Abstract
Econometric studies based on the STIRPAT framework suggest that carbon emissions respond more strongly to population size than to per capita income, yet this relationship has not been explicitly incorporated into the integrated assessment models used for climate policy analysis. We extend one of the most widely known framework, namely the DICE model, to allow population to directly determine emissions beyond its indirect effect through economic activity, calibrating the relevant elasticities on existing empirical estimates. We find that unabated emissions may exceed twice the standard DICE baseline by 2100, requiring substantially earlier and more intensive abatement effort. Full decarbonization appears necessary around mid-century to meet the 2(^{circ}) C temperature target, and socially optimal by 2070 when mitigation costs and benefits are weighed against each other. These results are primarily driven by a population elasticity above unity which amplifies emissions, combined with a sub-unitary response to per capita income which partly offsets this effect. Our analysis suggests that explicitly accounting for non-proportional effects of population and income on emissions can significantly affect conclusions about the urgency and cost of climate action.
Introduction
The dramatic consequences of climate change on our planet and worldwide societies have become more evident over the last decades, during which we have witnessed an increase in the frequency and intensity of natural disasters and extreme weather events, such as heat waves and droughts, hurricanes and tornadoes1,2. It is now widely accepted that anthropogenic activities are largely responsible for the rise in temperature at the global level as greenhouse gas emissions are predominantly driven by industrial production, land use, transportation and heating needs3,4, and indeed a large emphasis in the discussion of mitigation policies has been placed on the decarbonization of economic activities5,6. However, another essential and often underestimated driver of carbon emissions is represented by the size of human population, which determines the scale of consumption, waste and the demand for resources extraction7,8. Yet, the role of population dynamics in the climate mitigation discourse has been to a large extent neglected thus far9. Since population growth accounts for a large proportion of emissions growth over the last fifty years7,10, understanding whether and how demographic considerations may change the optimal mitigation strategy, along with the quantification of its cost, is essential to properly design effective policies to fight climate change. The goal of this paper is thus to reconsider the optimality and the cost of mitigation by explicitly accounting for the impact of population on carbon emissions in a traditional global climate-economy integrated assessment model.
In order to explain the determinants of global carbon emissions, economists and climate scientists as well have traditionally relied upon the IPAT identity which states that environmental impacts I depend on the multiplicative product of three different forces, namely population P, affluence A and technology T, such that (I=PAT)11,12. This formulation has been widely used as an accounting equation in which known values of impacts, population and affluence (typically quantified as carbon emissions, demographic size and per capita production, respectively) are used to solve for technology (quantifying thus the impact per unit of economic activity).
Despite the importance of the IPAT and its following refinements (such as the Kaya and the ImPACT identities proposed by Kaya13and Waggoner and Ausubel14,, respectively) in conceptualizing the driving forces of environmental degradation, they are not operationally effective as they cannot allow for empirical investigation and hypothesis testing by being mere mathematical identities15,16. For this reason economists have more and more frequently relied upon the STIRPAT (i.e., stochastic impacts by regression on population, affluence and technology) formulation, a stochastic extension of the basic IPAT, which does not assume a priori a proportional relation between the factors and does not represent an identity, allowing thus for an empirical quantification of how the different factors contribute to emissions17,18. Specifically, the STIRPAT model is based on the following equation (I=alpha P^{beta _P} A^{beta _A} T^{beta _T} epsilon) where (epsilon) is the error term, (alpha) a constant while (beta _P), (beta _A), (beta _T) are the so-called “ecological elasticities” (i.e., the elasticity of carbon emissions with respect to population, affluence and technology, respectively, measuring the percentage response of carbon emissions to a one-percent change in the relevant variable) which can be easily estimated by defining variables in logarithmic terms. In its basic specification, the technology variable is generally included in the error term rather than being estimated separately in order to ensure consistency with the IPAT approach.Footnote 1 The introduction of the STIRPAT framework has given rise to an extensive econometric literature which, despite the variability in the estimates according to the statistical methods employed and the controls included in the analysis, clearly shows that the population ecological elasticity is substantially (even seven times) larger than the affluence ecological elasticity24,25. Therefore, accounting for the specific role of human population in determining emissions is essential to reliably assess the effectiveness of alternative climate mitigation policies.
