# AØKA08007U Econometrics II

BSc programme in Economics - mandatory

Econometrics II is the final course in the compulsory BSc. course sequence in statistics and econometrics. The course Econometrics I focuses on linear regression and instrumental variables estimation of the linear regression model for cross‐sectional data. The current course discusses dependent observations and gives a detailed account of the econometric analysis of time series data. Econometrics II also goes into more detail with the estimation principles and the likelihood analysis, and it presents the generalized method of moments. Concepts such as stationarity, unit roots, cointegration and error correction, and autoregressive conditional heteroskedasticity (ARCH) are introduced. As an integral part of the course, students are introduced to statistical tools for analysing time series data and students will learn how to carry out, present, and discuss an empirical analysis based on economic time series on their own.

The outline of the course is the following:

- The linear regression model for time series data.
- Dynamic models for stationary time series.
- Unit root testing.
- Dynamic models for time series with unit roots. Cointegration and error correction.
- Models with time-varying conditional volatility.
- Generalized method of moments.

After completing the course, the student should be able to demonstrate the following:

__Knowledge:__

- Give an account for the important differences between (independent) cross-sectional data, analyzed in detail in Econometrics I, and time series data.
- Give a precise definition and interpretation of the concept of stationarity of time series data, and precisely describe the conditions under which the results from the linear regression analysis for cross-sectional data can be used also on time series data.
- Give an account for the motivation and intuition for different principles for estimation and inference – specifically the method of ordinary least squares (OLS), method of moments (MM), maximum likelihood (ML), and generalizes method of moments (GMM) – and discuss relative advantages and drawbacks.
- Give an account for the sufficient conditions for consistent estimation and valid inference in the statistical model.
- Give a precise definition of the concept of unit roots, explain the consequences of unit roots in economic time series data, and interpret statistical models for stationary and non-stationary time series.
- Give a precise definition and interpretation of the concepts cointegration and error correction, and give an account of statistical models based on cointegration and error correction.
- Give a precise definition and interpretation of the concept of autoregressive conditional heteroskedasticity (ARCH), and give an account of statistical models with ARCH in financial time series.

__Skills:__

- Identify the characteristic properties of a given data set of economic time series and suggest and construct relevant statistical models.
- Derive estimators of the statistical model’s parameters using the principles of method of moments (MM) and maximum likelihood (ML). Estimate and interpret the parameters.
- Construct misspecification tests and analyze to what extent a statistical model is congruent with the data.
- Construct statistical tests for unit roots in economic time series.
- Construct statistical tests for cointegration and error correction in economic time series.
- Formulate economic questions as hypotheses on the parameters of the statistical model and test these hypotheses.
- Use statistical and econometric software to carry out an empirical analysis.
- Present a statistical model and empirical results in a clear and concise way. This includes using statistic and econometric terms in a correct way, giving statistically sound and economically relevant interpretations of statistical results, and presenting results in a way so that they can be reproduced by others.

__Competencies:__

- Choose the relevant statistical model given the characteristics of a given data set of economic time series and apply the statistical tools to carry out, present, and discuss an empirical analysis and test specific economic hypotheses.
- Read research papers containing applied econometric time series analyses.

Marno Verbeek: A Guide to Modern Econometrics, 4th Ed., Wiley. ISBN 978-1-119-95167-4.

- Chapter 1-3 (cursory reading) p. 1-93 (93*).
- Section 4.1-4.5 (cursory reading) 94-112 (18*).
- Section 4.6-4.11: p. 112-136 (25).
- Chapter 5-6 p. 137-205 (69).
- Section 7.1.1-7.1.6 p. 206-217 (12).
- Section 7.3 p. 231-238 (8).
- Chapter 8 p. 278-337 (59).
- Section 9.1-9.3 p. 338-350 (13).
- Section 9.4-9.7 (cursory reading) p. 350-371 (22*)

**Lecture notes:**

1. Introduction to Time Series (13).

2. Linear Regression with Time Series Data (22).

3. Introduction to Vector and Matrix Differentiation (cursory reading) (6*).

4. Dynamic Models for Stationary Time Series (28).

5. Non-Stationary Time Series and Unit Root Testing (21).

6. Cointegration and Common Trends (31).

7. Modeling Volatility in Financial Time Series: An introduction to ARCH (16).

8. Generalized Method of Moments Estimation (31).

During the semester there are five written assignments covering each of the major topics in the course. After handing in each assignment students give peer feedback on each other’s assignments through the peergrade.io platform.

2x2 hours of lecturing and 2 hours of excercises per week for 14 weeks

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 (16E means Autumn 2016, F17 means Spring 2017). The lectures is shown in each link.

