### Model specification

Empirical literature reveals that energy intensity is influenced by several macroeconomic variables. Following Sadorsky (2013), this study used logarithm of income, logarithm of urbanization, logarithm of industrialization as potential determinants of intensity energy intensity in Ethiopia. Moreover, logarithm of import and logarithm of aid are included into equation of energy intensity based on Hübler and Keller (2010). In order to test the existence of energy-EKC hypothesis, logarithm of income squared is also included as an independent variable based on Deichmann et al. (2018b), Filipovic et al. (2015), Jiang and Lin (2012), Dong et al. (2016) and Zhang et al. (2016). Accordingly, the relationship between energy intensity (*E*) measured as the ratio of energy use to GDP, income (*Y*) proxied by GDP, income squared (*Y*^{2}) measured as GDP squared, urbanization (*U*) measured as percentage of urban population, aid (*A*) measured as the ratio of foreign aid to GDP, industrialization (In) proxied by the ratio of industrial sector GDP to total GDP and import (Im) measured as the ratio of import to GDP, all variables in natural logarithm form, is specified as:

$$\ln E_{t} = \alpha + \beta_{1} \ln Y_{t} + \beta_{2} \left( {\ln Y_{t} } \right)^{2} + \beta_{3} \ln U_{t} + \beta_{4} \ln In_{t} + \beta_{5} A_{t} + \beta_{6} \ln \text{Im}_{t} + \varepsilon_{t} .$$

(1)

### Data

This study uses annual time series data covering the period from 1970 to 2014. The following variables were considered for the study; energy intensity, GDP, square of GDP, urbanization, industrial sector GDP (industrialization), foreign aid and import. All variables except industrialization were obtained from the World Bank Development Indicators database. Industrialization variable was obtained from the Ethiopian Economics Association database.

### Estimation techniques

#### Unit root tests

Even though several conventional unit root tests are available to test the stationarity properties of the variables, they were not used in this study because Katircioglu (2014) and Muhammad et al. (2013) argued that they provide biased and spurious results due to ignoring structural break in the series. To this end, this study employed unit root tests which consider structural break/s in the series.

Zivot and Andrews (1992) (ZA hereafter) test the stationarity properties of the variables in the presence of single structural break point in the series with three options: a one-time change in variables at level form, a one-time change in the slope of the trend component and a one-time change both in intercept and the trend function of the variables. It can be captured by the following model.

$$\Delta x_{t} = \alpha + \alpha x_{t - 1} + \beta t + \phi DU_{t} + \sum\limits_{j = 1}^{k} {d_{j} \Delta x_{t - j} + \varepsilon_{t} }$$

(2)

$$\Delta x_{t} = \alpha + \alpha x_{t - 1} + \phi t + \beta DT_{t} + \sum\limits_{j = 1}^{k} {d_{j} \Delta x_{t - j} + \varepsilon_{t} }$$

(3)

$$\Delta x_{t} = \phi + \phi x_{t - 1} + \phi t + \gamma DU_{t} + \gamma DT_{t} + \sum\limits_{j = 1}^{k} {d_{j} \Delta x_{t - j} + \varepsilon_{t} }$$

(4)

where \(DU_{t}\) indicates dummy variable showing mean shift occurred at point with time break, while \(DT_{t}\) is trend shift variable. Model 4 is used for empirical estimation. Accordingly,

$${\text{DU}}_{t} = \left\{ {\begin{array}{*{20}l} {1 \ldots } \hfill & {{\text{if}}\;t > {\text{TB}}} \hfill \\ {0 \ldots } \hfill & {{\text{if}}\;t < {\text{TB}}} \hfill \\ \end{array} } \right.\;{\text{and}}\;{\text{DU}}_{t} = \left\{ {\begin{array}{*{20}l} {t - {\text{TB}} \ldots } \hfill & {{\text{if}}\;t > {\text{TB}}} \hfill \\ 0... \hfill & {\text{if}}\,{t < {\text{TB}}} \hfill \\ \end{array} } \right.$$

(5)

The null hypothesis of unit root break date is \(\phi = 0\) which indicates that the series is not stationary with a drift not having information about structural break point, while \(\phi < 0\) hypothesis implies that the variable is found to be trend-stationary with one unknown time break.

It is common for macroeconomic variables to exhibit the presence of multiple breaks. In this case, the unit root test method proposed by Clemente et al. (1998) (CMR hereafter) which takes two break dates was used in this study in addition to ZA method. The model has two forms: the additive outliers (the AO model) and the innovative outliers (the IO model).