Climate policy is traditionally analyzed in integrated assessment models (IAMs) which consist of computable general equilibrium frameworks linking economic and climatic sectors through bilateral feedback effects via carbon emissions and negative production externalities26,27. Several types and extensions of the basic IAMs have been developed over the years, but only a few specifically account for the role of population change28,29. These works mainly focus on how alternative demographic growth patterns by affecting economic production capability may alter the conclusions regarding the validity of different policy measures9,30,31,32. This is a crucial step forward in assessing the potential success of mitigation as it is now widely accepted that the optimality of climate change policy critically depends on population change at least as much as it depends on the discount factor33. However, as stressed by the STIRPAT literature, the effects of human population extend well beyond those related to the magnifying role of demographic growth on production as the population size represents an autonomous determinant of emissions influencing non-proportionally the scale of economic activities, through its effects on waste, littering and energy use25,34. To the best of our knowledge, all extant IAMs are built on the IPAT identity and thus unable to analyze how results may change by considering the population size as a separate driver of carbon emissions and thus that demography plays a twofold effect on environmental degradation by determining the magnitude of both production and emissions.Footnote 2 trends in which population affects affluence by determining the scale of consumption or production. As they do not specifically account for the direct effect of population on carbon emissions their quantification of the anthropogenetic impacts on the environment is substantially lower than ours. Indeed, by calibrating emissions according to the findings of the STIRPAT literature, our approach predicts that (without any form of abatement) emissions at the end of the century will be the double of what suggested by traditional IAMs, and this difference is reflected in the cost and urgency of mitigation.
We thus integrate the simplest IAM (the DICE; see Nordhaus28) with the STIRPAT framework allowing for the population size and per capita production to act as separate drivers of emissions and to affect them in a non-proportional way. According to empirical evidence, the population ecological elasticity is larger than one while the affluence ecological elasticity is smaller than one (Rosa and Dietz, 201235). With respect to what traditionally assumed in IAMs in which such ecological elasticities are both equal to one, in our setup the smaller affluence elasticity tends to reduce the impact of economic activity on the environment while the larger population elasticity tends to amplify it, such that it is not possible to state a priori which of these two effects may dominate. This suggests that emissions dynamics are shaped by the interaction between population and affluence, rather than by either factor in isolation, as also highlighted in recent empirical applications of the STIRPAT framework36,37. However, since the available estimates of the population ecological elasticity are much larger than those of the affluence ecological elasticity24, the population size effect largely dominates the affluence effect and thus emissions turn out to be substantially larger than those traditionally considered in IAMs. This leads to a faster accumulation of carbon concentration in the atmosphere which in turn generates a larger temperature increase and thus a higher cost of mitigation than in standard IAMs. Therefore, in order to effectively reduce the economic impacts of climate change more abatement efforts and earlier interventions are effectively needed than what currently believed. In particular, we show that unabated emissions will be more than two times higher than in DICE at the end of the century, and this requires to radically increase abatement in all scenarios, generating a substantial increase in the cost of carbon. The optimal policy prescribes instead a 100% abatement rate by 2070, while full abatement is needed around by mid-century if we wish to maintain the temperature increase with respect to the pre-industrial era below the 2(^{circ}) C target.
Our conclusions are thus substantially different from those traditionally derived in IAMs, which frequently prescribe a cautious optimal policy entailing relatively little early intervention and a gradual increase in the intensity of intervention over time28,38.
For example, DICE suggests an optimal abatement of greenhouse emissions of only 19.6% in 2030, increasing to 29.4% in 2050 to reach 65.9% in 210026. This is at odds with the conclusions from the climate science literature which advocates for more stringent mitigation measures in the near future in order to reduce the concentrations of greenhouse gas emissions by the end of the century, in an attempt to reduce the risk of tipping points and regime shifts39,40,41. Several works show that modifying crucial aspects of traditional IAMs, such as the size of the discount factor and the specification of the damage function, their results may become more consistent with the suggestions of the climate science literature42,43. Our analysis suggests that it is possible to reconcile economics with climate science also by simply accounting for the role played by human population in driving emissions. Indeed, the population-induced emissions channel substantially increases the optimal abatement, which needs to be 46.7% in 2030, increasing to 72.4% in 2050 to reach 100% in 2070. Our results clearly show that, by imposing proportional responses of emissions to population and income, extant literature strongly underestimates the detrimental environmental consequences of anthropogenic activities, and thus the cost and the urgency of mitigation.
