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Comments on Two KTM discussions - Organ Trade and Drugs

KTM has a discussion here on the organ trade. It isn't immediately apparent to me why so many people think that the legalization of organ trading would not lead to less information assymetries. With a legalized market, health authorities can make it compulsory for potential organ sellers to receive structured advice. Health authorities can also effectively monitor standards for transplants. Even if the authorities are able to curb all organ trade, one has to justify why it is reasonable to constrain the number of ways the poor can escape abject poverty. Of course, the existence of risks, high or otherwise, is not sufficient for such a paternalistic stance. If we were to extrapolate, acrobats and construction work should be prohibited as well.

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Since KTM brought up his discussion on drugs in his discussion on organ trade, I perused his arguments. I have a few comments on his general stance on the "war on drugs". Now let me be clear on my stance. I support the death penalty but I do think it is a cruel punishment on the lowly footsoldiers of the drug trade. Deterrence and effectiveness are not sufficient. There must also be proportionality. The deterrence and effectiveness properties still hold if we were to sentence litterbugs to death.

A comment on organ trade

I can't say that I comprehend all his points but I will comment briefly on the points I understand. Before that, I will like to clarify that I have not reached the conclusion that organ sales should be permitted. I will have to consider more arguments first.

Firstly, Jeremy refers to the von Neumann-Mogenstern which is the standard in the literature. He then claims that game theoretic equilibria is not socially optimal. I’m not sure about what game theoretic equilibria he is referring to since the structure of the game is not explicitly defined. Without resorting to game theory, it’s well known that under very few conditions, the absence of intervention is optimal. The details are quite technical and the math requires the use of Brouwer’s fixed point theorem (I can’t say I learned this in my topology class. We did go through this in my Economics class but I am not so sure about the generality of the proof. If you’re interested, check out Starr’s book on general equilibrium theory. MWG does not have the proof for this.)

Jeremy’s point about “market design” is not very accurate. The predisposition of economists towards free market is not a value-laden one. The economic arguments for “unfettered” markets have many roots, the most powerful of which stems from the technical theorems from general equilibrium theory. General equilibrium theory is not perfect but the assumptions are few (which is a good thing. Since any model one has off the bat is likely to have quite a number of assumptions even if one doesn’t realize it).

That is not to say that information asymmetries are unimportant. In this case, they could be critical. Nonetheless, it is important to distinguish the normative arguments from the positive ones.

Jeremy is concerned about organ theft. However, legal safeguards in these matters are not difficult to achieve. For example, it is not possible to sell a house that is not owned by you. The practical implementation may be difficult in developing countries with poor legal safeguards. However, this can be resolved by placing the burden on developed countries to enforce these rules. For example, hospitals in developed countries may be legally obliged to ensure that the organ are sold voluntarily by the “owners”. One might argue that this does not prevent intra-country organ trade in developing countries. However, there is no reason to expect that this would result in an increase in organ theft. In fact, with a legalized channel to sell organs, people who really do want to sell their organs can do it through proper channels, thus minimizing health risks.

If there is a market for organ trade, people in abject poverty can improve their livelihood. By prohibiting organ sales, these people are not better off. They would have one less avenue to lift themselves out of poverty. Think of it as optimization problem with an extra constraint. The potential organ donor does not have to donate his/her organs but if he/she chooses to do so, presumably it’s because he/she thinks that he/she will be better off.

One may legitimately argue that it is unfair that people born into abject poverty would have to undergo bodily mutilation to better their station in life. Indeed I agree that this is not ideal. However, people who wish to prohibit organ trade should at least provide some form of assistance such that no one would seek to do such a thing. I am not aware of any alternatives proposed.

Mathematics and Economics

I’m quite tired of Economics majors complaining that Economics is too mathematical. What they are saying is not that math has nothing important to teach us (since no one has taken up the challenge). All they are saying is that they don’t want to put in the hard work necessary to access the most powerful models and ideas in the field.

People in physics and engineering don’t ask the universe to become less complex so that they can understand it. Moreover what they are doing is much more mathematical than what we do in Economics.

