The International Bachelor Econometrics and Operations Research programme focuses on the application of mathematical and statistical techniques to answer economic questions. The academic year is divided into five eight-week blocks, in which you follow two or three courses. Your study load is measured in credits of 28 study hours each. Each academic year consists of 60 credits.
Year one: a diverse kick-off in every way
Your first-year courses contain topics in mathematics, statistics, and economics. You will also receive training in computer programming to learn how to build models and implement mathematical techniques. Your first experience with operational research will consist of analysing and solving optimisation problems by applying these mathematical models.
We work with tutorial groups of about thirty students, which allows for individual attention and intensive guidance. During many of the practical assignments, you will work in groups of around four students.
Year two and three: a topical and practice-oriented approach
During your second year you will focus on more advanced courses in different areas like mathematics, statistics, econometrics and business economics. You will divide your time equally between theory and practice, in small groups during lectures and assignments.
The third year offers many choices. First you get to take a minor (elective courses within or outside the field of Economics, such as Law or Psychology), study abroad at a partner university, or take an internship. In the second half of the year, you will choose a specialisation in one of the following four majors:
- Analytics and Operations Research in Logistics
- Business Analytics and Quantitative Marketing
- Econometrics
- Quantitative Finance
Your major involves two specialisations courses and a seminar. You will complete your programme with a bachelor thesis.
In class
The current 100m world record is 9.58 for men (Usain Bolt) and 10.49 for women (Florence Griffith- Joyner). Can you predict the next world record? You will need a model for this purpose, using the following data.
MEN WOMEN |
Year Time Year Time |
1968 9.95 1968 11.08 |
1983 9.93 1972 11.07 |
1988 9.92 1976 11.04 |
1991 9.90 1976 11.01 |
1991 9.86 1977 10.88 |
1994 9.85 1982 10.88 |
1996 9.84 1983 10.81 |
1999 9.79 1983 10.79 |
2007 9.74 1984 10.76 |
2008 9.72 1988 10.49 |
2008 9.69 |
2009 9.58 |
International character
We specifically aim for an international class room, with many students from abroad. Over the last three years we reached this goal with a very diverse group of students. We welcomed students from many European countries (Germany, France, UK, Italy, Spain, Poland, Romania, Russia), and Asian countries (China, Vietnam, Korea, Indonesia), but also from the US, Canada and Latin-America. This provides an interesting combination of backgrounds in the classroom and we actively stimulate that students with different backgrounds work together.
Study schedules
The Take-Off is the introduction programme for all new students at Erasmus School of Economics. During the Take-Off you will meet your fellow students, get acquainted with our study associations and learn all the ins and outs of your new study programme, supporting information systems and life on campus and in the city.
- Mathematical Logic
- Set Theory
- Mathematical and Strong Induction
- Sequences and Series
- Elementary functions and their graphs
- Combination, inverse and limits of functions
- Analytic Trigonometry and the unit circle
- The concept of the derivative of a function with a single variable
- Partial derivatives of a function of multiple variables
- The Lagrange multiplier method
- Integrals
Statistics is concerned with drawing solid conclusions from available data. Following a brief introduction to the different phases of scientific research, the main focus of this introductory course is on developing the mathematical basis (probability calculus, probability distributions, introduction to statistical testing) and with applications in solving practical questions. The topics are the following:
Introduction to statistics, mean and standard deviation, empirical rule, theorem of Chebychev, axioms of (discrete) probability calculus, sets, computation rules, counting rules, permutations, combinations, conditional probability, Bayes' rule, discrete probability distributions, expected value, variance, binomial distribution, geometric and negative binomial distribution, multinomial distribution, Poisson distribution, moment generating functions, introduction to testing, null hypothesis and alternative hypothesis, significance level, power, P-value, testing with the binomial distribution, sign test, normal distribution, central limit theorem, computations with the normal distribution, z-test for 1 and 2 proportions, goodness of fit test, cross table, test on independence, chi-square distribution.
Some of these topics (such as testing and the normal distribution) will be treated more extensively in later courses.
Guidance (econometrics) consists of two modules:
- Module A: Guidance includes lectures in block 1 plus study progress meetings in block 2 and 3. Each mentor group consists of max. 15 students, accompanied by one mentor (a senior student). Students are informed about studying at the ESE and about effective study methods during group meetings. In addition, three individual meetings will take place, in which the student can discuss the obtained study results with the mentor.
- Module B: Academic Communications Skills. This module takes place in block 2. Students work with online material to practice their presentation skills. Furthermore, students need to make assignments and give a presentation.
- Complex numbers
- Length and angles: the dot product
- Solving systems of linear equations
- Linear independence and spanning sets
- Matrix operations
- The fundamental theorem on invertible matrices
- Subspaces, bases and the dimension of subspaces
- Row space, column space, rank of a matrix: the rank theorem
- Determinants
- The first part of the course deals with the theory of the consumer. Topics covered include consumer choice under certainty and uncertainty, and individual and market demand.
- The second part focuses on the theory of the firm, and includes the topics of firm production and firm cost.
- The last part of the course turns to market structures (monopoly, imperfect competition and perfect competition), to the joint analysis of firm and consumer behavior within a market (general equilibrium theory) and to factor markets.
