Research Seminar I

2026/2027

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

Department of Economics

Course type:

Compulsory course

When:

1 year, 1, 2 module

Instructor

Molchanov, Pavel S.

Course Syllabus

Abstract

The purpose of the Research Seminar is to build the analytical competence that contemporary economic research requires: the ability to read a paper's methods section and judge whether its identification strategy and inference are sound, and the ability to design and defend such a strategy in a student's own work. In practice this competence rests on a specific, well-defined toolkit – linear algebra, probability theory, and mathematical statistics. The seminar assumes heterogeneous prior mathematical backgrounds among students and is delivered without the use of computers, in a lecture-and-seminar format. Each week is organised around a question a referee, discussant, or thesis advisor would actually ask of an applied paper (“is this specification identified?”, “why should I believe this standard error?”, “what if the regressor is correlated with the error?”), worked through on applied examples.

Learning Objectives

• To develop the capacity to critically read empirical economics papers – recognising identification assumptions, evaluating whether the reported inference is valid, and judging whether an estimate can be trusted. To build the mathematical and statistical foundation – linear algebra, probability theory, mathematical statistics – that underlies the methods section of contemporary applied and theoretical economics research. To connect every analytical tool to a concrete research decision – how to specify a model, whether an estimator can be trusted, how to defend a chosen identification strategy – using one running example throughout, in the same way these decisions arise in an actual paper. To prepare students to design, defend, and eventually execute their own empirical or theoretical research project, including the Master's thesis.

Expected Learning Outcomes

• recognise when a regression specification in a published paper is not identified (e.g. through redundant or collinear controls) and evaluate whether the authors' specification is sound, using rank and eigenvalue/condition-number arguments
• reproduce, from first principles, the derivation of the OLS estimator as an orthogonal projection
• correctly interpret the asymptotic claims that populate applied papers – “the estimator is approximately normal,” “standard errors follow from the Delta Method” – by being able to state and prove the underlying theorems (the Weak Law of Large Numbers, the Central Limit Theorem via convergence of moment generating functions, the Delta Method) rather than taking them on faith
• assess whether an estimator proposed in a paper is efficient, by deriving Maximum Likelihood estimators, computing the score and Fisher information, and checking efficiency against the Cramér–Rao lower bound
• construct, and correctly interpret, the hypothesis tests and confidence intervals that populate the results tables of empirical papers, under both normal and asymptotic sampling

Course Contents

• Week 1: Vectors, Inner Products, and the Geometry of Correlation
• Week 2: Rank, Determinants, and the Inverse
• Week 3: Eigenvalues, Projections, and Quadratic Forms
• Week 4: Probability Foundations
• Week 5: Random Variables, Distributions, and Moments
• Week 6: Parametric Families, Heavy Tails, and Jensen's Inequality
• Week 7: Multivariate Distributions and Conditional Expectation
• Week 8: Multivariate Normal Distribution and the Law of Large Numbers
• Week 9: The Central Limit Theorem (Proved) and the Delta Method
• Week 10: Maximum Likelihood Estimation
• Week 11: OLS as a Projection, the Gauss–Markov Theorem, and Instrumental Variables
• Week 12: Hypothesis Testing, Confidence Intervals, and Quantile Regression

Assessment Elements

• Weekly control tests (simple average of all tests held during the course, ≈10 in total)
• Midterm exam

Interim Assessment

• 2026/2027 2nd module
  0.7 * Weekly control tests (simple average of all tests held during the course, ≈10 in total) + 0.3 * Midterm exam

Bibliography

Recommended Core Bibliography

• The foundations of econometric analysis, , 1996

Recommended Additional Bibliography

• Modern econometric analysis : surveys on recent developments, , 2006

Authors

• Brodskaia Natalia Nikolaevna
• Молчанов Павел Сергеевич