This paper investigates whether there is energy intensity convergence in the Organization for Economic Cooperation and Development (OECD) countries or not by using annual data from the 1980-2011 period. OECD countries are Australia, Austria, Belgium, Canada, Chile, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, North Korea, South Korea, Luxembourg, Mexico, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK, and USA. Energy intensity is measured by the ratio of total energy consumption to total output. Energy intensity measures the energy consumption of an economy and its overall energy efficiency. We used linear and nonlinear unit root tests from the recent literature to accomplish this goal. An analysis of the test results shows that there is no convergence in Chile, Finland, Greece, Ireland, South Korea, Luxembourg, Mexico, Netherlands, New Zealand, Portugal, Spain, Sweden, Switzerland, and the UK. These countries should start implementing changes to their energy policies to achieve effective energy use.
Energy intensity is measured by the ratio of total energy consumption to total output, measured as Gross Domestic Product (GDP). It measures the energy consumption of an economy and its overall energy efficiency. High energy intensities indicate a high price or cost of converting energy into GDP. Low energy intensity indicates a lower price or cost of converting energy into GDP. This ratio is a measurement used in the comparison of the countries in this study. The oil crises experienced in the 1970’s have revealed the effects of energy on the economies of countries in different parts of the world. Several studies in this area focused on the correlation between energy consumption and growth [
Nilsson [
Pen and Sevi [
Ezcurra [
Since economic convergence can occur if poorer countries or regions grow more rapidly than the richer countries and regions, the notation of economic convergence deals with the important question of whether poorer countries grow at a faster rate than richer countries [
1 T log ( y i , t y i , t − T ) = a − [ 1 − e − β T T ] ⋅ log ( y i , t − T ) + u i , t
Here, y i , t − T indicates the real income per capita in the starting year and y i , t indicates the income per capita in the year of t. β is the coefficient that indi- cates the convergence rate. This coefficient must be statistically significant. If the coefficient is positively marked, occurrence of convergence is mentioned and if it is negatively marked, the divergence is mentioned.
The second convergence type is σ type convergence. In this convergence type, standard deviation value is used for measuring the expansion. The decrease of standard deviation in terms of time indicates occurrence of convergence. If the standard deviation increases in terms of the time, the divergence comes into question. Sigma stands for the standard deviation of log GDP per capita values. In case of convergence, sigma shows a negative trend in a time period. This also means that inequalities are diminishing. Sigma convergence refers to a reduction in the dispersion of income levels across economies.
The third convergence type is stochastic convergence. The stochastic conver- gence was introduced by Carlino and Mills [
lim k → ∞ Ε ( y i , t + k − y j , t + k | I t ) = 0
where y i is the log real GDP per capita in country i, I t is the information set available at period t. In other words, it means convergence of i and j economies to each other that the logarithms of production level per capita in a specific t time was equal for two countries. Stochastic convergence asks whether per- manent movements in one country’s per capita income are associated with permanent movements in other countries’ income [
In this study, we investigate the convergence of energy intensity among OECD countries (Australia, Austria, Belgium, Canada, Chile, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, North Korea, South Korea, Luxembourg, Mexico, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK, USA) and use a nonlinearity test established by Harvey et al., [
The outline of this paper as follows. In section two, we explain the data and the empirical methodology, section three presents the empirical results, and the last section provides the conclusions.
This paper investigates the convergence of energy intensity in OECD countries using annual data covering the 1980-2011 period (as Italy does not have data belonging to 1980, 1981-2011 data were used). The energy intensity is measured as Total Energy Consumption per Dollar of GDP (using purchasing power parity). All data are from the US Energy Information Administration. Stochastic convergence is introduced by Carlino and Mills [
y i j t = log Y i t − log Y j t
where y i j t is the analyzed variable, Y i t is the variable value for unit i at time t and Y j t is the variable value for unit j at time t.
Carlino and Mills [
y i t = ln ( x i t x ¯ t )
where x i t is energy intensity of country i, x ¯ t is the average energy intensity of OECD.