- Precise definition of limit and continuity of functions
- Pricise definition of bijectivity
- Proving (existence of) limits, continuity and bijectivity with the precise definitions
- Differentiation
- Sequences and series
- Taylor series
- Differential equations
- Multiple integrals
- For all these subjects the emphasis lies on concepts and proofs of the most important results.
The course includes:
- Interactions between money markets and goods markets;
- The impact of government policy on aggregate employment and output;
- Interaction between national economies through international trade and capital flows;
- Insights into the ways that the micro- and macroeconomic features of the economy interact through production, consumption, and economic policy.
Continuous random variables, continuous distributions, moment generating functions, discrete and continuous joint distributions, independence , conditional distributions, conditional expectations, variance, covariance, functions of random variables, transformation methods, Central Limit Theorem, stochastic convergence, sampling distributions.
The course starts by introducing the fundamental data types and operations. After that, control statements, i.e., decision and repetition, are presented. Then, methods, as computations consisting of multiple steps, are given. Lists and arrays, representing data structures storing multiple values, are depicted next. Last, the main concepts of object-oriented programming paradigm, i.e., class and instance, are described.
Meanwhile, students are expected to roll up their sleeves and acquire hands-on experience with the Java programming language. For this purpose, programming assignments will have to be completed by the students using a popular Integrated Development Environment (IDE). Students will develop an algorithmic way of thinking by implementing solutions for elementary computational problems in Econometrics.
- Acquiring knowledge of eigenvalues, eigenvectors, orthogonality, projections, diagonalization, quadratic forms, vector spaces, inner products, norms, distances and vector differentiation.
- Acquiring insight in abstract structures at the required level for Econometrics beyond doing merely computations.
- Acquiring the skills to determine eigenvalues, eigenvectors, diagonalizations, orthogonal bases, orthogonal decompositions, QR factorizations, spectral decompositions, optimal values of quadratic forms and vector derivatives.
- Acquiring skills in proving theorems in matrix algebra and vector calculus.
A typical phenomenon in empirical research is the wish to make statements about an unobservable population on the basis of an observed sample.
The course Statistics aims to facilitate the construction of statistical statements about the population on the basis of a random sample. The statements may concern statistical estimates or statistical hypothesis tests. Moreover, the statistical statements are typically accompanied by information concerning the level of (un)certainty.
In this course, the construction of "good" estimators and "good" tests in parametrical statistical models is considered. In particular, we will focus on the construction of method of moments estimators, maximum likelihood estimators, (uniformly) most powerful tests and likelihood ratio tests.
This course is an introduction in the theory and methods to solve linear programming problems. The topics of the course are:
- Modeling and solving linear programming problems
- Primal and dual (revised) simplex method
- Duality theory
- Sensitivity analysis
- Network simplex method
The topics that are discussed focus on:
- Developing mathematical methods and skills
- Abstract thinking
- Thinking algorithmically
- Acquiring mathematical intuition
The following topics are included:
- Combinatorics
- Recurrence relations
- Graph theory
- Game theory
Combinatorial optimisation deals with finding an optimal solution from a finite set of feasible solutions. Since enumerating this set is practically infeasible in general, one tries to exploit the problem structure to find an optimal solution in a computationally efficient way. In this course, we develop techniques for combinatorial optimisation problems. These techniques include:
- Branch-and-bound
- Lagrangean relaxation
- Maximum flow algorithm
- Hongarian method
- Dynamic programming
The course is primarily theoretical. In this course we use a lot of linear algebra and see its connection with statistics. After the univariate statistics studied in the previous courses, we move to multivariate statistical methods. We start with the geometry of multivariate samples. Then we generalize the univariate methods to multivariate setting. And finally, we study several techniques, which are useful in practice.
- Week 1: Refresh Object-oriented programming Java
- Week 2: Working with interfaces
- Week 3: Working with inheritance
- Week 4: Working with datastructes from the Collections API
- Week 5-6: Libraries, modern Java features
- Week 7: Summary, other programming languages (no exam material)
This course considers the optimisation of functions with and without constraints, both in theory and in practice. The following topics will be covered:
- Analysis of unconstrained problems
- Line search methods
- Newton’s method and variants
- Optimisation of non-differentiable functions
- Analysis of constrained problems
- Algorithms for constrained problems
- Discrete-time Markov chains
- Exponential distribution and the Poisson process
- Continuous-time Markov chains
- Basic queueing theory (M/M/c and variants)
- Gaussian processes (Brownian motion and others)(with applications in econometrics and operations research)
The course focuses on the strategic analysis of markets and contracts under asymmetric information. It does so by using Game Theory in a mathematical, rigorous way.
Econometrics is characterized by the combination of economic research questions, use of empirical data, application of statistical and mathematical methods, and the use of software to estimate and evaluate models. All these topics are extensively discussed in the lectures and practised in the tutorials.
- Lectures and exercise lectures: Introduction to econometrics, research questions, methods. The linear regression model (simple and multiple), method of least squares, testing. Non-linear models, maximum likelihood, some asymptotic theory of estimation and testing. The models and methods are motivated by economic applications and applied in practical examples. The required econometric methods make intensive use of earlier courses in the programme, in particular statistics, matrix algebra and analysis.