You can find the similar information partly in English at

https://skema.ku.dk/ku1617/uk/module.htm

-Select Department: “2200-Økonomisk Institut” (and wait for respond)

-Select Module:: “2200-E16; [Name of course]” or “2200-F17; [Name of course]”

-Select Report Type: List

-Select Period: “Efterår/Autumn – Weeks 30-3” or “Forår/Spring – Week 4-29”

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 in KUnet or can be seen in the app myUCPH and at the above link.

- 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.

- That all exercise classes will be taught in English.

for enrolled students. More information about registration,
schedule, rules, courses etc. can be found at the
*student intranet for courses
(MA-English)* and *student intranet for courses (BA-
Danish)**.*

Registration and information for prospective foreign
speaking students not enrolled at the University of
Copenhagen please find more information
at *Study
Economics**.*

For enkelfagsstuderende sker tilmelding via
*Åbent
Universitet* og
*Merit*.

- Credit
- 7,5 ECTS
- Type of assessment
- Portfolio, 7 daysThe final exam is a written assignment consisting of four parts. The first three parts are based on three of the assignments worked with during the semester. Students can use the peer feedback they receive during the semester to improve these assignments for the final exam. The forth part of the exam is a new assignment.

The written exam can be handed in individually or by groups of maximum three students. The exam is given in English and must be answered in English. The final exam must be uploaded to the Digital Exam portal in one file. - Exam registration requirements
To qualify for the exam a minimum of four out of five assignments must be handed in during the semester and approved by the teacher. Additionally, for a minimum of four of the five assignments written peer feedback based on specific criteria must be given to three other students and approved by the teachers. The assignments can be handed in individually or by groups of up to three students. However, the peer feedback must be given individually. The assignments and the peer feedback must be answered in English. Both the assignments and the peer feedback must be handed in through the peergrade.io platform.

- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
- Exam period
Autumn 2016: December 15, 2016 10:00 AM to December 22, 2016 10:00 AM.

Spring 2017: May 20, 10:00 AM to May 27, 10:00 AM 2017

For enrolled students more information about examination, exam/re-sit, rules etc. is available at the

*student intranet for Examination (English)*and*student intranet for Examination (BA-Danish)*.- Re-exam
The re-exam is oral (20 minuts) with 20 minuts preparation and all aids during the preparation. The questions cover the entire curriculum and are based on the cases in the five written assignments worked with during the semester. The language is Danish or English. Language must be chosen at the registration for the re-exam.

Autum semester 2016: The re-exam will take place in February 2017, week 7 and/or 8.

Spring semester 2017: The re-exam will take place in August 2017, week 35 and/or 36.

##### Criteria for exam assesment

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 he or she has acquired and can make use of the knowledge, skills and competencies listed in the learning outcomes.

- Category
- Hours
- Lectures
- 56
- Class Exercises
- 28
- Preparation
- 102
- Exam
- 20
- Total
- 206

### Course information

- Language
- English
- Course code
- AØKA08007U
- Credit
- 7,5 ECTS
- Level
- Bachelor
- Duration
- 1 semester
- Placement
- Autumn And Spring
- Schedule
- Teaching:

Autumn: Week 36-50

Spring: Uge 6-20

Timeschedule: See "Remarks"

Exam and re-sits: See "Exam" - Continuing and further education
- Price
- Study board
- Department of Economics, Study Council

##### Contracting department

- Department of Economics

##### Course responsibles

- Rasmus Søndergaard Pedersen (3-8283805075737f7e3e7b853e747b)

Spring - Morten Nyboe Tabor
(18-7c7e8183747d3d7d88717e743d8370717e814f74727e7d3d7a843d737a)

Autumn

##### Lecturers

Lectures: See ‘Course responsibles’

Autumn 2016:

Teachers of exercise classes:

Ex. Class 1: Cancelled

Ex. Class 2: Martin Vasilev Stoyanov

Ex. Class 3: Joachim Vilhelm Koch

Ex. Class 4: Dan Nolsøe Olsen

Ex. Class 5: Martin Vasilev Stoyanov

Ex. Class 6: Sebastian Schäber

Ex. Class 7: Dan Nolsøe Olsen

Ex. Class 8: Cancelled

Ex. Class 9: Cancelled

Ex. Class 10: Sebastian Schäber

Spring 2017:

Ex. Class 1: Dan Nolsøe Olsen

Ex. Class 2: Sebastian Schäber

Ex. Class 3: Sebastian Schäber

The schedule of the estimated pre-planned exercise classes can be
changed up to the start of the semester.

All classes will be taught in English.