The Graduate School of Finance and Financial Accounting

GSFFA


 

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The Graduate School of Finance and Financial Accounting (GSFFA) offers programmes for gaining a Doctoral (Ph.D.) degree in Finance or in Financial Accounting. The full programme is open for graduate students who fill the requirements for graduate studies at the Helsinki School of Economics, at the Swedish School of Economics and Business Administration, or at the University of Vaasa. Prerequisites are a Master´s degree in Finance or Financial Accounting or in a closely related field. Individual courses are open for all graduate students in Finland in Finance, Financial Accounting, or in a closely related field. The teaching language is English. Study time is expected to be 4 years.

The Graduate School of Finance and Financial Accounting co-ordinates Doctoral level education in finance and in financial accounting among three dominant research and educational units within the area; the Helsinki School of Economics (the Department of Accounting), the Swedish School of Economics and Business Administration (the Department of Finance and the Department of Accounting), and the University of Vaasa (the Department of Accounting and Finance). Currently there are 20 professors and around 15 Ph.D. level researchers involved in teaching and supervising activities, as well as a number of guest lecturers.

The Graduate School offers advanced level courses, and supervision of students within existing research projects, in two doctoral programmes:

Within a programme, a part of the courses (about 20 credit units) are mandatory and common for all students within that programme, while the remaining credit units can be chosen among the alternative courses offered within the specific programme. After one year, each student is assigned a supervisor from one of the two fields above, and a thesis committee with three members.

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Studies at GSFFA

Curriculum requirements

The curriculum for the degree of Ph.D. in Finance, or Financial Accounting, follows the Finnish standard requirements. Prerequisites are a Master´s degree. In addition, the student has to get an additional 40 credits in the form of courses, and do research leading up to a Ph.D. thesis.

A standard course, giving approximately 50 hours of lectures, 20 hours of assignments in class and a smaller project assignment will usually give 5 credits. There are also smaller courses and seminars, giving 1-3 credits.

Application procedure

Applicants wanting to enroll in the Graduate School of Finance and Financial Accounting should write a letter to the Board of the school. The letter should contain a formal application to the school, together with the following information:

  1. a short curriculum vitae (1 separate page),
  2. a more complete curriculum vitae including the list of publications and earlier research activity,
  3. the contact information of the candidate,
  4. a financing plan for studies,
  5. a letter of recommendation,
  6. copies of examinations earned (Master's or Licentiate's) and a transcript of courses taken,
  7. university and department for Ph.D. studies,
  8. a research plan, including a one page summary and time schedule,
  9. a description of the current status of the candidate's research, and
  10. the name(s) of the potential supervisor(s).

If the candidate already belongs to some other graduate school under KATAJA, he / she should tell it in the application.

Each year at the end of spring, preferably 10 Ph.D. students will be accepted, with the possibility to extend the amount to a maximum of 15 depending on the quality of the applicants. Accepted applicants are expected to formally be registered as Ph.D. students either at the Helsinki School of Economics, at the Swedish School of Economics and Business Administration, or at the University of Vaasa. For the next GSFFA application, see: Application announcement.

 

 

Financing the Studies

The school aims to offer grants (A18) each year to new students in need of financing. The grants are given mainly for 1 year at a time, with the possibility to extend successfull Ph.D. students' grants for an additional year at a time during a time period of maximum 4 years. In addition, these students are offered working facilities at the Helsinki School of Economics, at the Swedish School of Economics and Business Administration, or at the University of Vaasa.

There are no tuition fees.

The organisation of the studies

The first four terms will be centered on coursework and seminars. The doctoral student is expected to take 40 credits, and to come up with a thesis proposal by the end of the third term. At the end of the fourth term, the student is expected to present his thesis proposal at a workshop arranged by the programme. In order to stay on the programme, the students are required to have 40 credits and an accepted thesis proposal at the end of the fourth term.

After four terms on the programme, all students (henceforth called doctoral candidates) are assigned a main supervisor (from the school / university at which the student is officially registered) and a Ph.D. committee, consisting of three Ph.D. level supervisors. The purpose of the committee is to guide the doctoral candidates in their thesis work. Students are also assigned reaseach groups, within which seminars will be held on regular basis during these last four terms. One major workshop will be held at the end of each academic year (end of spring) and all students from their fourth term onwards are expected to present papers on this workshop. Also workshops on specific topics, with international participants, will be arranged in order to give the doctoral candidates sufficient feedback concerning their thesis work. Total study time is expected to be 4 years.

