Convergence and persistence in per capita energy use among OECD countries: Revisited using confidence intervals

    Convergence and persistence in per capita energy use among OECD countries: Revisited using confidence intervals Firouz Fallahi, Marcel Voia PII: DOI: Reference:

S0140-9883(15)00279-0 doi: 10.1016/j.eneco.2015.10.004 ENEECO 3175

To appear in:

Energy Economics

Received date: Revised date: Accepted date:

3 November 2014 21 September 2015 1 October 2015

Please cite this article as: Fallahi, Firouz, Voia, Marcel, Convergence and persistence in per capita energy use among OECD countries: Revisited using confidence intervals, Energy Economics (2015), doi: 10.1016/j.eneco.2015.10.004

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Firouz Fallahi∗

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Convergence and persistence in per capita energy use among OECD countries: Revisited using confidence intervals Marcel Voia†

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October 22, 2015

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Abstract

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This paper investigates the convergence in per capita energy use of a group of 25 OECD countries over the period 1960-2012. Unlike the previous studies, which mainly used unit root tests, in this study we construct subsampling confidence intervals to assess the convergence in the per capita energy use. These confidence intervals are more informative than the unit root tests, as they provide us with further information on the degree of persistence of the energy use. Our findings suggest that the per capita energy use in Australia, Austria, Belgium, Denmark, Finland, Greece, Italy, Japan, Luxembourg, Netherlands, Norway, Spain, and Switzerland has a convergent pattern. However, the per capita energy use in Greece, Luxemburg, and Spain appear to be very persistent. For the rest of the countries, i.e. 12 countries, we see a divergent pattern. Keywords: Energy Use; Convergence; Persistence; Confidence Interval; Subsampling JEL classification: C22, Q40

∗ Address for Correspondence: Firouz Fallahi, Department of Economics, University of Tabriz, 29 Bahman Bolv, Tabriz, Iran. Telephone: +98-9144190447, Fax: +98-4133392352, E-Mail: [email protected]. † Economics Department and Centre for Monetary and Financial Economics (CMFE), Carleton University. Mailing address: Economics Department, Carleton University, Loeb Building 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6 Canada. Tel (613) 520-2600-3546; FAX: (613)-520-3906; email: marcel-cristian [email protected].

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Introduction

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Energy is considered a key factor in the economic development of any country

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and understanding energy use pattern is important from different perspectives, namely: its link to economic growth and sustainable energy consumption; its relationships with greenhouse gas emissions and climate change; and energy

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security, amongst many. So, to better understand the impact of energy use, we examine the stochastic convergence of per capita energy use (PEC) among 25 OECD countries1 in a time series framework.2

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There are three major types of convergence: β−convergence, σconvergence, and stochastic convergence.3 The notion of β-convergence initiated from the neo-classical growth theory (Solow, 1956) and im-

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plies that poor countries grow faster than the rich ones and the gap between them shrinks over time. In energy use terms, it means that the PEC in countries with initially high PEC will tend to grow slower than the countries with low PEC. On the other hand, σ-convergence

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refers to a decline of disparity measured in terms of any economic variable such as output, energy use, and unemployment. It occurs when

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the standard deviation or the coefficient of variation of the variable of interest decreases significantly over time. Stochastic convergence as suggested by Carlino and Mills (1993) deals with the effect of shocks and

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means that shocks to PEC of country i relative to the average PEC would be temporary. In other words, stochastic convergence would be considered equivalent to the stationarity of the relative PEC, which means that following a

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shock to the relative PEC in country i, it will return to its deterministic

mean/trend and the difference between PECi and average PEC will be deterministic and predictable. Therefore, the long-term forecast of the difference between the PECi and the average PEC tends to zero as the forecast horizon grows (Bayer and Juessen, 2007).4 It is 1 The sum of energy use in this sample of countries amounts to approximately 40% of world’s final energy consumption in 2012 (EIA report). 2 This paper is among the few papers that examines the convergence in PEC, as most of the studies in the energy economic literature, have examined convergence in carbon dioxide emissions and energy intensities among countries, see Barassi, et al, 2008; Lee and Chang, 2008; Liddle, 2009; Mulder and Groot, 2012; Strazicich and List, 2003; inter alia. 3 For a good survey on convergence see Islam (2003). 4 It must be emphasized that objective of this paper is to examine the stochastic convergence only and we are not studying other types of convergence such as β-convergence or

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worth noting that the existence of stochastic convergence does not

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imply that the PECs will become equal, rather it means that the

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long-term differences between the PECi and the average PEC is deterministic and predictable. In addition, based on Carlino and Mills (1993) both stochastic and β-convergences are necessary to have a real convergence between PECi and the average PEC.

