Inscribirse aquí
All of our online courses are recorded and will be made available to all registrants for 90 days after the session ends.
- 2 días
- En línea a través de Teams
- Stata
Overview
This comprehensive two-day introductory mathematics course equips students with essential mathematical tools required for success in econometrics. With a focus on both linear algebra and calculus, students will gain the theoretical grounding and problem-solving skills needed to confidently tackle statistical modelling and data analysis.
Course Aims & Objectives
- Provide foundational knowledge in key mathematical areas including calculus and linear algebra.
- Prepare students to engage with advanced econometric techniques such as regression analysis and maximum likelihood estimation.
- Develop mathematical reasoning skills applicable across economics, statistics, and quantitative research.
Key Skills Acquired
By the end of the course, students will understand:
-
Systems of linear equations and solution methods.
-
Matrix operations, transposition, determinants, and inverses.
-
Vector spaces, eigenvalues, and quadratic forms.
-
Calculus basics: derivatives, differentials, concavity/convexity.
-
Techniques in unconstrained optimisation for functions of a single variable.
Learning Outcomes
- Mathematical Foundations: Gain essential knowledge in algebra and calculus to support the study of econometrics.
- Proficiency in Mathematical Techniques: Understand and apply key mathematical tools used in econometric analysis.
- Quantitative Skills: Develop skills in handling data, constructing models, and interpreting mathematical results.
- Critical Thinking: Apply logical reasoning and structured problem-solving approaches to real-world economic problems.
Course Structure
Delivery Format: Two-Day Intensive
- Lectures: 4 sessions (2 hours each)
- Tutorials/Workshops: 2 sessions (1 hours each)
Agenda
Day 1:
- Systems of linear equations
- Solving systems: substitution, elimination
- Matrix notation & basic operations
- Transposition
- Solving economic models using matrix equations (e.g., input-output analysis)
- Real-time problem-solving using short exercises
- Determinants and properties
- Inverse of 2.2 and 3.3 matrices
- Cramer’s Rule
- Intro to eigenvalues & diagonalisation (essential conceptual grounding)
- Working with matrix inversion in economic models
- Identifying stability via eigenvalues in simple dynamic systems
Day 2:
- Derivatives and differentials
- Rules of differentiation
- Concavity, convexity, inflection points
- Taylor expansion and Mean Value Theorem
- Marginal analysis
- Cost, revenue and profit functions
- Approximating functions with Taylor Series
- First and second-order conditions
- Unconstrained optimisation
- Optimisation over closed intervals
- Maximising/minimising utiity and profit functions
- Economic interpretation of first and second-order conditions
- Real-world problems using optimisation (e.g cost minimisation, revenue maximisation)
- Introduction to interpreting mathematical results in the context of econometric models (e.g. MLE intuition via univariate log-likelihoods)
Course Timetable
Reading List
Surveys for Background Reading:
- de Chaisemartin, C., and X. D'Haultfœuille (2023), “Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey,” Econometrics Journal 26, C1-C30
- Roth, J., P.H.C. Sant’Anna, A. Bilinksi, and J. Poe (2023), “What’s Trending in Difference-in-Differences: A Synthesis of the Recent Econometrics Literature,” Journal of Econometrics 234, 2218-2244.
- Baker, A., B. Callaway, S. Cunningham, A. Goodman-Bacon, P.H.C. Sant’Anna (2026), “Difference-in-Differencs: A Practitioner’s Guide,” Journal of Economic Literature 64, 498-557.
- Wooldridge, J.M (2026), “Recent Advances in Difference-in-Differences with Panel Data,” manuscript.
Journal Articles
- Borusyak, K., X. Jaravel, and J. Spiess (2024), “Revisiting Event Study Designs: Robust and Efficient Estimation,” Review of Economic Studies 91, 3253-3285.
- Callaway, B. and P.H.C. Sant'Anna (2021), “Difference-in-Differences with Multiple Time Periods,” Journal of Econometrics 225, 200-230.
- Goodman-Bacon, A. (2021), “Difference-in-Differences with Variation in Treatment Timing,” Journal of Econometrics 225, 254-277.
- Lee, S.J., and J.M. Wooldridge (2026), “A Simple Transformation Approach to Difference-in-Differences Estimation for Panel Data,” forthcoming, Journal of Business and Economic Statistics.
- Lee, S.J., and J.M. Wooldridge (2026), “Simple Approaches to Inference with Difference-in-Differences Estimators with Small Cross-Sectional Sample Sizes,” working paper. https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=5325686
- Roth, J. (2022), “Pre-test with Caution: Event-study Estimates After Testing for Parallel Trends,” American Economic Review: Insights 4, 305-322.
- Sun, L. and S. Abraham (2021), “Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects,” Journal of Econometrics 225, 175-199.
- Wooldridge, J.M. (2023), “Simple Approaches to Nonlinear Difference-in-Differences with Panel Data,” Econometrics Journal 26, C31-C66.
- Wooldridge, J.M. (2025), “Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators,” Empirical Economics Volume 69, 2545–2587.