The method frequently used for empirically testing the stochastic convergence is the use of unit root tests. If the series is stationary, a finding is obtained regarding that there is convergence, and if it is not stationary, a finding is achieved about that there is no convergence. The biggest problem in the studies that were carried out based on the unit root tests was the selection of the right test. Different tests selected yield different results and the findings obtained show differences. The standard tests for unit root and cointegration all have lower power in the presence of misspecified dynamics [
A unit root test appropriate for the data structure is selected to prevent biased results. The series are tested using nonlinearity test developed by Harvey et al., [
In this study, we used nonlinearity test developed by Harvey et al., (2008) for determination of nonlinearity properties of the series because it is not affected by stationary levels of the variables. The model to use under the assumption that time series is stationary (I(0)) for implementation of the test developed by Harvey et al., [
y t = β 0 + β 1 y t − 1 + β 2 y t − 2 2 + β 3 y t − 3 3 + ∑ j = 1 p β 4 , j Δ y t − j + ε t (1)
where Δ is the first difference operator, p is the number of lags. As suggested in the studies of Harvey et al., [
(number of lags) p max = int ( 8 ( T 100 ) 1 / 4 ) and optimal number of lags can be
determined by means of the sequential testing method using a 10% significance level. The null hypotheses to be used for the test are in the form of
H 0 , I ( 0 ) : β 2 = β 3 = 0 ( linearity )
moreover, the alternative hypothesis
H 1 , I ( 0 ) : β 2 ≠ 0 and / or β 3 ≠ 0 ( nonlinearity ) .
The test statistic is calculated as follows:
W 0 = T ( R S S 0 r R S S 0 u − 1 )
Here, T is the number of observations, R S S 0 r and R S S 0 u are the residual sum of squares from the unrestricted and restricted form of the model 1, respectively.
The model to use under the assumption of that time series is not stationary (I(1)) is shown as follows:
Δ y t = λ 1 Δ y t − 1 + λ 2 ( Δ y t − 1 ) 2 + λ 3 ( Δ y t − 1 ) 3 + ∑ j = 1 p λ 4 , j Δ y t − j + ε t (2)
The null hypotheses to use for the test are in the form of H 0 , I ( 1 ) : λ 2 = λ 3 = 0 ( linearity ) and alternative hypothesis
H 1 , I ( 1 ) : λ 2 ≠ 0 and / or λ 3 ≠ 0 ( nonlinearity ) .
The test statistic is calculated as follows:
W 1 = T ( R S S 1 r R S S 1 u − 1 )
where R S S 0 r and R S S 0 u are the residual sum of squares from the unrestiricted and restiricted form of the model 2, respectively.
In their studies, Harvey et al., [
W λ = { 1 − λ } W 0 + λ W 1
where λ is a function that convergences in probability to 0 if time series is I(0) and to 1 if time series is I(1). W λ is asymptotically distributed as χ 2 2 .