Mathematics is an important tool. There are several tests to a model. One of them is whether the model is consistent within its set of assumptions. Often this means it can be translated into a mathematical model. Based on my own experience, when you build a theoretical model, it can seem plausible but when you work out the math it turns out to be false. When you re-examine the model, you realize subtleties that you missed out. A lot of people don’t understand this because they never tried getting their hands dirty by extending or building models. Another reason why a technical model is necessary is because a technical model can be more easily transformed into a statistical one. Checking that the model is consistent with reality is important because your reasoning could be right but you could be missing a omitted variable and thus get absurd results when making predictions.

Sometimes a bit of technical detail is a good thing. I recall my first Econometrics course where we learned that we had to make degrees of freedom adjustment (number of parameters) to the expected sample variance. The lecturers were keen to avoid mathematical detail so they tried various ways to explain it. But I never really got it until I took the grad class. After all, why make the adjustment by division? There are many other ways to make adjustments. The reason turned out to be quite easy, requiring only some matrix algebra.

As you go on to do real things with your knowledge (ie. beyond understanding the models you learn in class), you tend to appreciate precision. A book that tells you how to solve a certain model but does not tell you the necessary and/or sufficient conditions for the method to work will cause you endless pain when you try to make extensions and borrow techniques.

Low Signal to noise ratio

I used to be determined to keep abreast with current affairs. In JC, I tried (although I was often unsuccessful) to read The Economist from cover to cover. Even in the Org, I continued my subscription. Towards the end of my undergraduate life, I gradually moved away from current affairs.

The recent for this is simple. The signal to noise ratio is extremely low. It takes way too long to (cumulatively) to read the news every day. Yet the marginal contribution from it is exceedingly. You will almost never be required to know the latest news. You can get by easily catching up with the news on a fortnightly or sometimes monthly basis. I really believe this.

Comments on Economics textbooks

Over the course of my undergraduate studies I have used quite a few economics textbooks. Now that I’m in my final year, some of my friends have asked me what books are good for certain topics. Book appreciation is a great hobby of mine so I’m posting some reviews of economics texts I have used.

The books classified “basic” or “intermediate” are undergraduate texts. The books that are classified “advanced” are advanced undergraduate level and sometimes beginning graduate level. I am not a graduate student and will not be going to graduate school. Therefore, I’m not a good source for graduate level references.

My second major is in mathematics but I have tailored my reviews to well-prepared economics undergraduates. When more advanced mathematics is needed I say so explicitly.

Some of these books are not the best books in the subject. For example I recommend Chiang’s Elements of Dynamic Optimisation to all my fellow economics undergraduates. This is because it’s easy to read and can be immediately applied. It’s clearly not the best book on optimal control! For that you may need Bertsekas but that would be two volumes of material and clearly not suitable for the average economics undergraduate. I also recommend Simon and Blume for people interested in matrix algebra but you should get Axler (tough problems) of Friedberg, Inse and Spence if you want a mathematical presentation.

I have used most of these books extensively. For those that I have not, I indicate quite clearly the amount I have read. For example, I have used most of Romer’s Advanced macro but only a few chapters in Sargent and Ljungquivst’s Recursive Macroeconomic Theory. I will continue to update these comments to incorporate new thoughts, especially if I ever get to read more of the texts that I don’t use that often. (The reason I include comments on some of the books that I’m only half way done with is because I think I have useful things to say about them that will help other economic undergrads. It’s a bit too demanding to expect one to read the entire textbook to post a review because how many of you have read a textbook from cover to cover? Out of the 50 plus courses I have taken, this has not happened except for those instances where I took it upon myself to read beyond the scope of the course. This applies for courses which I have taken a whole sequence of. For example I took 4 macroeconomics courses from undergraduate to graduate level.)

This first installment is on macroeconomics and mathematical economics, the two areas which I’m quite familiar with.

Favorite macroeconomics text

Basic to intermediate
My favourite text is Froyen’s “Macroeconomics”. This textbook is thinner than almost any other text in the market. It is succinct and very clear. At the basic and intermediate level, understanding IS-LM-BP is important. Froyen explains this extremely well. Furthermore, the difference between the Neoclassicals and Keynesians are well explained. You will want to know the broad strokes of these differences (all explained within the IS-LM-BP-AD-AS framework).

When friends from other departments ask me for recommendations, I tell them to get this book. Anyone can complete this book quickly and painlessly. It doesn’t have too many unnecessary text boxes of applications, something that has plagued the intermediate economics textbook markets for years.


