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Using the Box-Cox transformation to approximate the shape of the relationship between C[O.sub.2] emissions and GDP: a note.

I. Introduction

The international community agrees that, in order to avoid massive damages due to climate, the average increase of global temperature should be kept below 2 degree Celsius with respect to pre industrial levels (Copenhagen Accord, Point 1). To attain the carbon concentration in the atmosphere of 450 parts per million required for the 2 degree goal, developed countries' emissions should decrease by 2020 between 25 and 40% with respect to 1990 levels while developing countries' emissions need to be reduced substantially (Gupta et al, 2007).

Countries seem to understand more clearly the threat of climate change now that in the past. But, the division between developing and developing countries remains. Developing countries historically argue that they have the right to increase emissions in order to meet their development needs since they are not responsible for the GHG (greenhouse gases) concentration levels that resulted from developed countries' economic growth. (1) The analysis of the relationship between emissions and GDP plays an important role in that discussion.

Indeed, a large body of literature emerges around the beginning of the 90s under the name of "Environmental Kuznets curve" (EKC). It has its origin in the works of Grossman y Krueger (1991, 1995), Shafik and Bandyopadhyay (1992) and Panayotou (1993). The idea behind the EKC is that starting from low per capita income levels, emissions per capita tend to increase at a lower rate up to a "turning point", where those emissions begin to decrease as income per capita continues to evolve because of changes in people's waste as well as technological shifts. Those seminal articles are based on panel data or cross-section data for multiple countries and diverse pollutants, and are derived from reduced pollution-income regressions forms.

After "twenty-year fascination with the EKC" Carson (2010, p.3), several authors began to review the theoretical foundations of EKC as well as the empirical weaknesses behind the EKC (Dasgupta et al 2002; Stern 1998, 2004; Dinda 2005; Kijima et al 2010). Two of the main problems pointed out by the critics of the EKC are: 1) time-series problem associated to the data (ordinary least squares regression assumes that all the variables are stationary, so if they are not, further scrutiny is needed) and 2) the functional form used to estimate the relationship between emissions and GDP. Conventional estimations did not consider the time-series properties of the variables chosen and the standard EKC estimation was assumed linear, quadratic or cubic patterns.

To address the first concern, articles began to deal with time-series analysis. Until the late 90s, the EKC literature ignored that environmental degradation and income could be non stationary (their statistics are not constant through time), therefore, the EKC regressions could be spurious, unless the two series were cointegrated. Perman and Stern (2003) add to that analysis the consideration of panel data time series properties. In particular, with sulfur emissions and GDP data for 74 countries along 31 years (from 1960 to 1990), they found that for many of the countries emissions per capita or GDP are non stationary series and a long-run cointegrating relationship between those variables only exists in 35 of the countries, which as a consequence implies that the EKC cannot be estimated for the remaining countries or for the panel as a whole. Similarly, Wang (2013) tests the EKC for S[O.sub.2] and C[O.sub.2] emissions from 1850 to 1990 for several countries individually and within a panel and find that none of the EKC he estimates for single countries are cointegrated equations.

With respect to the second issue, a few articles have provided alternative formulations to the usual the functional form specifications. Wang (2013) uses different exponentials for income, from 0 to 2 (0 is the specific case of a linear EKC function and 2 is the case of a quadratic EKC function), Schmalensee et al (1998) and Vollebergh et al (2009) use semi parametric specifications of the B-spline method, (2) while Galeotti et al (2006) estimate a non-linear three parameter Weibull function in order to capture the EKC CO2 emissions-GDP relationship for groups of OECD and non-OECD countries. (3)

Another change in the EKC literature in the last few years has been the shift from cross-country and panel data analysis to individual countries' assessments (for example, Lindmark 2002 for Sweden; later on Ang 2007 for France, among many others). This is due to the fact that despite that the former provide a general understanding on how pollution variables are related to economic activity, they offer no guidance for predictions in each country. Individual countries do not possess neither the same pollution or income paths nor do the form of the relationship between income and CO2 emissions have the same shape. Hence, the emissions-income per capita relationships can be very different across countries.

