2. Data

This study uses a balanced panel of 104 countries over the period 1971 to 2013. All the variables are measured at the country level on a yearly basis. Given our focus on energy transition and the application of techniques allowing coefficient heterogeneity, it is important to gather the largest sample of countries for which it can be obtained for the longest period possible. This would return the most reliable variability both from the cross-sectional and temporal dimensions, useful for the estimations per country (for example for the application of Mean Group and Cross-Sectional dependence estimators, as well as for point estimation based on the Kernel Regularized Least Squares). Therefore, countries with fewer than 43 observations per variable were dropped from the panel.

In accordance with the energy ladder theory, the main independent variables are final use of the following energy categories: (a) traditional, including biomass; (b) transitional, including charcoal, coal and kerosene (as well as its equivalents such as paraffin or other liquid fuels); and (c) modern fuels, including electricity and gas.Footnote ^4, Footnote ⁵ The main independent variable is per capita gross domestic product (GDP) at purchasing power parity (PPP) in constant 2005 US dollars.

Energy prices are only available for a reduced sample; 51 countries have residential electricity prices and 32 countries have prices for natural gas. Moreover, our sub-sample with available prices has a high participation of countries classified as upper-middle and high-income with an average yearly per capita GDP of around US$17,000. Therefore, in the empirical analysis, we choose to control for international oil prices, in constant 2005 US dollars, to have a greater representation of countries at different income levels. Other variables used to control for differences between countries are the share of hydroelectricity and net fossil fuel exports. These controls capture to some extent heterogeneity in natural endowments that may affect energy consumption, mainly, through prices. Nonetheless, in a robustness check, we will show that the results do not change significantly when electricity prices (for which there is a larger sample) are included.

The sources of information for energy-carriers comes from the Extended World Energy Balances compiled/built by the International Energy Agency (IEA). Energy prices are obtained from the Energy Statistics of the U.S. Energy Information Administration (EIA), as well as BP annual statistics, and the Latin American Energy Organization. Other macroeconomic variables come from the World Development Indicators. The final dataset used in this paper, along with the replication files, are available in the online appendix.

3. Stylized facts about domestic energy consumption

This section presents some descriptive patterns to shed light on how domestic energy consumption evolves along the development ladder. It shows the relevance of distinguishing between energy sources when studying the relationship between energy consumption and income. Economic progress seems to drive the growing demand for modern fuels, particularly in the residential sector, while reducing the use of traditional and transitional fuels. Still, over the period under analysis, the pace of such growth has been highly heterogeneous between countries.

Figure 1 plots the relationship between energy consumption and per capita income, exploiting variability across countries and over time. The figure provides a historical view of patterns in domestic energy use over the world income distribution, showing how energy consumption (the bold line) tends to follow a nonlinear path depicted as a compressed S-curve. This shape seems to be explained by a marked shift in the composition of energy use. Energy consumption tends to be high at lower income levels, where the use of traditional fuels is prevalent. Moving to the right of the income distribution, traditional fuels are substituted with transitional and modern fuels. However, the use of transitional fuels tends to rise to a point from which it then starts to decline for further income increases. In contrast, consumption of modern energy grows nonlinearly until it accounts for most of the per capita consumption at the highest income levels. That is, as countries become wealthier, growth in overall per capita energy use tends to be explained mainly by larger consumption of better quality and more efficient fuels. Noticeably, this transition seems not to completely displace the use of traditional and transitional fuels in developed economies, a practice that may be attributed to cultural factors, or to consumption by low-income households within relatively rich countries.

Figure 1.

Consumption of domestic fuels along the world income distribution.

Notes: Axes in log scale. The curves are fitted with a 2-degree polynomial for observations of 104 countries over 1971–2013. Modern fuels = electricity and gas; transitional fuels = kerosene, paraffin, and so forth; and traditional fuels = biomass. GDP, gross domestic product; Kgoe, kilograms of oil equivalent; PPP, purchasing power parity.

Source: Authors' calculations based on data from the International Energy Agency.