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Convergence is said to be absolute if all countries converge to the same steady-state, however if each country converges to its own steady-state, it is called conditional convergence. Therefore, stochastic convergence will be condi-

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tional when a constant term is included in the models. Moreover, inclusion of a time trend in the model helps to distinguish two types of convergence. When PEC is stationary, a non-significant trend in the

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equation would imply long-run convergence. On the other hand, a significant time trend given the stationary of PEC would imply convergence as catching-up or lagging-behind type (Oxley and Greasley,

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1995; Bernard and Duarlauf, 1996). Most of the existing studies that analyzed the PEC, have used unit root tests or stationarity tests, with or without structural breaks, to infer convergence (or

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otherwise). Failure to reject the null hypothesis of unit root would be sufficient to conclude that the variable does not have a convergent pattern. Whereas, if we can reject the null of unit root, then the time series is stationary, the effect of

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shocks will dissipate over time, and the series will have a convergent behavior. However, it is widely acknowledged that these tests have low power especially in small samples and near-unit-root cases. The former issue is relevant in the

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energy related studies. As Narayan and Smyth (2014) have pointed out, most of the energy related data have 30-50 years of annual observations, which is considered a small sample size, and might adversely affect the power of unit root tests. To address these issues in a robust way, in this paper we take a different approach and study the convergence of PEC in the OECD countries using a confidence intervals type approach.5 To that end, we construct confidence intervals (CIs) for the sum of the coef-

σ-convergence. 5 To the best of our knowledge, this is the first paper that uses these approaches to examine the convergence of energy use.

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ficients in an AR(p) model, denoted by α.6 In an AR(p) model, the cumulative 1 1−α

over all time horizons and there is a

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impulse response (CIR) is measured by

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monotonic relation between α and the CIR (Andrews and Chen, 1994). Therefore, using α we could summarize the whole impulse response function into a single scalar measure. In addition, the parameter α determines the spectrum at the frequency zero of the series (Andrews and Chen, 1994).

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The asymptotic CIs can be constructed using α ˆ ± tσ, where σ denotes the

standard error; however, the limiting distribution of the OLS estimator depends on whether or not α = 1. To overcome this limitation, we construct CIs using

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subsampling approaches introduced by Romano and Wolf (2001). These approaches can handle the discontinuity of the limiting distribution of the OLS estimator, which is a function of α. Using these approaches instead of relying

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on point estimates of α, we can get an interval for α, which provides more information regarding the properties of the PEC compared with the unit root tests. In fact, the results from CIs not only show whether the null of a unit

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root can be rejected or not, but also as noted in Romano and Wolf (2001, p. 1283) they provide us a measure of sampling uncertainty and shows the range of models that are consistent with the data. In other words, not only they show

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the integration order of the variable, but also, unlike the unit root tests, they provide information on the persistence degree of shocks as well. In addition, these approaches perform well even at local-to-unity cases.

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Even though several papers have studied the integration property of PEC (Narayan and Smyth, 2007; Chen and Lee, 2007; Hsu et al., 2008; Mishra et al, 2009; Narayan et al, 2010; Aslan and Kum, 2011; Hasanov and Telatar, 2011;

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Meng et al, 2013; to name a few7 ), however, only a few of them have studied convergence in energy use. Maza and Villaverde (2008) studied the convergence of per capita residential

electricity consumption in a sample of 98 countries during the period 1980-2007. Based on parametric approaches they found evidences that support the σ and β convergence among these countries. However, according to the results from the non-parametric approach, the process of convergence is weak. Mohammadi and Ram (2012) using cross country data from 1971 to 2007 studied the convergence 6 α is a measure of how close the process is to being non-stationary (Andrews and Chen, 1994). 7 For a complete survey see Smyth, 2013.

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of per capita consumption of energy and electricity. They showed that global

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convergence in energy consumption is generally weak. Jakob et al (2012) exam-

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ined the change in the energy use pattern for 30 developing and 21 developed countries during the period 1971-2005. Using a difference-in-difference estimator on panel data, they found that the link between energy use and economic growth depends on the development level of the country. Meng et al (2013) studied the

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convergence of per capita energy use among 25 OECD countries over the period 1960-2010. They used newly developed unit root tests based on the residual augmented least square that allows for two break points. Their results show a

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rejection of the null hypothesis of a unit root for seventeen countries, concluding that most of these countries do converge. Mishra and Smyth (2014) using panel unit root tests showed that the per capita energy consumption among ASEAN

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countries over the period 1971-2011 had a convergent behavior. This paper aims to build on Meng et al (2013) and Mishra and Smyth (2014) to study the existence of stochastic convergence in the OECD countries

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using subsampling confidence intervals. We use a time series approach to study the same group of countries as Meng et al (2013), first to be able to compare the results, and second, because more data are available for these countries

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compared with the other members of the OECD.8 Our results indicate that the per capita energy use in Australia, Austria, Belgium, Denmark, Finland, Greece, Italy, Japan, Luxembourg, Netherlands, Norway, Spain, and Switzerland has a

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convergent pattern. These results are more robust than the results using unit root tests, as they are not sensitive to the start and end dates of the period analyzed.9

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The remainder of this paper is structured as follows. Section 2 outlines the

methodologies used in this study. In section 3, we report the data and the empirical results and section 4 concludes.