Don’t be fooled into thinking that more “examples” are necessarily a good thing. A lot of students make the mistake of assuming a correlation between content and weight of the book. Publishers include more and more text boxes into textbooks so that they can issue new editions. This prevents students from re-selling textbooks. Why anyone would want lug around a dumb bell of a textbook I’m not sure. In short, get Froyen’s Macroeconomics!

Other textbooks I have used
Abel and Bernanke – not bad but more lengthy. I got this when I was still in the ORG and was debating whether to get a degree in accounting or business. No, I didn’t change my mind because of this book.

David Gordon –there is some material presented quite differently from other textbooks, for example backward looking expectations. I used this in my second macro course. My opinion is that things like the above can be taught more rigorously with a mathematical presentation. A more mathematical presentation would be more compact and also a lot faster to pick up. I think the topics are quite hard to swallow for a first course in macro although the preface says that students with no economics background (not even a principles of economics course!) can use it for a first course!

Dornbusch, Fisher and Startz – Only used this for the growth chapter.

Summary: My recommendation is Froyen. If you ever forget the basics you will be referring to Froyen, not the other textbooks. In my programme, we used several economics textbooks including Gordon’s in the second course. The second course in intermediate macro is, in my opinion, a course that gives students graduating without honours all the concepts they need as economics majors, without the tough love that comes with our honours level macroeconomics. In retrospect, if we had a direct honours programme, we would probably do without the second course.

Honours/Senior year Macroeconomics.
In my programme we used several papers in conjunction with Romer. The graduate programme used Romer more extensively. I like Romer’s Advanced Macro because it has many, many models. There’s an extensive discussion of the literature so it makes great reading even if you don’t have to study the material for your exams. I enjoyed reading some of the chapters that weren’t assigned in my course (the later chapters in particular) and have read most of the book. (A nice tidbit for people who still cannot part with IS-LM is that Romer discusses that topic from a more mathematical perspective.)

A couple of things that I don’t like: I sometimes found it a little hard to follow the equations. That could be because I was still very green when I used Romer (a beginning year 3 student). On the other hand, it could be the presentation because I’m quite adept at following mathematical models. Either way, this book is almost certainly a requirement for advanced undergraduates and I’m pretty sure that even if graduate students didn’t use this, they would have a copy of it because it has so much good stuff.

Blanchard and Fischer
I actually think that there’s a lot of overlap between this and Romer. My lecturer claims that this text is more difficult. I think it’s true but not much. I used this for one chapter in my honours level course and read a bit here and there when I worked on my thesis. The last chapter on “useful” models was quite insightful when I was younger. The chapter on money made me run to find a better text on monetary economics (I like Walsh). If I had a choice I would stick to Romer. This text is extremely outdated. In comparison, Romer’s text has a recently issued third edition.

There’s some very basic dynamic programming and a lot of optimal control. One thing that annoys the hell of me is the extensive use of endnotes for technical points. Why does anyone use endnotes?????????????????

Minford and Peel
I have a copy of this but never used it beyond a superficial attempt. It was one of the readings when we learned the Muth method in studying Sargent and Wallace’s model. I recall the chapter being a real pain and hoped that the textbook would give me some anaesthesia. Nope. It did not help. This text is mathematically quite demanding (in the sense that you will need to know or will acquire several mathematical tools along the way). One of the authors was an early proponent of rational expectations.

This book is not really comparable with Romer or B/F. There’s a lot of time series, difference equations type of models. I will eventually get around reading this text from cover to cover one day and will update this section.

A note: Rational Expectations Macroeconomics is the older version of Advanced Macroeconomics: a primer. Please don’t get both.

Sargent’s Macroeconomic Theory
This book is really old. I’m not sure if anyone still uses it since Sargent has several new textbooks. The chapter on lag operators and difference equations is actually quite useful – and certainly more enlightening than other treatments I have seen in the course of my studies (I have never come across difference equations in my math courses for some reason). I enjoyed punishing myself with the dense treatment. The chapter on stochastic difference equations is extremely long.

The preface itself makes an enlightening read. Sargent talks about why he included some of the Keynesian models in the first part of the book and how he came to adopt rational expectations. The parts I have come across are technically demanding. Most of the book uses the language of difference equations (ie. Discrete time). You will be thankful for the chapter on difference equations which will get you up to speed.

