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Testing for Convergence in Carbon Dioxide Emissions Using a Bayesian Robust Structural Model

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Abstract

We address international convergence in carbon dioxide emissions per capita and per value added derived from emission inventories based on production and consumption patterns. We propose a Bayesian structural model that accounts for heteroscedasticity and endogeneity between emissions and economic growth, and tests for the existence of group-specific convergence via shrinkage priors. We find evidence for country-specific conditional convergence in all emission inventories, implying a half-life of 2.7–3.1 years for production-based emissions and 3.6–4.7 years for consumption-based emissions. When testing for global convergence without allowing for individual-specific convergence paths, the half-life of \(\hbox {CO}_2\) per capita increases to 15–26 years, whereas emission intensities show a half-life of 44–45 years. Our results highlight the current incompatibility between emission targets and economic growth and the need for faster diffusion of green technologies. Moreover, there is no evidence for specific convergence dynamics in the European Union, the OECD, or the countries that are subject to binding emission constraints specified in the Kyoto Protocol. The institutional frameworks implemented in industrialized countries did not induce faster convergence among developed economies.

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Notes

  1. See Knutti et al. (2015) for a critical analysis of the 2 °C target.

  2. Empirical studies that investigate the existence of an EKC in \(\hbox {CO}_2\) emissions usually fail to find such a relationship in samples covering a large group of countries (see e.g. Stern 2004, and Stern 2017, for exhaustive surveys, or Fernández-Amador et al. 2017, for a survey of empirical applications). Aslanidis and Iranzo (2009) and Fernández-Amador et al. (2017) provided evidence that the income elasticity of \(\hbox {CO}_2\) emissions decreases as income per capita rises above a threshold level though emissions continue growing, what challenges the sustainability of economic growth.

  3. The Paris Agreement recognizes the need to support developing countries in order to facilitate the effective implementation of the objectives identified in the Agreement (Paris Agreement, Art. 2).

  4. See Pettersson et al. (2014) and Stern (2017) for comprehensive surveys of the literature on convergence in pollution emissions.

  5. The findings of the literature range from evidence for convergence (Strazicich and List 2003; Nguyen 2005; Ezcurra 2007; Romero-Ávila 2008; Lee et al. 2008; Westerlund and Basher 2008; Lee and Chang 2009; Brock and Taylor 2010; Jobert et al. 2010; Huang and Meng 2013; Yavuz and Yilanci 2013; Anjum et al. 2014; Hao et al. 2015; Wu et al. 2016; Zhao et al. 2015) over the existence of convergence clubs (Nguyen 2005; Aldy 2006; Lee and Chang 2008; Panopoulou and Pantelidis 2009; Barassi et al. 2011; Ordás Criado and Grether 2011; Camarero et al. 2013; Herrerias 2013; Wang et al. 2014; Burnett 2016) to no evidence for convergence (Aldy 2007; Barassi et al. 2008; Nourry 2009).

  6. See Anjum et al. (2014), Camarero et al. (2013) and Panopoulou and Pantelidis (2009).

  7. Aldy (2007) investigated convergence of \(\hbox {CO}_2\) emissions across US states. This is the only study so far that also covers consumption inventories. The author did not find evidence for convergence for either \(\hbox {CO}_2\) production or for \(\hbox {CO}_2\) consumption per capita. In contrast to Aldy, our study covers economies at different development states, thus being the first one to evaluate global convergence patterns in \(\hbox {CO}_2\) consumption.

  8. Salois and Balcombe (2015) proposed a related model in the context of cross-sections, where t-distributed errors in an IV-model are represented by weighted errors of normals. Their modelization shares with ours the use of a scale mixture of normals representation, though the authors do not perform Cholesky-rotation of the system to represent it as a recursive system of equations but condition the weighted errors on each other and use a Wishart prior for the variance–covariance matrix.

  9. Earlier studies focused on unconditional convergence, while more recent studies tested for conditional convergence, i.e. convergence after allowing for heterogeneity across countries by accounting for additional determinants of economic growth. While unconditional convergence was often found for OECD countries, it was generally rejected for samples including non-OECD countries. If countries converge to different steady states, unconditional convergence models might result in biased coefficient estimates because the model used for estimation is miss-specified (Barro and Sala-i-Martin 2004). See for example Baumol (1986), Barro (1991), Barro and Sala-i-Martin (1992), Mankiw et al. (1992) and Barro and Sala-i-Martin (2004).

