What kinds of numerical models exist?

Economic models come in all shapes and sizes, ranging from small scale exercises to visualize conceptual findings, over firm and market models focusing on microeconomic interactions, to large scale energy system models and global economy models covering macroeconomic aspects. Generally those types of models can roughly be clustered in two streams: bottom-up (BU) and top-down (TD) models.

As the name suggests, BU models focus on the details of a market or system and aim to capture the technical or environmental details of the modelled system. They are basically disaggregated representations. In contrast, TD models aim to capture the interaction among several sectors or the whole economy. They are aggregated models in the sense that they work with representative production functions and elasticities to represent substitution between different technologies or products.

Both model clusters have their advantages and drawbacks. The high detail of BU models allows capturing specific market characteristics. In addition, they are well suited for policy impact assessments of a specific sector and for the evaluation of technology or market design shifts. They can be used both for short-term evaluations and long-term simulations. BU models have to omit the more general economic interactions and rely on a set of externally defined parameters capturing the elements not represented in the model. TD models allow capturing cross-sectoral effects, feedback effects across the economy and macroeconomic impacts like employment, trade and income effects. They cannot represent the same technological detail as BU models. They are suited for long-term evaluations but not for short-term operational simulations.

For real-world problems often the detailed as well as the aggregated dimension is important – especially for policy assessments. Therefore approaches to combine BU and TD models, so called hybrid models, are increasingly emerging. Furthermore, to capture relevant system constraints models often need to account for specific technological (ie power flows in electricity networks), environmental (ie diffusion of pollution) or behavioural (ie agent learning) aspects. Thus, economic modeling of energy and environmental topics is becoming more and more interdisciplinary.

Naturally, there are also other lines of reasoning to cluster numerical model approaches. An important differentiation is the mathematical nature of the model, namely whether they are linear, non-linear or mixed integer programs or mixed complementarity problems. The latter approach is used to represent equilibriums (we’ll learn more about equilibrium models in Step 3.4) while the former are all optimization problems (there will be more information about optimization problems in Step 3.3). Similar to the BU-TD debate the different mathematical model formulations have their advantages and disadvantages. We will go into more detail on the mathematics of models in Week 5.

Further differentiations can be made with respect to the underlying time frame (ie short- or long-term models), the choice variables (ie operational or investment models/ static or dynamic models), uncertainty (ie stochastic or deterministic models), the type of competition (ie perfect competitive, monopoly or oligopolistic) or the spatial dimension (ie network models).

Within this week we will use a differentiation that follows the underlying mathematical formulation of the model, namely optimization and equilibrium approaches. The two approaches provide a distinctive separation in terms of how to capture real world conditions while being highly interlinked in mathematical terms. Furthermore, they can be adopted to design both BU and TD models and capture the majority of existing numerical models out there. Understanding the principles of optimization and equilibrium models will enable you to understand and evaluate the different model approaches used by environmental and energy researchers.

Recommended readings:

To get more familiar with numerical models Herbst et al. (2012) and Krysiak and Weigt (2015), Section2, are good starting points. They provide comprehensive reviews on existing energy models and model approaches. Weigt (2009) provides a short overview for electricity market models that will be helpful for the numerical model assignment. If you have access to scientific journals you may also want to have a look at Ventosa et al. (2005). We will provide references with specific model examples within the following steps also offering more insights on the functionality of energy markets.

Herbst, A., Toro, F., Reitze, F., & Jochem, E. (2012). Introduction to energy systems modelling. Swiss Journal of Economics and Statistics, 148(2), 111-135.

Krysiak, F. C., & Weigt, H. (2015). The Demand Side in Economic Models of Energy Markets: The Challenge of Representing Consumer Behavior. Frontiers in Energy Research, 3, 24.

Ventosa, M., Á. Baíllo, A. Ramos, et al. (2005): Electricity market modeling trends. Energy Policy, 33(7), 897-913.

Weigt, H. (2009). A review of liberalization and modeling of electricity markets. Dresden University of Technology, WP-EM-34.