It is important to highlight that while in some developing countries the levels of total final energy consumption are high and even close to that of developed economies, their contexts are different. Not only is the quality energy mix dramatically different but so are the technologies that are used or accessible. For example, electricity provides greater efficiency for lighting than biomass, and access to more efficient light bulbs would increase this gap. Similarly, consumption of traditional fuels in developed countries would occur under very different circumstances, as for example, heating in better-off, isolated dwellings that use more efficient cook-stoves. All in all, this would imply considerable differences in the actual ‘useful energy’ enjoyed by the households.Footnote ⁶

Beyond the expected differences in energy-quality and -efficiency, we observe systematic differences in the levels of energy consumption by income classification. This can be appreciated in figure 2 that presents the composition of annual per capita residential energy use, averaged over 2009–2013, by income group. It shows that total final energy consumption in high-income OECD countries is almost three times what is observed in the low-income group. Also, and in accordance with the above, this figure also shows that in low-income countries, traditional and transitional fuels represent 90 per cent of per capita energy consumption, a share that tends to sharply decrease with rising incomes.

Figure 2.

Composition of per capita residential energy consumption by type of fuel and country income classification, average for 2009–13.

Notes: Countries are classified by their income level according to the World Bank income classifications. OECD: Organization for Economic Co-operation and Development; Kgoe: kilograms of oil equivalent.

Sources: Authors' calculations based on data from the International Energy Agency and World Development Indicators.

The resulting change in composition can be seen directly in figure 3, where the trend line of the share of modern fuels in domestic consumption follows a sigmoid shape –the gray dots are the scatter of the country-year observations. This reinforces the fact that modern fuels tend to displace other energy sources at the highest income levels. The switch toward modern fuels accelerates as countries develop, but the pace of substitution starts to decrease at higher-middle-income levels ($\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel\succ\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}}\ }$ US$10,000 per year). Still, a persistence of traditional and transitional fuels in the residential energy portfolio is observed. Such a slower pace may also be related to the last-mile problem, in which the difficulty of reaching isolated rural areas is an obstacle to achieving complete access to modern fuels.Footnote ⁷ On the other hand, the persistence of traditional and transitional fuels may also be the result of an optimal allocation by households, conditional on their preferences, resource availability, etc.

Figure 3.

Share of modern fuels along the world income distribution.

Notes: The axes are in log scale. Values are for 104 countries between 1971 and 2013. Modern fuels include electricity and gas. The curve is fitted with a 2nd-degree polynomial. GDP, gross domestic product; PPP, purchasing power parity.

Sources: Authors' calculations based on data from the International Energy Agency and World Development Indicators.

As inferred from the dispersion in the country-year observations, figure 3 also shows a pronounced heterogeneity in the energy transition paths. Such distinctive paths between countries can also be observed in terms of the relationship between the growth rates of modern energy consumption and GDP per capita. Figure 4 plots this relationship showing that it has been quite sparse, but also indicating that modern energy consumption has grown at a faster rate than income. This suggests that the estimation of income elasticities needs to take into account country-specific characteristics.

Figure 4.

Modern energy consumption versus income growth.

Notes: Values are for 104 countries from 1971 to 2013. GDP, gross domestic product; PPP, purchasing power parity.

Sources: Authors' calculations based on data from the International Energy Agency and World Development Indicators.

In a broader context, considering other economic sectors, residential modern energy consumption has not only grown at a higher rate than income but also at a higher rate than energy consumption by other sectors. Figure 5 illustrates that while per capita energy consumption in the residential sector has grown at relatively low rates in most regions, the modern fuel component has in fact grown faster than in other sectors, such as transportation and industry.Footnote ⁸ This pattern occurs in all regions, and it is especially marked in Sub-Saharan Africa, and the Middle East and North Africa.

Figure 5.

Average annual growth rate by fuel, sector, and region.

Notes: Values are average annual growth from 1971 to 2013. Modern fuels = electricity and gas; transitional fuels = kerosene, paraffin, and so forth; and traditional fuels = biomass. Regions follow the World Bank classification: SAS, South Asia; MEA, Middle East and North Africa; SSF, Sub-Saharan Africa; EAS, East Asia and Pacific; LCN, Latin America and the Caribbean; WDL, world; ECS, Europe and Central Asia; and NAC, North America; GDP, gross domestic product; TFC, total final consumption of all sectors. GDP per capita is in constant 2005 PPP prices.

Source: Authors' calculations based on data from the International Energy Agency and World Development Indicators.

