Skip to 0 minutes and 6 secondsHello, and welcome to the fifth week of our course on Modeling in Environmental and Energy Economics. In this week, we want to learn how to actually solve our numerical models, and produce all those numbers we want to interpret. Going back to the overall modeling structure from problem to interpretation, we are now on the second part where we actually derive the solution and interpret all the results. But keep in mind, this is a highly nonlinear process, so whatever we do on that side is going to have a feedback effect on the modeling design that we learned in week three. OK, now that we have modelled a nice representation of the real world, how do we actually get all those numbers?

Skip to 0 minutes and 56 secondsThere are two main aspects you need to consider. One is computational limitations. The other is data limitations. Let's start with the first one on computational limitations. With modern computers it is nowadays possible to design large scale numerical models of complex systems. That was still science fiction just a few decades ago. But nevertheless a good modeller will know what his model can and cannot do, and when it's too much. There's a multitude of possibilities why your model may throw an error. Your model can take forever and ever to solve. But even if you get a solution, you still need to know what the solution actually tells you.

Skip to 1 minute and 42 secondsTo handle these challenges, you have to have a basic understanding of the modeling mathematics behind and how those impact your results and the possible interpretation of those. But even if you design your model accordingly, accounting for all computational and mathematical limitations, there is still one big problem ahead We need input to produce output. In a conceptual model, it is normally sufficient to assume specific functional properties of external parameters. But in numerical modeling, you will need to put a number in there. So let's go back to our classic electricity market system. You see all those external parameters? You will need a number for each of those. No exceptions.

Skip to 2 minutes and 33 secondsIf you can't get the number, you can't use the corresponding equation, and need to adjust your model accordingly. Maybe you're simply not able to solve the model you want to build, because you can't get the data it would need. And be warned, getting data and processing data is oftentimes boring and frustrating. Don't get discouraged by that. We all need to go through it. It's part of the game.

Skip to 3 minutes and 4 secondsNow if we have ensured our model is computationally feasible, the mathematics make sense, and all the data is plugged in we can finally produce results, which means numbers. Plenty of numbers. Maybe millions of numbers. So what to do with those? Remember, we want to connect those with the problem we had, so we need to interpret our results with our problem in mind. To do so, we need number crunching. On the one hand, we need to filter all our results and boil them down to meaningful aggregates or representative cases. Maybe deriving yearly average prices out of hourly prices, or aggregate locational information to regional or national totals. On the other hand, we need to present them.

Skip to 3 minutes and 58 secondsNumerical models have the advantage that they are well suited to produce simple yet meaningful graphical representation of complex processes. Use that power wise - it will take you a long way.

# How to get numbers out of a model?

In this week we want to learn how to actually solve our numerical models, and produce the numbers we want to interpret.

In week 3 you learned how to design an optimization or equilibrium model. In week 4 you developed you first model ideas for your respective assignment and received feedback on your ideas. With this you are able to design your very first model.

Given your model formulation we will first have a look at the different model sub-types and what this means for the computation of your model (Step 5.2). Afterwards we will check what parts of you model you will need input data for (Step 5.4). Both restrictions may lead to a re-design of the model to ensure that you actually can get a numerical solution.

Once the model is computationally feasible, the mathematics make sense, and all the data is plugged in, results can finally be produced. Which means numbers. Numbers which have to be interpreted with our problem in mind (Step 5.5). On the one hand, all our results have to be filtered and be boiled down to meaningful aggregates or representative cases. On the other hand, they have to be presented.

Numerical models have the advantage that they are well suited to produce simple yet meaningful graphical representation of complex processes.

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