Spring semester 2026

Credits
5 ECTS

Teaching method
Classroom instruction.
2x2 lectures per week for 7 weeks + 2 tutorials.

Language
English.

Examination
Individual oral examination, no aids allowed.

Assessment
Pass/No pass, internal co-examination (re-exam oral)

Lecturers
Phillip Heiler
Chen Huang

Course description
The course is split into 2 modules:

Module one (3 weeks) covers probability theory and asymptotic analysis of extremum estimators and statistical tests. The class of extremum estimators includes but is not limited to maximum likelihood, (nonlinear) least squares and generalized method of moments, which may all be defined as solutions to maximisation/minimisation problems.

The second module (4 weeks) of the course is about asymptotic theory for nonparametric, semiparametric, and machine learning estimators. Examples include, but are not limited to, kernel methods for densities and regression, generalized random forests, and deep neural networks. It also covers semiparametric inference using machine learning and other methods for structural parameters, causal inference, missing data, and heterogeneity analysis. 

Both modules include programming applications.

Academic prerequisites
Students should have a basic understanding of probability theory, asset pricing, macroeconomics, econometrics. 

For PhD students at AU (ECON), this course has been pre-approved as an internal BSS PhD course equivalent to 5 ECTS.

Contents
Module 1:

• Modes of convergence
• Laws of large numbers and central limit theorems
• Uniform laws of large numbers
• Identification of econometric models and consistency of extremum estimators
• Asymptotic normality of extremum estimators, and asymptotic variance estimation
• Efficiency of maximum likelihood and GMM estimators
• Properties (size and power) of classical tests.

Module 2:

• Nonparametric density estimation
• Nonparametric regression models and estimation
• Advanced nonparametric regression and machine learning models for function approximation
• Semiparametric models, efficiency, estimation, and inference
• Debiased machine learning for causal/structural parameters and other semiparametric problems
• Machine learning for heterogeneity analysis

If time permits, additional material may be incorporated to reflect recent developments in the literature.

Description of qualifications
Knowledge and understanding of:

• of the mathematical and statistical foundations of large sample estimation theory
• of advanced estimation methods for empirical economic research and their properties
• of proofing techniques for deriving properties of econometric methods
• of fundamental challenges in the theoretical analysis of econometric methods
• of quantitative programming techniques using statistical software such as R.

Skills to:

• to derive, discuss, and compare the properties of parametric, nonparametric, semiparametric, and machine learning estimators
• to conduct estimation and statistical inference in econometric models
• to discuss and reflect technical assumptions and their consequences on estimation and inference
• to implement and interpret outputs of state-of-the-art methods using statistical software in empirical applications and simulation designs.

Competences to:

• to understand and to contribute to the development of frontier econometric techniques
• to select and implement appropriate methods for solving problems in empirical economic research.

Examination
Oral exam (30 mins.) with no aids and no preparation time. For this exam, the use of tools based on generative AI is not allowed. 

Prerequisites for examination participation
Prior to the exam, a number of homework assignments must be handed in. The solutions handed in must demonstrate a reasonable attempt at solving the assignments. The paper can be written individually or in groups of max. 4 students. 

Comments on the form of instruction
In the lectures, we will mainly see theoretical characterisation of various identification, estimation, and inference methods. There will also be sessions including applications and simulations of the discussed methodology in statistical software and additional exercises for practicing mathematical derivations and proofs.

Literature
The lectures are based on selected chapters of textbooks and research papers.  Potential textbooks and research articles include (but are not limited to):

Literature

Module 1, required: 

• Newey and McFadden (1994), “Large sample estimation and hypothesis testing”. In Handbook of Econometrics, vol. IV.
• Hayashi (2000), Econometrics, Princeton University Press. Chapters 2 and 7. 

Module 1, supplementary: 

• White (1999), Asymptotic theory for econometricians, Academic Press. Chapters 2-5. 

Module 2, required:

• Li and Racine (2007). Nonparametric Econometrics: Theory and Practice. Princeton University Press.
• Kennedy, E. H. (2023). Semiparametric doubly robust targeted double machine learning: a review. arxiv:2203.06469
• Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., & Robins, J. (2018). Double/Debiased machine learning for treatment and structural parameters. Econometrics Journal 21, C1–C68.
• Chernozhukov, V., Escanciano, J.C., Ichimura, H., Newey, W.K. and Robins, J.M. (2022), Locally Robust Semiparametric Estimation. Econometrica, 90: 1501-1535. 

Module 2, supplementary :

• Belloni, A., Chernozhukov, V., & Hansen, C. (2014). Inference on treatment effects after selection among high-dimensional controls. Review of Economic Studies, 81, 608–650.
• Knaus, M.C. (2022), Double machine learning-based programme evaluation under unconfoundedness, Econometrics Journal 25, 602–627
• Semenova, V., & Chernozhukov, V. (2021). Debiased machine learning of conditional average treatment effects and other causal functions, Econometrics Journal 24, 264–289
• Athey, S., & Imbens, G. W. (2016). Recursive partitioning for heterogeneous causal effects. Proceedings of the National Academy of Sciences 113(27), 7353–7360.
• Athey, S., Tibshirani, J., & Wager, S. (2019). Generalized random forests. Annals of Statistics 47, 1148–1178.
• A small selection of supplementary articles. 

Registration
Registration for PhD course: Econometrics

Schedule
Thursday 09-04-2026 at 10:00-12:00 in 1323-122
Thursday 16-04-2026 at 10:00-12:00 in 1816-128 
Monday 20-04-2026 at 14:00-16:00 in 1816-044
Thursday 23-04-2026 at 10:00-12:00 in 1816-128 
Monday 27-04-2026 at 14:00-16:00 in 1816-044
Thursday 30-04-2026 at 10:00-12:00 in 1816-128 
Friday 01-05-2026 at 13:00-14:00 in 1816-128
Monday 04-05-2026 at 10:00-12:00 in 1816-128 
Monday 04-05-2026 at 14:00-16:00 in 1816-044 
Thursday 07-05-2026 at 10:00-12:00 in 1816-128 
Thursday 07-05-2026 at 14:00-16:00 in 1816-028 
Friday 08-05-2026 at 14:00-16:00 in 1816-128
Monday 11-05-2026 at 10:00-12:00 in 1816-128 
Monday 11-05-2026 at 14:00-16:00 in 1816-044 
Wednesday 13-05-2026 at 14:00-16:00 in 1816-128 
Wednesday 13-05-2026 at 16:00-17:00 in 1816-128

Contact 
Susanne Christensen, sch@econ.au.dk