4. Empirical approach

The composition and sensitivity of domestic energy consumption are examined using parametric and machine-learning approaches. In the parametric setting, the general specification takes the following reduced forms:

(1)\begin{align}{y_{it}} & = \alpha {x_{it}} + W^{\prime}\beta + {\varepsilon _{it}}\end{align}

(2)\begin{align}{y_{it}} & = \theta {y_{it - 1}} + \alpha {x_{it}} + W^{\prime}\beta + {\varepsilon _{it}},\end{align}

where ${y_{it}}$ represents a dependent variable for country i in year t. The dependent variables are (separately) consumption of traditional, transitional, modern fuels, and the share of modern fuels, all measured in per capita terms. The share of modern fuels aims to capture the composition of domestic energy consumption, which is calculated as $s = m/E$, the ratio of modern fuels $(m)$ in total residential energy consumption $(E)$, and therefore is defined within the range $[{0,1} ]$. The main independent variable is per capita income $({x_{it}})$, with $\alpha$ the vector of parameters of interest.

The set of covariates, ${W_{it}}$, includes international petroleum prices, the share of power produced from hydro, net exports of fossil fuels, country-specific dummies and/or country-specific trends (for the MG and CCE estimators). This specification does not control for end-user energy prices (electricity and gas) for the entire sample. Since our main interest is estimating $\alpha$, we expect that the set of the other covariates captures differences in energy prices; for example, oil prices may be relevant in countries with a low natural capital endowment, while hydro participation and net exports of fossil fuels may help to account for differences in other cases. Besides, we expect that the country-specific trends will account for the absence of energy prices, among other time-variant unobservables (such as temperature and urbanization trends). Nonetheless, in a robustness check, we replicate the main results including electricity prices instead of oil prices.

We apply the following estimators: (i) the fixed effect (FE) estimator, which is the standard baseline and it is expected to perform well in the dynamic setting under samples with large T and N,Footnote ⁹ which is the case herein, since we restrict the sample to those countries with the longest time series. This estimator allows cross-country heterogeneity that is fixed over time, but assumes coefficient homogeneity and cross-sectional independence; (ii) the Pesaran and Smith (Reference Pesaran and Smith1995) mean group estimator (MG), which takes into account time-variant unobservables for each country and coefficient heterogeneity, while still assuming cross-sectional independence; and (iii) the Pesaran (Reference Pesaran2006) Common Correlated Effects (CCE) estimator, which further allows cross-sectional dependence (CSD), requiring only covariates with cross-sectional variation. The CCE model, therefore, does not include international oil prices.Footnote ¹⁰ Although a less restricted specification and estimator would be preferable, it is also interesting to evaluate the differences between these estimators. Also, the time variant unobservables in the MG and CCE estimators, would help to capture, among others, the effect of the technological and structural change.

The panel analysis requires examination of the properties of the series. Table 1 summarizes two characteristics of the series: cross-sectional dependence and cointegration. According to the Frees and Pesaran tests, the residuals of equation (1) present nonconstant variance and cross-sectional dependence, supporting the use of the CCE estimator. Regarding cointegration, two types of cointegration tests are applied: those proposed by Pedroni (Reference Pedroni1999) and those proposed by Westerlund (Reference Westerlund2007). Both types of tests are estimated with no intercept and no deterministic trends, and the optimal lags are determined using the Akaike information criterion.

Table 1.

CSD and cointegration tests for domestic fuels

Notes: E&G, electricity and gas; CSD, cross-sectional dependence; TFC, total final consumption of the residential sector; a, semiparametric test; adf, Augmented Dickey–Fuller test; G, group mean test; P, panel test; t, parametric test.

All CSD tests were performed after FE regressions. The null hypothesis is cross-sectional independence. The robust p-value is for a one-sided test based on a bootstrapped distribution (500 bootstrap replications). The Westerlund tests are applied with no intercept, no deterministic trends, and the optimal lags are determined using the Akaike information criterion.

Table 1 shows that both groups of tests return similar results for electricity, gas, and modern fuels, for LAC and all countries, suggesting a stable long-run relationship between income and modern residential energy sources. However, the results are less conclusive for the case of total final consumption (TFC) by the residential sector, specifically in the case of the Westerlund tests. Recall that in the tests proposed by Westerlund (Reference Westerlund2007), the null hypothesis (Ho) of no cointegration is evaluated for nonstationary cases with heterogeneous dynamics.Footnote ¹¹ The group-mean test (G) rejects the Ho if at least one country there is cointegration, while the panel tests (P) reject the Ho if there is cointegration for the panel as a whole. The Westerlund tests are applied to the main variables under analysis; moderns fuels and TFC as dependents, and income per capita as independent. The panel tests and the group mean parametric test tend to not accept Ho for electricity, gas, and modern fuels, suggesting a stable long-run relationship between income and modern residential energy sources. The null cannot be rejected in the case of group mean semi parametric test (Ga), and for any test, in the case of the TFC of the residential sector.