The paper proceeds as follows. The “Methods” section briefly introduces our setup which is basically a DICE model extended to allow for a STIRPAT formulation of emissions. The “Results” section discusses our main findings to stress the large underestimation of the cost and the urgency of mitigation policy in traditional IAMs.
In “Sensitivity and robustness” section shows that our conclusions hold true under a broad range of alternative parametrizations of the ecological elastiticities and of the population dynamics.
Section “Discussions and conclusions” present concluding remarks and suggests directions for future research.
Methods
We extend the DICE model to account for the conclusions of the STIRPAT literature. Specifically, industrial emissions, (EI_{t}), depend both on per capita production, (frac{Y_t}{N_t}), where (Y_t) denotes aggregate production and (N_t) human population, and the population size as follows:
where (sigma _t) represents technologyFootnote 3, while (phi ge 0) and (psi ge 0) measure the ecological elasticities with respect to population and affluence, respectively. If the ecological elasticities are both equal to one ((phi =psi =1)), emissions are defined as in the IPAT framework and the equation above reduces to the standard emissions formulation employed in IAMs, (i.e., (EI_{t} = sigma _{t}Y_t)).
Apart from this novelty, all other elements of the DICE model are entirely preserved, and the complete specification of the economic and climatic sectors is reported in appendix The DICE-STIRPAT Model. We rely on the same set of parameters and the same scenarios employed in the standard DICE model, calibrating the ecological elasticities as follows: (phi =1.85) and (psi =0.87)25.Footnote 4Footnote 5
We consider the following business-as-usual (BAU), optimal (OPT) and temperature (TEMP2C) scenarios.
- a.
Business as usual (BAU): this scenario assumes that current policies as of 2015 are extended indefinitely. Specifically, abatement is determined in order to ensure that the carbon price follows an exogenously given path increasing at an yearly rate of 2%. The carbon price in the BAU is equal to the Hotelling rents on carbon fuels.
- b.
Optimal benefit-cost comparison (OPT): this scenario determines the share of emissions to abate in order to maximize social welfare, accounting for the impacts of climate change on output and therefore consumption. The carbon price in OPT is determined as the marginal welfare effect of an additional ton of carbon emissions in terms of consumption, which coincides with the social cost of carbon.
- c.
Temperature-target (TEMP2C): this scenario imposes a constraint on the global temperature level, requiring temperature not to exceed 2(^{circ}) C with respect to the average temperature in the pre-industrial era. This scenario is crucial to quantify the efforts and the costs needed to effectively reach a target consistent with those imposed by international climate agreements.
Results
We now present the results of our scenario analysis and we focus on some key variables: per capita GDP net of damages and abatement costs, industrial emissions, emission abatement rate, temperature level, and carbon price (which quantifies in monetary terms the relative price of an additional ton of carbon emissions).
Table 1 compares the variables evolution until 2100 in the standard DICE ((phi =psi =1)) and in our STIRPAT-extended DICE ((phi =1.85) and (psi =0.87)) models, respectively. As a matter of expositional simplicity in what follows we shall refer to our extended model as the DICE-STIRPAT model. We can observe that in DICE and DICE-STIRPAT the variables follow a similar pattern across scenarios, and the main difference relies in the assessment of emissions which generates important discrepancies in the intensity and the timing of policy interventions. By underestimating emissions dynamics DICE predicts that abatement is not very sizeable and till mid-century it is less than 50% in the BAU and OPT scenarios, reaching almost 100% only in the TEMP2C scenario and at the end of the century (in the BAU it is less than 1% while in the OPT scenario about 65% in 2100). Since in DICE-STIRPAT gross emissions (i.e., unabated emissions) are higher (+20% in 2030 reaching even +101% in 2100) the abatement effort needs to be substantially larger earlier in time: in the BAU it does not change with respect to DICE since abatement is exogenously given and does not respond to unabated emissions, while in the other scenarios abatement is much more sizeable since 2030 (about 47% and 60% in the OPT and TEMP2C scenario, respectively) to then reach 100% (in 2070 in the OPT and in 2055 in the TEMP2C scenarios, respectively).
