationships in dynamic heterogeneous panels. DAE Working Papers Amalgamated Series 9721. Pesaran, M. H., Shin, Y., and Smith, R. P. (1999). Pooled mean group estimation of dynamic heterogeneous panels. Journal of the American Statistical Association, 94(446):621–634. Pesaran, M. H. and Smith, R. P. (1995). Estimating long-run relationships from dy- namic heterogeneous panels. Journal of Econometrics, 68(1):79–113. Phillips, P. C. B. and Moon, H. R. (2000). Nonstationary panel data analysis: An overview of some recent developments. Econometric Reviews, 19(3):263–286. 280 Journal of Business Strategies BIOgrAPhICAl sKETCh OF AuThOrs Edward Blackburne (PhD, Texas A&M University) currently serves as Chair of the Department of Economics and International Business at Sam Houston State University. Dr. Blackburne has published a dozen articles in journals including the Journal of Business Strategies, Journal of Developing Areas, Journal of Econom- ics and Finance Education, Journal of Finance Case Research, Stata Journal, and Advances in Economics of Energy and Resources. A popular speaker, Dr. Black- burne has over three dozen presentations to regional and national organizations. His research interests include regional economic development, energy, partial pooling of panel data, and asymmetries in structural relationships. Donald L. Bumpass (BA, MS, PhD, Oklahoma State University) currently serves as Professor of Economics at Sam Houston State University. Dr. Bumpass has published over 30 articles in numerous journals including Atlantic Economic Jour- nal, B.E. Journal of Economic Analysis & Policy, Journal of Business Strategies, Review of Industrial Organization, American Economist, Antitrust Law & Econom- ics Review, Journal of Economic Education, and Journal of Economics. His research interests include regional economic development and energy.