With respect to the proposed specification, the energy consumption, income, and price variables are expressed in logarithmic, so the estimates from equation (1) can be interpreted as short-run elasticities. However, a relevant distinction is the long-run effect of income changes on energy consumption and its composition. The long-run relationship is captured by including the lagged dependent variable as a regressor in equation (2) and then calculating the long-run elasticity as the corresponding derivative, which in a linear setting is ${\varepsilon _{E,x}} = \alpha /({1 - \theta } )$, where $\theta$ is the coefficient of the lagged variable.

These regressions return average elasticities which are informative by type of fuel but not for the suspected changing association between income and energy consumption along the income distribution. To address this issue, the regressions are also performed by income group, which allows for the evaluation of the change in income elasticities across groups at different development stages at the cost of reducing the sample per estimation and not accounting for changes in the sample composition (i.e., countries that may move from one income classification to another).

To further examine the change in consumption of modern fuels, we replace the linear income regressor with an income polynomial, with its degree being chosen based on cross-validation procedures.Footnote ¹² In a linear setting, $\alpha$ is expected to be positive, while a polynomial can capture potential nonlinearities, approximating the shape of the responsiveness to income changes. From a conceptual viewpoint, in a nonlinear setting, the sign and significance of $\alpha$ are less clear but may have relevant implications for capturing how energy consumption patterns change along the income distribution. Notice that this framework still assumes a functional form and constant parameters for each country.

The next step is to completely relax the functional form and to allow for complete heterogeneity of the income elasticity along the world income distribution. This problem is quite complicated in semiparametric or nonparametric settings, where the returned coefficients are difficult to recover and interpret. An efficient approach for discovering patterns, when the correct functional form is unknown, is the application of machine-learning methods. In particular, a flexible and interpretable method, described by Hainmueller and Hazlett (Reference Hainmueller and Hazlett2014), is the Kernel Regularized Least Squares (KRLS), which allows estimation of the full distribution of $\alpha$ without relying on parametric assumptions such as linearity or additivity. The KRLS estimator states and solves the following problem:Footnote ¹³

(3)\begin{equation}{\omega ^\ast } = argmin{({y - K\omega } )^T}({y - K\omega } )+ \lambda {\omega ^T}K\omega ,\,\; \omega \epsilon {\mathrm{\mathbb{R}}^D},\end{equation}

where ${\omega ^\ast }$ = test point coefficients or weights, containing $\alpha$ and $\beta$; y = outcome variable; and K = matrix of kernel functions $({{z_j},{z_i}} )$ where z represents the vector of covariates, previously defined as x and W.

In equation (3), the loss function takes the least-squares form using the Gaussian kernel function K. The kernel function, $k(. )$, measures the similarity between observations for each ${z_i}$. A greater similarity translates to a greater influence of ${z_i}$ over the outcome. Therefore, $K\omega$ represents a space of functions that aim to approximate the outcome point to point, such that similar observations would tend to have similar outcomes. λ weights the complexity of the function, such that greater values represent larger penalties for complexity.Footnote ¹⁴

This problem is solved computationally, and the search for the best fit of the KRLS does not impose any functional parametric form, such that it does not assume constant marginal effects. That is, the estimated vector $\alpha$ contains the pointwise income elasticities by country at each point of the income distribution. This is important in our context as the returned distribution of coefficients will display long-run information without requiring transformation. However, and in contrast with the MG and CCE estimators, such pointwise estimates can be interpreted in local terms as reflecting the structural conditions and available technology (and technology adoption) in each point of the income distribution.Footnote ¹⁵

In line with the above, an important aspect of the empirical analysis is determining whether the estimates have a causal interpretation or represent conditional correlations. It is expected that the inclusion of the covariates and fixed effects helps to clean the relationship between energy and income of omitted factors. However, potential econometric problems are not being addressed, such as income endogeneity or measurement error. Therefore, since there is a conceptual and empirical basis to argue for bi-directionality between income and consumption of modern energy sources, we attach no causal interpretation to the estimates.