Climate Econometric Analysis of Energy Balance Models:Cointegrating Relations Revisited

Abstract

　　Research on climate change mainly focuses on detecting whether the climate is actually changing and if so, detecting possible causes of such change.　Climate models, constructed on laws of physics, have played a central role in detection and attribution of climate change.　To accomplish those goals, simulation experiments based on climate models are intensively conducted.　In simulation experiments, how accurate climate models can reproduce internal natural variability is of importance.　Moreover, the model outcome is sensitive to initial values due to the chaotic nature of the model.　To alleviate sensitivity with respect to initial values, ensemble experiments are performed with the cost of computational burden.

　　Climate econometrics, on the other hand, has attracted much attention in recent years where statistical models are built through statistical properties of observed climate variables in conjunction with the physical laws in order to capture a causal relationship between external drivers of the climate and the observed data.　Climate econometrics has an advantage in that it can avoid problems arisen from simulation experiments.　In climate econometrics, climate models expressed by differential equation system, such as energy balance model which describe the relationship between temperature and radiative forcing, are transformed into statistical models.　The past literature shows that the stochastic energy balance model constructed by adding noise term to energy balance model is equivalent to a vector error correction model under a certain assumption of statistical properties of the time series of climate variables.

　　In this article, our aim is to re-investigate statistical properties, in particular, the stationarity of the extended time series of climate variables.　This is important because the way the statistical model is constructed is different whether the data are generated by stationary processes or not.　Our major finding is that the earth’s surface temperature anomaly is detected non-stationary with a stochastic trend, which is in contrast to the finding in the past literature.　This may lead to an incompatibility with the physical theory based statistical model of the climate.　Our result indicates that data-driven statistical models can reject the relationships between climate variables deduced from physical laws that the past literature assumes.　This implies that the validity of restrictions the past literature of climate econometrics imposes a priori must be statistically tested.

JEL Classifications:Q54, C32, C51