We wish to test the null hypothesis:

\(H_{0} :y_{t} = y_{t - 1} + \delta_{1} DTB_{1t} + \delta_{2} DTB_{2t} + u_{t}\) as against the alternative hypothesis:

$$H_{1} :y_{t} = \mu + d_{1} DU_{1t} + d_{2} DU_{2t} + \varepsilon_{t}$$

where \(DTB_{it}\) is a pulse variable that takes the value 1 if \(t = TB_{i} + 1 \, (i = 1,2)\) and 0 otherwise, \(DU_{it} = 1{\text{ if }}t > TB_{i} \, (i = 1,2)\) and 0 otherwise.\(TB_{1}\) and \(TB_{2}\) are the time periods when the mean is being modified.

The unit root hypothesis testing if the two breaks belong to the innovational outlier takes place by first estimating the following model and testing whether \(\rho = 1\):

$$y_{t} = \mu + \rho y_{t - 1} + \delta_{1} {\text{DU}}_{1t} + \delta_{2} {\text{DU}}_{2t} + d_{1} {\text{DT}}_{b1,t} + d_{2} {\text{DT}}_{b2,t} + \sum\limits_{i = 1}^{k} {c_{i} \Delta y_{t - i} + \varepsilon_{t} }$$

(6)

If the shifts are supposed to be better represented as additive outliers, then we can test the unit root null hypothesis through the following two steps. The first step is to remove the deterministic part of the variable by estimating the following model:

$$y_{t} = \mu + \delta_{1}^{{}} {\text{DU}}_{1t} + \delta_{2} {\text{DU}}_{2t} + \tilde{y}_{t}$$

(7)

Second, we carry out the test for the \(\rho = 1\) hypothesis in the following model:

$$\tilde{y}_{t} = \sum\limits_{i = 0}^{k} {\omega_{1i} {\text{DTB}}_{1t - i} + \sum\limits_{i = 0}^{k} {\omega_{2i} {\text{DTB}}_{2t - i} + \rho \tilde{y}_{t - i} + } } \sum\limits_{i = 1}^{k} {C_{i} \Delta } \tilde{y}_{t - i} + \varepsilon_{t}$$

(8)

#### Cointegration: ARDL approach

Due to the merits that the ARDL bounds testing approach to cointegration has over the traditional approaches to cointegration (Chindo et al. 2014; Halicioglu and Ketenci 2016; Hundie 2018; Shahbaz et al. 2015; Shahbaz et al. 2013); this study applied the ARDL approach to test the long-run cointegration among the variables under consideration.

The unrestricted error-correction model (UECM) version of the ARDL model for Eq. (1) is specified as follows:

$$\begin{aligned} \Delta \ln E_{t} & = \alpha_{1} + \sum\limits_{i = 1}^{p} {\beta_{1i} \Delta \ln E_{t - i} + \sum\limits_{i = 0}^{{q_{1} }} {\eta_{1i} \Delta \ln Y_{t - i} + \sum\limits_{i = 0}^{{q_{2} }} {\gamma_{1i} \Delta (\ln Y)_{t - i}^{2} + } \sum\limits_{i = 0}^{{q_{3} }} {\theta_{1i} \Delta \ln U_{t - i} } } } + \sum\limits_{i = 0}^{{q_{4} }} {\pi_{1i} \Delta \ln In_{t - i} } + \sum\limits_{i = 0}^{{q_{5} }} {\phi_{1i} \Delta \ln A_{t - i} } + \sum\limits_{i = 0}^{{q_{6} }} {\omega_{1i} \Delta \ln \text{Im}_{t - i} } \\ & \quad + \delta_{1} \ln E_{t - 1} + \delta_{2} \ln Y_{t - 1} + \delta_{3} \left( {\ln Y_{t - 1} } \right)^{2} + \delta_{4} \ln U_{t - 1} + \delta_{5} \ln In_{t - 1} + \delta_{6} \ln A_{t - 1} + \delta_{7} \ln \text{Im}_{t - 1} + \varepsilon_{1t} \\ \end{aligned}$$

(7)

The parameters \(\delta_{i} \, (i = 1,2,3,4,5,6,7)\) are the corresponding long-run multipliers, while the parameters \(\beta_{i} ,\eta_{i} ,\gamma_{i} ,\theta_{i} ,\pi_{i} ,\phi_{i} ,\omega_{i}\) are the short-run dynamic coefficients of the underlying ARDL model.