  10. See e.g. Barro and Sala-i-Martin (1992), Quah (1993), Sala-i-Martin (1996) and Young et al. (2008). Phillips and Sul (2007b) developed a test for identifying club-convergence groups, which corresponds to a test for conditional \(\sigma \)-convergence (see Phillips and Sul 2007b). Phillips and Sul (2007a) provided a short empirical application of the test in the context of economic growth convergence.

  11. See e.g. Ravallion (2003) who applied \(\beta \)-convergence tests to international income inequality.

  12. See e.g. Carlino and Mills (1993), Quah (1993), Bernard and Durlauf (1996) and Evans and Karras (1996).

  13. See also Panopoulou and Pantelidis (2009), Jobert et al. (2010) and Ordás Criado and Grether (2011) for surveys on \(\beta \)-, \(\sigma \)- and stochastic convergence.

  14. Studies for OECD countries focused mainly on stochastic and \(\beta \)-convergence. For more details on the concept of convergence used by the respective studies, see Table A.1 in the Online Appendix.

  15. Panopoulou and Pantelidis (2009) and Herrerias (2013) applied the Phillips and Sul (2007b) test for convergence clubs. Ordás Criado and Grether (2011) found evidence for income-specific and regional convergence clubs especially for the sub-period 1980–2000.

  16. See Dasgupta et al. (2002), Kaika and Zervas (2010), and Stern (2004, 2017) for reviews, and Fernández-Amador et al. (2017) for a summary of the most recent evidence.

  17. Schmalensee et al. (1998) is an exception, finding support for an inverse-U relationship using non-parametric techniques. More recently, Aslanidis and Iranzo (2009) and Fernández-Amador et al. (2017) found that the income-elasticity of \(\hbox {CO}_2\) emissions decreases slightly after income per capita passes a certain threshold, such that relative decoupling increases with economic growth, though there is no evidence of absolute decoupling and an EKC relationship. Fernández-Amador et al. (2017) also provided evidence for a similar pattern in \(\hbox {CO}_2\) consumption-based inventories.

  18. Anjum et al. (2014) reported that the negative correlation between initial emissions and subsequent emission growth is stronger for \(\hbox {CO}_2\) intensity than for \(\hbox {CO}_2\) per capita.

  19. All these studies define \(\hbox {CO}_2\) intensity as \(\hbox {CO}_2\) per GDP. In our analysis we refer to \(\hbox {CO}_2\) intensity as \(\hbox {CO}_2\) per value added.

  20. A description of the countries included in the composite regions is available in Fernández-Amador et al. (2016). The dataset has been recently extended by the authors to cover the year 2014.

  21. This corresponds to calculating average annual growth rates. For a similar method see Ravallion (2003), who accounts for the unequal spacing in time between measures of income inequality for large-N, small-T panel data by regressing the difference in inequality between time t and the initial period \(t_1\) on a constant and initial inequality at time \(t_1\), both multiplied by a time-trend (\(t-1\)). In contrast to Ravallion’s data, our panel is balanced in the sense that for every individual we observe all variables at the same points in time. Thus, we can also exploit the variation of the data across time and use initial emissions in year \(t-s\) instead of in year \(t_1\) as a regressor.

  22. Bernard and Durlauf (1996) pointed out that the power of time-series tests may be weak when the dynamics do not occur near the steady state. In this sense, time-series approaches to test for stochastic convergence may not be particularly suitable in our context, since data on \(\hbox {CO}_2\) emissions covering a global sample of countries are very likely to be driven by transition dynamics rather than being near the steady state.

  23. Detailed information on the sector aggregation from the original GTAP sectoral disaggregation is available from the authors upon request.

  24. Ordás Criado et al. (2011) tested for convergence in sulfur oxides and nitrogen oxides. Their theoretical model assumes optimal control of pollution emissions at the national level, making it particularly suited for applications to local air pollutants. Nevertheless, the structure of the empirical model they specify is compatible with the green Solow model by Brock and Taylor (2010), which the authors applied to \(\hbox {CO}_2\) emissions. Ordás Criado et al. (2011) regressed the average growth rates of emissions over the period \(t-5\) to t on the level of emissions at the initial period of the growth rate (\(t-5\)), the growth rate of GDP over \(t-5\) and t, GDP in \(t-5\), and time- and individual-dummies using OLS and a non-parametric model. The authors also addressed endogeneity between emissions and GDP by instrumenting GDP and its growth rate with their lagged values (following Barro and Sala-i-Martin 1992). Brock and Taylor (2010) developed a theoretical model that also predicts conditional \(\beta \)-convergence, which the authors applied to \(\hbox {CO}_2\) emissions. Although Brock and Taylor’s model is applicable to global pollutants, in our empirical approach we follow Ordás Criado et al. (2011) since their empirical analysis makes use of the panel structure of the data and accounts for the potential endogeneity of GDP per capita.