These results are striking: full abatement by the end of the century is needed not only to avoid the temperature level to exceed the 2(^{circ}) C target (and in this case full abatement is required just after mid-century) but also to allow an optimal balancing of the benefits and costs of climate change (which requires reaching full abatement a couple of decades later). The mechanism leading to such more sizeable abatement efforts is straightforward. The asymmetric emission elasticities combined with demographic growth lead
unabated emissions in DICE-STIRPAT to be much higher than in DICE, resulting thus in a higher carbon concentration and thus temperature level in the absence of mitigation. To avoid incurring in a stronger environmental damage yielding an important reduction in economic production capabilities, earlier and stricter abatement is required.
In order to better understand the differences in the abatement motives between DICE and DICE-STIRPAT we report in Table 2 the carbon concentration and the damages generated by climate change, measured in terms of aggregate GDP loss. As in the BAU the abatement rate is the same in both the models this helps to quantify the differential in the carbon concentration and thus in the damage between DICE and DICE-STIRPAT. The interaction of a population elasticity above unity and an affluence elasticity below unity combined with demographic growth leads emissions to grow faster in DICE-STIRPAT than in DICE resulting at the end of the century in a higher carbon concentration (+7.49%) and damages (+10.00%), which requires to increase abatement in the OPT scenario in order to achieve at the end of the century lower carbon concentrations (−71.51%) and damages (−67.14%) with respect to what happens in DICE.
The full evolution of three key variables, emissions (measured in gigatonnes of carbon, GtC), temperature (measured in degrees Celsius) and the carbon price (measured in dollars per ton of (CO_2), $/ton(CO_2)) is shown in Fig. 1 both for the DICE (dotted curves) and DICE-STIRPAT (solid curves) models, distinguishing among the BAU (black), OPT (green) and TEMP2C (blue) scenarios.
Evolution of key variables in DICE (dotted lines) and DICE-STIRPAT (solid lines).
The larger emissions in DICE-STIRPAT induce important abatement efforts which allow emissions to be substantially lower than in 2020 by the end of the century, not only in the TEMP2C but also in the OPT scenario (in DICE instead the decrease in emissions in the OPT scenario is more limited). The substantial abatement efforts allow to limit the temperature increase with respect to the pre-industrial era, which in DICE-STIRPAT reaches 2.3(^{circ}) C in the OPT scenario (substantially lower than in DICE, in which it reaches 3.1(^{circ}) C in the OPT scenario). The size of the abatement efforts in DICE-STIRPAT gives rise to a carbon price which is substantially higher than in DICE, especially in the OPT scenario. By the end of the century the carbon price in the OPT scenario reaches $350, the same value as in the DICE’s TEMP2C scenarios but much higher than in its OPT scenario where the carbon price is about $220. In DICE-STIRPAT’s OPT and TEMP2C scenarios the pattern of the carbon price is very similar, but it changes its peak which is much higher and achieved much earlier in the TEMP2C (about $450 in 2055) than in the OPT (about $410 in 2070) scenario.
Our results clearly show that, by imposing proportional responses of emissions to population and income,
extant literature strongly underestimates the detrimental environmental consequences of anthropogenic activities, and thus the cost and the urgency of mitigation. Accounting for the asymmetric elasticities requires since 2030 important abatement efforts both in the OPT and TEMP2C scenarios, in order to achieve full decarbonization either by 2070 (in the OPT scenario) or in 2055 (in the TEMP2C scenario).
Decomposition analysis
To better understand the mechanisms underlying these results, we now decompose the effects of the STIRPAT specification into their two key components. In the baseline comparison, both the population and affluence elasticities differ from the standard DICE benchmark ((varphi = psi = 1)), making it difficult to attribute the observed changes in emissions and optimal mitigation to a specific channel. To address this, we isolate the contribution of each elasticity by considering two counterfactual cases: one in which only the population elasticity exceeds unity while the affluence elasticity remains at its benchmark value, and another in which only the affluence elasticity differs from unity while the population elasticity is fixed at one. This decomposition allows us to disentangle the respective roles of population dynamics and per capita economic activity in driving emissions and shaping optimal climate policy. The results of this analysis are reported in the table below.