Investigating the presence of long-run relationship among the variables in Eq. (7) using Fisher (F) or Wald (W) statistics is the first step in the ARDL bounds testing approach to cointegration. Shahbaz et al. (2015) contended that the *F*-statistic is much more sensitive to lag order selection. Therefore, the proper lag length was chosen based on the Schwartz Bayesian Criterion (SBC).^{Footnote 1} Then, a joint significance test that implies no cointegration hypothesis, \((H_{0} :\delta_{1} = \delta_{2} = \delta_{3} = \delta_{4} = \delta_{5} = \delta_{6} = \delta_{7} = 0)\), counter to the alternative hypothesis, (H_{1}: at least one of \(\delta\)’s is different from zero) is performed for Eq. (7). *F*-statistic is compared to the critical bounds generated by Narayan (2005) because it better fits small sample observations (Narayan 2004, 2005; Narayan and Narayan 2004). If the calculated *F*-statistic greater than the upper critical bound, the null hypothesis is rejected; it indicates that cointegration exists among the variables.

If the presence of long-run relationships (cointegration) among the variables is established, the second step is to estimate the following long-run and short-run models that are represented in Eqs. (8) and (9), respectively.

$$\begin{aligned} \ln E_{t} & = \alpha_{2} + \sum\limits_{i = 1}^{p} {\beta_{2i} \ln E_{t - i} + \sum\limits_{i = 0}^{{q_{1} }} {\eta_{2i} \ln Y_{t - i} + \sum\limits_{i = 0}^{{q_{2} }} {\gamma_{2i} \left( {\ln Y_{t - i} } \right)}^{2} + \sum\limits_{i = 0}^{{q_{3} }} {\theta_{2i} \ln U_{t - i} } } } \\ & \quad + \sum\limits_{i = 0}^{q4} {\pi_{2i} \ln A_{t - i} } + \sum\limits_{i = 0}^{{q_{5} }} {\phi_{2i} \ln In_{1i} } + \sum\limits_{i = 0}^{{q_{6} }} {\omega_{2i} \ln \text{Im}_{t - i} } + \varepsilon_{2t} \\ \end{aligned}$$

(8)

$$\begin{aligned} \Delta \ln E_{t} & = \alpha_{3} + \sum\limits_{i = 1}^{p} {\beta_{3i} \Delta \ln E_{t - i} + \sum\limits_{i = 0}^{{q_{1} }} {\eta_{3i} \Delta \ln Y_{t - i} + \sum\limits_{i = 0}^{{q_{2} }} {\gamma_{3i} \Delta \left( {\ln Y_{t - i} } \right)^{2} + } \sum\limits_{i = 0}^{{q_{2} }} {\theta_{3i} \Delta \ln U_{t - i} } } } + \sum\limits_{i = 0}^{{q_{3} }} {\pi_{3i} \Delta \ln A_{t - i} } \\ & \quad + \sum\limits_{i = 0}^{{q_{4} }} {\phi_{3i} \Delta In_{t - i} } + \sum\limits_{i = 0}^{{q_{5} }} {\omega_{1i} \Delta \ln \text{Im}_{t - i} } + \psi ECT_{t - 1} + \varepsilon_{3t} \\ \end{aligned}$$

(9)

where \(\psi\) is the speed of adjustment parameter and \(ECT_{t - 1}\) is the lagged residuals that are obtained from the estimated cointegration model.

It is good idea to apply more than one estimator if there is concern about the robustness of the results (Narayan 2005). To this aim, the ARDL bounds test of cointegration is accompanied by an alternative single cointegration equation known as the fully modified ordinary least squares (FMOLS hereafter) estimator of Phillips and Hansen (1990) for the robustness check. The FMOLS has a benefit of fixing endogeneity and autocorrelation effects and it removes the sample bias error (Adom and Kwakwa 2014; Gokmenoglu and Taspinar 2018; Narayan 2005).