The EKC literature has become a very fruitful and independent research area. However, there are other narrower fields in the environmental economics literature that also analyze the CO2 emissions-income relationship. That is the case of the studies on the relationship between carbon emissions and GDP which were introduced to discuss the advantages of GDP linked CO2 quantified reduction targets. (4) For example, Hohne and Harnisch (2002) with IEA data from 1971 to 1999 looked at GDP and emissions over time for four countries (India, the former Soviet Union, USA and the UK). They find significant GHG emissions to GDP elasticities (except for the UK) between 0.45 and 1.48 depending on the period and the country. Kim and Baumert (2002) calculate an elasticity of 0.95 for Korea based on EIA data for 1981 to 1998, Barros and Conte Grand (2002) estimate a 0.5 elasticity for Argentina with local data for 1990 to 2005. In all those cases, the relationship between emissions and GDP is assumed to have the form of a specific log-log functional form. That shape results from taking logarithms to both sides of the following equation: [E.sub.t] = b x [GDP.sub.t.sup.a], where [E.sub.t] denotes emissions and [GDP.sub.t] is the gross domestic product and a is the elasticity of emissions with respect to GDP.

The main innovation of this note is to use the Box-Cox specification to capture the C[O.sub.2] emissions-GDP link, taking into consideration the time-series properties of both variables depending on the transformation that is considered more appropriate for each individual country. The advantage of this formulation is employing a nonlinear transformation of variables that subsumes several other functional forms as nested cases (for example, both the linear model and log-log model). We use CAIT-WRI international database to analyze the behavior of C[O.sub.2] emissions with respect to GDP for those countries who submitted quantified reductions under the Copenhagen Accord. We select that group of countries in order to capture if the metric they used for the Accord has to do with the shape of their emissions-GDP long-run relationship.

This note is organized as follows. Section II describes the empirical strategy and describes the data sources. Section III shows our results and Section IV concludes.

II. Empirical strategy

It has been acknowledged in econometric studies that the determination of the functional relationship that may exist between some variables of interest could be derived applying the Box-Cox transformation technique (Box-Cox, 1964). Applied to our research, the functional form would be:

[E.sup.[theta].sub.t] = [[delta].sub.0] + [[delta].sub.1] x [GDP.sup.[lambda].sub.t] + [u.sub.t] (1)

where [E.sup.[theta].sub.t] = [[E.sup.[theta].sub.t] - 1/[theta]] and [GDP.sup.[lambda].sub.t] = [[GDP.sup.[lambda].sub.t] - 1]/[lambda]] and [theta], [lambda] [not equal to] 0. Then, d and X can be estimated in

order to "choose" a functional form sufficiently flexible to "fit" the data.

Then, it is possible to test if more usual (restricted) relationship between emissions and GDP are preferred to the Box-Cox flexible model: [theta] = [lambda] = 1 (linear model) and [theta] = 0, [lambda] = 1 (log - lin model), while if [theta] = [lambda] = 0, the function is defined as log - log). Those are usual functional forms that can make emissions and GDP positively related and preclude negative emissions as could be the case for some alternative models (e.g., the lin-log functional form). Box-Cox regressions are run here using STATA 11 and the tests performed are Likelihood Ratio tests based on the log-likelihood estimates for the unrestricted (Box-Cox) versus the restricted (lin-lin, log-log, or log-lin) models (Greene, 2003). A high calculated [chi square] statistics implies rejection of the null hypothesis that the restrictions to the functional form are correct. More specifically, the test we use is:


Where ln[??]* is the log likelihood evaluated at the restricted estimates, ln[??] is the log-likelihood evaluated at the unrestricted Box-Cox estimates, and J are the number of restricted parameters. The Box-Cox method begins by computing the maximum likelihood estimation (MLE) score when the parameters [theta] = [lambda] = 1. Then, other values for the parameters are tried and, at the end, the method reports the values of [theta] and [lambda] that maximizes the MLE score.

Once selected the functional form that best fits emissions and GDP data of each country, it is crucial to test for time-series properties of the variables used in the regression because a distinction has to be made between the true relation between GDP and pollution and the change in emission levels occurring merely due to the passage of time. More specifically, if dependent and independent variables are stationary, they can be used in a regression. If they are not stationary, but are integrated of the same order and cointegrated, they can also be included in a regression and the estimation of the model by OLS and the classical analysis of series is valid (Greene, 2003). If neither of the two conditions holds, the regression would be spurious (Granger and Newbold, 1974). This means that results would indicate that the two variables are related when in fact they are not, it is only their dependence to time that relates them. Separating the relationship between pollution and income from the correlation between both variables and the passage of time is difficult. It can be the case that they are related by time and not by themselves.

