Archive for October, 2015

Roller coaster

UPDATE 13-11-2015: A new .pdf has been uploaded

I upload here an educational application of the standard Ramsey model of long-run growth, to show that it predicts correctly, in a qualitative sense, what has happened and is still happening in the Greek economy due to the recent crisis and current depression.

Even though the model is concerned with long-run growth rather than with short- and mid-term fluctuations, still it is important to see that by shifting our horizon-focus in economic analysis, we do not end up with incompatible conclusions.

Current Greek Depression and the Ramsey growth model 13-11-2015

Robert Dorfman, Economist, 1916-2002

Robert Dorfman, Economist, 1916-2002

Almost 50 years after its publication, late Robert Dorfman’s paper on explaining to then-innocent economists the principles of Optimal Control theory,

Dorfman, R. (1969). An economic interpretation of optimal control theory. The American Economic Review, 59(5): pp. 817-831

remains a classic example of masterly knowledge (and perhaps of scientific imperialism also): reading it from Dorfman, one may get the impression that Optimal Control is just the mathematical formalization of basic economics principles.

And how better an opening sentence can be than (quote), “Capital Theory is the economics of time” ?

For any aspiring student of Economics, it is still required reading.

phase diagram

I upload here an updated and considerably expanded  older pamphlet of mine, about dynamic stability in economic models, one- or two-dimensional. The standard results are combined and tabulated compactly to provide a coherent picture, while I also treat in detail the  (many) cases of “Saddle-path stability” in systems of difference equations. Saddle-path stability is a central concept in dynamic economics, being the mathematical concept that is consistent with dynamic adjustment that results from purposeful behavior, and can accommodate structural shifts.

Dynamic Stability for economic models




Two good tutorials:

The first is on the Taylor-series expansion of a function which is used for linearizing a non-linear function (1st-order Taylor expansion), and also, usually in a stochastic context, for “mean-variance” analysis (2nd-order, Taylor expansion). Among other things we use it to linearize non-linear differential and difference equations in order to study their stability properties.

Taylor Series tutorial


The second is about log-linearization, which is another linearizing technique often used in Economics, and especially in macroeconomic models.

Log-linearizing Guide


ConnectedFor those of you who don’t use it already: having an account gives you access to most of the scientific journals and economics papers you may need to read during your studies. How?

Install in your computer the  VPN service that the University offers. Then activate it, and then go to a scientific search engine (Google Scholar is the most frequently used one, but there are others), type in the title of the paper you are looking for and hit the link the browser will provide: It will send you to one of the online repositories of scientific papers, like, or a scientific publisher’s site, where, because you arrive there through the University VPN, in most cases you will have free access to the paper (as well as the right to legally download it), since the University has purchased blanket-subscriptions for all its members (and you are a member of the University).

The Course Structure contains a Reading List, where apart from books, scientific papers are also listed. Irrespective of whether the professor uses them or not, go find them and download them, and read them even if only lightly, to get familiar with how Economics is actually done.


According to the course structure , 30% of your grade will come from the grading of “Class Assignments”. These are essentially the “Exercises” we review in our TA meetings. Specifically:

  1. You are to hand in at least four (4) Exercises for grading. If you deliver less, you will lose 7.5/100 points from your course grade for each one that is not delivered. If you deliver more, we will consider the 4 top-graded among them.
  2. You are to “hand in” your assignments written in a computer (and so you can send them to me by e-mail if you want). No matter how clear your hand-writing is, learning to write in a computer using software for mathematical symbols is part of your education. There are “equation editors” freely available over the web, or already embedded in typewriting programs. Diagrams can be hand-made, then scanned and merged with the rest of the assignment.
  3. The course schedule is such that: on a Wednesday the professor presents a new model, and two days later I present the relevant Exercise. This means that my presentation will be “guidance to solve” rather than “complete solution”, since realistically you will not have the time to do and hand-in the exercise before  it is presented in our sessions.
  4. Time to deliver each exercise: You are to deliver an exercise no later than a week after it has been presented in our meetings, i.e. by the next TA meeting. This is pressing, but you must “get it off your chest” and move on to the next model. My suggestion is to try to complete an exercise no later than the next Wednesday course lecture (so that you can focus on the new material the professor will present). So I expect the Solow model exercise(s) no later than  Friday Oct 30th, and the Ramsey model exercise no later than Friday Nov 6th.
  5. This is Social Sciences. Mathematics adds rigor and transparent accountability for a model’s assumptions, but things remain approximate. This holds for your grades too. There is no microscopic formula that produces your grades -rather, there is, but it is in my brain and I am not fully aware of it. I can argue up to a point as to why your grade was what it was -but after that point an overall assessment is involved, which is not decomposable further.
  6. I plan on grading and publishing grades gradually, as time passes, so that you are aware of how are you doing (in terms of understanding and knowledge, not grades) -and if I see a common weakness in an exercise, I will discuss it in class, or post a note here.
  7. Doing the exercises is much more important for understanding the material, than it is for your course grade. This is a cliche that happens to be true.

I just got back from our first TA meeting – and I am worried. The fact that you did not review differential calculus or Optimal Rodin thinkerControl techniques during the preparatory classes of September, but you are only scheduled to review them later in the semester, means that you are ill-prepared to follow the basic Growth models of Solow and Ramsey (and Dynamic Macroeconomics in general), at their mathematical levels.

The professor has uploaded in the main site of the course some material on these matters. Also, there are abundant relevant resources freely available over the web. The coming week during which you will not have a new class, please focus on reading about these mathematical techniques, and try to solve and understand the solution of the Solow and Ramsey models of optimal growth. Note that while the Solow model involves only a single differential equation (or difference equation) of the first order, the Ramsey model involves both Optimal Control techniques and a system of two differential equations of first-order.

I would recommend also Barro & Sala-i-Martin (2004) Economic Growth (2nd ed.) book. I find it a very good educational resource for graduate beginners on Growth Theory, with accessible and intuitive mathematical appendices. Try it.

I will also upload here some notes on these matters, to help you cope.

Macroeconomic Theory

alogoskoufis.george_1394213166_54This is the first part of the compulsory graduate course in Macroeconomics, taught by Professor George Alogoskoufis. It assumes some familiarity with undergraduate macroeconomics and basic mathematical tools.

We focus on the theory of economic growth, consumption and investment, the theory of money and alternative theories of aggregate fluctuations, unemployment and inflation.

The course aims to present the main models used in modern macroeconomic analysis and research, and to familiarize students with them as well as with current analytical methods and techniques.

The course covers the following topics: 1. Models of exogenous and endogenous growth. 2. Models of consumption and investment under uncertainty. 3. Models of the money market, the price level and inflation. 4. New Classical models of aggregate fluctuations. 5. New Keynesian models of aggregate fluctuations, unemployment and inflation.

The detailed notes of lectures and exercises, communications and supplementary material are continuously posted on the course website.


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