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Research Groups

Asset pricing. Anders Löflund (leader), Tom Berglund, Johan Knif, Eva Liljeblom, Martti Luoma, Seppo Pynnönen, and Marianne Stenius.

Corporate finance. Matti Keloharju (leader), Mats Hansson, Kenneth Högholm, Eero Kasanen, Stefan Sundgren, Arto Suvas, Sami Torstila, and Paavo Yli-Olli.

Derivatives and hedging. Jari Käppi (leader), Tom Berglund, Antti Kanto, Johan Knif and Vesa Puttonen.

Financial ratios. Timo Salmi (leader), Bo-Göran Ekholm, Kari Järvikari, Juha Kinnunen, Erkki K. Laitinen, Teija Laitinen, Arto Suvas, Jan Wallin, Ilkka Virtanen, and Paavo Yli-Olli.

Financial reporting. Pontus Troberg (leader), Bo-Göran Ekholm, Markku Koskela, Jarmo Leppiniemi, and Jan Wallin.

Market microstructure and institutions. Eva Liljeblom (leader), Kaj Hedvall , Kenneth Högholm, and Benny Jern.

Faculty and Researchers

Departments

The following departments partcipate in the Graduate School of Finance and Financial Accounting:

Faculty

The faculty of the Graduate School of Finance and Financial Accounting consists of persons with a tenured position: professors, associate professors, and lecturers. The staff from fall 2000 onwards is listed below, with their affiliation and areas of interest.

Researchers

The following Ph.D. level researchers are actively involved in the Graduate School of Finance and Financial Accounting, as lecturers, members of research teams, and supervisors and thesis commitee members for Ph.D. students.

Visiting faculty

During the recent years, the following persons, among others, have been actively enrolled in teaching / supervisor activities for gradual students in Finance and Financial Accounting. The Graduate School of Finance and Financial Accounting intends to continue the co-operation with them if possible.

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The structure of the Ph.D. exam

The Graduate School of Finance and Financial Accounting offers a Ph.D. exam which includes the following moments:

Depending on the selected programme (Programme of Finance or Programme of Financial Accounting), 40 credits should be obtained so that both the requirements of the programme, as well as the requirements of the school / university at which the student is registered, are fulfilled.

A student who is accepted to a programme should, within one months time from the acceptance, present to the programme commitee member of the student´s own school an acceptable study plan describing the courses planned for the exam. An accepted plan must be consistent with the requirements of 1.) the school / university at which the student is registered, and 2.) the selected programme. The decision to accept a study plan is made by the programme commitee member in question, who also decides upon potential deviations from mandatory moments of the programme (compensatory courses).

Includes thesis work and the parts of the research process (such as the thesis proposal, participation in research seminars, and presentations at workshops) according to the following schedule:

The coursework (40 credits) within the Programme of Finance should include

The coursework (40 credits) within the Programme of Financial Accounting should include

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Courses 2002-2003


Managing the Doctoral Research (and GSFFA Research Workshop) (HKKK & VY)

An intensive course and tutorial for doctoral students. Part "Managing the Doctoral Research (an introduction to doctoral studies)", a 2-day course is compulsory to the first year students of the Graduate Program (part of the 120 credits of research work). The second part "GSFFA Research Workshop" is for students with presentable research plans and reports, with full faculty present.

Course objectives:
Part "Managing the Doctoral Research" is to introduce the doctoral candidates to the realities of doing scientific research, and to strengthen the students´ knowledge of scientific methods and research in finance and financial accounting. The research tutorial is to provide feedback and guidance to the doctoral students in planning and proceeding with their doctoral research.

Literature:
DAVIS, G.B. & PARKER, C. A. : Writing the Doctoral Dissertation. A Systematic Approach, Barron´s Educational Series, Inc. STERNBERG, D.: How to Complete and Survive a Doctoral Dissertation, St. Martin´s Press. GOTHONI, R.: Oletko neuvoton. Lohdutuksen sanoja opinnäytteen laatijalle, Yliopistopaino. RYAN, B. & SCAPENS, R. W. & THEOBALD, M. : Research Method and Methodology in Finance and Accounting. Assigned material.