A time series is stationary if it has a constant mean and its covariance between t and t-s does depend on s but not on time (t) (or, which is the same, the variance of the series is not growing with time). One of the most popular tests of stationarity is the Dickey-Fuller (DF) test. The starting point is the following general model:

[Y.sub.t] = [a.sub.0] + 0 x [Y.sub.t-1] + [a.sub.1] x t + [u.sub.t], (3)

Where [a.sub.0] is a constant (also called "drift"), [Y.sub.t] is the serie whose stationarity we test, t is a trend and [u.sub.t] are taken to be independently normally distributed. Based on the significance of the constant and the trend test we then, on the remaining model, contrast the null hypothesis [H.sub.o]: 0 = 1 (unit root or non-stationarity). But we cannot estimate a model regressing the series on its lagged value to see if the estimated 0 is equal to 1 because in the presence of a unit root the t-statistics for that coefficient is severely biased. Therefore, Eq. (3) is expressed in terms of differences subtracting the lagged value from both sides. Then,

[Y.sub.t] - [Y.sub.t-1] = [a.sub.0] + [0 - 1] x [Y.sub.t-1] + [a.sub.1] x t + [u.sub.t], (4)

In this model we test the null hypothesis [H.sub.o]: (0 - 1) = 0 (i.e. there is a unit root and the series is nonstationary) against H1: [H.sub.o]: (0 - 1) < 0 (i.e. there is no unit root and the series is stationary). Under the null hypothesis, the statistic of the regression has a distribution which was first estimated by Dickey and Fuller (1979) and then obtained analytically by Phillips (1987). If the series is stationary in levels, it is integrated of order 0: I(0). If the series became stationary after differentiating it d times, the series is integrated of order d: I(d).

However, the Dickey-Fuller test assumes that the error terms are uncorrelated. When the residuals are serially correlated, the Augmented Dickey-Fuller (ADF) test proposes to include in the regression several lags of the dependent variable AYt to eliminate the serial correlation. In this paper we perform the modified Dickey-Fuller t test (known as the DF-GLS test) proposed by Elliott, Rothenberg, and Stock (1996) to test for a unit root. Essentially, the test is an augmented ADF test except that the time series is transformed via a generalized least squares regression. Elliott et al (1996) and later studies have shown that this test has significantly greater power than the previous versions of the ADF test (Elliott et al 1996, p. 813).

The testing procedure for the DF-GLS test is the same as for the ADF test and is applied to the model with constant term and trend. This would imply (when applied to (4)):

[DELTA][Y.sub.t] = [a.sub.0] + [delta] x [Y.sub.t-1] + [a.sub.1].t + [[summation].sup.m.sub.i=1] [[beta].sub.i] [[DELTA].sub.t-i] + [u.sub.t] (5)

The lag lengths were chosen for each variable in each of the countries using the procedure suggested by Ng-Perron (1995). This criterion starts with a maximum lag length as selected by Schwert (1989) and test the highest lag coefficient for significance. When the p-value of that lag falls below 0.1, the lag is retained and is chosen as the optimal lag. (5)

After the DF-GLS tests, we learn the order of integration of the series. But, regressions between series that are not stationary in levels can only be run if they are integrated of the same order and cointegrated. Cointegration indicates a long run relationship between non-stationary time series. If the series are cointegrated it means that although they move together over time they do it in a harmonized way so that the error between the variables does not change. The long run relationship is represented by a linear combination of the variables that is stationary:

[c.sub.i] x [Y.sub.t] + [c.sub.2] x [X.sub.t] is I(0), where [Y.sub.t], [X.sub.t] are I(d), d [not equal to] 0 (6)

Where c = ([c.sub.1], [c.sub.2]) is the cointegrating vector.

Cointegration is tested by the Engle-Granger test. Engle-Granger (1987) "residual approach" implies running a regression of [Y.sub.t] against [X.sub.t] (where both variables have the same order of integration) and extract the residuals. (6) Then, if the estimated residuals have a unit root (or, which is the same, are non-stationary), then cointegration is rejected. If residuals are I(0), cointegration cannot be rejected. To do so, we run Eq. (5) and obtain the residuals, then the first difference of the residuals is regressed on the lagged level of the residuals without a constant. As the cointegration test is based on the estimated residuals of the long run relationship, the usual Dickey-Fuller table is not longer valid, so critical values employed for the Engle-Granger test are those calculated by MacKinnon (1990, 2010). If the residuals are stationary the two series do not drift too much apart from each other and hence, there is a cointegration between the two variables.

