We now come to the final stages of modeling, the interpretation of the results. When we interpret the results of a model, we have to accomplish three things. We have to phrase results that are usually contained in mathematical expressions in words that can be understood and remembered. We have to provide a sound intuition of what happens in economic terms, and argue why the underlying mechanism is relevant for real world cases. And we have to embed the results in the storyline of our analysis, and into the literature. These three parts of interpreting results help to convince our audience that our results are not only consistent, but are interesting and relevant, and that they contain new and or original ideas.
Furthermore, it helps if we can point to real world cases that can be seen as examples of what happens in our model. Remember, we want to show that our models are models of credible worlds. Let me use an example from one of my papers to highlight these points. In one paper, I’ve analysed the question whether prize based policies, such as taxes, and quantities based policies, like permit trading, lead to the same direction of technological change. Using a rather complex model, I have shown that this is not the case. Different policies lead to different directions of technological change. Given this, I raise a question, which policy is better, which yields the following proposition.
With a fixed quantity, and with a tradeable quantity regulation, the firm’s technology choice is socially optimal. In contrast, with a price based regulation, the firm’s choice of technology is always socially suboptimal. This proposition is already stated in fairly simple words, and not in equations, so that it is already the first step of interpretation. To provide an intuition, I explain the results in terms that are similar to what is known in the literature. With the price based regulation, the total amount of emission reductions varies over time if the firm’s costs change with time. This reduces expected welfare. Those points are well known in the literature on environmental policy.
The new point is that by choosing their technology, firms can influence the extent of this variation. But they do not bear the costs of the more strongly varying emission reductions. Thus, they tend to invest in the wrong technology. This effect is robust, in the sense that it always exists if there is cost uncertainty, and if firms can change the slope of their marginal cost function via investing in new technologies. This paragraph does most of what is needed for interpreting results. It explains the economic mechanism. It links the results to a well known scientific discussion, and it explains that the result is likely to be very robust, as addressed on two rather undemanding assumptions.
This example comes from a paper written for an economic journal. For an interdisciplinary outlet, or for communicating with the general public, the interpretation would have to be stated in different terms, and would most likely be much longer. However, the example highlights the three most important aspects of interpreting results. State them in simple terms, explain the underlying mechanism, show how robust they are. Let me finally mention two pitfalls, when interpreting results from a theoretical model. The probably greatest pitfall is to stay too close to the formal derivation of the results. A formal result is a bit like a jewel that is discovered in the dark underworld of formal models, and thus need to be brought to the light to be seen.
If you want your audience to appreciate what you have done, you have to interpret your results in a way that makes them accessible, and that shows their scope and their applicability to real world problems. You will find many examples in the literature that contain highly interesting insights that have remained mostly hidden, because the authors were not able, or did not care to do this. The second pitfall is to overstate the generality and importance of your results. Be honest. If your results rest on restrictive assumptions, point this out. If it is only of interest in special cases, point this out as well. You are in good company.
The literature contains thousands of results that have small scope, but that are highly valuable within their range of applicability. If you find a hidden jewel in your models, do not break it by overtaxing its strength. Finally, interpreting a model is tough work. Often, it takes more time to understand a result than to derive it. Take this time. You can only interpret your results for others if you have understood them yourself.