Is faster economic growth compatible with reductions in carbon emissions? The role of diminished population growth

The first step of our analysis is to estimate the elasticity of carbon emissions with respect to income per capita and population. To do so, we estimate the STIRPAT equation:

$$\begin{eqnarray}&&{I}_{i,t}={P}_{i,t}^{a}{A}_{i,t}^{b}{T}_{i,t}^{\tilde{c}}{e}_{i,t},\end{eqnarray} \tag{ 1 }$$

where ${I}_{i,t}$ is environmental impact in country i at time t, P is population, A is affluence (income per capita), T is technology, and e is the residual error term. A substantial literature analyzes STIRPAT regressions to examine the determinants of many measures of the environmental impact of human activity [7]. We focus on total carbon emissions.

The STIRPAT equation is derived from the IPAT accounting identity [17, 18], and most applications of STIRPAT are focused on decomposing environmental impacts between explanatory variables. This decomposition can be aimed at explaining past emissions or predicting future emissions. Our goal is different. We want to understand the effect of changes in fertility on both environmental and economic outcomes, accounting for the effect of fertility on population levels, population age structure, and income per capita. Thus, we use the partial elasticities from the regression equation to parameterize the economic-demographic model (see section 3).

Given our goal, the difference between the coefficients on population and affluence is of primary importance. Thus, in all regressions, we test the null hypothesis that these coefficients are equal (i.e., a = b). While the literature provides a wide range of estimates for both coefficients—depending on the dependent variable under consideration and the choice of regression specification—we are the first to test for a difference in coefficients between population and affluence [7]. If the coefficient on population is significantly larger than the coefficient on income per capita, then decreases in population could potentially lower carbon emissions even while substantially increasing income per capita, overcoming the trade-off central to most environmental policies.

To estimate equation (1), it is necessary to assume a specification for technology (T). We make the following assumption:

$$\begin{eqnarray}&&{{\rm{l}}{\rm{n}}{T}}_{i,t}={\tilde{f}}_{i}+{\tilde{g}}_{t}+{{h}{\rm{ln}}{S}}_{i,t}+{x}_{i,t}^{\prime }\tilde{\delta },\end{eqnarray} \tag{ 2 }$$

where $\tilde{{f}_{i}}$ is a fixed effect capturing time-invariant differences between countries, ${\tilde{g}}_{t}$ is a fixed effect capturing differences in global technology over time that affect all countries, ${S}_{i,t}$ is a measure of the age structure of the population, and ${x}_{i,t}$ is a set of control variables including urbanization and trade. All three of the time-varying explanatory variables have been found to affect carbon emissions in the existing literature [2, 15, 19]. The inclusion of age structure, ${S}_{i,t}$, is important for our results since changes in fertility patterns mechanically alter the age structure of the population, implying that we need to capture this effect in the economic-demographic model. In the appendix (available at stacks.iop.org/ERL/12/014003), we also include income per capita squared to capture the environmental Kuznets curve (EKC), but the term is insignificant in our main specification.

Recent advances in the STIRPAT literature have demonstrated the importance of correcting for potentially non-stationary variables [15, 20]. Thus, our main specification estimates a log-linearized version of (1) in first differences. Thus, our estimating equation becomes:

$$\begin{eqnarray}&&{{\rm{\text{ln}}}{I}}_{{i},{t}}-{{\rm{\text{ln}}}{I}}_{{i},{t}-1}=a({{\rm{\text{ln}}}{P}}_{{i},{t}}-{{\rm{\text{ln}}}{P}}_{{i},{t}-1})\\ &&\quad +b({{\rm{\text{ln}}}{A}}_{{i},{t}}-{{\rm{\text{ln}}}{A}}_{{i},{t}-1})\\ &&\quad +c({{\rm{\text{ln}}}{S}}_{{i},{t}}-{{\rm{\text{ln}}}{S}}_{{i},{t}-1})+{({x}_{{i},{t}}-{x}_{{i},{t}-1})}^{\prime }\delta \\ &&\quad +({g}_{{t}}-{g}_{{t}-1})+({{\rm{\text{ln}}}{e}}_{{i},{t}}-{{\rm{\text{ln}}}{e}}_{{i},{t}-1}),\end{eqnarray} \tag{ 3 }$$

where $c=\tilde{c}h$, $\delta =\tilde{\delta }\tilde{c}$, and ${g}_{t}=\tilde{c}\tilde{{g}_{t}}\ \forall t$. It is important to note that the coefficients on population and affluence are still the same as in equation (1).

Our equation is estimated on an unbalanced yearly panel of countries. We use standard sources for all data. Our dependent variable is carbon emissions from production, which are from Oak Ridge National Laboratory [21]. Our measures of population and income per capita come from the Penn World Tables (PWT) version 8.0 [22]. We employ the newly created output-side measure of income per capita, which is the best match for our emissions measure. Age structure, urbanization and trade data are all from the World Bank's World Development Indicators (WDI) database. To capture age structure, we use the fraction of population of between the ages of 15–64, which we denote as 'working age'. In the appendix, we show that all our results are robust to alternate measures of income, alternate samples, and alternate estimation strategies. Summary statistics are provided in appendix table A1.