Our data are 1980-2008 CAIT 2012 International data for emissions (measured in thousands of metric tons of C[O.sub.2] equivalent) and GDP (in million constant 2005 international dollars converted by Purchasing Power Parity) from the World Bank Development Indicators. We limit our analysis to those countries having submitted pledges under the Copenhagen Accord because we try to associate if the metric of their pledges to the Accord has to with the shape of the relationship between emissions and GDP for each of the countries.

Developed countries have submitted emission reduction pledges to be attained in 2020 and whose base years differ among the proposals but in all cases refer to a year in the past (see Table 1). On the other side, some developing countries have submitted proposals, which include economy-wide caps. Developing countries' proposals are of four types (Levin and Finnegan, 2011). Some of those targets are set as percentage reductions of emissions with respect to a given base year (the same metric of developed countries' caps). In many cases, commitments are absolute emissions reductions from the (future) business as usual (BAU) levels in 2020. Other countries set reductions in emissions intensity in comparison to a base year. For example, China made a pledge to cut in C[O.sub.2] emissions per unit of GDP by 40 to 45% below 2005 level by 2020 and India proposed a 20 to 25% emissions intensity reduction over the same period. (7) And, finally, there are nations (e.g., Costa Rica) whose aim is to achieve carbon neutrality by 2020 (i.e., zero net emissions: emissions do not exceed sequestration). Table 1 shows the different types of caps. We observe that only two countries have submitted voluntary reductions to Copenhagen that depend of GDP (i.e., China and India), and, that those specific quantified limits on emissions depend linearly of GDP.

III. Results

Regarding the functional form of the relationship between C[O.sub.2] emissions and GDP, the results of the Log-likelihood Ratio test reported in Table 2 indicate that the model specifications differs among countries. More precisely, the log-log shape is the one that predominates among developed countries (it provides the best fit in 4 of the 11 countries), while the Box-Cox functional form provides the best adjustment in many of the developing countries (i.e., in 8 of 15 nations). (8) Overall, the linear model and (to a lesser extent) the log-linear functional form are the ones that less fit the individual countries' data. More precisely, the linear shape is only preferred in the case of 3 countries in the overall sample (Canada, Mexico and Republic of Moldova).

Regarding the stationarity and cointegration of our series, the order of integration of transformed emissions and GDP series (as well as the cointegration among them) differs for the different countries (see Table 3). In all nations, emissions and GDP transformed are integrated of the same order. Moreover, in less than 20% of developed and of developing countries the hypothesis of non-stationarity is rejected for series in levels and, in the remaining countries, the series are stationary after taking the first difference. Hence, the series are I(0) only for 4 cases (2 developed and 2 developing countries) and are for the remaining ones validating the long-run cointegration possibility between emissions and GDP. As can be seen in Table 3, for those economies whose series are not integrated in levels but are stationary in first differences, the null hypothesis of no cointegration within the Engle-Granger test is rejected for 3 developed countries and for 4 developing ones. Hence, a valid regression analysis searching for the functional form between C[O.sub.2] emissions and GDP levels can only be performed for less than half of the countries who submitted quantitative caps under the Copenhagen Agreement (more precisely, for 4+7=11, of the 26 countries in our sample).

Note that for those individual countries for which the regression between emissions and GDP is not spurious, the Box-Cox functional form predominates (it constitutes 7 of the 11 cases). This result is clearly depicted in Table 4 and Figure 1.

Finally, as shown in Table 4, the Emissions-GDP elasticities vary greatly among countries. This result is consistent with the literature that analyzes dynamic targets (Hohne and Harnisch 2002, for example, find quite different elasticities depending on the country analyzed). Average elasticities are lower than 1 (emissions increases in a lower % when GDP increases) in most nations (8 out of 11). As seen in Table 1, only India and China chose for their Copenhagen submission a GDP related reduction target. The Emissions-GDP elasticity cannot be calculated for India since transformed Emissions and GDP are not cointegrated, but the result for China (an elasticity of 0.56 on average for the 1980-2008 period) would not support the choice of a linearly adjusted target to GDP. Emissions in China do not seem to be moving linearly with GDP over the whole period as shown in Figure 1.A. of the Appendix, which describes the path of emissions, GDP and emissions intensity. However, it is fair to acknowledge that the few last years of the period seem to show a different path.

