Integrated Assessment Models
Why such a simplified model? Nordhaus’s approach was to condense and simplify state-of-the-art knowledge about global carbon circulation and the climate system into a set of (close-to) linear equations that was tractable enough to handle in an economic model. To understand the need for drastic simplifications of the natural-science elements of the IAM, note that the economic model assumes that agents are forward-looking. Indeed, people’s concern with climate change is in itself evidence of the forward-looking capacity of humans. Like Romer, Nordhaus assumes rationality as a benchmark. Under rational forward-looking behavior, the optimality conditions that pin down the laws of motion for endogenous variables (including fuel prices and interest rates) imply that current variables like consumption depend on the entire path of future endogenous and exogenous variables.
A key step in economic model building is therefore to solve the model. To do so, one needs to find a mapping from the “state”, i.e., the predetermined variables (e.g., the capital stock and the level of technology at the beginning of a certain time period), to the endogenous variables (e.g., consumption) that satisfies the forward-looking conditions. This step is absent in models of climate and carbon circulation, as the differential equations that determine the model dynamics are recursive: they have no forward-looking components. That is to say, particles in natural-science models – unlike humans in economic models – do not choose
their paths based on expectations about future events (including how other particles will act, today as well as in the future).
This fundamental difference makes the standard large-scale models of climate and carbon circulation incompatible with economic models. Just joining a set of standard (sub)models, would yield a model much too complicated to solve, given the large state space of conventional natural-science models. The incompatibility is reinforced when models are used to find optimal policy, since the set of possible policies to consider and compare is very hard to reduce to a manageable size. For this reason, Nordhaus’s demonstration that a compact and easy- to-analyze climate and carbon circulation system could be made compatible with a forward- looking economic model is a fundamental contribution. Obviously, the simplifications on the natural-science side have some costs.
Nonphysical Nature of DICE2007
For example, if you set t = 2015, then warming
between 2015 and 2025 is affected by the stock of atmospheric CO2 in 2035,
implying that emissions between 2025 and 2035 will increase warming during the ten years between 2015 and 2025.