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A. Courses in Finance (F) and in Financial Accounting (FA)

Advanced Corporate Finance (HKKK)

5 credits. 19. – 23.11.2002, Helsinki. Instructor: Professor S.A. Ravid (Rutgers University).

Course Objectives:
To familiarize the students with recent advances in corporate finance. In particular, the following topics will be discussed: 1) Basic tools of game theory; 2) Review of agency theory, signalling, and irrelevance theorems; 3) Capital structure; 4) Interactions; 5) Mergers; 6) Dividends; 7) Design of securities; 8) Bankruptcy; 9) Debt maturity; 10) Other features of debt; and 11) IPOs.

Literature:
A reading package will be distributed to the participants of the course.

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Advanced Financial Statement Analysis

(HKKK)

5 credits. Fall 2003, Helsinki. Instructor: Professor Joshua Livnat (New York University), tentative.

Course objectives: To familiarize the students in recent theoretical and empirical developments in financial statement analysis, covering the following main topics: 1) Earnings and security prices; 2) Valuation-relevant information beyond earnings; 3) Valuation; 4) Investment strategies; 5) Selection of accounting methods; 6) "New economy" research.

Literature: A package of readings provided by the lecturer.

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Stochastic Discount Rate Approach to Asset Pricing (HKKK)

5 credits. Spring / Fall 2003, Helsinki. Instructor: Professor Tuomo Vuolteenaho (Harvard University), tentative.

 

Course Objectives: This course covers some of the basic asset pricing machinery: The stochastic discount factor (SDF) present value formula. First, the course develops the basic mechanics of the SDF formula as applied to one-period asset returns and multi-period cash flows. Second, the course examines some famous empirical puzzles using the SDF framework. All effort is made to minimize technicalities and maximize economic intuition.

 

Literature: A package of readings provided by the lecturer.

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Analysis of Financial Time Series (SHH & VY)

5 credits. 13.1. – 25.4.2003, Vaasa. Instructors: Professor Johan Knif (SHH) and Professor Seppo Pynnönen (VY).

Aim: To provide the students with sufficient skills to apply modern time series methods in analyzing financial time series. The course is suitable on graduate as well as post-graduate level. The course covers the following four inter-related parts: basic univariate time series analysis, vector autoregressive models, state space modeling and frequency domain analysis.

Requirements: Research Methods in Finance (SHH codes 1725 and 1771) or a corresponding course is recommended.

Literature: Mills, T.C.: The Econometric Modelling of Financial Time Series. Cambridge University Press, 2000, 2nd ed. Articles and additional material according to instructions.

 

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Volatility Modelling and Empirical Methods in Asset Pricing

(SHH)

5 credits. 13.1. – 25.4.2003, Vaasa. Instructor: Professor Gregory Koutmos (Fairfield University).

 

Aim: This seminar explores recent developments in modelling time-varying second moments and crossmoments as they relate to dynamic asset pricing with primary emphasis on equities.

Requirements: Basic knowledge of financial econometrics

Literature: Research articles according to instructions.

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Mathematics of Financial Derivatives (SHH)

5 credits. 9.9 – 13.12.2002, Vaasa. Instructors: Professors Johan Knif (SHH) and Seppo Pynnönen (VY).

Aim: The objective of this course is to introduce the student to the mathematics utilised for pricing of financial derivatives and to provide the student with a basic understanding of the mathematical ideas and technical tools used in modelling the characteristics of derivatives, interest rates, and currencies with continuous time stochastic processes.

Requirements: Basic knowledge in economic mathematics and risk management.

Literature: Neftci, S.N.: An Introduction to Mathematics of Financial Derivatives. Academic Press, London 2000, 2nd ed. Selected parts of Duffie, D.: Dynamic Asset Pricing Theory. Princeton University Press, 1996. Pliska, S.R.: Introduction to Mathematical Finance: Discrete Time Models. Blackwell Publishers, 1997.

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An Introduction to Mathematical Finance

(SHH)

5 credits. Spring 2003, Helsinki. Instructor: Dr. Andriy Andreev (SHH).