Table 1 presents the results of the regression using equation (3). In column 1, we present a simple regression with only population and income per capita as explanatory variables. This specification highlights the potential for lower population to decrease emissions and increase income per capita simultaneously. Specifically, the coefficient on income per capita is 0.203, while the coefficient on population size is 1.364, a 6.7-fold difference. The difference is statistically significant at the 0.1% level. The difference in coefficients implies that a decrease in population could potentially decrease emissions and raise income per capita as long as the elasticity of income per capita with respect to population is less than 6.7. Thus, decreases in population growth could mitigate environmental concerns while permitting further economic growth. To ensure that this result is not driven by outliers, figure 1 presents the residual scatter plots from the regression in column 1.

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Column 2 adds the share of the working age population, the other key variable to be affected by a change in fertility. While statistically significant, the inclusion of the working age population has little effect on the population and income per capita coefficients. To ensure that our results are not driven by omitted variables, the final two columns add controls for urbanization and trade. Again, the key results are unchanged. In all cases, the equality of coefficients can be rejected at the 0.1% level. Importantly, the regression coefficients are not substantially altered by the inclusion of urbanization or trade. If urbanization was an important channel through which population led to increases in emissions, the coefficient on population would likely have decreased substantially once urbanization was included as a control variable in the regression. Our preferred specification is column 4, which includes controls for the major confounding variables identified in the literature. Thus, we use this specification to parameterize the economic-demographic model in the second phase of our analysis.

In the appendix, we show that our key qualitative result—the large difference in coefficients between population and income per capita—holds in a number of other settings. To ensure that the results are not driven by attenuation bias, which can be exacerbated by differencing, we demonstrate that the results hold when estimating the equation in levels (table A2). In this case, the squared term on income per capita becomes significant. While our goal is not to provide a detailed examination of the EKC relationship, the fact that first differencing removes the significance of the squared term is consistent with existing literature [23]. We also show that the results are unaffected by moving to a balanced sample of countries, indicating that the results are not driven by the changing sample (table A3). We also re-estimate the STIRPAT equation using total income, instead of income per capita (table A4). The population coefficient is statistically significant in this specification, further supporting the finding that population matters beyond simply increasing total output. Finally, we show that the qualitative results are unchanged if we use several other measures of income per capita. We use the consumption-side (table A5) and national accounts (table A6) measures from the PWT, indicating that our results are not driven by the use of the output-side measure. We also use the exchange-rate based measure from the WDI (table A7), demonstrating that our results are not a byproduct of the adjustments for price differences across countries.

The regression coefficients presented in table 1 capture the effect of the explanatory variables on carbon emissions through two key channels, the energy intensity of output and the carbon intensity of energy, in addition to their direct effects. Unfortunately, regressions of this type cannot tell us more about the specific mechanism through which population and output affect carbon emissions. Since the employed economic-demographic model does not explicitly capture the energy intensity of output or the carbon intensity of energy, we rely on the simplified reduced-form relationship provided by the STIRPAT regression to parameterize the effects of population, age structure, and income per capita on carbon emissions. Understanding the exact causal mechanisms underlying these regression results is an interesting and important way forward for future work in this area.

While we are the first to formally test for the difference in coefficients between population and income per capita, these results are consistent with the existing literature. Jorgensen and Clark estimate an equation similar to ours, and the results display the same qualitative pattern [19]. Specifically, they find a population elasticity of 1.43 and an income per capita elasticity of 0.65 in their first-differenced specification with similar results in alternate specifications. Our major differences in specification, in addition to formally testing for different coefficients, include the use of new data, differing time scales, the inclusion of age structure, and the use of time fixed-effects in all specifications. They also find that the elasticities are relatively stable across time and space [19, 24]. Knight et al also find similar results when focusing on alternate population measures such as employed persons and hours worked [25]. For example, when also controlling for hours worked, they find a population elasticity of 2.25 and an income per capita elasticity of 0.59. Earlier work, which did not use panel data to mitigate omitted variable bias, finds similar coefficients for population and income per capita [5, 6]. More exhaustive reviews of elasticities found in the existing literature, as well as discussions of different estimation techniques and specifications, can be found in existing work [2, 7, 15].