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Methodology

Stochastic convergence implies that the deviation of each variable from the average of all countries must follow a stationary process. In order to distinguish a 8 More data helps to overcome the sample size issues as stated by Narayan and Smyth (2014). 9 Because of the subsampling nature of the methods.

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stationary variable from a non-stationary one, we can use the root of the data

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generating process (DGP). Any series with a root on a unit circle is considered

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a non-stationary series. For stationary series, the roots lie inside the unit circle implying that any shock to the series would dissipate over time and will not last long. In other words, a nonstationary variable has at least one root equal to 1 or −1, but all the roots of a stationary series would be less than unity in

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absolute value. To differentiate these two types of series from each other, we

can use unit root tests. If we could reject the null hypothesis of a unit root, we conclude that the series is stationary and has a convergent pattern.10 Even

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though unit root tests are very popular in the energy economics literature, there are sample size limitations associated to this approach. As Narayan and Smyth (2014) pointed out most of the energy related data have 30-50 years of annual

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observations, which might adversely affect the power of unit root tests. Moreover, it is widely acknowledged that the unit root tests may fail to reject the null hypothesis of unit root when the root is close to the unity.11 One way

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to overcome this limitation is through employing panel data unit root tests; however, as Narayan and Smyth (2014, p. 2) states, ”the panel data will not be appropriate if the research question and resulting policy implications focus on

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results for individual countries”. Therefore, new approaches are needed to address these issues. Constructing confidence intervals (CIs) is an alternative way to infer the stationarity of a variable of interest. The series is called stationary

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if the upper bound of the constructed CI is less than 1, but if the CI contains 1 the series would be considered non-stationary. The results from this CI not only show the stationarity or non-stationarity of data but also they show the

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degree of persistence of the variable, which makes the results from the CIs more informative than those of the unit root tests. In an AR(p) model, CIs can be estimated for the largest coefficient (ρmax ) or

for the sum of the coefficients (α). However, the results using α provides more 10 Carlino and Mills (1993), who introduced the concept of stochastic convergence, assume that variable of interest consists of two parts: a time-invariant equilibrium level and the deviation from this equilibrium. The deviation part could be trending over time, so it is necessary to include a time trend in the model (see Carlino and Mills, 1993, p.336). 11 It is well known that the least square estimates of the autoregressive parameters in small samples are downward biased (Andrews, 1993; Cashin et al, 2000). This issue arises because the distribution is skewed to the left, so its median exceeds the mean. Therefore, it is better to use median instead of mean through median-unbiased estimators in the least square estimates of the models (see Andrews, 1993 for details).

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accurate information compared with the results from ρmax (Andrews and Chen,

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1994; Rapach and Wohar, 2004). There are several ways of building the CIs

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in the literature. Asymptotic CI is the conventional way; in this approach the lower and upper bounds of the 90% CI can be calculated as the point estimate of the root ±1.645 times the standard error. However, as noted by researchers

this way of calculating the CI is not appropriate when the root is near to unity

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and its value is large. In addition, this method is not useful in constructing the CI when the variable is integrated and has a unit root, since the traditional asymptotic theory is discontinuous at this case (Torous et al., 2004, p. 943).

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In order to overcome this deficiency, new methods have been developed that are robust to the presence of a root close to or on the unit circle. Stock (1991) using the local to unity framework developed a method to construct the CI

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of the largest autoregressive root by inverting ADF t-tests. According to this method, the largest autoregressive root modeled as ρmax = 1 + c/T , where c is a real valued constant, which shows the deviation from unit root case and T is the

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sample size. Hall (1992) introduced the percentile -t method, which uses OLS to estimate the value of autoregressive coefficient and uses this estimated value as the true value to evaluate the sampling distribution of the t-statistic and

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build the CI. However, as noted by Hansen (1999) the CIs built based on the percentile-t method has incorrect first order asymptotic coverage, that is, the interval constructed using this approach cannot control the typeI error prop-

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erly.12 Therefore, Hansen (1999) proposed using grid bootstrapping procedure. This procedure gives a CI that is asymptotically valid and can control for type I error even in the cases that the root is in the neighborhood of one. In 2001

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Romano and Wolf proposed two alternative approaches, based on the subsampling method of Polities and Romano (1994), that unlike the grid bootstrapping procedure of Hansen (1999) do not rely on the assumption of independent innovations. In other words, these procedures require very weak assumptions, can be applied to dependent innovations, and they also provide correct first-order asymptotic coverage. These approaches take subsamples or blocks without replacement from the observed data (y) and compute the coefficients of the following regression13 12 This

is true even for large samples. and Wolf (2001) have shown that the inclusion of a time trend even when the true β is zero will not affect the coverage property of their approaches. 13 Romano

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γ j ∆yt−j + ut .

j=1

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yt = µ + βt + αyt−1 +

p−1 X

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using the least square method,

(1)

TX −b+1

√ 1{ b (ˆ αb,m − α ˆ )) ≤ y}.