The decomposition in Table 3 helps to clarify the relative contribution of the two elasticities by isolating the population channel ((varphi> 1), (psi = 1)) and the affluence channel ((varphi = 1), (psi < 1)). It shows that the increase in the population elasticity above unity is the main driver of the higher emissions and the substantially stronger and earlier abatement observed in the full STIRPAT specification, whereas the reduction in the affluence elasticity below unity partly offsets this effect by dampening the emissions response to economic growth. Importantly, the combined outcome of the two channels is not strictly additive, as the emissions function is multiplicative and the interaction between population and per capita output introduces nonlinear effects. Overall, the comparison indicates that the population channel accounts for most of the deviation from the standard DICE benchmark, while the affluence channel moderates this effect without overturning it. Consistent with this, the outcomes of the full STIRPAT specification lie between the two channels but closer to the population channel, implying that the stronger mitigation requirements are primarily driven by the amplification effect associated with population dynamics.
A direct comparison between Tables 1 and 3 helps clarify how the full STIRPAT specification relates to the two isolated channels. In Table 1, the DICE–STIRPAT model ((varphi = 1.85), (psi = 0.87)) implies substantially higher abatement in the OPT scenario (e.g., 46.7% in 2030 and 72.4% in 2050) compared to standard DICE. When we turn to Table 3, these values lie much closer to those generated by the affluence channel in early periods (47.86% in 2030 and 74.39% in 2050), while the population channel alone implies considerably stronger and earlier intervention (68.8% already in 2030 and full abatement by 2050). This comparison indicates that the full STIRPAT outcome reflects a balance between the two forces: the population elasticity pushes toward much higher emissions and aggressive early abatement, whereas the lower affluence elasticity dampens this effect, bringing the optimal policy closer to (but still above) the standard DICE benchmark. At the same time, the population channel clearly sets the upper bound for mitigation intensity, confirming that it is the primary driver of the deviation from the baseline, while the affluence channel moderates its magnitude.
Sensitivity and robustness
The main assumptions employed in our analysis are related to the role of population in driving emissions and the evolution of human population. First, the affluence and population ecological elasticities are set equal 0.87 and 1.85 respectively, following recent empirical estimates25. Second, human population evolves as suggested by the UN in the mid variant of their population projections such that population growth will gradually decrease in order for the population size to stabilize at the end of the century to a level of 11.5 billions people44. In order to assess the robustness of our analysis, we now explore how relaxing these assumptions might modify our conclusions.
We start by modifying the ecological elasticities by borrowing from the literature on STIRPAT to consider a larger set of estimates. Based on the studies discussed in Liddle’s25 literature review, we compute the mean m and the standard deviation s of the empirical estimates of (psi) and (phi) from a number of econometric works, to then determine some lower and upper bound for these parameters by adding (subtracting) one standard deviation from the mean estimate (mpm s). Table 4 reports the determined upper, central and lower values for (psi) and (phi).
The results of our sensitivity analysis are reported in Fig. 2 where we show the evolution of the key variables when either the parameter (psi) (top panels) or (phi) (bottom panels) is set according to the above upper (dotted curve), mean (solid curve) or lower (dashed curve) value, while the other parameter remains as in our baseline analysis (either (phi =1.85) or (psi =0.87)). While we vary each elasticity independently for expositional clarity, it is important to stress that the results in the full model depend on their joint interaction. We can observe that independently of the value of the ecological elasticities, from a qualitative point of view the results are identical to those presented in our baseline analysis, and also the quantitative differences are moderate.
Evolution of key variables in STIRPAT-DICE under different parametrizations of (psi) (top) and (phi) (bottom), in which they take the upper (dotted), central (solid) and lower (dashed) values reported in Table 4.
From the top panels we can see that when (psi) takes its mean value our previous conclusions still apply to a large extent, while when the parameter increases (decreases) by taking its upper (lower) value emissions turn out be higher (lower) leading to a higher (lower) temperature increase which demands larger (smaller) abatement efforts, resulting thus in a larger (lower) carbon price. This type of conclusion applies to all the scenarios, and the only relevant differences which may be worthy to mention are the following. (i) Emissions decrease with respect to their initial level whenever (psi) takes its upper value, generating a slower increase in the temperature level, which exceeds 3(^{circ}) C only at the end of the century. (ii) Full decarbonization may not be achieved in the OPT scenario before 2110 whenever (psi) takes its mean value, while if it takes its upper level full decarbonization is required by 2055. (iii) The ceiling on the temperature level becomes no longer binding when (psi) takes its mean or upper value, and in such a case the temperature increase stabilizes at 1.9 (^{circ}) C, lower than the temperature target.