Sargent and Ljungqvist’s Recursive Macroeconomic Theory.
I have not finished this book. Some day I will. In fact, I’m such a fan of Sargent’s work that I have read the first half of his monograph with Lars Peter Hansen on Robustness (very, very difficult for someone with only a limited math background like myself).

The parts I’ve used are the chapters on dynamic programming and time series and also the few chapters that were related to my own thesis research on monetary policy. This book frightens me a lot and is pitched at the graduate level. Advanced students may be interested in reading the appendix on the duality between Dynamic programming and the Kalman Filter.

Summary: Get Romer’s Advanced Macro. You don’t really have a choice. This textbook is pitched at the most reasonable level for undergraduates and is really good. You will also keep it for life.

Mathematics for Economics majors

Let’s face it. Modern Economic theory is mathematical and technical. If you’re not interested in knowing more than what’s found in your undergraduate programme, I highly recommend the following books. It’s always good to know more math since deficiency in your mathematical toolbox is a huge barrier to more advanced models which presumably you’re interested in since you chose to major in economics. As I’m not a graduate student, I’m not in a position to recommend the desired course of mathematical preparation for graduate school but you should know that the books below will not be sufficient.

Alpha Chiang’s Mathematical methods
This is the book my macro lecturer recommends. I recommend it too. The book is a great reference with heuristic proofs at best. Learn all you need to know about calculus, linear algebra, constrained and unconstrained (static) optimization, difference and differential equations.

Simon and Blume
I hear from many sources that many graduate schools use Simon and Blume’s text. The material on linear algebra is especially good. I don’t recommend it to my fellow undergraduates because it’s kind of an over-kill. It’s a much thicker book and has real proofs. Having said that, the analysis material (advanced calculus would be a more apt description) isn’t really enough.

As mentioned earlier, the linear algebra chapters are surprisingly rigorous and can pass off as a first course in linear algebra. I don’t think it has anything on difference equations (either that or it must have been very skimpy).

It’s a good idea to get one of these even if you’re taking a full dose of math courses. They are handy references and they include all you need for an undergraduate course. I don’t think it’s really reasonable to learn whatever math you need from the math department. Firstly, you will learn a lot of material that you will not use in your undergraduate study for example, have you ever changed the order of integration, used spherical coordinates or used Stokes theorem in any of your economics courses? I didn’t think so. Yet you would have to learn these in multivariable calculus which you need to register for the course in differential equations. Go ahead and take the math courses but pick up some useful tools for economics on the way by reading Chiang or S&B.

For (deterministic) continuous time dynamic optimization, I recommend Alpha Chiang’s Elements of Dynamic Optimisation. Again there are very few real proofs here. It’s easy to read and there are nice examples. I treat it as a cookbook and I learned most of the deterministic continuous time dynamic optimization here. Note that the book covers optimal control and calculus of variations. You won’t get to see the Bellman equation here. Another popular text recommended by lecturers is Kamien and Schwartz. I haven’t used the latter extensively so I can’t say much, except that it’s more theoretical than Chiang. Chiang wrote his book as a continuation of his Mathematical Methods. If you like his style you will like this book.

A comment about the material in Chiang’s book. I have read people dissing Chiang’s Dynamic Optimisation but I think the criticism is overly harsh. The material in Chiang fulfils an important niche – 1) advanced undergraduate programmes 2) elementary graduate level programmes. I’m quite skeptical of people saying that dynamic programming is the best way to go.

If you’re not dealing with randomness, it’s much easier to use optimal control. I learned this from my own painful experience. After a long arduous period of writing a model in discrete time and using the dynamic programming (by the way, you can consider using the Lagrangian also. Gregory Chow is a proponent of this.), my professor asked me to reformulate the problem using optimal control. I realized two things: my discrete time model was completely wrong because I made a mistake when solving the dynamic programming problem. And, I could have saved a lot of time by just working in continuous time for the same results. If you’re a beginner and you’re setting up a baseline model, you definitely want to see how it works out in this easily tractable case first.

(Note: Dynamic programming does have a continuous time analog. See the Hamiltonian-Jacobi-Bellman equations.)

There’s a book by de la Fuente that’s at a much higher level than the above books. It has metric spaces in the beginning for example. I didn’t refer to this a lot. I learned most of my “pure mathematics” from the math department – Analysis, Metric Spaces and Topology using books by Bartle and Shebert, Rudin, Parzynski and Zipse, Sutherland and Munkres. I’ll update this section if I ever get around reading it. From what I have seen, it looks very good.