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Lb (y) = (T − b + 1)−1

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√ αb,m − α ˆ ) /ˆ σ b,m forDoing so, the t-statistic for α is calculated using b (ˆ mula, where b shows the block size, α ˆ is the OLS estimate of α for the mth b,m √ block. In addition, σ ˆ b,m = b × s.e (ˆ αb,m ), where s.e shows the standard error, and m = 1, 2, ..., T − b + 1.14 Next, the approximate distribution of the subsample t-statistic can be calculated using the following formula

m=1

(2)

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This approximation of subsampling distribution can be used to get the 90% two-sided equal-tailed confidence interval for α as following (3)

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ˆ + T −0.5 cb,0.050 ] [ˆ α − T −0.5 cb,0.950 , α

where cb,0.950 and cb,0.050 show the 0.95 and 0.05 quantiles of the subsampling distribution as approximated before.

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In addition, Romano and Wolf (2001) propose an alternative approach to construct the confidence interval called the two-sided symmetrical confidence interval. In order to obtain the symmetrical confidence interval, instead of

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equation (1) the following equation is used to approximate the empirical distri-

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bution

Lb,|.| (y) = (T − b + 1)−1

TX −b+1 m=1

√ 1{ b |ˆ αb,m − α ˆ |) ≤ y}.

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If the quantiles from this approximate distribution is used, the constructed confidence interval is called the symmetric confidence interval. Romano and Wolf (2001) and Mikusheva (2007) have shown that the two-sided symmetric confidence interval is superior to the equal-tailed two-sided confidence interval. Because the results from the symmetric confidence intervals are uniformly asymptotically valid, while the results from equal-tailed method are only point wise consistent; therefore, it is recommended to use the results from the twosided symmetric confidence interval. √ 14 b is called the normalizing constant.

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Selection of subsample or block size is the other issue that needs to be

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addressed before proceeding this approach. Romano and Wolf (2001) propose

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the following algorithm to select the block size.

First, compute the 90% confidence interval for α for each b ∈ [bsmall , bbig ]

and denote the endpoints with Ib,low and Ib,up .15 Next, for every b calculate the standard deviation of the interval endpoints and select the value of b with the

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smallest standard deviation as the optimum block size, b∗ , and report [Ib∗ ,low , Ib∗ ,up ] as the final confidence interval for the α.16

Data and empirical results

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Our data set17 includes relative PEC (kg of oil equivalent) over the period countries.

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1960-2012 to study the stochastic convergence of energy use among 25 OECD These countries are: Australia (AUS), Austria (AUT), Belgium

(BEL), Canada (CAN), Denmark (DNK), Finland (FIN), France (FRA), Germany (GER), Greece (GRC), Iceland (ISL), Ireland (IRL), Italy (ITA), Japan

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(JPN), Luxembourg (LUX), Netherlands (NLD), New Zealand (NZL), Norway (NOR), Poland (POL), Portugal (PRT), Spain (ESP), Sweden (SWE), Switzer-

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land (CHE), Turkey (TUR), United Kingdom (UK) and the United States (USA).18 Relative PEC of country i is defined as the natural logarithm of the

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ratio of PEC in country i to the average PEC of the group as follows: yit = ln(P ECit /P EC t ).

The relative PECs are presented in Figures 1 to 4. Moreover, the descriptive

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statistics of the PEC at the beginning of different decades are shown in Table 1. As it can be seen from this table, the mean of PEC has been constantly increasing, but at a declining rate. From 1960 to 1970 the PEC has risen 54%, but from 1970 to 1980 it has increased only 15%.19 Moreover, it has experienced a single-digit rise over the next few decades.

15 Romano and Wolf (2001) recommend to set b η and b η small = c1 T big = c2 T . Based on the simulation results, they suggest to consider 0.5 ≤ c1 ≤ 1 and 2 ≤ c2 ≤ 3 and η = 0.5. 16 The choice of block size, b, plays a crucial role. Selecting a very small or very large b would result in a poor approximation of the actual distribution. 17 The data were obtained from the World Development Indicators (WDI). 18 We use the same group of OECD countries studied by Meng, Payne, and Lee (2013). These countries are selected based on data availability from 1960 to 2012. 19 This might be related to the effect of energy crises in 1970s.

