Learning economics needs math (3)

    I have written two posts so far on why learning economics needs mathematics. The first is for science-stream students who have learned the mathematical methods of maximization in high school. The second is for students who have no such math background but have learned some basic economics (including money multiplier) in high school. This appears to be an interesting topic to our readers, and thus warrants me writing more on this. That's why this post is written.

   Both the first and second posts are written to explain why undergraduate economics education uses much more math than that in high school. Hence, in the present post, I want to write something about post-graduate economics education. Perhaps this is not so suitable for the readers of "hi, economics" because most of them will not pursue post-graduate study in economics. Nonetheless, they may be curious. Furthermore, they need to be better informed to make a decision for themselves: to pursue post-graduate study or not. 

   In fact, the content of this post is based mainly on a past conversation between me and my undergraduate student, who was in the final year and thought about pursuing a Master's or Doctorial degree in economics. An innocent question was asked: Do these programmes require lot more advanced math, and why? Though I said this was an innocent question, this was a question given by a top student. Hence, this is not a stupid question. In contrast, this is a question that will trouble even a smart student although one is already very good at economics and math. 

   Then, what's my answer? My answer is "yes". As to why, it is more complicated.

   In a way, I can give a highbrow answer, such as illustrating how these advanced math can help us better do scientific study in the economics. But at that time, I choose to give a lowbrow, but practical or perhaps more understandable, answer to the student. The point is: the schools that offer higher degrees in economics aim mainly at training academic economists who work at universities as teachers and researchers, not mainly for applied economists who work at banks, governments or think tanks. Although some of their graduates will work at banks, governments or think banks, most of the job opportunities are for those who take these higher degrees are for academic positions. Thus, the syllabus will be dominated by the needs in the academic world. 

   Admittedly, applied economists working at banks, governments or think tanks do not need so much more math (as what is required in these post-graduate programmes). But that's not true for academic economists.

   Then, why academic economics must be so mathematical? The point is: for one to demonstrate that they are a good academic, they must publish their research papers at respected peer-reviewed journals. Peer-reviews are done outside any single universities. The reviewers are also anonymous. Hence, there is no way, at least no easy way, for anyone to manipulate the reviewing process to secure publications. As such, this is an objective and a reliable way to demonstrate one's academic quality. Now most world-class universities adopt journal publications as their (almost) only standard for recruitments and promotions for their employees. 

   When journal publications become so important for job evaluations, submissions to journals are tremendous. There is a need to screen out most of the submissions. But how? Put it simply. A good submission that deserves reviewers' recommendations should be either good at offering innovative ideas, demonstrating some existing ideas with better techniques, or both. Now, everyone will say one has a good new idea. But it is not easy to objectively determine if an idea is really good. If an idea is published and then widely cited by other academics, the idea is at least widely recognized though you can still argue it is not a (really) good idea. But before an idea is published, the "objective" evaluation process via citation is not even kick-started. The reviewers have to make a judgement before the idea can be published. 

   In fact, reviewers' judgments for publications are often criticized -- good ideas (confirmed by post-publication citations) often are missed (initially) by reviewers who rejected these submissions. There is even a whole book, known as "rejected", documenting these rejected submissions (see also my past post). The problem is that editors and reviewers have to handle so many submissions whose authors always claimed that they have good ideas. It will be very easy to miss something good, or many things good. In a way, this also means containing good ideas may not be a reliable or an effective screening criterion. 

    Let me emphasize. I don't mean that journals will not publish good ideas. They of course publish many good ideas. I simply mean that journals may also often screen out good ideas. Hence, as a screening criterion, it may not be reliable to expect that all good ideas can be published.

   Turning to technique, the job is much more straightforward and reliable. The required technique in economics is either math (for theory works) or econometrics/statistics (for empirical studies). You can easily demonstrate that your paper has achieved something in this way. Suppose that there is a good idea published in a respected journal already but the authors use only the minimally necessary math technique to present the idea. Now, you work with the original idea with more advanced mathematical technique and so can demonstrate that the original idea work more generally or more beautifully or more convincingly. This is clearly a contribution. No doubt. Hence, the paper is accepted. 

   Again, let me emphasize. I don't mean that it is bad to assess a paper by its technique employed. In contrast, I think technique is very relevant and indeed important. I simply mean that, relative to assessing the quality of an idea, it is more reliable as a screening criterion to assess technique employed.