Aim: The structure of the course is as in Ross, S. R. We start with probability basics. Then proceed by introducing Geometric Brownian Motion (GBM). Discrete approximation of GBM is used for derivation of Black-Scholes call option formula and for algorithmic evaluation of price of American put option. Concept of Arbitrage is discussed and extended by introducing utility functions. Pricing of exotic options are treated in two ways: by Monte Carlo simulations (with special emphasis on variance reduction) and by multiperiod binomial approximations. Finally, we will consider examples of real data (simple and small) when GBM is not flexible enough for modelling purposes, and hence, suitable extensions will be discussed. Some topics will be covered in more generality than in Ross, S.R.

Requirements: Ekonomisk Matematik

Literature: Ross, S.M.: Introduction to Mathematical Finance. Cambridge University Press, 1999. Arrow, K.J.: Aspects of the Theory of Risk-Bearing. Yrjö Jansson Säätiö. Research papers (to be announced).

 

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Workshops in Finance and in Financial Accounting

The Annual GSFFA Research Workshop (HKKK, SHH & VY)

May 2003, Helsinki.

A research workshop where fourth term GSFFA students present their research proposals, and GSFFA doctoral candidates their research reports. Arranged in connection to the course "Managing Doctoral Research". Mandatory for all GSFFA students.

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The 4th NoonToNoon Meeting in Insurance and Financial Mathematics – Theory and Practice

10.10 – 11.10.2002, Åbo Akademi University, Department of Mathematics

 

The aim of the meeting is to bring together practitioners of mathematics and statistics in insurance and financial markets and researchers and graduate students in different academic institutions doing research in or related to insurance and financial mathematics.

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B. Courses in Research Methodology and Research Philosophy

Estimation and Inference in Econometrics (SHH)

5 credits. 13.1 – 25.4.2003, Helsinki. Instructor: Professor Gunnar Rosenqvist, part 1, and Professor Seppo Pynnönen, part 2.

 

Aim: The course considers estimation and inference in econometrics at an intermediate level. Estimation and inference in econometrics relies heavily on maximum likelihood methods. The course considers the general theory of maximum likelihood estimation and testing, general linear models and econometric applications of maximum likelihood methods. The course consists of two parts, which can be taken separately. Part I considers basic material like general maximum likelihood theory. Part 2 considers econometric applications of maximum likelihood methods.

 

Requirements: Introduction to Research Methods (SHH code 7777) and Econometrics (SHH code 3606). Probability Theory (SHH code 3614) is strongly recommended.

 

Literature: To be announced.

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Kvantitatiivinen empiirinen tutkimus (HKKK)

4 credits. Spring 2003, Helsinki. Instructor: Professor Pekka Korhonen.

 

Tavoite: Opiskelija tuntee tavanomaisten havaintoaineiston tilastollisten analysointi-menetelmien perusteet ja osaa opastettuna soveltaa niitä erityisesti liiketaloudellisia ilmiöitä kuvaavien havaintoaineistojen käsittelyyn.

 

Kirjallisuus: Agresti, A. and Finlay, B.: Statistical Methods for Social Sciences. Prentice Hall. Agresti, A: Categorial Data Analysis. John Wiley. Sharma, S.: Applied Multivariate Techniques. John Wiley & Sons. Mardia, K.V., Kent, J.T. and Bibby, J.M.: Multivariate Analysis. Academic Press.

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Taloustieteen matemaattiset menetelmät (HKKK)

4 credits. Fall 2002, Helsinki. Instructor: Professor Tomi Seppälä.

 

Sisältö: Mallin tasapaino, komparatiivinen statiikka, optimointi, dynamiikka ja niiden tarvitsemat matemaattiset menetelmät, differentiaali- ja differenssiyhtälöt.

 

Kirjallisuus: Klein, M.W.: Mathematical Methods for Economics, Addison-Wesley Longman Publishing Co, 1998. Lambert, P.J.: Advanced Mathematics for Economists, Static and Dynamic Optimization, Blackwell Publishers, 1995. Simon, C.P., and L. Blume: Mathematics for Economists, W.W. Norton & Co, New York, 1994.

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Matemaattinen optimointi (HKKK)

4 credits. Spring 2003, Helsinki. Instructor: [TBA].

 

Tavoite: Opiskelija oppii tuntemaan lineaarisen optimointiprobleeman rakenteen keskeiset ominaisuudet ja ratkaisutavat, hallitsemaan epälineaarisen optimoinnin keskeiset käsitteet, optimiehdot ja ratkaisutavat sekä tutustuu peliteorian ja monitavoiteoptimoinnin alkeisiin.