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Figures 1 and 2 show the relative PEC for the first group of countries, which

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has a PEC lower than the average PEC in the OECD countries. Figure 3 shows

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the evolution of the relative PEC in the second group of countries that during the time-span of the study, have a higher PEC than the average PEC. Finally, Figure 4 shows the third group of countries that the logarithms of their relative PEC are both lower and higher than the average during the period from 1960 to

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2012. In fact, Austria, Finland, France, Greece, Iceland, Ireland, Italy, Japan, New Zealand, Norway, Portugal, Spain, and Turkey have a positive relative PEC trend; while, the relative PECs in Canada, Denmark, Luxemburg, UK, and US

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trending downwards.

The dynamics of the PEC are visualized in Figure 5, which shows a 45-degree line and the ranking of countries according to their PECs at the beginning and

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end of the sample period. As most observations are located next to the 45degree line, we could say that the rank order of countries in terms of their PEC has been quite stable from 1960 to 2012. In other words, the pattern of the PEC

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displays some sort of persistence. Luxemburg has the highest PEC among the 25 OECD countries and ranked 25 and 24, respectively in the beginning and end of the sample period. In fact, the rank of Portugal, Italy, Ireland, Belgium, and

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Canada are the same; however, the rank of Poland, Denmark, and the UK from 1960 to 2012 has decreased drastically.20 On the other hand, all the countries above the 45-degree line have risen in ranking.

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To study the existence of stochastic convergence, hereafter convergence, in the sample of OECD countries, we start the analysis with testing unit root properties of the relative PECs.

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The calculated ADF statistics are reported in the second column in Table 2.21

Based on the ADF results we are able to reject the unit root null hypothesis in

favor of the stationary alternative at the 10% level for the following countries: Austria, Denmark, and Italy. So the PEC in these three countries shows a convergent pattern. Looking at the coefficient of the time trend in the ADF models we found that the trend is not significant in the case of Italy but it is significant in Denmark and Austria. Therefore, the convergence of PEC in Italy is of long-run type; while the convergence

rank of the UK was 20 in 1960, while it ranked 8th in 2012. results from these tests only act as benchmarks, because it is widely known that these tests suffer from both power and size distortions. 20 The 21 The

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in Denmark and Austria is of catching-up or lagging-behind type. It

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is worth noting that Italy will be classified as a divergent country if we

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consider the results at the 5% significance level.

The third column shows the median-unbiased αs, which have been calculated using the approach introduced by Andrews and Chen (1994). In contrast to the least square estimates of the AR parameters, the median-unbiased αs are not

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downward biased. As it can be seen from these results, most of the estimated αs are close to unity. This closeness to unity possibly could cause size and power distortions in the results from ADF unit root test.

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Next, we calculate the 90% and 95% confidence intervals for the sum of the autoregressive coefficients (α) for each yit .22 The results are provided in the columns 5-8 of the Table 2.23 To choose the lag lengths, we used the Akaike

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information criterion (AIC) and estimated two-tailed CIs and also symmetric CIs for all the countries examined in this study. However, we focus on the symmetric CIs, which is the preferred approach due to its advantageous properties

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as mentioned earlier. The upper bounds of the 90% CIs for Australia, Belgium, Finland, Greece, Italy, Japan, Luxembourg, Netherlands, Norway, Spain, and Switzerland are less than unity, so PEC in these countries are stationary and

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show convergent behavior, at least at 10% significance level. Moreover, the estimated CIs are narrow, indicating that the results are fairly precise. Another point that is worth noting is that even though these countries have had a con-

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vergent PEC, the lower bounds of the CI for Greece, Luxembourg, and Spain are higher than 0.9; therefore, these variables are very close to non-stationary process and any shock to these series would have a very persistent effect.24

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In order to assess the robustness of the results, we also consider the 95%

CIs and arrive at largely similar findings, with the exceptions of Luxembourg, Netherlands, and Norway, which now appear to have a unit root. So based

22 As one of the referees of the paper pointed out, this is true when the characteristic roots of the model are real. Presence of complex roots will require other conditions beside the α < 1 to ensure stationarity. Therefore, we calculated the roots of the models and all of them were real numbers. 23 The presence of potential break points in the series does not affect these results. Because we have used a subsampling method and estimated a CI for each subsample or block and then moved the block and estimated the CI again. We repeated this until end of the sample. Potential break points may only affect a few of these estimated CIs, but these few CIs will affect the lower and upper ends of the approximated distribution, which get discarded in constructing the 90% and 95% confidence intervals. 24 Gospodinov, 2002; Juvenal and Taylor, 2008; and Baldini, 2005 are among the scholars that have considered 0.9 as a measure of high or substantial persistence.

