# Advanced Microeconometrics

### Course content

Advanced Microeconometrics gives a detailed account of principles for estimation and inference based on the most conventional methods for estimation of both linear and non-linear parametric models, such as non-linear least squares, maximum likelihood estimation (MLE) and generalized method of moments (GMM). These methods are used to estimate a range of microeconometric models for panel and cross-sectional data covered in the course.  The course provides both the theoretical foundations of these estimation methods, as well as the practical tools to implement them in a relatively low-level programming language (MATLAB).

The course will be developed along the following four axes:

1) Linear unobserved effects panel data models:

• Estimation with strictly exogenous regressors.
• Random and fixed effects, first differences.
• GMM estimation of dynamic models with sequentially exogenous regressors.

2) Estimation methods and numerical tools for non-linear parametric models:

• M-estimators (e.g., NLS, MLE, LAD) and two-step M-estimators.
• Generalized Method of Moments (GMM) and Minimum Distance (MD).
• Simulation-based estimation methods.
• Numerical optimization algorithms (e.g., Nelder-Mead, Newton-Raphson, BHHH).

3) Discrete-outcome models and models for demand:

• Binary choice models for cross-sectional and panel data
• Multinomial choice models (e.g., logit, nested logit, probit, mixed logit)
• Censoring, selection models (e.g., tobit-type models)
• Structural models which combine discrete and continuous choices.
• Structural models for discrete demand in oligopolistic markets

4) Traditional semi-/non-parametric methods and introduction to machine learning:

• Kernel and series regression.
• Regularized linear regression (e.g., LASSO, Ridge).
• Classification and regression trees.

The course will provide the student with a statistical toolbox that can be used for estimation of and inference in a wide range of reduced-form and structural microeconometric models.

Education

MSc programme in Economics – elective course

The PhD Programme in Economics at the Department of Economics:

• The course is an elective course with research module. PhD students must contact the study administration AND the lecturer in order to register for the research module and write the research assignment.
• The course is a part of the admission requirements for the 5+3 PhD Programme. Please consult the 5+3 PhD admission requirements.
Learning outcome

After completing the course the student is expected to be able to:

Knowledge:

• Define the data generating process (including model (un)observables and parameters), the appropriate estimation method(s) and the assumptions ensuring consistency (including identification) for the models in axes 1, 3 and 4.
• Define the principles of estimation and inferences for the paradigms in axis 2.
• Identify the most common numerical optimization algorithms and their implementations in MATLAB.
• Account for the key opportunities and challenges that arise in models for panel versus cross-sectional data.
• Discuss merits and drawbacks of different estimators for a specific problem.
• Discuss validity of model assumptions. For concrete data examples, the student must be able to precisely relate the mathematical assumptions to economic intuition about the behavior that is underlying the data.

Skills:

• Assess which estimator is suitable for a given model.
• Estimate model parameters through programming in MATLAB.
• Test formal statistical hypotheses.
• Replicate, extend and critically discuss microeconometric research.
• Code an estimator from a research paper up from scratch and conduct estimation and inference.
• Exploite the added value of panel datasets over purely cross-sectional datasets.
• Master estimation using probability theory and (asymptotic) statistics.

Competencies:

• Assess which economic research questions can be answered when faced with a new dataset.

• Independently carry out and present empirical analysis e.g. in the master’s thesis and future jobs.

• Independently formulate and answer empirical economic questions and economic research question with a given dataset e.g. in a government agency or in the private sector.

• Initiate, be responsible for and receive constructive feedback in future colaborations.

The course is a combination of lectures, exercise classes and mandatory homework assignments. The lectures cover the theory and the intuition behind the estimators and the methods.

Exercises classes as well as homework assignments span a mix of theoretical, empirical and computational topics and allow students to put theory into practice in both supervised and unsupervised environments.

Homework assignments furthermore allow students to obtain hands-on coding experience by implementing estimators in MATLAB while using real datasets and addressing real economic questions. Students are expected to have (at least) attempted the exercises prior to attending exercise classes.

Restrictions due to Coronavirus:
The teaching in this course may be changed to be taught either fully or partly online due to COVID-19. For further information, please see the course room on Absalon (for enrolled students).

A. Colin Cameron & Pravin K. Trivedi

Microeconometrics: Methods and Applications July 2005 ISBN 9780521848053

Pre-requisites are the econometrics course Econometrics I at the Bachelor of Economics, University of Copenhagen or similar course.