 

Kirjallisuus: Salo, S.: Matemaattinen optimointi, luentomoniste, Hki 1998, Luenberger, D.; Linear and Nonlinear Programming, 2nd ed. Addison-Wesley, Inc., 1984.

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Ekonometria (HKKK)

4 credits. Spring 2003, Helsinki. Instructor: Professor Antti Kanto.

 

Tavoite: Opiskelija hallitsee yleisimmät ekonometriset menetelmät ja tuntee niiden käytön rajoitteet.

 

Kirjallisuus: Dougherty, C.: Introduction to Econometrics, 2002. ISBN 0-19-877643-8.

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Rahoitusmarkkinoiden ekonometria (HKKK)

4 credits. Spring 2003, Helsinki. Instructor: Hannu Kahra.

 

Tavoite: Opiskelija pystyy itsenäisesti käsittelemään rahoitusteorian malleja R-kieltä käyttäen.

Kirjallisuus: Gourieroux, C., and J. Jasiak: Financial Econometrics, Princeton University Press, 2001.

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Econometrics (VY)

3 credits. Fall 2002, Vaasa. Instructor: Professor Seppo Pynnönen (VY).

 

Tavoite: Perehdyttää opiskelija (empiirisen) ekonometrian tutkimuksen perusteisiin, mallintamiseen ja käytännon toteuttamiseen.

 

Kirjallisuus: Rama-Nathan, R.: Introductory Econometrics with Application, 4th ed. HJB, 1998.

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Lineaarialgebra (VY)

3 credits. Fall 2002, Vaasa. Instructor: Lecturer Juha Vuolle-Apiala (VY).

 

Tavoite: Perustiedot lineaarisista vektoriavaruuksista, determinanteista, matriiseista, ominaisarvoista ja lineaarisista yhtälöryhmistä, sekä antaa valmiudet niiden soveltamiseen taloustieteissä ja tekniikassa.

 

Kirjallisuus: Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons.

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Todennäköisyyslaskenta ja stokastiikka (VY)

3 credits. Spring 2003, Vaasa. Instructor: Lecturer Juha Vuolle-Apiala (VY).

 

Tavoite: Täydentää todennäköisyyslaskennan tietoja ja johdattaa stokastisten prosessien käyttöön satunnaisilmiöiden mallintamisessa.

Kirjallisuus: [TBA].

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Econometric Analysis of Panel Data (FPPE)

Fall 2002, Helsinki. Instructor: Professor Steve Bond (The Institute for Fiscal Studies / Nuffield College).

 

Aim: The course will cover estimation methods and specification tests for linear panel data models. The implementation of these methods using DPD98 for Gauss will be covered, and an application to the estimation of production functions will be discussed.

Literature: see http://www.valt.helsinki.fi/staff/jzrytkon/ER202/ER202_sb_rl.doc.

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C. Courses in Economics

Microeconomic Theory (FPPE)

Fall 2002, Helsinki. Instructors: Professor Juuso Välimäki (HKKK).

 

Literature: Mas-Colell, Whinston and Green: Microeconomic Theory, Oxford University Press, 1995.

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Topics in Applied Microeconometrics (FPPE)

5 credits. Fall 2002, Helsinki. Instructors: Professor Almas Heshmati (The United Nations University, WIDER).

 

Litetarture: Textbook and handbook chapters. Selection of journal articles.

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Mikroteoria (HKKK)

4 credits. Fall 2002, Helsinki. Instructor: Mikko Leppämäki

 

Tavoite ja sisältö: Syventää mikrotaloustieteen opintoja sekä analyysimenetelmien että talouden instituutioiden tarkastelun osalta. Kuluttajan teoriassa perehdytään dualiteetti-teoriaan, yrityksen ja markkinoiden analyysissä epävarmuuden ja täydellisen informaation ongelmiin. Lisäksi johdatellaan talouden yleisen tasapainon ja hyvinvoinnin analyysiin.

 

Kirjallisuus: Jehle, G. and Reny, P.: Advanced Microeconomic Theory.

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Avotalouden makroteoria

(HKKK)

4 credits. Fall 2002, Helsinki. Instructor: Jouko Vilmunen.