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on the results from 95% CIs, PEC for Luxembourg, Netherlands, and Norway

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has a divergent behavior. Again, the lower bound of the CI for Greece and

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Spain is higher than 0.9, which provides evidences of high persistency in these countries.25

To examine the sensitivity of the results to the selected lag length of autoregressive process for a series, we also used Schwarz (SIC) and Hannan-Quinn

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(HQ) information criteria to determine the optimal lag lengths. The SIC selects one lag for all series and 2 for the UK. The results from HQ is the same as the AIC except for the Japan which is 1 now. Therefore, the only differences

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between using different information criteria are related to Switzerland, Finland, Japan, Norway, Poland, and the UK. The new results for these six countries are reported in the Table A1 in the appendix. According to this table, we see that

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the results for Switzerland, Japan, Poland, and the UK remain unchanged. For Finland and Norway, the new results are in contrast with those obtained earlier using AIC. Now, the PEC in Finland and Norway show a divergent pattern. But

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this is not that surprising, because the upper bounds of the confidence intervals for these two countries calculated based on the AIC were very close to unity. Figure 6 shows the frequency of lower and upper bounds in different ranges

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based on the 90% and 95% CIs. According to this figure, it can be seen that most of the lower bounds are in the [0.9 − 1) range and only two countries have

a lower bound in the range 0.6 - 0.7. In addition, more than half of the series

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have an upper bound larger than unity. In sum, based on the results from the ADF unit root test and the 90% CIs, we found evidence of stationarity in the relative PEC in Australia, Austria,

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Belgium, Denmark, Finland, Greece, Italy, Japan, Luxembourg, Netherlands, Norway, Spain, and Switzerland.26 That is, 13 countries27 out of 25 studied here, are converging and 12 of them have a divergent behavior. Among the

countries with a divergent pattern, the PECs in New Zealand, Portugal, and Turkey are increasing more rapidly than the average growth rate of the PEC; while, in Canada, Sweden, and the US it is growing at a slower pace. At the 25 The case of Finland and Japan also worth noting, as the lower bound of the CIs are higher than 0.8. 26 If we consider 5% significance level, Australia, Austria, Belgium, Denmark, Finland, Greece, Italy, Japan, Netherlands, Spain, and Switzerland appear to be I(0) and convergent. 27 It worth noticing that Denmark and Austria appear to have a convergent pattern only based on the ADF test, and the CIs show that these countries have a divergent behavior.

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same time, PEC in Luxemburg and the UK is declining.

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A very important point to be emphasized here is that the stationarity (non-

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stationarity) of the relative PEC does not necessarily imply the stationarity (nonstationarity) of PECi if the average PEC of the OECD countries does not follow a stationary process. Because even if the average PEC follows a nonstationary process it is possible to have a stationary relative PEC when the national

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PEC shares the same stochastic trend as the average OECD PEC, that is, when they are cointegrated. The same logic implies that when the average PEC is nonstationary and the national PEC is stationary then the relative PEC would

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be nonstationary. Thus it is very important to know the integration properties of the average PEC as well.28 Therefore, we examined the stationarity of the average PEC in the OECD countries. The result from the ADF unit root test,

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with a t-statistic of -2.608, cannot reject the null of unit root for the average PEC. However, the calculated symmetric CI is (0.894, 0.975), which shows that the series is stationary. Therefore, the stationarity of the relative PEC will

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imply the stationarity of the national PEC. In comparing our findings to those of Meng et al (2013) who studies the relative PEC in the same countries, there are many similarities but also some

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differences. We failed to reject the unit-root null for France, Germany, New Zealand, Sweden, Turkey, UK, and the US, whereas the results from Meng et al (2013) show that these series are I(0) and these countries are converging. At

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the same time, contrary to their findings we provide evidence of convergence in

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Greece, Italy, and Spain.29

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Conclusion

In this study, we analyze the stochastic convergence of per capita energy use (PEC) in the 25 OECD countries over the period 1960-2012. To this end, unlike the previous studies that usually have used unit root tests, without or with structural breaks, we constructed confidence intervals for the sum of autoregressive coefficients in AR(p) model to examine the convergence in the PECs. 28 We

thank an anonymous referee for pointing this to us. other words, in 14 countries the results are the same but for the rest, i.e., 11 countries the findings are contradictory. 29 In

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These confidence intervals (CIs) provide more information than point estimates,

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such as unit root tests. Because the results from CIs not only show whether the

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null of a unit root can be rejected or not, but also they provide us a measure of sampling uncertainty and show the range of models that are consistent with the data. In addition, these approaches perform well even at local-to-unity cases. Based on the results from the ADF unit root tests and the 90% CIs, we

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found that the PEC in Australia, Austria, Belgium, Denmark, Finland, Greece, Italy, Japan, Luxembourg, Netherlands, Norway, Spain, and Switzerland are stochastically converging. In other words, the findings indicate that the PECs

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of 13 countries are consistent with stochastic convergence; while, the PECs for the rest of countries show a divergent behavior. Among the countries with a divergent pattern, the PECs in New Zealand, Portugal, and Turkey are increas-

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ing more rapidly than the average growth rate of the PEC. Therefore, these countries should adopt appropriate policies and regulations to control their PECs, because a higher PEC would create more pollutions

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which will raise the share of these countries in international environmental issues. On the other hand, in Canada, Sweden, and the US the PEC is growing at a slower pace. At the same time, PEC in Luxemburg and the

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UK is declining. This desirable pattern30 observed in Canada, Sweden, Luxemburg, the US, and the UK might be resulted from the improvements in energy efficiency.