IV. Conclusions

With CAIT WRI data for those countries which submitted quantifiable reduction limits under the Copenhagen Agreement, this note supports the existence of a long run relationship between C[O.sub.2] emissions and GDP in 11 of the 26 countries in our sample over the period 1980-2008. However, the functional specification of that relationship is not homogenous among nations, being linear for 2 countries, log-log for 2 other cases, while the relationship follows a Box-Cox functional form for 7 nations. Moreover, mean elasticities of the emissions-income relationship differ among countries, independently of the shape of the relationship. But in most cases (8 out of 11), the magnitude of the average elasticity is lower than 1, which means that emissions increase less that the GDP.

The contributions of our findings are twofold. First, this note reinforces the fact that the analysis of the time series properties of the variables is crucial not only in the study of the EKC, but also in the analysis of the relationship between emissions and GDP (in levels, not in per capita terms). We reject 15 of the 26 individual countries regressions between C[O.sub.2] emissions and countries' income level for considering them spurious.

Secondly, this note highlights the importance of considering an appropriate functional form for each individual country. This fact is already acknowledged in the EKC related literature (for example, by Piaggio and Padilla 2012, who reject the assumption of equality in countries' functional forms). But, this note goes a step further since instead of hypothesize quadratic or cubic transformations for income, use different exponentials for income from 0 to 2 (as in Wang 2013) where 0 is the specific case of a linear EKC function and 2 the case of a quadratic EKC function, this note introduces the Box-Cox functional form to deal with the different shape of the C[O.sub.2] emissions and GDP relationship in different individual countries. As a result, we conclude that in most of the countries for which a non spurious relation is possible (8 of the 11 cases), the Box-Cox shape is more appropriate than other more traditional shapes (e.g., linear or log-log).



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Mariana Conte Grand y Vanesa D'Elia *

(Universidad del CEMA)

* Las opiniones de este trabajo son personales y no representan necesariamente las de la Universidad del cema.

(1) GHG gases are of six types, being the carbon dioxide (C[O.sub.2]) the most important in term of GHG emissions.

(2) B-splines take the form of piecewise polynomials. B is related to the smoothness of the function. If B = 0, there is no smoothness, if B=1, the function used is piecewise linear, if B=2, it is piecewise quadratic, and so on (de Boor, 2001).

(3) A few papers have used non-parametric approaches through the use of kernel models (for example, Azomahou et al 2006).

(4) Intensity caps, contrary to fixed caps, do not set country's allowable emission level, but define it as a linear function of GDP. Those "pure" intensity targets define emission intensity while fixed caps imply fixing emissions. At the moment, two countries submitted linearly indexed pledges to the Copenhagen Accord: China and India.

(5) We also run the Kwiatkowski, Phillips, Schmidt and Shin (1992) test to verify our results. The evidence is in all cases supportive of the results.

(6) Note that the constant and coefficient estimated by the regression are the estimates of the cointegrating coefficients.

(7) China's target has received a high level of attention in the empirical literature in part because it is based on an intensity indicator, but also because China represents a very large share of total global emissions. It has grown at an exceptionally high rate over the last years, and so has grown its emissions, but its emissions intensity has declined. China's target has raised the issue of whether or not it just represents the business as usual trend. There are no unanimous conclusions in that regard.

(8) For those cases where the LR tests were not significant in more than one model (e.g., Croatia and Japan) we compare the log-likelihood values to select the model that fits best to the data.

Table 1. Quantified reductions proposed under the Copenhagen Accord

States        Country                Base    Target

Developed     Australia              2000    2020
              Belarus                1990    2020
              Canada                 2005    2020
              Croatia                1990    2020
              Iceland                1990    2020
              Japan                  1990    2020
              Kazakhstan             1992    2020
              Liechtenstein          1990    2020
              Monaco                 1990    2020
              New Zealand            1990    2020
              Norway                 1990    2020
              Russian Federation     1990    2020
              Switzerland            1990    2020
              Ukraine                1990    2020
              USA                    2005    2020

Developing    Antigua and Barbuda    1990    2020
              Marshall Islands       2009    2020
              Republic of Moldova    1990    2020
              Brazil                 BAU     2020
              Chile                  BAU     2020
              Indonesia              BAU     2020
              Israel                 BAU     2020
              Mexico                 BAU     2020
              Republic of Korea      BAU     2020
              Singapore              BAU     2020
              South Africa           BAU     2020
                                     BAU     2025
              China                  2005    2020

