### Course content

The overall purpose of the course is to provide a fundamental understanding of microeconometric methods and of their applications. It gives a detailed overview of the available estimation methods, from the classical approach to the Bayesian approach, providing both the theoretical foundations of these methods, as well as practical tools to implement them empirically. Microeconomic models that are widely used in practice to model individual behaviors and decisions will be introduced and used to illustrate how the various estimation methods can be applied.

The course will be developed along the following three axes:

1) Core estimation methods

• Extremum estimation (e.g., M-estimators, nonlinear estimation)
• Numerical optimization (e.g., grid search, Newton-Raphson, BHH algorithm)
• Non- and semi-parametric methods

2) Simulation-based estimation methods

• Simulation estimation methods (e.g., simulated maximum likelihood, simulated method of moments)
• Bootstrap
• Bayesian inference
• Markov chain Monte Carlo methods (e.g., Gibbs sampling, Metropolis-Hastings algorithm)

3) Applications

• Censored and selection models (e.g., tobit model, Roy model)
• Binary outcome models (e.g., probit, logit)
• Multinomial models (e.g., conditional and multinomial logit, multinomial probit)
• Quantile regression
• Latent variable models (e.g., factor modeling)

Learning outcome

The course will provide the student with a statistical toolbox that can be used for the estimation of a wide range of microeconometric models. After completing the course, the student will be able to:

Knowledge:

• Understand how the estimated parameters rely on specific identifying assumptions.

• Understand the principle of M-estimation in terms of estimation and inference, as well as key examples of M-estimators.

• Get a grasp of how the most common numerical optimizers work.

• Get an overview and understand the fundamental features of the available estimators depending on the nature of the data (e.g., binary, multinomial, censored, sample selection problem).

• Understand the fundamental differences between the classical approach and the Bayesian approach, and the advantages and drawbacks of each approach for a given estimation problem.

Skills:

• Be able to discuss the identifying assumptions and use regressions or descriptive data analysis to assess the assumptions.

• Given an economic problem and a data set, be able to select an appropriate econometric model and a suitable estimation approach.

• For a given model, be able to derive the corresponding likelihood function, the gradient and the information matrix (classical approach), or select a prior distribution and derive the corresponding posterior distribution (Bayesian approach).

• Be able to implement the estimation approach numerically: Maximize the objective function (using optimization methods in the classical framework), or implement an appropriate sampling method (Bayesian approach).

• Be able to take an estimator from an academic paper or book, code it up in Matlab and estimate parameters as well as obtain standard errors.

Competencies:

• When faced with a new dataset (whether in academia or in the real world), students should be able to:

• assess which estimator is best suited to answer a given question,

• code up the estimator and estimate parameters,

• test statistical hypotheses.

• Students should learn how to develop arguments supporting an identification strategy.

• Students should learn how to assess the identification strategies in existing research papers as well as in their own analyses.

• The acquired skills in microeconometric theory and practice provide a strong background that enable students to do empirical analyses at a high level suitable for the master thesis, but also relevant for answering empirical economic questions that could be encountered in a government agency or in the private sector.

The course is a combination of lectures and exercise classes.
The lectures cover the theory and the intuition behind the estimators and the methods. The exercise classes allow students to put into practice the theory through exercises, and also to obtain hands-on coding experience by implementing the estimators on real datasets, primarily in Matlab. Students are expected to prepare the exercises before coming to the exercise classes.

Cameron, A. C. and P. K. Trivedi (2005), “Microeconometrics: Methods and Applications”, Cambridge University Press, ISBN: 978-0521848053.

Greenberg, E. (2013), “Bayesian Econometrics”, Second Edition, Cambridge University Press, ISBN: 978-1-107-01531-9.

Pre-requisites are the bachelor-level econometrics courses, Econometrics I
and II. Prior knowledge about programming in Matlab is not required, but some programming experience will be an advantage. Students will be required to do mathematical derivations for the exam.

Schedule:
2 hours lectures even weeks and 2x2 hours odd weeks from week 36 to 50 (except week 42).
2 hours exercise classes a week from week 36/37 to 50 (except week 42).

The overall schema for the Master can be seen at https:/​/​intranet.ku.dk/​economics_ma/​courses/​CourseCatalogue-E17/​Courseschema/​Pages/​default.aspx

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

You can find the similar information partly in English at
https:/​​/​​skema.ku.dk/​​ku1718/​​uk/​​module.htm
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-E17; [Name of course]””
-Select Report Type: “List – Weekdays”
-Select Period: “Efterår/Autumn – Weeks 31-5”
Press: “ View Timetable”

Please be aware regarding exercise classes:
- The schedule of the exercise classes is only a pre-planned schedule and can be changed until just before the teaching begins without the participants accept. If this happens it will be informed at the intranet or can be seen in the app myUCPH and at the above link
- That 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, because the room has only seats for the amount of registered student.
- 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.
- That all exercise classes will be taught in English.

ECTS
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
individual closed book exam at the computers of Copenhagen University. The exam assignment is in English and must be answered in English.
Aid
Without aids
Marking scale
Censorship form
External censorship
##### Criteria for exam assessment

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 be able to demonstrate in an excellent manner that she or he has acquired and can make use of the knowledge, skills and competencies listed in the learning outcomes.

So in order to obtain the grade 12, students should meet the following criteria:

Knowledge:

• The student should be able to give a detailed account of the estimators in the course.

• The student should be able to derive the estimator and other relevant statistics, including how standard errors are obtained.

• The student should be able to describe how the estimation is conducted.

Skills:

• The student should be able to discuss the use of an estimator in an empirical context.

• The student should be able to write up the data generating process of the model and to derive the likelihood function.

• For Bayesian methods, the student should be able to choose an appropriate prior distribution, to derive the likelihood function and the corresponding posterior distribution.

Competencies:

• The student should be able to select a suitable estimation approach for answering an empirical question.

• The student should be able to present arguments for or against a given research strategy.

Single subject courses (day)

• Category
• Hours
• Lectures
• 42
• Class Exercises
• 24
• Preparation
• 137
• Exam
• 3
• English
• 206