Econometrics of Climate Change

For many of us, it is an unquestionable fact that climate change requires immediate action. Increase in the atmospheric carbon dioxide (CO₂) levels, rising global temperatures, changes in the level of solar radiation that reaches the earth; all these and changes in many other climate variables are argued to be the result of human activities. Experts are saying that if we do not take any actions, the damages of climate change will soon become irreversible. This has been known and debated for many years. In the Joint science academies' statement, published by Intergovernmental Panel on Climate Change in 2001, it is written that

There will always be uncertainty in understanding a system as complex as the world's climate. However there is now strong evidence that significant global warming is occurring. The evidence comes from direct measurements of rising surface air temperatures and subsurface ocean temperatures and from phenomena such as increases in average global sea levels, retreating glaciers, and changes to many physical and biological systems. It is likely that most of the warming in recent decades can be attributed to human activities.

Econometricians and data scientists can contribute to the fight against climate change by turning climate data into useful pieces of information. In particular, by using econometric theory we can

1. Investigate the relationships between climate related variables and try to forecast how these variables will behave in the future;
2. Analyze the relationships between climate and economic/financial variables;
3. Evaluate the effectiveness of the actions taken to alleviate the damaging effects of climate change.

Our findings can be used to design policies that respond to climate change. There has been a growing literature on econometric methods and modelling approaches that can be used to answer climate change related questions.

One of the most debated topics in climate sciences is earth's climate sensitivity (ECS). Earth's climate sensitivity is the amount of increase in the global temperatures that might occur at the time when CO₂ concentration doubles. It tells us by how much global temperatures will rise in response to human-caused CO₂ emissions. Pre-industrial level of CO₂ was around 280 parts per million (ppm). It increased to around 409 ppm today. Without any interventions to reduce the emissions, concentrations are likely to reach 560 ppm (double pre-industrial levels) around 2060. By using simple physics, we can claim that the earth will be around 1^oC warmer once CO₂ concentration doubles. However, this would be an inaccurate claim because of the existence of feedback effects. Climate feedbacks are processes that can either amplify or decrease the effects of changes in the CO₂ concentrations. Climate feedbacks include water vapour, cloud covers, ice and snow cover. They introduce a substantial amount of uncertainty and invalidates the results obtained by simple physics. Indeed, it has been argued that, due to climate feedback effects, possible change in the global temperature will be  1.5^oC to 4.5^oC at the time the CO₂ doubles. Questions:

1. Can we obtain an (accurate) estimate of earth's climate sensitivity by using econometric methods?
2. Can we decompose the changes in the global temperature to the changes caused by increasing CO₂ levels and to the changes caused by certain feedback effects, such as changes in surface radiation?

The answer to both questions is: Yes. Let's see how we can formulate ECS by using econometric models.

Most of the climate variables are observed and recorded in multiple locations/stations. For this reason it is natural to consider models and methods that are developed to analyze panel data sets. A panel data set contains observations on multiple units obtained over multiple time periods. Let T_i,t be the local temperature at time t, measured at location i and R_i,t be the local surface radiation at time t at location i. Furthermore, let CO_2,t be the CO₂ concentration in the atmosphere at time t. Assume that we have data for temperature and radiation for T time periods, from N locations. So, we have a panel data set for these two variables. Also, assume that we have a time series of CO₂ concentration of length T. We can use the following panel data model to relate the one period ahead local temperature to current local temperature, surface radiation and to some global factors:

Here α_i accounts for location specific effects and it accounts for heterogeneity across locations in the levels of the temperatures. In panel data literature, α_i is known as individual specific effect. The coefficients of temperature and radiation are β₁ and β₂. These coefficients are not allowed to vary across locations. It could be the case that they were allowed to vary across locations. Then, one would need to denote them by i index, in particular by β_1,i and β_2,i, respectively. In the model above, we rule out heterogeneous coefficients. The third term is φ_iλ_t. Here, λ_t is the time specific effect. This time specific effect is allowed to affect each location's one-period-ahead temperature differently. This is ensured by allowing the coefficient φ_i to be different for each location i. Finally, the error term u_i,t+1 accounts for the unexplained variation in the one period ahead temperatures. This error term can be correlated across locations and across time. The model in (1) is a dynamic panel data model for local temperature.