              India                  2005    2020

              Bhutan                         2020
              Costa Rica                     2021
              Maldives                       2020
              Papua New Guinea               2030

States        Metric

Developed     GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions

Developing    GHG Emissions
              CO2 emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              GHG Emissions
              Carbon dioxide emissions per unit of GDP
              Share of non-fossil fuels in primary energy consumption
              Forest coverage and forest stock volume
              Emissions intensity of its GDP (grams of CO2eq
              excluding agriculture, per Rs. of GDP)
              Emissions do not exceed its sequestration capacity
              Carbon neutrality
              Carbon neutrality
              GHG emissions
              Carbon neutrality

States        Stringency (8)

Developed     -5/-25%

Developing    -25%
              No less than 25%
              Up to -30%
              - 40/-45%
              Reach 15%
              + 40 mill.has./+ 1.3 bill.[m.sup.3]


Source: Kyoto Protocol
to the UNFCCC, United Nations 1998 (Article 3, Annex A,
Annex B). Appendix / Quantified economy-wide emissions targets for 2020 Appendix
II Nationally appropriate mitigation actions of
developing country Parties

Notes: Rs. = Rupees. * Targets of Kyoto Protocol in carbon dioxide
equivalent. ** EU-15=15 States who were EU members in 1997 when
the Kyoto Protocol was adopted. *** Includes non-Annex I countries who
submitted a pledge with their NAMAS. Guyana and Thailand
are not included: they submitted pledges, but not NAMAs.

Table 2. Functional form tests with respect to the Box-Cox

Country                Calculated [chi square] of Log-likelihood
                                  Ratio Test

                         Linear      Log-Log      Log-lin

Australia              13.52 ***       0.96      31.12 ***
Canada                    2.08       4.64 **      6.17 **
Croatia                   1.66         0.93       6.84 ***
Iceland                13.32 ***     9 17 ***     8.63 ***
Japan                     2.53       9 11 ***       0.42
Kazakhstan              5.08 **        1.69         0.88
New Zeland             23.18 ***    24.19 ***    30.48 ***
Norway                   3.60 *        1.03        3.32 *
Switzerland             6.67 ***     6 91 ***     8.35 ***
Ukraine                10.84 ***    11.93 ***       1.22
USA                     6.86 ***       2.62       8.37 ***


Antigua and Barbuda    34.96 ***    59 21 ***    65.57 ***
Bhutan                 27.35 ***    13.41 ***    21 72 ***
Brazil                  4.32 **        0.63       6.96 ***
Chile                   5.38 **        0.86      25.74 ***
China                   5.52 **        0.03      23.37 ***
Costa Rica             21 97 ***    20.53 ***    42.38 ***
India                   4.39 **        0.06      89 57 ***
Indonesia              13.75 ***     4 12 ***     8.43 ***
Israel                 50.86 ***    44.88 ***    43.00 ***
Maldives                4.89 **      4.84 **     10.37 ***
Mexico                    0.72       4.90 **      1449 ***
Papua New Guinea       29 91 ***    16.75 ***    15.87 ***
Republic of Korea      16.14 ***       1.16      39.65 ***
Republic of Moldova       1.56      12 22 ***     8.03 ***
Singapore              40.11 ***    22.69 ***    19.66 ***
South Africa           27.88 ***    16.69 ***    10.67 ***

Notes: *, **, *** denote rejection of the null-hypothesis (the
model in each column against the corresponding Box-Cox functional
form) with 10%, 5% and 1% significance. There is no C[O.sub.2] data
available from CAIT-WRI International data for Liechtenstein,
Monaco and Marshall Islands. Belarus results are not reported
because coefficients of the relationship between emissions and GDP
are not significant for any of the alternative functional forms.
The Russian Federation is not included because when trying to
perform the Box Cox transformation to the dependent variable only,
the data presents discontinuities that do not allow maximum
likelihood to be reached and the comparison between the Box Cox and
the log-lin transformations cannot be performed.

