Why do we need numerical models?

Hello and welcome to the third week of our course on Modeling in Environmental and Energy Economics. In this week, we want to get more familiar with numerical modeling and how to design a model that is able to capture the real world– well, at least parts of the real world. Going back to the overall modeling structure from problem to interpretation, we want to address the point how to transfer a real-world problem into a numerical model. The actual process of solving the model and interpreting the results will be covered in week 5.

So what is a numerical model? Essentially, a numerical model is a theoretical model with numbers. So a basic understanding of theoretical modeling is not only a nice add-on but a prerequisite for successful numerical modeling. A numerical model is a representation of a real-world system via mathematical equations that can be solved with computational methods. So let’s take our electricity market example with generation, transport, and demand. In this system, we have power plants generating electricity. So we need to find a way to capture their decision process, like a classical company profit representation. The electricity needs to be transported, so we need a representation of the physics of power flows.

Finally, we use electricity to heat our homes, to cook, or watch online courses on our computers. So we need a representation of our own demand behaviour. And that’s it. We now successfully transferred the real wold into a few simple equations for a numerical model. Naturally, there are some distinctions to theoretical modeling. The driving difference is the focus of numerical models on quantification. We want to know whether it’s 5, 50, or 500 millions and not highlight a specific argument or concept. Consequently, the models need to capture the real world we want to analyse. You will learn a set of different approaches how to achieve that.

But we still follow the same guideline as in theoretical modeling– as simple as possible, as complex as needed. In addition, the whole numerical modeling process is impacted by limitations on the computational side, data restrictions, and you will have a lot of numbers that you need to analyse. We will address those points in week 5.

Now that we have a first rough idea about numerical models, why should we care? What are numerical models good for? If we look into the past, we hopefully have data to analyse. If we want to understand what drives the world, we have our theoretical models capturing concepts and ideas. But if we want to look into the future, numerical models enter the stage. Numerical models and simulations are the crystal balls of our modern age. Instead of sacrificing animals, reading palms, or looking into the stars, we can design mathematical representations of possible futures and explore those. Every long-term forecast of economic developments is based on some form of numerical modeling.

Every investment decision a company has to make needs some numerical analyzers in there. And every policy evaluation should be based on numerical modeling. Those models help us to answer a different kind of question. So for example, would a higher carbon price lead to a shift away from oil? What would happen if we implement renewable support systems? How much should we get? Would we get? And finally, what happens with all those nice new applications on the demand side?

OK. So we need numerical models to quantify different kind of effects, from forecasts to policy evaluations. The important thing to keep in mind for any good modeller is to know where the limits of the models are and what you can, and more important, what you cannot say based on your model results. Remember, all models are wrong, but some are useful. So let’s start.