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Decision-making under risk and “statistical thinking” in the 20th century (selected models and persons)

100%
Rybicki W.
Mathematical Economics
|
2018
|
issue 14(21)
71-94
EN
The paper is the second part of the series of articles surveying chosen models of decision-making under “risky circumstances”. The first segment concerned the earlier period of development of so-called “statistical thinking” (up to the times of J. Neyman and E. Pearson) and has been published elsewhere. These “twins” of papers as a whole, are intended as essays (consciously avoiding any formalization) to introduce the subsequent parts of the cycle – conducted in a more formal style. Several problems were discussed in the first part of the series. The leitmotifs, i.e. Bayesian vs. “orthodox” approaches, and the subjective vs. objective probability meaning are continued in this article, and developed towards the “modern needs and directions”. The role of some outstanding scientists is stressed. The possibility of the unification of the different philosophies on the grounds of statistical decision theory (thanks to A. Wald and L.J. Savage) is noted. “Dynamic” or multistage statistical decision procedures will be also indicated (in contrast to “static, “one-shot” problems). The primary role in developing these ideas played by mathematicians A. Wald, L. Shapley, R. Bellman, D. Blackwell and H. Robbins (plus many others) is stressed. The outline is conducted in a “historical perspective” beginning with F. Ramsey’s work and finishing at H. Robbins achievements – as being very influential in the further development of the stochastic methodology. The list of models, to be discussed in the subsequent (“formal-mode”) article/s, is added at the end of the paper. The central role in the notes is played by the “procession” of the prominent representatives of the field. The first “series” of them was presented in the previous part of the cycle. The subsequent (nine) are placed here. These scientists built the milestones of statistical science, “created its spirit,” exquisitely embedding the subject in the “general stochastic world”. The presentation is supplemented with their portraits. The author hopes that some keystones determining the line-up can be recognized in the course of reading. It is not possible to talk about mathematics without mathematics (formulas, calculations, formal reasoning). On the other hand − such beings as probability, uncertainty, risk can be, first of all, regarded as philosophic and logic in their heart of hearts (as well as being somewhat “mysterious”). So, it can turn out illuminating (sometimes) to reveal and to show merely the ideas and “their” heroes (even at the expense of losing the precision!). The role of the bibliography should also be stressed – it is purposely made so large, and significantly completes the presentation.
2
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O „metamorfozach” ekonomii dobrobytu

100%
Rybicki W.
Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu
|
2017
|
issue 481
73-93
PL
W artykule naszkicowano historię ekonomii dobrobytu (ED), podkreślając „hybrydowy” charakter tej koncepcji teoretycznej i odwieczne swary dotykające racji naukowego bytu tej konstrukcji myślowej, głównie „starej ED” – „normatywnej herezji”, pozbawionej mocy objaśniającej („folklor” omawianej tematyki). Impulsem do zaistnienia „nowej” ED była idea porządku Pareta i ordynalnego ujęcia użyteczności. Od czasów „wczesnego Arrowa” środek ciężkości „nowej” ED przesuwa się w kierunku teorii wyboru społecznego, agregacji preferencji, a następnie: polityki energetycznej, bio-ekonomii i ekonomii środowiska. Celem pracy jest zwrócenie uwagi na „horyzontalną mutację” ED. Idee trwałości (sustainability) rozwoju ekonomiczno-społecznego można włączyć do obszaru badawczego „najnowszej” ED: „Dynamic Welfare Eonomics” (Goeffreya Heala), „New Welfare Economics for Sustainability” (Johna Gowdy’ego). W pracy przywołano klasyczne koncepcje Hotellinga, Hartwicka i Solowa, dylemat granic zastępowalności (weak vs strong sustainability), „zielone” mutacje kanonicznych reguł ekonomicznych oraz podkreślono rolę technik dyskonta.
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Dyskontowanie jako przedmiot badań interdyscyplinarnych: ekonomii behawioralnej, etyki oraz teorii zrównoważonego rozwoju