More recently, a growing literature has included intensity variables, such as the energy intensity of output, in STIRPAT regressions and found more similar coefficients between population and income per capita [7, 20, 26]. This addition is an important step forward in accounting applications of STIRPAT, but is not appropriate for our purpose. Our goal is to determine whether decreases in fertility can simultaneously achieve economic and environmental policy priorities. As noted above, the economic-demographic model does not have an explicit energy sector, and therefore, the appropriate regression coefficients must include the effect of population and income on carbon emissions via the energy intensity of output and the carbon intensity of energy. Earlier results including intensity variables suggest that the difference in elasticities between population and income per capita could be explained by a greater effect of population on the energy intensity of output, which is an interesting area for further study. As discussed in section 3.2, the careful modeling of fertility and omission of an explicit energy sector in the economic-demographic model represent a trade-off when compared to modeling strategies based on PET [2, 3, 16]. Section 4 discusses several ways that the current analysis could be extended in future work, including more explicit modeling of the energy sector.

The second step of our analysis quantifies the effect of lower fertility on economic and environmental outcomes. STIRPAT regressions, while useful for decomposition exercises, are insufficient for determining the overall environmental impact of an exogenous change in an explanatory variable [3, 8]. The regression cannot tell us about the relationship between the explanatory variables. To fully account for these interdependencies, we use the economic-demographic model developed by Ashraf, Weil, and Wilde (AWW) [9]. The model was constructed explicitly to evaluate the effect of changes in fertility on income per capita, making it well-suited for our purposes. We examine the effect of an exogenous reduction in fertility on both economic and environmental outcomes in Nigeria. As in the original analysis, our exogenous change in fertility is a movement from the medium to the low variant of the UN fertility projections. We use the most recent projections [27].

The AWW model examines the effect of fertility on economic growth through several channels, which can be divided into three main categories. We call the first category composition effects. Changes in fertility alter the age structure of the population, which affects economic output through the number of people of working age (the 'dependency effect'), savings behavior (the 'life-cycle saving effect'), and labor supply differences within the working age population (the 'life-cycle labor supply effect'). We deem the second category behavioral effects, which encompasses changes in economic behavior for an individual as a direct result of having children. When fertility is reduced, parents have more time to work (the 'childcare effect') and can invest more resources in the education of each child (the 'child-quality effect'). The third category is factor accumulation. High fertility reduces the amount of physical capital per person (the 'Solow effect') and natural capital per person (the 'Malthus effect'). Moreover, the increase in labor force participation caused by lower fertility leads to greater human capital via work experience (the 'experience effect').

We use the AWW model to measure the effect of the change in fertility on the total population level, the age structure of the population, and income per capita. We then combine the model output with our regression results from column 4 in table 1 to estimate the impact on carbon emissions. Since we do not know the future values for the time fixed effects, we estimate the ratio of carbon emissions between the two scenarios.

Our work is closely related to analyses that estimate the effect of exogenous changes in population and urbanization on carbon emissions using the PET model [2, 3, 16]. The key difference between the analyses is that the present paper is expressly interested in the effect of fertility on both economic and environmental outcomes. Thus, we use an economic-demographic model specifically designed to estimate the effects of fertility on economic growth, accounting for all of the channels discussed above. The earlier works focus on composition effects and do not report economic outcomes.

This approach involves trade-offs. The PET model captures rich details of the population composition and energy sector, but only examines some of the channels through which fertility affects economic outcomes. Another strength of the AWW model lies in the careful selection of well identified parameters taken from the existing microeconomic literature. Thus, the parameters are strongly grounded in the historical experience of Nigeria. The strict requirements for parameterizing the model, however, imply that it can only be applied in a single country, unlike the PET model. Also, the demographic model does not explicitly model the energy sector. Instead, we use the STIRPAT regressions to capture the reduced-form effects of population, age structure, and income per capita on carbon emissions.

The results of our analysis are presented in figure 2. In all cases, results are presented as the ratio of the outcome under the low fertility scenario compared to the outcome under the medium fertility scenario. Panel A presents the outcomes of the major variables in the analysis. Emissions are sharply lower under the low fertility scenario, while income per capita increases. This is the key qualitative message of our analysis. Specifically, relative emissions are 10% lower by 2055 and 35% by 2100. Income per capita, meanwhile, is 10% higher in 2055 and 15% in 2100. Thus, the income gains occur sooner, while emission reductions are back-loaded.

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The share of the population that is of working age increases slightly as a result of the change in fertility patterns. At its highest point, the share is 4.5% higher than it would have been under the medium fertility scenario. Relative population follows a path very similar to that of total emissions, demonstrating how strongly changes in population levels drive emissions.

Panel B translates these effects into their impact on emissions. As suggested by panel A, emission reductions due to lower population drive the results. Increases in the working age fraction of the population and income per capita have only small positive effects on relative emission levels. Between the two, the change in the working age share has a bigger effect on emissions than does the increase in income per capita, though the effects become more similar over time.

The appendix includes results when using alternate specifications and measures of income per capita (figures A3–A5). In all cases, the qualitative effects are similar. The most significant difference occurs when using the balanced regression sample (figure A2) or estimating the regression in levels (figure A1). In these cases, relative emissions increase in the low fertility scenario briefly, due to the increase in the share of the working age population. By 2100 C.E., there is a substantial decline in relative emissions, leaving our key results unchanged.