1) Kapetanios, Shin, Snell (2003) Unit Root Test
Kapetanios et al., [
y t = β y t − 1 + γ y t − 1 Θ ( θ ; y t − d ) + ε t , t = 1 , ⋯ , T (3)
in which β and γ are unknown parameters and ε t ~ i i d ( 0 , σ 2 ) . The transition function adopted exponential form, Θ ( θ ; y t − d ) = 1 − exp ( − θ y t − d 2 ) where they assumed that θ ≥ 0 , and d ≥ 1 is the lag parameter. The exponential transition function is limited to be between zero and one. Using (10) and (11) obtained an ESTAR model, y t is shown as follows:
y t = β y t − 1 + γ y t − 1 [ 1 − exp ( − θ y t − d 2 ) ] + ε t , t = 1 , ⋯ , T
where using parameter conveniently, it is rewritten as,
Δ y t = ϕ y t − 1 + γ y t − 1 [ 1 − exp ( − θ y t − d 2 ) ] + ε t , t = 1 , ⋯ , T (4)
In which ϕ = β − 1 . If θ is positive, it effectively determines the speed of mean reversion. Kapetanios et al., [
Δ y t = γ y t − 1 [ 1 − exp ( − θ y t − 1 2 ) ] + ε t (5)
In test procedures, specific parameter θ , which is zero under the unit root null hypothesis and positive under the globally stationary ESTAR alternative hypothesis is H 0 : θ = 0 , H 1 : θ > 0 Testing the null hypothesis directly is not feasible, γ is not identified under the null. To overcome this problem, t-type test statistics are used. They demonstrate a first-order Taylor series approximation to the ESTAR model under the null, the auxiliary regression,
Δ y t = δ y t − 1 3 + error (6)
They obtain the t-statistic for δ < 0 against δ < 0 as t N L = δ ^ / s . e . ( δ ^ ) where δ ^ is the OLS estimate of δ and s . e . ( δ ^ ) is the standard error of δ ^ . Kapetanios et al., [
2) Kruse (2011) Unit Root Test
Kruse’s [
Δ y t = ϕ y t − 1 ( 1 − exp { − γ ( y t − 1 − c ) 2 } ) + ε t (7)
This equation is transformed into the below form by using Taylor approximation as utilized in the study by Kapetanios et al., [
Δ y t = δ 1 y t − 1 3 + δ 2 y t − 1 2 + ∑ j = 1 p φ j Δ y t − j + ε t (8)
Concerning this, Kruse [
3) Sollis (2009) Unit Root Test
KKS test is based on the assumption of that mean reversion is symmetric at every point. This assumption means that negative and positive deviations have the same effect. Sollis [
Δ y t = G ( γ 1 , y t − 1 ) { S t ( γ 2 , y t − 1 ) ρ 1 + ( 1 − S t ( γ 2 , y t − 1 ) ) ρ 2 } y t − 1 + ∑ i = 1 k k i Δ y t − i + ε i (9)
Here, G ( γ 1 , y t − 1 ) = 1 − exp ( − γ 1 ( y t − 1 2 ) ) with γ 1 ≥ 0 and S t ( γ 2 , y t − 1 ) = { 1 + exp ( − γ 2 y t − 1 ) } − 1 with γ 2 ≥ 0 .
The model for Taylor approximations as it was for KSS tests is as follows [
Δ y t = a ( ρ 2 * − ρ 1 * ) γ 1 γ 2 y t − 1 4 + ρ 2 * γ 1 y t − 1 3 + η i (10)
where ρ 1 * ve ρ 2 * are linear function of ρ 1 and ρ 2 . Where a = 1 / 4 , which can be written
Δ y t = ϕ 1 y t − 1 3 + ϕ 2 y t − 1 4 + η i (11)
where ϕ 1 = ρ 2 * γ 1 and ϕ 2 = a ( ρ 2 * − ρ 1 * ) γ 1 γ 2 . An augmented version is
Δ y t = ϕ 1 y t − 1 3 + ϕ 2 y t − 1 4 + ∑ i = 1 k k i Δ y t − i + η i (12)
where y t , similar KSS test, is raw, demeaned or detrended data. The null hypothesis of nonstationarity is H 0 : ϕ 1 = ϕ 2 = 0 . Sollis [
F = ( R β ^ − r ) ′ [ σ ^ 2 R { ∑ t x t x ′ t } − 1 R ′ ] − 1 ( R β ^ − r ) / m (13)
The critical values of F statistic are tabulated by Sollis [
Narayan and Popp [
d t M 1 = α + β t + Ψ * ( L ) ( θ 1 D U ′ 1 , t + θ 2 D U ′ 2 , t ) (14)
d t M 2 = α + β t + Ψ * ( L ) ( θ 1 D U ′ 1 , t + θ 2 D U ′ 2 , t + γ 1 D T ′ 1 , t + γ 2 D T ′ 2 , t ) (15)
where D U ′ 1 , t = 1 ( t > T ′ B , i ) , D T ′ 1 , t = 1 ( t > T ′ B , i ) ( t − T ′ B , i ) , i = 1 , 2 . T ′ B , i , i = 1 , 2 , denotes the true break dates. The parameters, θ i and γ i indicate the magnitude of the level and slope breaks, respectively.