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For the 13 countries with a convergent pattern, shocks to the PEC due to policies designed for demand management would have temporary effects and there is no need to intervene at any single deviation of the PEC from

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the average PEC. However, for the rest of the countries, the effects of these shocks would last for a longer period and any intervention in the PEC would be effective. This would help these countries to control the emissions of greenhouse gases and also the pattern of energy use through the implementation of appropriate energy-related policies. Moreover, for the countries that we have found stochastic convergence, the idiosyncratic country-specific factors cannot explain the differences that we observe in the PECs. Whereas, for the countries with divergent PEC, country-specific factors are highly persistent and play an important role in the pattern

30 The slower growth rate or declining PEC is desirable because the energy use is directly related to the greenhouse gases and climate change.

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of energy use. In other words, the divergence shows that even though

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the common shocks have been diffusing widely across the countries,

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there are some country-specific factors (such as different product mix, fuel mix, energy intensity) that makes PECs more persistent (Pesaran, 2007). Therefore, for these countries a uniform policy or regulation will not be effective and policy makers have to consider the

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heterogeneity of these countries. But for the convergent countries a uniform policy is adequate to achieve the policy makers’ objectives. Abundance of energy, economic activity mix, energy intensity, efficiency, and

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existence of environmental regulations are among the factors that might affect the pattern of energy use of countries. Therefore, a further extension of this paper would be to study the importance of these factors on the convergence of

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1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

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T

0

SC

-0.5

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-1

Austria Switzerlans

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-1.5

Spain France Greece

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-2

-2.5

Ireland

-0.2 -0.4 -0.6

1970

1975

CE

0

1965

1980

1985

1990

1995

2000

2005

2010

AC

1960

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Figure 1: Relative per capita energy use (group 1)

-0.8 -1 -1.2 -1.4 Italy Japan New Zeland Poland Portugal Turkey

-1.6 -1.8 -2 Figure 2: Relative per capita energy use (group 1 continued)

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1.6

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T

1.4 1.2

Belgium

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1

Australia

0.8

Finland Iceland

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0.6

Canada

Swden USA

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0.4

Luxemburg

0.2 0 1965

1970

1975

1980

1985

ED

1960 -0.2

1990

1995

2000

2005

2010

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Figure 3: Relative per capita energy use (group 2)

CE

0.3

AC

0.2 0.1 0 1960

1965

1970

1975

1980

1985

1990

1995

-0.1 -0.2 Denmark

-0.3

Germany Netherlands

-0.4 Norway

-0.5

UK Figure 4: Relative per capita energy use (group 3)

2000

2005

2010

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25

LUX CAN

FIN NOR USA

20

T

BEL

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AUT

15

AUS

SWE

SC

GER

JPN

FRA

CHE

DNK

10

UK

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IRL ESP ITA

POL

5

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GRC PRT TUR

0

ED

0 5

10

15 Rank in 1960

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Figure 5: Countires’ rank in terms of the per capita energy use

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Rank in 2012

NLD NZL

20

25

ACCEPTED MANUSCRIPT 18 90% confidence intervals

16 95% confidence intervals

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T

14 12

SC

10 8

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6

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4 2

[0.6-0.7)

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0 [0.7-0.8) [0.8-0.9) Lower Bounds

[0.9-1)

[0.8-0.9) [0.9-1) Upper Bounds

>=1

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Figure 6: Frequency of lower and upper bounds in different ranges based on the 90% and 95% confidence intervals

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Mean

SD

Min

Max

1960

2294

2116

289

10523

1970

3540

2431

524

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Table 1: Descriptive Statistics of per capita energy use

1980

4055

2183

716

9775

1990

4296

2048

977

8874

2000 2010

4693 4905

2227 3076

1209 1457

11023 16882

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SC

NU MA ED PT CE AC

12106

ACCEPTED MANUSCRIPT Table 2: Results using ADF unit root test and subsampling confidence intervals 90% confidence interval

95% confidence interval

k*

MUα

equal-tailed

symmetrical

equal-tailed

symmetrical

-2.747

1

0.902

1

0.591

(0.628, 0.912) (0.801, 1.072)

(0.750, 0.921) (0.952, 1.084)

(0.659, 0.881) (0.790, 1.084)

Belgium

-4.219*** -2.574

(0.746, 0.890) (0.955, 1.110)

1

0.917

Canada

-1.982

1

0.992

(0.692, 0.880) (1.006, 1.160)

(0.680, 0.888) (0.853, 1.144)

(0.665, 0.901) (1.001, 1.167)

(0.672, 0.895) (0.843, 1.154)

1

0.769

(1.017, 1.113)

(0.872, 1.101)

(1.015, 1.125)