It is strongly recommended to have taken the econometrics course Econometrics II at the Studies of Economics, University of Copenhagen or similar course before taking Adv. Microeconometrics..

Students will be required to do mathematical derivations in order to complete both the exercise classes, homework assignments and exam. So students should have a sound knowledge of linear algebra and calculus (e.g., matrix algebra, differentiation) e.g. from the course "Mathematics B" at the Bachelor of Economics, University of Copenhagen or similar course.

Programming will be an important component of the exercise classes, homework assignments, and exam. Prior experience with MATLAB is not a pre requisite to begin at this course. However students are strongly encouraged to complete the short course “Online MATLAB Course for Students of Economics” (available on Absalon at bit.ly/3cX4nXm) before the start of the semester.

Schedule:
2 hours lectures one to two times a week from week 36 to 50 (except week 42).
2 hours exercise classes a week from week 36/37 to 50 (except week 42).

Schema:
The overall schema for the Master can be seen at KUnet:
MSc in Economics => "Courses and teaching" => "Planning and overview" => "Your timetable"

Timetable and venue:
To see the time and location of lectures and exercise classes please press the link/links under "Timetable"/​"Se skema" at the right side of this page (E means Autumn). The lectures are shown in each link.

You can find the similar information partly in English at
https:/​/​skema.ku.dk/​ku2122/​uk/​module.htm
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-E21; [Name of course]”
-Select Report Type: “List – Weekdays”
-Select Period: “Efterår/Autumn”
Press: “ View Timetable”

Please be aware:
- The schedule of the exercise classes is only a pre-planned schedule and can be changed until the teaching begins without the participants´ acceptance. If this happens you can see the new schedule in your personal timetable at KUnet, in the app myUCPH and through the links in the right side and the link above.
- The study administration allocates the students to the exercise classes according to the principles stated in the KUnet.
- If too many students have wished a specific class, students will be registered randomly at another class.
- It is not possible to change class after the second registration period has expired.
- If there is not enough registered students or available teachers, the exercise classes may be jointed.
- The student is not allowed to participate in an exercise class not registered.
- The teacher of the exercise class cannot correct assignments from other students than the registered students in the exercise class except with group work across the classes.
- All exercise classes will be taught in English.
- It is the students´s own responsibility to continuously update themselves about their studies, their teaching, their schedule, their exams etc. through the curriculum of the study programme, the study pages at KUnet, student messages, the course description, the Digital Exam portal, Absalon, the personal schema at KUnet and myUCPH app etc.

Oral
Individual
Collective
Peer feedback (Students give each other feedback)

Assignments handed in for anonymous peer feedback will receive written feedback from fellow students based on criteria set up by the lecturers.

If deemed relevant, the lecturers will provide oral collective feedback in lectures based on a sample of the assignments.

Office hours: Are offered by Anders Munk-Nielsen and Jesper Riis-Vestergaard Sørensen, who inform day and time.

ECTS
7,5 ECTS
Type of assessment
Portfolio, 48 hours
The exam is a written assignment consisting of two parts:
- Part 1: The first part is based on one of the mandatory assignments worked on during the course. The student can use the peer feedback received during the course to improve the assignment. This can be done before the exam period begins. The repeat assignment is chosen at random and reveals with the release of the exam.
- Part 2: The second part is a new assignment given in English.

Please be aware that:
- The new assignments can be written individually or by groups of maximum three students.
- The students are allowed to communicate about the given problem-set for the new assignment but must work on the assignment individually.
- The plagiarism rules and the rules for co-written assignments must be complied.
- All parts must be answered in English
- All parts must be uploaded to Digital Exam in one file.
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Aid

All aids are allowed for the written exams.

Regarding aids for the oral reexam, please go to the section "Reexam" for further information about allowed aids.

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Marking scale
7-point grading scale
Censorship form
No external censorship
for the written exam.

Oral re-examination may be with external assessment.
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##### Criteria for exam assessment

Students are assessed on the extent to which they master the learning outcome for the course.

To receive the top grade, the student must with no or only a few minor weaknesses be able to demonstrate an excellent performance displaying a high level of command of all aspects of the relevant material and can make use of the knowledge, skills and competencies listed in the learning outcomes.

Single subject courses (day)

• Category
• Hours
• Lectures
• 42
• Class Instruction
• 24
• Preparation
• 92
• Exam
• 48
• English
• 206