Model example and model types

Economic models are useful and often necessary to answer pressing questions. But like all models, they have limitations that need to be understood. Let us look at an example of an environmental economic model to highlight common advantages and limitations. Models of the European emission trading system provide a good example. This system is a main instrument for reducing CO2 emissions in Europe. At the moment, it is the world’s largest environmental policy scheme. In this system, firms have to own emission permits to emit CO2. They are granted a limited amount of such permits, which can be traded among firms. When this system was first implemented, economists were asked what will be the price of emission permits?

As this is a new policy, so that no data was available for empirical work, an answer to this question could only be based on models. Fairly sophisticated models were built, most of which rest on the simple basic model that I will show you now. Two firms, both alike in emissions, in a sector regulated by emissions trade. Both firms receive the same amount of permits. One firm invests in new technology and one does not. The question is will they trade permits and if, at which price? Imagine that one of these firms has marginal costs of reducing its emissions that are described by this simple graph.

The graph shows how much this firm has to pay to reduce its CO2 emissions by one unit. For high emissions, these costs are small, but they increase if the firm has to meet more demanding targets. The other firm, drawn from right to left, has higher costs, as it did not invest in new technology.

Both firms receive the same amount of permits.

Due to the different technologies, emission reductions are much more expensive for the second firm than for the first one. Thus, both firms can benefit from trading permits. The first firm reduces its emissions further and sells permits to the second firm, with a gain. The second firm buys permits and emits more, also gaining from this exchange. The best outcome is reached where the marginal cost curves intersect.

If there’s perfect competition on the permit market, this will be the outcome. And here we have the permit price.

In most cases, we use more sophisticated models than such graphs. Here we have the same model. The optimisation problem of both firms. This model can be solved to derive an expression for the permit price. Furthermore, we can use data on technological options for reducing emissions in different firms to estimate those equations and thus, come up with a number for the permit price. This is a useful model, as it gives us information - the price at which permits will be traded - that cannot be gained in any other way. The model is even more useful, as it also describes what determines the permit price.

We can use it, for example, not only to predict permit prices, but also to see what would happen to the permit price in a recession or in a boom. However, the model is not a detailed description of what happens in reality. It does not tell us which technologies will be used to reduce emissions. If such information is required, this is a wrong type of model. Furthermore, our model is based on assumptions that might not be true. For example, we have assumed that the permit market is competitive. If this is not the case, our model might give us misleading results. Therefore, it is a very important to build models in a way that they are fit for the purpose in question.

In economics, we use three general types of models for different purposes. First, we have explanatory models. These models are used to make an argument. For example, we could use such a model to argue that a bad design of a permit market, where some firms have market power, could lead to too high permit prices. Such models are usually theoretical models. That is, they are not fully quantified. Their purpose is to make consistent arguments. For example, what consequences different climate policies might have for technological change. They do not give quantified results, but rather aim at capturing economic mechanisms. Second, we have simulation models. These models are used to describe plausible scenarios.

Scenarios of different pathways towards a renewable energy system or a low carbon society are often derived from such models. These models are usually based on simpler economic mechanisms than explanatory models. But they are calibrated so that they yield quantitative insights. Their purpose is to provide a detailed picture of future developments. But they only show what is possible. They do not make predictions. Finally, we have prediction models. They are usually econometric models, often with some theoretical model in the background. Their purpose is to predict future developments or the results of policy measures. As this is rather demanding, most models focus on short run predictions and are thus of limited use to most topics relevant in environmental and energy economics.

Thus, in this course, we will cover the first two types of models. That is explanatory models and simulation models.