   Okay, now you can appreciate why advanced math is required for higher degrees in economics. This is indeed for students' own good. If students cannot master these math skills, their chance for getting their works published in respected journals is low. Eventually, they cannot find a job, or will be fired. Hence, most programmes require students to learn some advanced math that is elementary for journal publications. In fact, what these schools can teach their students are really elementary. The math skills exhibited in academic journal are actually advancing over time. This is also an understandable trend. To demonstrate that one has contributed to the literature, advancing the techniques used is one such method. But once your technique used has become common, using it again is no longer an advancement. Thus, you should use an even more advanced technique. So, using the technique learned from graduate school is simply elementary. If graduates don't keep up with the upward-moving standard, they will lose out one day. Thus, students should require more math instead of less. 

   At this point, perhaps you know better why math is needed in advanced education of economics. In a way, it has nothing to do with undergraduate education. So, if you don't like math in your undergraduate courses, you shouldn't blame what happens in "advanced" programmes, or economics as a whole. What I want you to know is that you should prepare for more math if you aspire to higher degrees in economics.

   I also want to emphasize that I don't intend to say this situation is good or bad. I simply describe what things, in my view, are. If asked for comments, I will say the situation is good in some aspects but bad in some aspects. In general, I think using (more) math is good for economics. But in some cases more math is really not necessary. Meanwhile, the real world is always not ideal. We can't cut off math simply because sometimes it is excessively used. Finally, I hope students now understand why so much more math is required in post-graduate study in economics. Don't blame the schools. They do what are supposedly good for your academic career. What you need to evaluate is: If you really don't like math skills, you should not consider pursuing post-graduate studies in economics.  

What economics models students (should) have learned?

    I recently have had a look of the high-school economics curriculum in Hong Kong. I've found that students have been taught very small number of economics models, which are the essential elements in economics. 
    Economics models represent economists' understanding of how the real world works. A description of what happens in the real world or in a hypothetical world must be involved. This involves how typically an issue will happen in some ways, and, if the model is useful, we expect that similar things will happen in similar circumstances. Simply explaining a concept and saying that a concept can be applied in some circumstances is not a model. For example, explaining what is inflation, long term vs short term, opportunity cost, etc is NOT a model although these concepts may be used in a model. 
   By this standard, I find that the high-school economics teach students only three models: demand and supply of goods, demand and supply of money, and aggregate demand and supply. In short, it is only demand-supply model in several contexts. 
   There are also two models that students may learn but it is not necessary for them to learn. In the elective part of the curriculum, students may need to learn how a monopolist sets the price for profit-maximization. This is a model. Also, they may need to learn how countries can specialize and trade with each other to attain a mutual gain. This is also model. 

   In my view, of course, I think they have learned too little about models. When these students study at university, typically they will find it difficult to learn much more models. In fact, they will find that they need only to learn many more models, and no more. They will find that economics is not what they expect (as their impression about economics is mainly from high schools). 

   Perhaps that's what things should be. High-school students may not need to learn so many models. They are too ignorant of what the economy is about. So, their urgent task is to learn some concepts that can be used to do simple economic analysis and some facts about the economies. Well, I am not expert in high school teaching. I cannot comment on whether this is the justification for the current curriculum design. But as an university teacher, I am worrying about the wide gap between high school and university education may potentially generate severe impact on students' learning experience in economics. 

   I am not proposing the high-school curriculum should incorporate more models. But I am here to explain what extra models should be taught if one wants to get sufficient tools for doing essential economic analysis. 

   The point is, demand-supply model belongs to the class of equilibrium models in economics. Equilibrium models explain how forces in opposing sides (or with conflicts of interests) may arrive at a stable outcome when different sides interact under some rules of games. Be it for a single good, or for the whole economy, equilibrium tells you the whole picture, given your understanding of how individuals will take actions. 

   However, equilibrium models do not tell you how individual will take actions. If individual actions are not explained, we may need to take some patterns of actions for granted. For example, students are told that when price of a good increases, the quantity demanded for this good will decrease. This is a pattern of individual actions. But why individuals will follow this pattern? If we don't explain it, we don't know if there will be exception, and we don't know if this pattern may change. If the real world is changed, not like the world we encounter today, will the individual action pattern change? We don't know if we don't have a model of individual action. 

   Hence, you can see: the point is that you need more models. In particular, how individual consumers or producers make decision and take some actions? We need to understand the mechanisms behind their decision-making. Thus, at university, students will be taught the model of consumer behaviours and firms' behaviours. Of course, some more parties' behaviours under different circumstances will also be taught. But it is basic that students need to understand consumers' and producers' behaviours. 

   I hope my students understand why they need to go through the trouble in learning so much more.