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Rybicki W.
Studia Ekonomiczne
|
2015
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vol. 242
142-166
PL
W artykule rozważa się implikacje postulatów etyczno-pragmatycznych w zakresie wyceny strumieni wielkości ekonomicznych. Imperatyw respektowania idei trwałości rozwoju społeczno-gospodarczego, z jednej strony, a z drugiej - bogata dokumentacja empiryczna zachowań podmiotów decyzyjnych (ewolucji wycen przyszłych zdarzeń - celów, odwracanie preferencji), prowadzą do podważenia paradygmatu zdyskontowanej użyteczności (Samuelsona-Bergsona).Uchylenie założenia stałości stopy dyskontowej (stacjonarnej niecierpliwości) skutkuje niezgodnością dynamiczną programów - taka jest "cena realizmu" w modelowaniu. Z kolei, implementacja dyskonta wykładniczego do modelu Dasgupty, Heala i Solowa (D-H-S) skutkuje paradoksalnymi konsekwencjami - pogwałceniem idei sprawiedliwości międzypokoleniowej. Odnotowuje się również interakcje biologii i ekonomii ("naśladownictwo mechaniki ogólnoprzyrodniczej" przez rzeczywistość ekonomiczno-społeczną). Po części "eseistycznej" i krótkim przypomnieniu nieklasycznych formuł dyskontowania (hiperboliczne, quasi-geometryczne, CADI) przedstawiono się koncepcje dyskontowania log-normalnego i "nad-hiperbolicznego". Podkreśla się następnie rolę agregacji w dyskontowaniu: agregacja indywidualnych czynników dyskontujących ma stwarzać "pomost" łączący ekonomię behawioralną (skala "mikro"), z problematyką społecznej, międzypokoleniowej stopy dyskontowej (skala "makro"). Jest to operacja uśredniania, determinująca pewny równoważnik (immanentnej) niepewności) wielkości "przyszłych" stóp procentowych (stochastyczne ujęcie scenariuszy rozwoju).
EN
In the article the implications of ethical and pragmatic postulates regarding the evaluation of economic quantities streams are discussed. There are two spheres involving the increasing interest in the above mentioned problems: the general ideas of sustainability of socio-economic development, and the second one, finding their roots in the domain of psychology (based on the large empirical material, evidencing the behavior of various subjects). The special emphasis have been put on the evolutions of evaluation of the "validity" of future events and acts when the time passes (in the extreme cases the preference reversal is observed). These findings lead to rejecting the Samuelson- -Bergson paradigm of exponentially discounted sums of utilities (DU) . The main point is questioning the idea of stationary (constant) discount rate (or - a rate of impatience). However, such a change causes loosing of the dynamic consistency of multi-period plans, which, might be viewed as a price for an adequacy in describing of the real processes. The direct implementation of the geometrical discounting into the Dasgupta- -Heal-Solow (D-H-L) model results in the violation of intergenerational equity (paradoxical consequences concerning long-term consumption paths). The interactions between the economics and the biological benchmarks are also mentioned - "socioeconomic processes mimic biological processes". After "essayistic" part, and the short mentioning non-classic discounting formulas (hyperbolic, quasi-geometric, generalized hyperbolic, "CADI") the so called log-normal and "super-hiperbolic" discounting conceptions are present. Subsequently, the role of aggregation of individuals' discount rates for obtaining the social discount rates is stressed: this average operation makes a "bridge" joining the micro- and macroeconomic areas. It also provides the partial antidote against intrinsic uncertainty, characterizing the future.
4

Some reasons why we should teach matrices to students of economics

100%
Rybicki W.
Didactics of Mathematics
|
2012
|
issue 9(13)
55-74
EN
The paper makes up the second part of the series of articles aimed at establishing the usefulness of matrices in the study of contemporary economic sciences. The series was initiated by the present author in his previous article of this subject (Rybicki, 2010). The items chosen to be presented here concern applications of (operating with) matrices in the field of welfare economics and to the description dynamics of economic systems. The first class of matrices we discuss serves as tools for indicating the inequalities of distributions of (finite) commodity bundles (and as devices to “equalize” these distributions). Other considered families of matrices consist of transition matrices of Markov chains. The presented statements are of an elementary character – they are intended to help students feel (and believe in) some uniformity of the content of lectures on mathematics and economics and (in a wider sense) operations research.
5

Further examples of the appearance of matrices (and the role they play) in the course of the economists’ education

100%
Rybicki W.
Didactics of Mathematics
|
2012
|
issue 9(13)
75-90
EN
The paper makes up the third part of the series of articles aimed at establishing the usefulness of matrices for the study of contemporary economic sciences. The series was initiated by the present author in his previous articles of the subject (Rybicki, 2010, 2012). The themes discussed in the present article concern two areas: (i) the surface description of the Markov-type, continuous time stochastic dynamics (with special emphasis placed on “Poisson dynamics” and on families of transition probability matrices and intensity matrices – finite or denumerable spaces of states); (ii) the second is devoted to showing the role of eigenvectors in modeling the economic dynamics.
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