  25. For the first period in our sample, 1997–2001, we use the average growth rate for a period of the same length, 1993–1997, as instrument.

  26. In the original dynamic model of emissions, once we undo the average growth rate, the relevant parameter for the case of regular sampling every period is \((1+\beta )\). The precision elicited ensures that the hypothesis of an unit root in our autoregressive model with explanatory variables is not an extreme event in our prior for \(\beta \).

  27. The precision is defined as the inverse of the variance. A precision of 0.2 implies a variance of 5.

  28. Note that the precision of the individual-dummies is larger than the precision of the rest of the parameters. A uniform prior on the individual fixed effects would lead to improper posterior distributions for the parameters of interest, while very diffuse priors would lead to very slow convergence of the MCMC algorithm used for inference (see e.g. Lancaster 2008, Chap. 7).

  29. Scale mixture of normals with the weights specified as in (9) are equivalent to a t-student distribution (see e.g. Andrews and Mallows 1974; West 1987; Ding 2016). The degrees of freedom of the t-student are equal to the hyperparameter governing the distribution of the weights \(\omega _{i}\), \(\nu \). With growing \(\nu \) the distribution converges to a normal distribution, as less probability mass is concentrated at the tails of the distribution. The prior for the weights in the scale mixture of normals, \(\omega _{i}\), together with the prior for the components of the variance matrix \(\Sigma \) that we will define below, imply a form of cross-sectional heteroscedasticity of the gamma type (Andrews and Mallows 1974; Geweke 1993; Koop 2003, Chap. 6; Lancaster 2008, Chap. 3). There are two main advantages of modeling the problem in terms of scale mixture of normals rather than as a t-student distribution. The first one is that the type of heteroscedasticity, cross-sectional in our case, can be explicitly stated. The second is that it is less computational demanding for the numerical algorithm to estimate the posterior distributions of the parameters.

  30. We regard the priors for the parameters of interest \((\beta , \pi _0, \pi _1, \{\theta _r\}, \{\delta _t\}, \alpha _{iv}, \beta _{iv}, \{\alpha _i\},\{\beta _j\})\) as informative. Geweke (1993) shows that under informative (normal) priors for the slopes, both the first and the second moments of the slopes exist. When the priors of the slopes are uninformative, \(\nu >2\) ensures existence of the first moments, while \(\nu >4\) ensures existence of the second moments. Thus, the truncation defined contains roughly \(80\%\) of the density around the mean of the prior, while ensuring existence of first moments even in the case of noninformative priors for the parameters of interest.

  31. We explain the derivation of the IV-prior in terms of covariance matrices because this is common in the literature, though the specification of the priors is in terms of precisions, as carried out in the software. Alternatively, we could use an inverted Wishart prior for \(\Sigma \), \(\Sigma \sim IW(v_0, \Sigma _0)\), with parameters \(v_0\) and \(\Sigma _0\). Priors for covariance matrices and variances have usually been addressed by means of inverted Wishart and inverted Gamma distributions, respectively, while Wishart or Gamma distributions have been used as priors for precision matrices and precisions. Wishart priors have been extensively used in the framework of Bayesian instrumental variable models under normal-distributed errors (see e.g. Kleibergen and Zivot 2003; Lancaster 2008, Chap. 8; Rossi et al. 2005).

  32. Ding (2016) used the representation of a multivariate t-student distribution as a scale mixture of multivariate normals to derive the conditional distribution of the multivariate t-student, which can be represented by the conditional normal distribution times the conditional distribution of the weights.

  33. See George and McCulloch (1993) for details on the Gibbs sampler for the SSVS prior, and Lopes and Polson (2014) for the details of the Gibbs sampling for IV-estimation in the context of the normal distribution.

  34. That was sufficient for the chains to show mixing and the estimates of the coefficients to show convergence to their ergodic distribution.