- Tutorials: Exercises on theory and applications. Further, some tutorials consist of computer sessions to apply econometric techniques by means of the software package EViews.
The following simulation techniques will be covered:
- Basic set-up of a Discrete-event simulation model
- Formulating complex econometric and OR problems in a simulation model.
- Model validation
- Random number generators
- Methods to generate realisations of random variables
- Discrete event simulation
- Monte Carlo method
- Statistical analysis of simulation results.
- The time-value of money and appropriate discount rate.
- The role of arbitrage in finance
- The value of bonds and stocks
- Market efficiency and financial markets as information processor.
- Risk and return models
- Portfolio theory.
The lectures are a follow-up on the lectures in Econometrics 1. The following topics will be discussed:
- Models with heteroskedasticity and/or serial correlation
- Models with endogenous regressors
- Models for limited dependent variables (logit, probit, multinomial)
After this course the student will have practical and theoretical knowledge of various extensions of the linear model (among which: heteroskedasticity, serial correlation, endogeneity). The student will also have knowledge of models for limited dependent variables (logit model, probit model, multinomial).
The student will be able to apply the theory in practice, and will also gain experience in the analysis of economic data using Eviews.
The objective of the course will be to demonstrate the benefits of using a systematic and analytical approach to decision-making in marketing.
This course teaches and trains writing, presentation and research skills.
- Translating a practical economic decision problem into a mathematical and statistical model
- Solving/estimating model parameters
- Translating the model results into practical implications
- Presenting research findings (both orally and in writing)
Time series analysis concerns modelling sequential observations on economic variables, such as monthly unemployment figures. A suitable time series model can be used for making forecasts and for policy analysis. A key issue in developing a suitable model for time series concerns the dynamic features of economic variables, such as trends, seasonal fluctuations, and business cycles.
The main topics covered in this course are:
- Theory of stationary dynamic processes
- Linear time series models (ARMA)
- Model selection
- Parameter estimation
- Evaluating time series models
- Handling special observations (outliers)
- Forecasting methods and evaluation
- Nonlinear time series models
Students are allowed to replace the Minor with studying abroad, or with an internship.
The elective space is 12 ec when the Minor is rounded off at 12 ec, and 9 ec when the Minor is rounded off at 15 ec.
The Career Skills programme consists of the obligatory course ‘Your Future Career’ and several other 1-credit elective courses from which you can choose one preferred course. In the online course ‘Your Future Career’ you will learn to identify which professional environment and culture are the best match for you and work on various practical job searching skills.
There are many different Career Skills elective courses, for example Personal Effectiveness, Project Management, Managing Complexity and language courses. Some courses are organised jointly with our study associations, such as Model United Nations and the Debate Workshop Cycle.
An Econometrics Major consists of one seminar and two major courses.
Econometricians use methods and techniques drawn from mathematics and statistics to address economic issues and questions. These questions can concern the macroeconomy, finance, microeconomic issues, labor, and various business economic settings. Typically, econometricians examine economic theories, create forecasts, develop multiple scenarios, propose optimal decisions, or evaluate policies. When the examinations are substantially novel and relevant to share with academics, the research findings can be published in academic literature, where other econometricians judge the merits of the work. In many other settings, however, the studies end up in an advice to an end user who can use the forecasts, who decides on the continuation or a change of the policy, who implements a proposed decision, or who picks one of the scenarios for making further plans.
It is important to recognize that such an end user rarely is an econometrician too. An end user can for example be an employee (top level or middle level) in a government, in a company, or in a bank. This implies that rarely an end user can fully grasp every single step that an econometrician has set when creating the product. At the same time, it is often also not possible to present every single step, and perhaps it is also not instrumental for the end user’s intentions. This means that the end user must trust that the econometrician made the right choices during the analysis.
There are various ethical guidelines around, and these usually concern honesty related to for example data cleaning (from raw data to the data to be analyzed), estimation methods, decisions based on statistical inference, trial and error and the reporting. Basically, these guidelines should establish that the final product can be reproduced when a list of choices and also the programming code is provided.
In this course I will initially discuss these guidelines but after that, in the main content of the book, I will address more specific ethical issues that follow from the fact that there is a knowledge asymmetry between the end user and the econometrician. Loosely said, even when the standard ethical guidelines are obeyed, it is still possible to provide an advice that meets a specific request of an end user. For example, it is not difficult to create a forecast that comes close to a desired target of an end user.
This course provides a range of cases where the knowledge asymmetry can be exploited intentionally, even though reproduction still is possible. There are cases where the result crucially depends on a single observation, cases where the statistical test is performed such that an outcome is manipulated, and for example cases where initial configurations dominate the result, even though it is very difficult to see.
The thesis in an individual piece of research about a subject of the Bachelor programme. More information about topics, supervisors and the writing process can be found on the thesis hub on Canvas.
Disclaimer
The overview above provides an impression of the curriculum for this programme. It is not an up-to-date study schedule for current students. They can find their full study schedules on MyEUR.