Similar conclusions arise from the analysis of the bottom panels in which the parameter that changes is (phi). When the parameter takes its mean value our previous conclusions still apply, while when the parameter increases (decreases) by taking its upper (lower) value emissions are higher (lower) leading to a higher (lower) temperature increase demanding larger (smaller) abatement efforts, resulting thus in a larger (lower) carbon price. In this case however whenever (phi) takes its lower value full decarbonization is not achieved by the end of the century in the OPT scenario and the temperature target becomes no longer binding.
We now modify population dynamics by allowing human population to evolve alternatively according the low, medium and high variant of the population projections, in which at the end of the century the population size stabilizes at 9.0, 11.5 and 12.5 billions people respectively. Figure 3 compares the evolution of the key variables in the DICE-STIRPAT frameworks under the low (dashed), medium (dotted) and high (solid) population variants. It is straightforward to observe that independently of the specific assumption regarding the evolution of human population the results are qualitatively identical to those earlier discussed, even if in quantitative terms the differences may be substantial.
Evolution of key variables in DICE-STIRPAT under the low (dashed), medium (dotted) and high (solid) population variants.
Intuitively, a larger population size generates a higher emissions level which results in a higher temperature increase, demanding thus for more stringent abatement efforts. According to the population variant the carbon price peaks at values varying between $430 and $450 between 2050 and 2060 in the TEMP2C scenario, and at values varying from $390 to $420 between 2065 and 2085 in the OPT scenario. The timing of full decarbonization in TEMP2C is similar under all population variants (between 2050 and 2060) while it slightly changes across population variants in OPT (it occurs around 2065 under the high population variant, while around 2085 under the low population variant).
Monte Carlo analysis
We now perform some further robustness checks by running a Monte Carlo analysis to understand the extent to which our conclusions might differ by relying on alternative parametrizations of the ecological elasiticities. We keep relying on Liddle25 as a reference point for our analysis and we employ his estimates to determine the mean and the standard deviation of the normal distribution which our parameter values will be extracted from. Specifically, the mean is given by his point estimate while the standard deviation is derived from the extremes of his interval estimates for the emissions elasticities with respect to per capita production and population, which yields: (psi sim N(0.87, 0.13)) and (phi sim N(1.85, 0.56)). From these distributions we randomly extract 1,000 values of (psi) and use these values to run the DICE-STIRPAT model by keeping the value of (phi) fix to its mean; we then repeat the analysis by extracting 1,000 values of (phi) to run the DICE-STIRPAT model by keeping the value of (psi) fix to its mean. Therefore, while one parameter remains as in our baseline analysis, the other is varied following a random extraction procedure.
Evolution of key variables in STIRPAT-DICE in the BAU (black), OPT (green) and TEMP2C (blue) scenarios under different parametrizations of (psi) (top) and (phi) (bottom).
The results of our Monte Carlo simulations are shown in Fig. 4 in which we present the point and the 95% interval estimates of the evolution of emissions, temperature and carbon price in the BAU (black), OPT (green) and TEMP2C (blue) scenarios, focusing on the effects of variations in (psi) (top panels) and (phi) (bottom panels). We can observe that the evolution of the variables show a large degree of variability in the OPT scenario where both emissions and the carbon price span across a wide range of values, while much more limited is their variability in the other two scenarios (in BAU this is mainly reflected in the evolution of emissions as the carbon price is exogenously given, while in TEMP2C it is very limited).
Despite the large variability in the dynamics it should be clear that from a qualitative point of view our main results are confirmed: the introduction of asymmetric elasticities
leads unabated emissions (and also emissions in the BAU in which abatement is exogenously given) to be substantially higher than what traditionally believed in IAMs and this requires much stronger and earlier abatement, which may make it optimal to achieve full abatement by (or shortly after) the end of the century. The full decarbonization date in the OPT scenario varies between 2050 to 2110 according to the specific value of (psi) and between 2040 to 2120 according to the value of (phi), and in this latter case the full abatement date in OPT could even occur before the full abatement date in TEMP2C suggesting that it may be optimal to limit the temperature increase well below 2(^{circ}).