  35. The concept of incidental parameters and the problem of limited information to estimate incidental parameters was first defined by Neyman and Scott (1948). Lancaster (2000) and Moon et al. (2015) offer rigurous treatments of the incidental parameters problem.

  36. Several authors have shown the connection between the non-parametric bootstrap, the parametric (Bayesian) bootstrap and MCMC, respectively (see e.g. Rubin 1981; Efron 1982, 2011; Newton and Raftery 1994; Hastie et al. 2009, Chap. 8).

  37. The results from our simulations are available from the authors upon request. These simulations did not include the null of endogeneity between explained and explanatory variables and thus do not introduce an IV structure in the model. A more detailed simulation-based analysis of the Bayesian estimator in comparison with alternative dynamic panel estimators can be found in Fernández-Amador and Oberdabernig (2018).

  38. Furthermore, we report the results of the DV-conditional and conditional homoscedastic models (normal-distributed errors with and without individual-dummies) in Tables A.4 and A.5 in the Online Appendix.

  39. The underlying data cover 468 observations. Because we use the growth rate of emissions as dependent variable, our final sample includes 390 observations.

  40. It should be noted that Bayesian estimation does not aim at minimizing the sum of square residuals and thus, it does not maximize the \(R^2\). However, we consider it together with the DIC when assessing how well our models fit the data and whether they can be regarded as consistent with our data. The DIC penalizes the number of parameters and is often regarded as a better measure of fit in the Bayesian context than the \(R^2\).

  41. The half-life provides an indication of the speed of convergence. It is defined as the time required to eliminate half of the initial gap between actual emissions levels and the steady state. The half-life is calculated as \(\frac{-ln(0.5)}{-ln(1+\beta )}\) (see Allington and McCombie 2007, p. 206).

  42. The half-life in their sample of developed countries was estimated to lie between 4.2 and 6.2 years; this is longer than the half-life estimated in their pooled sample including developing countries.

  43. These figures correspond to estimates of conditional convergence. For unconditional convergence the authors reported a half-life between 4 and 8.5 years.

  44. The negative effect of democracy on emissions growth is not robust to using alternative measures of democracy, such as the democracy measure sourced from the FSD1289 Measures of Democracy 1810–2014 database (see Finnish Social Science Data Archive 2018) or the average of the Freedom House indices of political rights and civil liberties (see Freedom House 2018). The main results are not sensitive to these alternative specifications and are also robust to the exclusion of the democracy variable.

  45. The negative impact of the construction sector may be related to the low carbon intensity of this sector during the period analyzed. We take the value added share of agriculture as the benchmark sector and exclude it from the specifications in order to avoid multicollinearity.

  46. The results of the models without individual-dummies could be affected by omitted variables and should be taken with care (see Barro and Sala-i-Martin 2004).

  47. Tables A.4 and A.5 in the Online Appendix report the results for the models with homoscedastic errors. The main results do not change qualitatively. The only important qualitative change is that income growth becomes significant for emissions per value added in the DV-conditional models. The convergence coefficient only changes slightly, though this change is amplified in the half-lives, decreasing them in the specifications for emissions per value added in the conditional models.

  48. A more detailed analysis of this mechanism is out of the scope of this paper.

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Acknowledgements

The authors thank Carlos Ordás Criado for valuable insights and the participants of the SWSR for inspiring discussions. The authors acknowledge support of the NRP 73 project Switzerland’s Sustainability Footprint: Economic and Legal Challenges, grant No. 407340-172437, University of Bern, supported by the Swiss National Science Foundation (SNSF) within the framework of the National Research Programme “Sustainable Economy: resource-friendly, future-oriented, innovative” (NRP 73).

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  1. World Trade Institute, University of Bern, Hallerstrasse 6, 3012, Bern, Switzerland

    Octavio Fernández-Amador, Doris A. Oberdabernig & Patrick Tomberger

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  1. Octavio Fernández-Amador
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  2. Doris A. Oberdabernig
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  3. Patrick Tomberger
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Correspondence to Octavio Fernández-Amador.

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Fernández-Amador, O., Oberdabernig, D.A. & Tomberger, P. Testing for Convergence in Carbon Dioxide Emissions Using a Bayesian Robust Structural Model. Environ Resource Econ 73, 1265–1286 (2019). https://doi.org/10.1007/s10640-018-0298-9

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