We can incorporate the global factors to our model by assuming the following time series model for λ_t:

Note that λ_t is not observed. We see that in the model for λ_t there are three global, spatially aggregated variables, which are T_bar,t, R_bar,t and ln(CO_2,t). Here, T_bar,t is the average global temperature, R_bar,t is the average global radiation. They are obtained by

and ln(CO_2,t) is the logarithm of the CO₂ concentration. Equation (2) can be seen as an energy balancing equation. This equation captures the relation between global radiation, CO₂ concentration and global temperature. Any imbalance between these variables will affect the local temperatures of the subsequent period through λ_t because λ_t is in the model for T_i,t+1.

We can use model (1) and (2) to measure earth's climate sensitivity. ECS has the following analytic form.

A derivation of this formula can be found in Phillips et al. (2020). If we want to estimate earth's climate sensitivity, we need to estimate the parameters: γ₃, β₁ and γ₁. This means that we need to estimate models (1) - (2). This means that if the models are correctly specified and if appropriate estimation methods are chosen, we can estimate the earth's climate sensitivity accurately.

Storelvmo et al. (2016) use standard dynamic panel data and cointegration methods to infer about ECS. They disentangle the changes in the temperature that are caused by increases in the CO₂ concentrations and that are caused by changes in the radiation levels. Changes in the radiation that reaches earth's surface is largely explained by the aerosol loading in the atmosphere (climate feedback). Then, when there is a decrease in the temperature due to changes in the radiation, we can call it "aerosol cooling''. Storelvmo et al. (2016) disentangle these "greenhouse warming'' and "aerosol cooling'' effects to see how much of the change in temperature is due to greenhouse warming and how much of is due to aerosol cooling. They use historical data collected from many stations and find that the aerosol cooling masks one third of the global warming. By accounting for this aerosol cooling masking, they find a higher climate sensitivity, that is around 2 ± 0.8^oC. Estimation methods used in Storelvmo et al. (2016) rely on certain independence assumptions placed on u_i,t+1 of (1).

Some future research can be conducted by developing and/or using alternative estimation methods that can yield accurate estimates when certain independence assumptions placed on u_i,t+1 are relaxed. In order to avoid bias and inconsistency of the estimators, we need to be careful about what we assume about u_i,t+1. For instance, when we are dealing with climate data, there are strong reasons to believe that there is a "spatial'' correlation between u_i,t+1 and u_j,t+1 when j ≠ i. This spatial correlation will depend on how far location i is from location j. Temperature changes in neighbouring locations will depend on each other. Given this, it would be unrealistic to assume independence between u_i,t+1 and u_j,t+1 for any j ≠ i. We might assume that the dependence dies out as the distance between i and j increases. However, even that might not be so realistic. We know that gases and solids thrown into the atmosphere travels around the globe within only three week. So, some shocks such as the effects of volcanic eruptions can affect all locations. An estimator that takes all these into account can be a more accurate estimate of earth's climate sensitivity.

Estimating earth's climate sensitivity is important as it provides policymakers or intergovernmental institutions a guideline of how to deal with global warming. This is relevant especially when institutions are setting upper limits for CO₂ emissions and determining carbon budgets. An accurate estimation of it will lead to effective policies and eventually to a safer world to live in for humans and animals. Econometricians can make valuable contributions to climate research by searching for/finding/using correct modelling approaches, accurate estimation methods that take into account the nature of the climate data.

References

Phillips, P.C., T. Leirvik, and T. Storelvmo (2020). Econometric estimates of Earth's transient climate sensitivity. Journal of Econometrics, 214(1), 6--32.

Storelvmo, T., T. Leirvik, U. Lohmann, P. C. Phillips, and M. Wild (2016). Disentangling greenhouse warming and aerosol cooling to reveal Earth's climate sensitivity. Nature Geoscience, 9(4), 286--289.