Table 3. Unit root and cointegration tests

                                           Model in levels

Countries              Functional     Dep. Var.      DF-GLS
                          form                      Statistic


Australia                Log-Log        log(E)       -2.179
Canada                   Linear           E          -2.751
Croatia                  Log-Log        log(E)       -1.658
Iceland                  Box-Cox     [[??].sub.E]    -4.541     ***
Japan                    Log-lin        log(E)       -1.198
Kazakhstan               Log-lin        log(E)       -2.602
New Zeland               Box-Cox     [[??].sub.E]    -2.405
Norway                   Log-Log        los(e)       -3.175      *
Switzerland              Box-Cox     [[??].sub.E]    -3.660     **
Ukraine                  Log-lin        log(E)       -3.080      *
USA                      Log-Log        log(E)       -2.080


Antigua and Barbuda      Box-Cox     [[??].sub.E]    -2.162
Bhutan                   Box-Cox     [[??].sub.E]    -3.042
Brazil                   Log-Log        log(E)       -1.822
Chile                    Log-Log        log(E)       -2.122
China                    Log-Log        log(E)       -2.538      *
Costa Rica               Box-Cox     [[??].sub.E]    -2.609
India                    Log-Log        log(E)       -1.717
Indonesia                Box-Cox     [[??].sub.E]    -0.982
Israel                   Box-Cox     [[??].sub.E]    -2.646      *
Maldives                 Box-Cox     [[??].sub.E]    -1.305
Mexico                   Linear           E          -1.999
Republic of Korea        Log-Log        log(E)       -0.760
Republic of Moldova      Linear           E          -1.435
Singapore                Box-Cox     [[??].sub.E]    -1.611
South Africa             Box-Cox     [[??].sub.E]    -2.957

                           Model in levels

Countries              Indep. Var.    DF-GLS


Australia               log(GDP)      -1.875
Canada                     GDP        -2.303
Croatia                 log(GDP)      -1.721
Iceland                  ([??])P      -3.508     **
Japan                      GDP         0.365
Kazakhstan                 GDP        -3.222     **
New Zeland               ([??])P      -0.203
Norway                  log(GDP)      -0.648
Switzerland              ([??])P       3.328     ***
Ukraine                    GDP        -2.002
USA                     log(GDP)      -2.088


Antigua and Barbuda      ([??])P      -0.736
Bhutan                   ([??])P      -3.285     **
Brazil                  log(GDP)      -2.434
Chile                   log(GDP)      -3.181     **
China                   log(GDP)      -4.152     ***
Costa Rica               ([??])P      -2.923      *
India                   log(GDP)      -1.170
Indonesia                ([??])P      -1.586
Israel                   ([??])P      -2.588      *
Maldives                 ([??])P       -3.52      *
Mexico                     GDP        -1.466
Republic of Korea       log(GDP)      -0.760
Republic of Moldova        GDP        -3.256     **
Singapore                ([??])P      -1.685
South Africa             ([??])P      -1.943

                            Model in first difference

Countries                  Dep. Var.        DF-GLS


Australia                [DELTA]log(E)      -4.578     ***
Canada                 [increment of E]      -4.93     ***
Croatia                  [DELTA]log(E)      -4.147     ***
Japan                    [DELTA]log(E)      -4.732     ***
Kazakhstan               [DELTA]log(E)      -3.232
New Zeland               [[??].sub.E]       -7.439     ***
Norway                   [DELTA]log(E)      -5.384     ***
Ukraine                  [DELTA]log(E)      -2.747     ***
USA                      [DELTA]log(E)      -3.807     ***


Antigua and Barbuda      [[??].sub.E]       -8.039     ***
Bhutan                   [[??].sub.E]        -6.53     ***
Brazil                   [DELTA]log(E)      -3.679     **
Chile                    [DELTA]log(E)      -3.743     ***
Costa Rica               [[??].sub.E]       -4.924     ***
India                    [DELTA]log(E)      -3.007     ***
Indonesia                [[??].sub.E]       -4.154     ***
Maldives                 [[??].sub.E]       -3.658     **
Mexico                 [increment of E]     -7.839     ***
Republic of Korea        [DELTA]log(E)       -4.97     ***
Republic of Moldova    [increment of E]      -3.91     ***
Singapore                [[??].sub.E]       -4.731     ***
South Africa             [[??].sub.E]       -3.614     **

