**3. Data and Methods**

The paper examines annual data for four South Asian countries: India, Bangladesh, Sri Lanka, and Pakistan. The period for the analysis (1971–2014), was selected based on data availability. The annual time series data came from the World Bank collection of development indicators, and include the following variables: C—carbon dioxide (CO2) emissions per capita (in metric tons); Y—GDP per capita (in constant 2010 US\$); E—energy consumption per capita (kg of oil equivalent), and T—trade openness (% of GDP). Carbon dioxide emissions are defined as emissions that result from cement manufacturing and fossil fuel combustion. They also include CO2 emissions produced during the consumption of gas fuels and gas flaring, and liquid and solid fuels. Energy consumption refers to primary energy use; i.e., before it is transformed to other end-use fuels. It is equal to domestic production plus imports and stock changes, minus exports and fuels used in international transport (World Bank Development Indicators). Trade openness is defined as the sum of imports and exports of services and goods measured as a share of GDP.

Table 2 shows a data description. According to the skewness and kurtosis measures, we found that the series of some countries showed evidence of asymmetry, fat tails, and high peaks for all variables. These results indicated that the non-linear ARDL approach is suitable for our analysis. Additionally, we performed the test for parameter instability by Andrews [63] and the Brock, Dechert, and Scheinkman (BDS) test [64] to check the data. The test for parameter instability confirmed the instability for all variables in all countries (Table A1). The BDS test confirmed the failure of the assumption of iid residuals (linear model) for some variables in some countries (Table A2). These results also show that applying the non-linear ARDL approach is appropriate for this study.


**Table 2.** Descriptive statistics of the variables.

Sources: The authors' estimation. Note: \*, \*\* and \*\*\* show the significance at the 10%, 5% and 1% level, respectively.

Our model is based on the EKC hypothesis, which postulates an association between economic growth and environmental degradation. The pattern of economic growth can affect environmental quality in many ways. According to Grossman and Krueger [65], this influence can occur through three channels: scale effect, composition effect, and technique effect. Following the literature (e.g., Soytas et al. [66], Shahbaz et al. [67], Kyophilavong et al. [68], Kisswani et al. [69], Józwik et al. [ ´ 70], and Soylu et al. [71]), we assume that the EKC has an inverted U-shape. This means that at the initial stage of development, countries focus more on economic growth, which results in increasing environmental pollution and decreasing environmental quality. Once their threshold level of income (i.e., beyond some level of per capita income) has been achieved, they become more concerned about the environment by implementing more restrictive environmental laws and regulations and encouraging investment in eco-friendly projects. As a result, the pollution level is reduced and environmental quality increases.

Our aim is to identify the long-run relationship and causality between environmental degradation, economic growth, energy consumption, and trade openness in South Asian countries. This association can be expressed as follows:

$$CO2 = f\left(E, Y, Y^2, T\right) \tag{1}$$

All data in the model have been transformed into natural logarithms. Thus, the ARDL model (Equation (2)) and NARDL model (Equation (3)) are rewritten as:

$$
\ln{CO\_{2}}\_{t} = \mathfrak{a} + \beta\_{1}\ln{E\_{t}} + \beta\_{2}\ln{Y\_{t}} + \beta\_{3}(\ln{Y\_{t}})^{2} + \beta\_{4}\ln{T\_{t}} + \varepsilon\_{t} \tag{2}
$$

$$\ln{CO\_{2}}\_{t} = \mathfrak{a} + \beta\_{1}\ln{E\_{t}} + \beta\_{2}\ln{Y\_{t}} + \beta\_{3}(\ln{Y\_{t}})^{2} + \beta\_{4}^{+}\ln{T\_{t}^{+}} + \beta\_{4}^{-}\ln{T\_{t}^{-}} + \varepsilon\_{t},\tag{3}$$

where *CO*<sup>2</sup> is carbon dioxide emissions in metric tons per capita in year *t*, *Et* is energy consumption in kilogram of oil equivalent per capita, *Yt* is real GDP per capita (in constant prices 2010 US\$), *Y*<sup>2</sup> *<sup>t</sup>* is real GDP per capita squared, *Tt* defines trade openness (% of GDP), *T*+ *<sup>t</sup>* and *T*<sup>−</sup> *<sup>t</sup>* represent positive and negative shocks of foreign trade (trade openness), and *ε<sup>t</sup>* is the error term. As was pointed out earlier all the data were collected from the World Bank (World Development Indicators).

The sign of the coefficient *β*1, which is associated with energy consumption, is usually positive, indicating that an increase in energy consumption, which leads to higher economic growth, triggers *CO*<sup>2</sup> emissions. But recent research has suggested that the impact of energy consumption on environmental quality is heavily conditional and dependent on energy sources; for example, Fatima et al. [72], Saidi and Omri [73], Ma et al. [30], and Shahbaz [29]. In our research, it is essential to note that the majority of South Asian countries have traditionally been overwhelmingly dependent on non-renewable fossil fuels to meet their increasing energy demand [20,74].

The signs of coefficients *β*2, and *β*<sup>3</sup> associated with GDP per capita can have positive and negative values. According to the inverted U-shaped EKC hypothesis, the relationship requires that *β*<sup>2</sup> should be positive and *β*<sup>3</sup> should be negative [75,76]. If coefficient *β*<sup>3</sup> is statistically insignificant, there is a monotonic increase in the relationship between CO2 emissions per capita and real GDP per capita.

In liberalized South Asian countries, the expected sign of coefficient *β*<sup>4</sup> associated with GDP per capita is positive. According to Copeland and Taylor [39], the environmental effects of trade liberalization can be classified into five categories: scale effects, structural effects, technology effects, direct effects, and regulation effects. Three of them were explained earlier. The expected sign of the coefficient for trade openness is negative if trade openness promotes energy-efficient technology through the import of new technologies, encouraging cleaner domestic products, and imposing stricter environmental regulations [77]. On the other hand, the coefficient is positive if trade openness increases pollution-intensive export and promotes a pollution haven for foreign direct investment [56,67,78].