The test equation used for Model 1 (M1) that allows for two structural breaks in level in mean is presented below.
y t M 1 = ρ y t − 1 + α 1 + β * t + θ 1 D ( T ′ B ) 1 , t + θ 2 D ( T ′ B ) 2 , t + δ 1 D U ′ 1 , t − 1 + δ 2 D U ′ 2 , t − 1 + ∑ j = 1 k β j Δ y t − j + e t (16)
where α 1 = Ψ * ( 1 ) − 1 [ ( 1 − ρ ) α + ρ β ] + Ψ * ′ ( 1 ) − 1 ( 1 − ρ ) β , Ψ * ( 1 ) − 1 being the mean lag, β * = Ψ * ( 1 ) − 1 ( 1 − ρ ) β , ϕ = ρ − 1 , δ i = − ϕ θ i and D ( T ′ B ) i , t = 1 ( t = T ′ B , i + 1 ) , i = 1 , 2 , ⋯ .
T ′ B , i , i = 1 , 2 , denotes true break dates. The break dates are selected using sequential procedure that selects the break dates when the absolute t-value of the break dummy coefficients is maximized.
The test equation used for Model 2 (M2) that allows for two structural breaks n level on average and in trend is presented below.
y t M 2 = ρ y t − 1 + α * + β * t + κ 1 D ( T ′ B ) 1 , t + κ 2 D ( T ′ B ) 2 , t + δ 1 * D U ′ 1 , t − 1 + δ 2 * D U ′ 2 , t − 1 + γ 1 * D T ′ 1 , t − 1 + γ 2 * D T ′ 2 , t − 1 + ∑ j = 1 k β j Δ y t − j + e t (17)
where κ i = ( θ i + γ i ) , δ i * = ( γ i − ϕ θ i ) and γ i * = − ϕ γ i , i = 1 , 2 .
The t statistics of the ρ ^ parameter is used to test the null hypothesis of unit root against the ρ = 1 , ρ < 1 alternative hypothesis. The test critical values are tabulated in Narayan and Popp [
We reviewed whether the series to examine at the first stage of the study for convergence were linear or not by using the test developed by Harvey et al., [
According to the results in
| Country | Harvey Statistics |
|---|---|
| Australia | 5.31* |
| Austria | 1.25 |
| Belgium | 2.79 |
| Canada | 3.20 |
| Chile | 2.48 |
| Denmark | 0.08 |
| Finland | 0.66 |
| France | 4.76* |
| Germany | 7.59* |
| Greece | 1.64 |
| Ireland | 1.25 |
| Italy | 314.17* |
| Japan | 5.55* |
| North Korea | 6.95* |
| South Korea | 3.95 |
| Luxembourg | 6.25* |
| Mexico | 1.64 |
| Netherlands | 3.48 |
| New Zealand | 1.31 |
| Norway | 1.68 |
| Portugal | 2.96 |
| Spain | 5.64* |
| Sweden | 6.69* |
| Switzerland | 0.49 |
| Turkey | 13.03* |
| UK | 12.94* |
| USA | 5.47* |
Note: The symbols *, **, and *** mean rejection of the null hypothesis of linearity at the 1%, 5%, and 10% respectively. Harvey et al. (2008) test critical values, 9.21, 5.99 and 4.60 respectively.