                            Model in first difference

Countries                Indep. Var.       DF-GLS


Australia              [DELTA]log(GDP)     -4.248     ***
Canada                    [DELTA]GDP       -2.293      *
Croatia                [DELTA]log(GDP)     -2.522      *
Japan                     [DELTA]GDP       -2.605      *
Kazakhstan                [DELTA]GDP       -3.125     ***
New Zeland               [DELTA][??]P      -3.437     **
Norway                 [DELTA]log(GDP)     -2.519     **
Ukraine                   [DELTA]GDP       -3.143     **
USA                    [DELTA]log(GDP)     -3.772     ***


Antigua and Barbuda      [DELTA][??]P      -2.945
Bhutan                   [DELTA][??]P      -3.674     ***
Brazil                 [DELTA]log(GDP)     -3.886     ***
Chile                  [DELTA]log(GDP)      -2.54
Costa Rica               [DELTA][??]P      -3.068     ***
India                  [DELTA]log(GDP)     -3.561
Indonesia                [DELTA][??]P      -3.802     ***
Maldives                 [DELTA][??]P      -4.667     ***
Mexico                    [DELTA]GDP       -4.743     ***
Republic of Korea      [DELTA]log(GDP)     -5.371     ***
Republic of Moldova       [DELTA]GDP        -3.52     ***
Singapore                [DELTA][??]P        -4       ***
South Africa             [DELTA][??]P      -3.871     ***

Countries              Integration order both series      EG


Australia                                               -3.106
Canada                                                  -3.241      *
Croatia                                                 -1.719
Iceland                I(0)    Stationary in levels
Japan                                                   -2.725
Kazakhstan                                              -1.373
New Zeland                                              -3.635     **
Norway                                                  -4.265     **
Switzerland            I(0)    Stationary in levels
Ukraine                                                 -3.218
USA                                                     -2.927


Antigua and Barbuda                                     -5.143     ***
Bhutan                                                   -3.53      *
Brazil                                                  -2.505
Chile                                                   -2.950
China                  I(0)    Stationary in levels
Costa Rica                                              -3.069
India                                                   -2.331
Indonesia                                               -1.595
Israel                 I(0)    Stationary in levels
Maldives                                                -5.352     **
Mexico                                                  -3.779      *
Republic of Korea                                       -1.954
Republic of Moldova                                     -2.255
Singapore                                               -2.999
South Africa                                            -3.140

Countries              Cointegration


Canada                 Cointegrated
New Zeland             Cointegrated
Norway                 Cointegrated


Antigua and Barbuda    Cointegrated
Bhutan                 Cointegrated
Costa Rica
Maldives               Cointegrated
Mexico                 Cointegrated
Republic of Korea
Republic of Moldova
South Africa

Note: *, **, *** denote 10%, 5% and 1% of significance.

Table 4. Slopes and elasticities under alternative functional forms

Country                Fn. Form    Slope       Elasticity    [??]


Canada                 Linear      0.30 ***       0.52
Iceland                Box-Cox                    0.41        2.36
New Zeland             Box-Cox                    1.04        1.59 **
Norway                 Log-Log     0.11 ***       0.54
Switzerland            Box-Cox                    0.27        2.38 ***


Antigua and Barbuda    Box-Cox                    0.74        3.15 ***
Bhutan                 Box-Cox                    1.46        0.06
China                  Log-Log     0.69 ***       0.56
Israel                 Box-Cox                    0.92       -0.29
Maldives               Box-Cox                    1.67        0.67
Mexico                 Linear      0.28 ***       0.85

Country                [??]          CO2 mean     GDP mean


Canada                                481,254      843,101
Iceland                -1.09            2,009        7,403
New Zeland             -0.62           25,771       76,857
Norway                                 33,542      164,941
Switzerland            -1.75 ***       43,227      234,585


Antigua and Barbuda     1.50 ***          305        1,071
Bhutan                 -0.49 *            272        1,287
China                               3,211,251    2,607,619
Israel                 -1.35 ***       44,089      110,824
Maldives               -0.28              343        1,412
Mexico                                325,068      989,133

Notes: *, **, *** denote 10%, 5% and 1% of significance. The
elasticities have been evaluated at the mean values of C[O.sub.2]
and GDP. Papua and New Guinea was not included in the Table because
the relationship between the emissions and the GDP shows more
complex patterns than the ones observed for the other countries.
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Title Annotation:articulo en ingles
Author:Conte Grand, Mariana; D'Elia, Vanesa
Publication:Serie Documentos de Trabajo
Date:Jul 1, 2013
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