(0.857, 1.117)

Finland

-4.295*** -1.281

2

0.928

France

-0.969

1

1

(0.844, 0.990) (0.879, 1.011)

(0.811, 0.978) (0.778, 1.005)

(0.832, 0.991) (0.845, 1.053)

(0.800, 0.988) (0.776, 1.008)

Germany

-1.717

1

1

(0.842, 1.096)

(0.841, 1.076)

(0.819, 1.575)

(0.814, 1.104)

Greece

-1.117

1

1

Iceland

-1.189

1

1

(0.929, 0.969) (1.013, 1.150)

(0.914, 0.959) (0.960, 1.110)

(0.925, 0.973) (1.015, 1.199)

(0.918, 0.956) (0.940, 1.130)

Ireland

-1.136

1

1

(0.823, 1.064)

(0.779, 1.047)

(0.813, 1.069)

(0.769, 1.057)

0.990

(0.798, 0.888)

(0.781, 0.875)

3

1

(0.838, 0.969)

Luxembourg

-1.725

1

1

(0.88, 0.992) (0.955, 1.021)

(0.816, 0.903) (0.879, 1.023)

(0.772, 0.884)

Japan

-3.305* -2.653

1

(0.926, 0.999)

(0.947, 1.026)

(0.836, 0.971) (0.910, 1.015)

Netherlands

-3.080

1

1

(0.845, 1.034)

(0.715, 1.026)

-2.245

1

1

(0.907, 1.004)

(0.798, 0.944) (0.814, 1.013)

(0.806, 1.095)

New Zealand

(0.908, 1.035)

(0.828, 1.000)

Norway

-2.427

2

0.899

(0.880, 1.006)

(0.870, 1.010)

(0.831, 1.002)

Poland

-1.629

2

1

(0.975, 1.058)

(0.837, 0.997) (0.921, 1.031)

(0.973, 1.064)

(0.906, 1.045)

Portugal

0.095

1

Spain

-0.488

Sweden

-2.065

Switzerland

-1.422

1

Turkey

-2.780

1

UK

-1.564

1

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SC

NU

ED

Italy

PT

Denmark

1

(0.966, 1.021)

(0.941, 1.007)

(0.966, 1.019)

(0.938, 1.010)

1

1

1

0.966

(0.944, 0.977) (0.865, 1.081)

(0.928, 0.975) (0.707, 1.056)

(0.941, 0.985) (0.853, 1.074)

(0.923, 0.979) (0.719, 1.044)

2

(0.745, 0.933) (0.953, 1.079)

(0.763, 1.064)

0.829

(0.766, 0.984) (1.014, 1.081)

(1.025, 1.087)

(0.714, 0.964) (0.955, 1.078)

1

(0.939, 1.022)

(0.940, 1.026)

(0.952, 1.042)

(0.939, 1.026)

CE

Austria

AC

Australia

T

τ

MA

ADF

USA -3.142 1 0.769 (0.990, 1.038) (0.962, 1.028) (0.987, 1.046) (0.966, 1.025) The lag length is chosen using the Akaike information criterion. *, **, and *** show significance at the 10%, 5%, and 1% level, respectively. All the stationary cases are shown in Bold. MUα shows the median unbiased estimate of α computed following Andrews and Chen (1994).

ACCEPTED MANUSCRIPT Table A1: Results of subsampling confidence intervals 90% confidence interval 95% confidence interval k* equal-tailed symmetrical equal-tailed symmetrical 1

(0.890, 1.015)

(0.818, 1.010)

(0.868, 1.018)

(0.809, 1.019)

Japan

2

(0.876, 0.967)

(0.855, 0.938)

(0.870, 1.001)

Norway

1

(0.885, 1.049)

(0.817, 1.036)

(0.878, 1.054)

(0.825, 1.028)

Poland

1

(0.966, 1.076)

(0.929, 1.040)

(0.978, 1.109)

(0.893, 1.077)

Switzerland

1

(0.804, 0.989)

(0.729, 0.929)

(0.805, 1.050)

(0.684, 0.974)

UK

2

(0.940, 1.030)

(0.946, 1.022)

(0.937, 1.032)

(0.937, 1.031)

SC

RI P

T

Finland

(0.847, 0.946)

AC

CE

PT

ED

MA

NU

The lag length is chosen using the Schwarz and Hannan-Quinn information criteria. All the stationary cases are shown in Bold.

Research Highlights

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The paper studies the convergence of per capita energy use in 25 OECD countries. Unlike the previous studies, which mainly used unit root tests, in this study we construct subsampling confidence intervals to assess the convergence. We construct the 90% and 95% confidence intervals for sum of the AR(p) coefficients. The results show that the per capita energy use in Australia, Austria, Belgium, Denmark, Finland, Greece, Italy, Japan, Luxembourg, Netherlands, Norway, Spain, and Switzerland has a convergent pattern.

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· ·