The useless model Challenge

In economics we use mathematical models. Mathematical models do not tell the whole story. The most accurate depiction of reality is the real world itself. When you resort to economic modeling, you’re seeking simplifications. Constructing a mathematical model is a way to check that your argument passes at least one test. Another test is econometrics. However, the functional forms and the dynamics of the analytical model determine how you go about applying econometrics.

Mathematics is a deductive science. We work from a few axioms and build up theorems. From simple theorems, we obtain more complicated and beautiful ones. Theorems are true because we have to prove them. Most of the other sciences are empirical sciences. You come up with a hypothesis and then you test it. Experiments can support or refute your hypothesis but cannot prove it. Similarly, in Economics, we come up with hypotheses and then find evidence (a consistent model or econometric tests) to support it (but never to prove it.)

(Please note that I’m not saying that economics is a science. I’m not sure whether that topic is worth discussing)

Despite every other economics undergraduate complaining about how mathematical economics is, I have yet to hear of any examples of an economic models learned during the course of their undergraduate studies that is unnecessarily mathematical. This suggests that the mathematical framework yields useful insights. Do you have a counterexample? Please leave a comment.

NOTE: I’m not saying that all economic models that use math are insightful. There are definitely loads of papers with fancy math with no economic insight around. That’s not surprising at all. In every field, there will be papers with results that are not useful. At the cutting edge of research there will be a lot of failed attempts and a lot of ideas that do not stand the test of time. I’m asking for models learned in your undergraduate courses. Stuff that you are forced to study!

Hello I have sent my first (personal) blog post out on email. More than one of you told me that you thought my mail was spam. I got a new nick- Gaussitokreps - so bear that in mind!

I will try to type a subject line next time so that you will recognise me.

Update

Hi everyone. Some of you asked me about my locked entries. I signed up for a LJ account but I decided against making any locked entries because it's just incredibly unfair to ask you all to get an LJ account to read my crap. I think I'll probably blog the personal stuff by emailing you all instead.

A response: Trade

Han has posted an interesting discussion about globalization. I agree with some of his points and would like to qualify a few others in this post. I’m not interested in the larger issue of globalization because it includes issues outside of economics and public policy. Instead I will focus on trade liberalization.

If we take the simplest model, perfect competition and a few other reasonable assumptions, zero trade barriers make perfect sense. In the absence of any possible distortion, the fundamental theorems of welfare economics follow (with a very parsimonious set of assumptions). I prefer this way of looking at free trade rather than the two country model or various variants of small economy trading with the “world”.

The reason for my distrust of many international trade models (that I learned in the two courses at the undergrad level) is that many of the models use the community indifference curve. This concept makes sense only in very restrictive conditions. If you have studied some basic general equilibrium theory you will notice that the utility function is constructed with a small and reasonable set of assumptions. This is sort of a mathematician’s cheap thrill – trying to get the same result with as few axioms as possible. But in this case, it’s actually important. You don’t want to build an elaborate model explaining the world that fails just because your utility function is founded on crappy assumptions. I don’t think the idea of a community indifference curve pass this test. I’m not even sure if you can build such a function using any framework remotely similar to that of the usual utility function we use for the individual (If I’m wrong, I would love to see some references)

Even if community indifference curves make sense, we still don’t get very robust results. For there to be an improvement in welfare, you need to make assumptions on the relative price level in the case of imperfect competition. A large country may have off-setting terms of trade gains when they impose tariffs. These departures suggest that we need empirical evidence to back up the analytical models.

If we persist and assume that the country as a whole gains from international trade, we must analyse what sort of gain this is. Trade liberalization seldom results in pareto improvement (Nobody loses and at least one person gains). We assess trade policies by the “compensation criterion.” The key word is “compensation.” Do we intend to assist those who are clearly worse off?

Of course you may argue, why are we obligated to compensate those who suffer under free trade. Indeed you may not be. And that’s really the point. This becomes a question of political economy. Why should someone who perceives that s/he will suffer when there is trade liberalization support free trade? A rational self-serving person is not obliged to support policies to his/her detriment.

Having said this, I’m pro-free trade. It’s just that I understand why people may be opposed to it.