Nature: Estimating the trajectory of CO₂ emissions, an important part of planning for climate change mitigation and adaptation, depends in part on understanding how these emissions are influenced by the economy. Although researchers have developed sophisticated models of the connections between the economy and CO₂ emissions, prominently used modelling approaches implicitly assume that the effect on emissions of declining GDP per capita is symmetrical with the effect of growth in GDP per capita^{1, 2}. Here, analysing available data from 1960 to 2008 (see Methods), I find that in years where GDP per capita shrinks, CO₂ emissions per capita do not decline in equal proportion to the amount by which they increase with economic growth. One important implication of this finding is that CO₂ emissions depend not only on the size of the economy, but also on the pattern of growth and decline that led to that size.

I estimated two separate models of CO₂ emissions (from fossil-fuel combustion and cement manufacturing) per capita using first-differenced (that is, change from year to year) variables. I estimated different slopes for when the change in GDP per capita was positive (economic growth) and when it was negative (economic decline). All variables were converted to natural logarithmic form before first-differencing, making these elasticity models. The use of first-differenced data controls for factors that vary across nations but do not change over the period of observation, such as many aspects of physical geography.

The coefficients for both models are presented in Table 1 (full results are presented in Supplementary Table S1). In Model 1 no control variables were included. This model indicates that for each 1% of growth in GDP per capita, CO₂ emissions per capita grew by 0.733%, whereas for each 1% decline in GDP per capita, CO₂ emissions per capita declined only by 0.430%. Both of these coefficients are significantly different from 0 and from each other. In Model 2, the percentage of the population living in urban areas and the percentage of GDP from the manufacturing sector were included as control variables. This model has lower data coverage than Model 1 (154 versus 160 nations, and 4,134 versus 5,630 nation-year observations) owing to missing data on the control variables. The coefficients, at 0.752 for growth and 0.346 for decline, are similar to those from Model 1 and, as in Model 1, are both significantly different from 0 and significantly different from each other. I also examined models, not presented here, with other control variables (international trade as a percentage of GDP, foreign direct investment as a percentage of GDP and the age-dependency ratio) that have been examined in other studies of CO₂ emissions^{1, 2, 3}. These variables did not, however, have significant effects in the models I estimated. Therefore, I omitted these additional control variables in this analysis so as to improve statistical efficiency and the parsimony of the models.

Note that because these are elasticity models, they already allow for a nonlinear relationship between CO₂ emissions and GDP per capita. The inelastic coefficients (that is, <1) indicate diminishing returns, where, for example, an increase in GDP per capita in an affluent nation increases CO₂ emissions per capita less than an equal increase in a low-income nation. Because it is possible, however, that in highly affluent nations the connection between GDP per capita and CO₂ emissions per capita may diminish more than is indicated by this inelastic relationship, I also constructed models examining whether the coefficient changes over the range of GDP per capita values (see Supplementary Information). These models suggest that the effect of change in GDP per capita on CO₂ emissions per capita does not vary significantly over the range of GDP per capita values. To assess whether these results are overly influenced by observations earlier in the period, I have also estimated versions of the models presented here using only data from 1990 to 2008. These models produce very similar coefficients to the models that include data for all years and point to the same conclusions.

Why does economic decline not have an effect on CO₂ emissions that is symmetrical with the effect of economic growth? There are various reasons that this may occur, but the asymmetry is probably due to the fact that economic growth produces durable goods, such as cars and energy-intensive homes, and infrastructure, such as manufacturing facilities and transportation networks, that are not removed by economic decline and that continue to contribute to CO₂ emissions even after growth is curtailed. This may help to explain in part the observation that the reduction in global CO₂ emissions in 2009 following the global financial crisis was modest compared with the increase in emissions in 2010 (Refs 4,5). This finding is consistent with previous research examining post-Soviet states in the 1990s, which found that in the context of economic decline that followed the collapse of the Soviet Union, CO₂ emissions dropped substantially but not at the same rate as emissions grew elsewhere with economic growth³. Thus, the present study, building on previous work, shows that economic decline is not simply the reverse of economic growth and needs to be understood in its own terms.

The asymmetric effects of economic growth and decline on CO₂ emissions have important implications for modelling emissions. This asymmetry indicates that history matters: that is, to estimate CO₂ emissions one needs to measure not only GDP per capita values for nations but also how those values came about. Models of CO₂ emissions per capita that account for asymmetric effects of GDP per capita growth and decline will diverge from those that do not, to varying degrees depending on the pattern of economic change. In a model equivalent to asymmetric Model 2 (Table 1), but where the assumption of symmetry is imposed, the estimated coefficient for GDP per capita is 0.569 whether it is expanding or contracting (model presented in Supplementary Table S2), which is in between the growth and decline coefficients from the asymmetric Model 2. It is important to note that the symmetric and asymmetric models estimate different annual trends in CO₂ emissions per capita independent of other factors in the model. This is represented by the y intercept (presented in Supplementary Tables S1 and S2) in the models (that is, the y intercept in first-difference models indicates the expected change in CO₂ emissions per capita if all factors in the model remain unchanged). In the asymmetric model, the intercept indicates an independent annual trend of about −1.50%, whereas the symmetric model produces an estimate of about −0.73%. The difference in the estimated change in CO₂ emissions per capita between the asymmetric and symmetric models will vary over the range of change in GDP per capita, as illustrated in Fig. 1. As Fig. 1 shows, when the change in GDP per capita is between −3.34% and 4.23%, the symmetric model overestimates the growth in CO₂ emissions per capita, but for GDP changes beyond this range, the symmetric model will systematically underestimate growth in CO₂ emissions per capita.