Discussion and conclusions
The dramatic effects of human activities on climate change and the consequences of growing temperature levels on world economies and societies have become more clear than ever over the last decade. Understanding thus what drives emissions, which are the primary contributor to climate change through carbon concentrations in the atmosphere, is essential in order to design effective policy aiming to reduce the detrimental economic consequences of climate change. However, despite an extensive econometric literature documents that the population size is a key driver of emissions, this issue has never been accounted for in traditional IAMs. Our paper aims at filling this gap by extending the most widely known IAM, the DICE, to allow human population to directly determine emissions. We show that since DICE largely underestimates emissions by neglecting to account for the asymmetric role of population and affluence as separate drivers of industrial emissions, it also gives rise to important distortions in the determination of the intensity and timing of the policy measures required to effectively mitigate climate change. Indeed, in our extended framework the temperature increase and the cost of climate mitigation are all much larger than what traditionally believed, and thus more abatement efforts and earlier interventions are effectively needed in order to reduce the economic consequences of climate change.
It is important to emphasize that our results should not be interpreted as advocating population control as a climate policy instrument. Rather, the contribution of this paper is to highlight how alternative specifications of the emissions function, particularly allowing for non-proportional responses to population and income, can materially affect the estimated timing and intensity of optimal mitigation. The policy implication is therefore not demographic intervention, but rather the need for improved representations of emissions drivers in IAMs, which may point toward earlier and more ambitious decarbonization efforts.
Despite our qualitative conclusions are robust to different parametrizations and alternative specifications of key functional forms, we need to stress that our analysis is built on the STIRPAT literature which shows a large degree of variability in the estimates of the emissions elasticities36,45. While some agreement seems to have emerged on the fact that the population elasticity is sizeably larger than the affluence elasticity, more debated is the issue related to their exact magnitude. In particular, several studies document the existence of important regional heterogeneities in the size of these parameters which largely changes with the stage of economic development25,28). This should not be a surprise as poor and rich countries substantially differ in the phase of the demographic transition they are experiencing and thus in the specific role that population plays as a driver of carbon emissions33,46. But this also suggests that the most appropriate framework to account for the environmental impacts of demographic patterns may be a regional model accounting for the possibility that the ecological elasticities may change over time as different countries and regions move along different phases of development. Our analysis based on a global model (i.e., an extended DICE) with constant ecological elasticities clearly cannot fully capture the complexity underlying the determinants of demographic and environmental processes, but nevertheless we believe it is informative in pinpointing the importance of asymmetric population and affluence elasticities along with their implications on the quantification of the cost of climate change along with the urgency and intensity of mitigation policy.
Data availability
Code to reproduce figures and tables available upon request.
Notes
In extensions of the basic STIRPAT formulation, technology is separately specified to identify the contribution to environmental impacts of a variety of variables such as energy intensity mix, dependence of fossil fuels, demographic age structure, urbanization and trade19,20,21. Recent contributions have emphasized both the heterogeneity of emissions elasticities and the role of additional socio-economic drivers, suggesting that the relationship between population, income and emissions is more complex than implied by the proportional IPAT formulation (e.g22,23).
All the IAMs works examining how human population affects climate mitigation consider the implications of different exogenous9,32 or endogenous30,31 demographic
The technological variable captures the effects on emissions of all other factors different from per capita production and population, and its initial value (sigma _{0}>0) is calibrated to allow emissions to match their 2015 level.
It is possible to show (details available upon request) that our results are robust to different parametrizations and alternative functional forms.
This parametrization follows25, based on the augmented mean group estimator applied to a panel of 80 countries. As that study documents, elasticity estimates vary across specifications and samples. We therefore interpret our baseline parametrization as a representative calibration within the range reported in the literature and assess robustness by considering alternative parameter values, which yield qualitatively similar results (see the Sensitivity and Robustness section).