The ARDL framework of Equation (2) can be written as:

$$\begin{aligned} \Delta \ln CO\_{2\_t} &= a + \beta\_0 \ln CO\_{2\_{t-1}} + \beta\_1 \ln E\_{t-1} + \beta\_2 \ln Y\_{t-1} + \beta\_3 (\ln Y\_{t-1})^2 + \beta\_4 \ln T\_{t-1} \\ &+ \sum\_{i=1}^p \zeta\_0 \Delta \ln CO\_{2\_{t-i}} + \sum\_{i=0}^r \zeta\_1 \Delta \ln E\_{t-i} + \sum\_{i=0}^{r1} \zeta\_2 \Delta \ln Y\_{t-i} \\ &+ \sum\_{i=0}^{r1} \zeta\_3 \Delta (\ln Y\_{t-i})^2 + \sum\_{i=0}^{r1} \zeta\_4 \Delta \ln T\_{t-i} + \varepsilon\_t \end{aligned} \tag{4}$$

where Δ denotes the operator, *r* denotes the lag lengths, and *ε<sup>t</sup>* is the error term. The null hypothesis is that there is no relationship (cointegration) between CO2 emissions and the determinant variables, and the alternative hypothesis states that a long-run relationship (cointegration) between the variables exists.

Additionally, we investigate an asymmetric impact of trade openness on CO2 emissions. To do this, we apply the NARDL approach, which has been widely used in empirical studies since the mid-1990s, when a substantial body of work considered the joint issues of non-linearity and non-stationarity. Among the recently published studies, we can mention Rahman and Ahmad [79], Qamruzzaman et al. [80], Sheikh et al. [81], and Mujtaba et al. [82]. The main idea of an asymmetric impact is that a positive shock may have a larger absolute effect in the short run while a negative shock has a larger absolute effect in the long run (or vice-versa). The NARDL has several advantages compared to the ARDL model [83]. First, the ARDL approach does not consider the asymmetric relationship between the variables. The positive and negative variations of independent variables have the same effect on the dependent variable. Second, the NARDL approach enables us to test for hidden cointegration, which helps differentiate between linear cointegration, non-linear cointegration, and lack of cointegration. The concept of hidden cointegration (which means that no cointegration is detected when using conventional techniques, but cointegration is found between positive and negative components of the series) was developed by Granger and Yoon [84].

The NARDL framework of Equation (3) can be written as:

$$\begin{aligned} \Delta \ln \text{CO}\_{2i} &= \mathfrak{a} + \delta\_0 \ln \text{CO}\_{2\_{t-1}} + \delta\_1 \ln E\_{t-1} + \delta\_2 \ln Y\_{t-1} + \delta\_3 (\ln Y\_{t-1})^2 + \delta\_4^+ \ln T\_{t-1}^+ \\ &+ \delta\_4^- \ln T\_{t-1}^- \\ &+ \sum\_{i=1}^p \zeta\_0 \Delta \ln \text{CO}\_{2\_{t-i}} + \sum\_{i=0}^r \zeta\_1 \Delta \ln E\_{t-i} + \sum\_{i=0}^r \zeta\_2 \Delta \ln Y\_{t-i} \\ &+ \sum\_{i=0}^r \zeta\_3 \Delta (\ln Y\_{t-i})^2 + \sum\_{i=0}^r \left( \zeta\_4^+ \Delta \ln T\_{t-i}^+ + \zeta\_4^- \Delta \ln T\_{t-i}^- \right) + \varepsilon\_t \end{aligned} \tag{5}$$

where *T*<sup>+</sup> *<sup>t</sup>* and *T*<sup>−</sup> *<sup>t</sup>* represent positive and negative shocks of foreign trade (trade openness). The long-run and short-run changes are represented by coefficients *δ<sup>i</sup>* and *ζi*, respectively.

The short-run NARDL model estimations with an error correction mechanism can be estimated with the following equation:

$$\begin{split} \Delta \ln CO\_{2\_t} &= a + \sum\_{i=1}^p \varrho\_0 \Delta \ln CO\_{2\_{t-i}} + \sum\_{i=0}^p \varrho\_1 \Delta \ln E\_{t-1} + \sum\_{i=0}^p \varrho\_2 \Delta \ln Y\_{t-1} \\ &+ \sum\_{i=0}^p \varrho\_3 \Delta (\ln Y\_{t-1})^2 + \sum\_{i=0}^p \left( \varrho\_4^+ \ln T\_{t-1}^+ + \varrho\_4^- \ln T\_{t-1}^- \right) + \psi ECM\_{t-1} \end{split} \tag{6}$$

The long-run symmetry and asymmetry are tested with the standard Wald test. The asymmetric cumulative dynamic multipliers effect on ln *CO*<sup>2</sup> of a unit change in ln *T*<sup>+</sup> *<sup>t</sup>* and ln *T*− *<sup>t</sup>* can be obtained as follows:

$$\begin{aligned} m\_h^+ &= \sum\_{i=0}^h \frac{\Delta \ln \text{CO}\_{2\_{t+i}}}{\Delta \ln T\_t^+}\\ m\_h^- &= \sum\_{i=0}^h \frac{\Delta \ln \text{CO}\_{2\_{t+i}}}{\Delta \ln T\_t^-} \end{aligned} \tag{7}$$

Finally, we applied the asymmetry causality test developed by Hatemi [85]. The causality testing is asymmetric in the sense that positive and negative shocks may have different causal impacts.