#### Toda–Yamamoto (TY) approach to granger causality

The existence and direction of causal relationship between variables in the model are analyzed using Toda–Yamamoto (1995) (TY hereafter) method because it has several statistical merits over conventional Granger causality testing methods (Chindo et al. 2014; Gokmenoglu and Taspinar 2018). The basic idea behind TY method is estimating a \((k + d_{{\rm max} } )\)th-order VAR where k is the correct lag length of the VAR model and \(d_{{\rm max} }\) is the maximal order of integration. The TY representation of Eq. (1) is given as below:

$$\begin{aligned} \ln E_{t} & = \beta_{10} + \sum\limits_{i = 1}^{k} {\theta_{1i} } \ln E_{t - i} + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\varOmega_{1i} \ln E_{t - i} + \sum\limits_{i = 1}^{k} {\delta_{1i} \ln Y_{t - i} } } + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\phi_{1i} \ln Y_{t - i} } + \sum\limits_{i = 1}^{k} {\gamma_{1i} \ln U_{t - i} } \\ & \quad + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\psi_{1i} \ln U_{t - i} } + \sum\limits_{i = 1}^{k} {\mu_{1i} \ln A_{t - i} } + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\eta_{1i} \ln A_{t - i} + \sum\limits_{i = 1}^{k} {\vartheta_{1i} \ln In_{t - i} + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\omega_{1i} \ln In_{t - i} } } } \\ & \quad + \sum\limits_{i = 1}^{k} {\varphi_{1i} \ln \text{Im}_{t - i} + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\mu_{1i} \ln \text{Im}_{t - i} } } + \varepsilon_{1t} \\ \end{aligned}$$

(10)

$$\begin{aligned} \ln Y_{t} & = \beta_{20} + \sum\limits_{i = 1}^{k} {\theta_{2i} } \ln E_{t - i} + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\varOmega_{2i} \ln E_{t - i} + \sum\limits_{i = 1}^{k} {\delta_{2i} \ln Y_{t - i} } } + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\phi_{2i} \ln Y_{t - i} } + \sum\limits_{i = 1}^{k} {\gamma_{2i} \ln U_{t - i} } \\ & \quad + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\psi_{2i} \ln U_{t - i} } + \sum\limits_{i = 1}^{k} {\mu_{2i} \ln A_{t - i} } + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\eta_{2i} \ln A_{t - i} + \sum\limits_{i = 1}^{k} {\vartheta_{2i} \ln In_{t - i} + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\omega_{2i} \ln In_{t - i} } } } \\ & \quad + \sum\limits_{i = 1}^{k} {\varphi_{2i} \ln \text{Im}_{t - i} + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\mu_{2i} \ln \text{Im}_{t - i} } } + \varepsilon_{2t} \\ \end{aligned}$$

(11)

$$\begin{aligned} \ln U_{t} & = \beta_{30} + \sum\limits_{i = 1}^{k} {\theta_{3i} } \ln E_{t - i} + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\varOmega_{3i} \ln E_{t - i} + \sum\limits_{i = 1}^{k} {\delta_{3i} \ln Y_{t - i} } } + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\phi_{3i} \ln Y_{t - i} } + \sum\limits_{i = 1}^{k} {\gamma_{3i} \ln U_{t - i} } \\ & \quad { + }\sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\psi_{3i} \ln U_{t - i} } + \sum\limits_{i = 1}^{k} {\mu_{3i} \ln A_{t - i} } + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\eta_{3i} \ln A_{t - i} + \sum\limits_{i = 1}^{k} {\vartheta_{3i} \ln In_{t - i} + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\omega_{3i} \ln In_{t - i} } } } \\ & \quad + \sum\limits_{i = 1}^{k} {\varphi_{3i} \ln \text{Im}_{t - i} + \sum\limits_{i = p + 1}^{{k + d_{{\rm max} } }} {\mu_{3i} \ln \text{Im}_{t - i} } } + \varepsilon_{3t} \\ \end{aligned}$$

(12)

The modified Wald (MWald) test is used to test the direction of causal relationship among the variables under study.

#### Innovative accounting approach to test dynamic Granger causality

Economic literature argued that the Granger causality approaches such as the VECM and TY Granger causality test fail to consider the relative strength of causal relation between the variables beyond the selected time period (Chindo et al. 2014; Hundie 2014). This makes the credibility of causality results obtained by the VECM and TY Granger approaches questionable. To this end, the study applied innovative accounting approach (IAA), i.e., variance decomposition method and impulse response function. Generalized forecast error decomposition and generalized impulse response developed by Pesaran and Shin (1998) which are invariant to the ordering of variables in VAR system were employed in this study.

The impulse response function is alternate of variance decomposition approach and shows the reaction in one variable due to shocks stemming in other variables. The generalized forecast error variance decomposition method shows proportional contribution in one variable due to innovative shocks stemming in other variables.