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Acknowledgements
We are grateful to the participants in the EAERE23 (Limassol, Cyprus) and HEDGE2024 (Pisa, Italy) conferences, and seminars at the Paris School of Business and Rennes School of Business for insightful discussions. All remaining errors and omissions are our own sole responsibility. Moreover the authors acknowledge the support of the APC central fund of the university of Milan.
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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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V.L., D.L., S.M. all equally contributed to the model conceptualization, the analysis and interpretation of the results.
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Appendix A: The DICE-STIRPAT model
Appendix A: The DICE-STIRPAT model
The social planner maximizes social welfare, W, which is the product between per capita utility and population size, (N_{t}), discounted by the rate of time preference, (rho):
In Eq. (2) per capita utility depends on per capita consumption (c_t) and it is specified as follows:
where (zeta) is the marginal elasticity of consumption. per capita consumption is the ratio between the aggregate consumption, (C_{t}) and the population size, (N_{t}):
Population, (N_{t}), and labor perfectly coincide since there is no unemployment. Demographic dynamics is captured by the following equation:
where its growth rate (g_{t}) exogenously decreases at a constant rate (delta _{N}) as follows:
The output net of damages and abatement is denoted with (Q_t) and is equal to:
where (Omega _{t}) represents the damage function linking the effects of climate change on the production process, (Lambda _{t}) is the abatement cost and (Y_t) is gross output. Gross output is produced according to a constant returns to scale capital Cobb-Douglas production function combining capital, (K_{t}) and labor, (N_{t}) as follows:
where (A_t) denotes the total factor productivity, which grows at an exogenous rate (g^{A}_{t}) as follows:
where (delta _{A}) determines the decline in the growth rate of the total factor productivity:
The economy is closed and its resource constraint is given by:
where (I_t) is investment. The law of motion of capital depends on investment and capital depreciation as follows:
where (delta _{K}) is the constant depreciation rate.
Total emissions, (E_{t}) are given by the sum of land-use (ELU_{t}) and industrial (EI_t) emissions as follows:
where land-use emissions are exogenous and modelled as:
where (delta _L) is the constant declining rate of land use emissions. Industrial emissions (EI_{t}), instead, are a by-product of gross production and population size determined as follows:
where (mu _{t}) is the optimal emission-abatement rate, (psi>0) and (phi>0) measure the elasticity of emissions with respect to per capita production and population respectively, and (sigma _{t}) is the exogenous level of carbon intensity which evolves as:
where (g_{sigma t}) is the growth rate of (sigma _{t}) which reads as:
where (delta _{sigma }) is the exogenous rate of energy efficiency. Equations (18) – (20) reflect the evolution of carbon concentration in the atmosphere, (MAT_{t}), shallow ocean concentration, (MUP_{t}), and lower oceans concentration, (MLO_{t}):
where (phi _{ij}) is the transfer rate from reservoir i to reservoir j. Accumulation of emissions in the atmosphere leads to global warming, through changes in radiative forcing. Specifically, the increase in radiative forcing, (F_{t}), since 1900 in watts per square meter (W/(m^{2})) is given by:
where (O_{t}) is the forcing of other GHGs (CFCs, CH4, N2O,…) and (MAT_{t}^{PI}) is the pre-industrial level of atmospheric concentrations of CO2 (equal to 596.4 GtC, about 280 parts per million). Changes in radiative forcing are linked to atmospheric temperature, (T_{t}), as follows:
where (c_1), (c_2) and (c_3) are the climate coefficients for the upper level, the transfer from upper to lower stratum, and for the lower level, respectively. The parameter (lambda _1) represents the forcing of equilibrium doubling CO2 and (lambda _2) the equilibrium temperature impact. (TLO_{t}) is the increase of temperature in the deep oceans. The relationship between global-temperature increase and income loss is described by the following damage function, (Omega _t):
Finally, the cost of emissions abatement, (Lambda _{t}), in terms of income loss is given by:
The complete list of parameters and their specific values used in the simulations is reported in Table 5.
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Liuzzi, D., Lupi, V. & Marsiglio, S. Population driven emissions call for earlier climate mitigation.
Sci Rep 16, 30511 (2026). https://doi.org/10.1038/s41598-026-57960-x
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DOI: https://doi.org/10.1038/s41598-026-57960-x
Keywords
- DICE
- Climate change
- STIRPAT
- Human population
- Affluence
Source: Ecology - nature.com
