The Cambridge Economics Tripos is deemed to be rigorous because of the depth of material covered in each paper, but the course as a whole also offers breadth in the subject of study. While I am taking a diverse range of papers in the Economics Tripos this year, I’m strangely seeing more connections and relationships across the papers. Of these, I’ll just touch on three (1) how important math and micro foundations are (2) the similarity of mathematical and philosophical reasoning (3) how academic papers overlap across papers.
It’s the first day of week 3, and I’ve done at least one supervision piece for each of the papers I’ve taken this year, and I think it’s an appropriate time to talk about the papers I’m taking. In Year 2, we have three compulsory papers in microeconomics, macroeconomics, and econometrics. We are also required to choose one optional paper from the following: trade and development, labour, math and statistics, and history and philosophy of economics. To understand the subject better, I opted to take two optional papers instead, and these lie on the two ends of the math-essay spectrum: mathematics and statistics for economists (MSE), and history and philosophy of economics (HPE).
The first thing that struck me this year was how foundational mathematics and microeconomics are. The first topic that we are doing this year in macroeconomics is intertemporal macroeconomics, and we built the entire model from micro-foundations, starting with the Robinson Crusoe model and the consumer choice for intertemporal substitution in consumption and labour. The way that macroeconomics is now rooted in the microeconomics we learned last year made me appreciate last year’s material a lot more, and appreciate macroeconomics a lot more. Our first topic in microeconomics this year is game theory, and when we looked at Cournot games and optimisation again, we had to invoke the Lagrangian constraint optimisation technique, which was drilled as an algorithm last year. This year, when we looked at optimisation under constraint again in MSE, I finally appreciated how the Lagrangian actually worked based on the constraint qualification and the Weierstrass theorem, which I had taken for granted last year. With the extension into the Kuhn-Tucker theorem for inequalities rather than pure equalities, the multiplier interpretations and complementary slackness conditions that our microeconomics lecturer briefly talked about suddenly made a lot more sense. As such, I am also very excited to learn how the foundations in statistics that we learn in MSE might be applied to the econometrics that we are currently doing. The foundations in mathematics are in its axioms and definitions. After the painful process of contemplating on the nature of epsilon balls in n-dimensional space in order to prove some results, I’m gradually appreciating how these axioms and definitions in mathematics feed into our economic results and algorithms. Thus, I’d say that mathematics is probably the most foundational and transferable. It is with proper understanding of mathematics that microeconomics is grounded, and it is with grounding of microeconomics that models in macroeconomics makes sense.
After working on the first supervision sets, I found the similarity between mathematical and philosophical reasoning very interesting. While mathematics proceeds in a long line of hieroglyphs (for those who don’t understand them), and philosophy proceeds in a long line of English words (that might still be vaguely understandable), the way reasoning and deduction works are very similar. That’s what I have learnt when I worked out mathematical proofs (assuming they are correct) and when I wrote my first philosophy essay on the assumptions on rational choice theory. Deduction proceeded from definitions and assumptions, and in order to get to the conclusion that we want, more assumptions have to be built in. It is from this air-tight reasoning process that we can examine the argument to see how it might crumble if some assumptions are proven false (or non-falsifiable, which results in another philosophical complication for sciences). This latter part is what people generally associate with critical thinking. I also found that many argument forms are similar, but are just known by different names: modus tollens in philosophy is similar to proof by contradiction in mathematics for instance. Beyond the material, I find that engaging with these two disciplines fundamentally changes and hones the way we think about issues and logic. To this end, I’m quite glad to observe this relationship and that I have the opportunity to take both papers rather than just either of these.
When I think of academic publishing, I usually associate them with having a very narrow focus. There is some area of specialisation that this economist is good at, and he fills a rather obscure part of our knowledge gap. As such, since undergraduate papers are cursory and broad in the fields that they explore, we should expect academic papers to fall neatly into any one of these papers that I’m taking. But the papers clearly overlap, and the way each paper grants a different perspective to that academic paper is really interesting. There was this seminal work by Friedman in our macroeconomics reading list for the Permanent Income Hypothesis (PIH). In setting up the PIH, Friedman had to appeal to microeconomic foundations before setting up the macroeconomic theory. The empirical US data cited and conclusions drawn can be understood and evaluated from the “econometrics” lens. The way his propositions follow from the definitions and intuition can be understood and evaluated from the lens of mathematics and philosophy. The history part of HPE also situates the paper in its historical context – monetarist view, post-war period in US, where scientific and socio-cultural circumstances could have influenced this theory. While each paper grants a particular perspective, the material of the paper was still clearly macroeconomic, and perhaps that is all that most students see. It really excites me to see how these ideas converge, and I hope that when I write (now and in the future) I will be able to use these transferable skills learnt in each paper to produce original work of the highest quality.
It’s definitely difficult trying to cope with five papers, apart from the many other things I’m doing, from starting a society, to doing research and consultancy during term through the social innovation programme, to the commitments as a prayer secretary in CF, to simply caring for and being available for people in general. But it’s always great to work while the sun in still up, and the blessing and learning is definitely worth it!