# Econometrics II

### Course content

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.
Education

BSc programme in Economics - mandatory

Learning outcome

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.

The course is based on a combination of lectures (4 hours per week) and exercises (2 hours per week). Activities to challenge and activate students, such as Socrative quizzes and peer-discussions, are an important part of the lectures. Students are required to prepare before lectures by reading, watching online videos, and completing online quizzes. Finally, peer feedback is used to provide detailed feedback on the assignments.

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.

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).

The course requires knowledge equivalent to that achieved in 'Probability Theory and Statistics' and Econometrics I.

Schedule:
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.

ECTS
7,5 ECTS
Type of assessment
Portfolio, 7 days
The 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.
Aid
All aids allowed
Marking scale
Censorship form
No external censorship
##### 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 he or she has acquired and can make use of the knowledge, skills and competencies listed in the learning outcomes.

Single subject courses (day)

• Category
• Hours
• Lectures
• 56
• Class Exercises
• 28
• Preparation
• 102
• Exam
• 20
• English
• 206