 

Tavoite ja sisältö: Kokonaistaloudellinen tasapaino avoimessa taloudessa: katsaus keskeisiin makroteoreettisiin malleihin avotalouden näkökulmasta. Painotus kansantalouden vakauden, valuuttakurssijärjestelmien ja vaihtoehtoisten talouspolitiikkojen välisissä kytkennöissä.

 

Kirjallisuus: Romer, D.: Advanced Macroeconomics, McGraw-Hill 1996.

 

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Avancerad Mikroekonomisk Teori med Tillämpningar (SHH)

5 credits. 13.1. – 25.4.2003, Helsinki. Instructor: [TBA].

 

Mål: Att ge deltagarna en översikt över den moderna mikroekonomiska teorins analysverktyg och applikationsmöjligheter. Deltagarna får uppöva sin förmåga att strukturera och lösa empiriska problem utgående från den sammanhängande referensram som mikroekonomisk teori erbjuder. Deltagarna lär sig också utnyttja ekonometrins verktyg till att få fram information ur existerande ekonomisk statistik.

 

Förkunskaper: Prisbildning och marknader, Economics of Information and Organisation, samt Economics of Strategy.

 

Kurslitteratur: Hoffman, E. och Binger, B. R.: Microeconomics with Calculus. Addison-Weslsey. Molho, I.: The Economics of Information. Blackwell. Philips, L.: Competition Policy: A Game-Theoretic Perspective. Cambridge University Press. Studenmund, A.H.: Using Econometrics, A Practical Guide. Addisson Wesley Longman

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Fördjupad Makroekonomisk Teori och Metod (SHH)

5 credits. 9.9. – 13.12.2002, Helsinki. Instructor: Professor (acting) Staffan Ringbom (SHH).

 

Mål: Kursen avser att erbjuda en orientering i modern makroekonomi i syfte att utveckla deltagarnas förmåga att tillgodogöra sig makroekonomiska forskningsresultat såsom de typiskt presenteras för professionella ekonomister. Speciell vikt fästs vid att utveckla deltagarnas metodologiska kunskaper i enlighet med vad som krävs för ett framgångrikt avhandlingsarbete.

 

Kurslitteratur: Romer, D.: Advanced Macroeconomics. McGraw-Hill. Persson, T. and Tabellini, G.: Political Economics – Explaining Economic Policy. MIT Press. Berndt, E.: The Practice of Econometrics: Classics and Contemporary. Addison-Weslsey..

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Mikrotalous II

(VY)

5 credits. Spring 2003 (starting 6.3.2003), Vaasa. Instructor: [TBA].

 

Tavoite: Perehdyttää opiskelija tuoreimpaan mikrotalousteoriaan ja sen sovellutusmahdollisuuksiin. Syventää opiskelijan valmiuksia mikrotaloustieteelliseen analyysiin.

 

Edeltävät opinnot: Mikrotalous I. Suositellaan Matemaattinen analyysi.

 

Kirjallisuus: Gravelle, H, R. Rees, "Microeconomics", 2 painos. Longman 1992. H. Varian, "Microeconomic Analysis", 3 painos. W. W. Norton & Company, 1992. New York. London.

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Makrotalous II

(VY)

5 credits. Fall 2002 (starting 5.11.2002), Vaasa. Instructor: [TBA].

 

Tavoite: Perehdyttää opiskelija tuoreimpaan makrotalousteoriaan ja sen sovellutusmahdollisuuksiin.

Edeltävät opinnot: Makrotalous I. Suositellaan vahvasti Dynaamiset systeemit ja Matemaattinen analyysi.

 

Kirjallisuus: Scarth, W.M.: Macroeconomics, An Introduction to Advanced Methods. Harcourt Brace & Company. Branson, W.H.: Macroeconomic Theory and Policy. Harper & Row.

 

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Organisation

The Graduate School of Finance and Financial Accounting has a Board, with three members, one from each of the three schools. Among its members, the Board selects each year a Director (from one of the three schools). The Board also selects, for each of the two programmes, a Programme committee, consisting of three members (one representant for each of the three schools).

The current Board is:

The Programme committees are:

The external financing to the programme is directed to each of three schools / universities in direct proportion to 1.) the number of grants offered to students of that school (if the external financing is to be used for student grants), or 2.) the costs for courses given by that school (if the external funding has been obtained to finance specific graduate courses).

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