| KSS | Kruse | Sollis | ||||||
|---|---|---|---|---|---|---|---|---|
| k | Stat | k | Stat | k | p value | |||
| Australia | 1 | −1.96816 | 1 | 9.388311c | 1 | 7.795929a | 3.567142 | 0.0697 |
| France | 2 | −1.88583 | 2 | 3.647676 | 2 | 3.534421 | 0.101031 | 0.7532 |
| Germany | 1 | −2.59058 | 1 | 8.088011 | 1 | 8.148822a | 1.353101 | 0.2549 |
| Italy | 1 | 0.271862 | 1 | 3.016651 | 1 | 2.529186 | 2.451304 | 0.1295 |
| Japan | 3 | −1.4322 | 3 | 2.305626 | 3 | 2.140589 | 0.161094 | 0.6919 |
| North Korea | 1 | −2.19993 | 1 | 4.688372 | 1 | 5.149429b | 0.411479 | 0.5266 |
| Luxembourg | 1 | −1.73606 | 1 | 2.924167 | 1 | 3.031412 | 0.112972 | 0.7394 |
| Spain | 2 | −0.67941 | 2 | 1.688755 | 2 | 0.611304 | 0.164543 | 0.6885 |
| Sweden | 2 | 0.478338 | 3 | 1.74167 | 3 | 1.402575 | 1.393938 | 0.2498 |
| Turkey | 2 | −0.79225 | 1 | 15.49859a | 1 | 12.79519a | 3.065895 | 0.0913 |
| UK | 1 | 0.004095 | 1 | 7.713567 | 1 | 3.707096 | 3.707077 | 0.0648 |
| USA | 2 | −2.92075c | 2 | 8.302401 | 2 | 8.302401a | 0.075079 | 0.7863 |
Note: The symbols a, b and c mean rejection of the null hypothesis of unit root at the 1%, 5% and 10% respectively. KSS: −3.48, −2.93, −2.66; KRUSE: 13.75, 10.17, 8.6; Sollis: 6.883, 4.954, 4.157.
nonlinear, Austria, Belgium, Canada, Chile, Denmark, Finland, Greece, Ireland, South Korea, Mexico, Netherlands, New Zealand, Norway, Portugal, Switzerland are not nonlinear. By using this basic finding, convergence is investigated for the countries having nonlinear data using the tests of Kapetanios et al., [
The first part of
According to the results in
The oil crises experienced in the 1970s revealed the importance of the energy in the world economy and how energy impacts global markets in so many different ways. The energy intensity is the measurement used for the energy efficiency. Energy intensity is measured by the ratio of total energy consumption to total
| Country | k | t-statistic | TB1 | TB2 |
|---|---|---|---|---|
| Austria | 5 | −4.907b | 1994 | 2000 |
| Belgium | 3 | −4.797b | 1991 | 1996 |
| Canada | 0 | −4.392b | 1991 | 1999 |
| Chile | 0 | −1.968 | 1990 | 1996 |
| Denmark | 0 | −4.232c | 1995 | 1999 |
| Finland | 2 | −3.262 | 1990 | 1994 |
| Greece | 5 | −2.833 | 1997 | 2003 |
| Ireland | 2 | −2.296 | 1987 | 2002 |
| South Korea | 0 | −1.859 | 1988 | 1996 |
| Mexico | 0 | −2.662 | 1989 | 1996 |
| Netherlands | 4 | −2.796 | 1997 | 2003 |
| New Zealand | 2 | −3.819 | 1995 | 2002 |
| Norway | 3 | −4.527b | 1993 | 1995 |
| Portugal | 0 | −2.351 | 1990 | 1993 |
| Switzerland | 0 | −1.500 | 1998 | 2000 |
Note: The symbols *, **, and *** mean rejection of the null hypothesis of a unit root at the 1%, 5%, and 10% respectively. Critical values are −5.259, −4.514, −4.143 at the 1%, 5%, and 10%, respectively. TB1 and TB2 denote the structural break dates suggested by the tests.
output (GDP). In this study, we reviewed the convergence of energy intensity in OECD countries.
We used nonlinearity test developed by Harvey et al., [
Canel, C., Guris, S., Guris, B., Öktem, B. and Oktem, R. (2017) Convergence of Energy Intensity in OECD Countries. Modern Economy, 8, 946-958. https://doi.org/10.4236/me.2017.87066