Archive for April, 2014

Άνευ απροόπτου, μετά την Τρίτη 6/5 ο κος Αλογοσκούφης θα ανεβάσει στο blog του μαθήματος την 1η άσκηση για το Β’ μέρος που σχετίζεται με το κεφ. 14 του βιβλίου, (Διαχρονική Προσέγγιση στο Ισοζύγιο Πληρωμών).  Θα υπάρξει και άλλη άσκηση από το κεφάλαιο αυτό, αλλά η 1η θα αφορά Οικονομίες χωρίς παραγωγή. Η άσκηση αυτή έχει 4 ζητούμενα. Όπως και για το Α’ μέρος, μπορείτε να παραδίδετε λυμμένες ασκήσεις πριν παρουσιαστούν στην τάξη. Σε κάθε περίπτωση, προσπαθείστε να επιλύσετε το Ζητούμενο 1, και τα Αριθμητικά Παραδείγματα (Ζητούμενο 4).


Αλέκος Παπαδόπουλος

Χάνονται δύο φροντιστήρια του Β’ μέρους.

Τετάρτη 30/4

Ολοκλήρωση ασκήσεων που αφορούν το Α’ μέρος του μαθήματος

Τετάρτη 7/5

Κενό λόγω εκλογών

Τετάρτη 14/5

15:00-17:00 Αμφι-Γ : ΠΡΟΟΔΟΣ στο Α’ μέρος (προαιρετική)

19:00-21:00 Αμφι-Α : 1o φροντιστήριο Β΄ μέρους

Τετάρτη 21/5

15:00-17:00 Αμφι-Γ : 2ο φροντιστήριο (αναπλήρωση)

19:00-21:00 Αμφι-Α : 3o φροντιστήριο Β΄ μέρους


Ακολούθως βασική ώρα και μέρα η Τετάρτη, Αμφι-Α, 19:00-21:00. Η 2η αναπλήρωση θα ορισθεί αργότερα.


Αλέκος Παπαδόπουλος



Paper ideaMore often than not science (and statistics especially) is counter-intuitive. Since the human world is built on and maintained by science (and to a larger and larger extent, on and by statistics), this should tell us something about the value of “common sense” (of which I am not particularly fond of). I was just reminded of that by an excellent paper by Zhu and Lu (2004), where the authors present, with students in mind, the strongly counter-intuitive/confusing/hard-to-believe, case of the uninformative prior distribution in the context of Bayesian estimation related to the apparently simple case of a Bernoulli random variable where we want to estimate the probability that the variable will take the value 1.


Now almost everybody (myself included), using -what else- common sense, view a Uniform prior (ranging in (0,1) in our case), as the bona fide uninformative one (which goes back to The Principle of Insufficient Reason). In our case, using such a prior distribution reflects a prior belief that the probability we want to estimate can take any value in (0,1) with equal probability –how more uninformative can you be?

Oh, but you can. In fact Zhu and Lu paper shows clearly that for the case at hand, such a prior  influences rather distinctly the posterior results -and so it is not-uninformative at all. They also derive the actual uninformative prior for this case.

Download the paper :

Zhu and Lu – Non Informative priors for Bernoulli rv


I have always found that tabulating information, cases and sub-cases, is very useful in providing a coherent picture of the situation, making interlinks visible, as well as general rules.

In the context of Dynamic Economics, stability of differential equations that describe laws of motion of economic variables are of primary interest. Since in Economics we are almost exclusively concerned with the existence of “saddle-path stability“, we usually do not provide the whole picture and possibilities, of which saddle path stability is just one case.

So I wrote and I attach here a summary of what can happen (and when) in a 2 by 2 system of differential equations, in terms of the system’s stability. While writing it, I hit upon an interesting way to show how important is the actual arrangement of equations when one wants to use matrix algebra -arrangements that are equivalent in the “plain” formulation of a system of equations, become totally different if viewed through the lenses of matrix algebra, and lead to different results.

The summary can be downloaded here:

Stability of Systems of Diferrential Equations

Maybe in the future I will do the same for Difference Equations, since they are more convenient when one wants to work in a stochastic framework.

I think it is fitting to kick off this blog with the publication of my first …bona-fide research paper in a peer-reviewed journal (I have publications of conference papers and a book chapter, that all relate to the Management of Health Systems, but they live in this strange land between “professional” and “academic” publications). The paper is in the field of Stochastic Frontier Analysis, and deals with the Two-tier stochastic frontier model (2TSF model). It presents a new stochastic specification for the three-component composite error term of this model, and it contains a complete toolkit to implement the specification in an applied study. Unavoidably, it mostly consists of a series of complicated mathematical expressions -but the literature review in the beginning is quite interesting I think, since it shows how wide is the applicability of the 2TSF model -the uses of which I plan to extend in the near future, in the context of my PhD research.

The paper can be  downloaded from the link below:

Papadopoulos Al. (2014) The half normal specification for the two-tier stochastic frontier model

Journal of Productivity Analysis,  DOI 10.1007/s11123-014-0389-8

Submitted August 01 2013, accepted March 10 2014, published online April 04 2014