# Econometrics II

### Course content

Autumn 2018:

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.

Spring 2019:

Econometrics II gives a detailed account of principles for estimation and inference based on the likelihood function and based on generalized method of moments estimation with application to cross-sectional data and time series data.

In addition, econometrics II presents the econometric analysis of time series data, applying the concepts of non-stationarity, unit roots, co-integration, vector autoregressions, and autoregressive conditional heteroskedasticity (ARCH).

As an integral part of the course, students will learn how to carry out, present, and discuss an empirical analysis on their own.

Education

Bacheloruddannelsen i økonomi – Obligatorisk fag på 3. år

The Danish BSc programme in Economics - mandatory course at the 3rd year

Learning outcome

Autumn 2018:

After completing the course in autumn 2018, 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.

Spring 2019:

After completing the course in the spring 2019, the student should be able to demonstrate the following:

Knowledge:

• Give an account for the different principles for estimation and inference – specifically the method of maximum likelihood, the (generalized) method of moments – and discuss relative advantages and drawbacks.
• Give a precise definition and interpretation of the concept of stationarity of time series data, and precisely describe the conditions for consistent estimation and valid inference in a 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 and maximum likelihood. 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 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.

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 assignments.

The exercise classes will primarily be performed through workshops with all students together with the teaching assistants and the lecturer.

A number of assignments must be handed in individually or by groups of up to three students. The plagiarism rules must be complied and please be aware of the rules for co-writing assignments.

After handing in each assignment students give individual peer feedback on each other’s assignments.

The assignments and the peer feedback must be answered in English and must be handed in through the peergrade.io platform.

Autumn 2018:
During the semester there are five written assignments covering each of the major topics in the course.

Spring 2019:
During the semester there are four written assignments covering important topics in the course.

Autumn 2018:

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).

Spring 2019:

Marno Verbeek: A Guide to Modern Econometrics, 5th Ed., Wiley. ISBN 978-1-119-472117.

Lecture notes.

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

Schedule:
An overall schema for BA 3rd year can be seen at https:/​/​kunet.ku.dk/​study/​economics-ma/​Pages/​topic.aspx?topicid=662a6f35-7859-40c7-a3ee-8d147d8c18cd -> Your Timetable

Autumn 2018:
2x2 hour lectures each week from week 36 to 50 (except week 42).
2 hours of workshops/exercise classes each week from week 36/37 to 50 (except week 42).

Spring 2019:
2x2 hour lectures each week from week 6 to 20 (except holidays).
2 hours of exercise classes each week from week 6/7 to 21 (except holidays).

Timetable and venue for autunm and spring:
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, F means Spring). The lectures is shown in each link.

You can find the similar information in English at
https:/​/​skema.ku.dk/​ku1819/​uk/​index.htm
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-E18; [Name of course]” or “2200-F19; [Name of course]”
-Select Report Type: “List – Week Days”
-Select Period: “Efterår/Autumn – Weeks 31-5” or “Forår/Spring – Week 5-30”
Press: “ View Timetable”

Please be aware of the rules regarding exercise classes:
- The schedule of the exercise classes is only a pre-planned schedule and can be changed until the teaching begins without the participants accept. If this happens changes can be seen in your personal timetable at KUNet or in the app myUCPH and at the links in the right side.
- 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 students.
- 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.

ECTS
7,5 ECTS
Type of assessment
Portfolio, 7 days
Autumn 2018:
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 (all four parts) can be handed in individually or by groups of maximum three students. The plagiarism rules must be complied and please be aware of the rules for co-writing assignments. 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.

Spring 2019:
The final exam is a written assignment consisting of three parts. The first two parts are based on two 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 third part of the exam is a new assignment.

The written exam (all three parts) can be handed in individually or by groups of maximum three students. The plagiarism rules must be complied and please be aware of the rules for co-writing assignments. 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.
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Aid

All aids are allowed for the regular written exam.

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Marking scale
Censorship form
No external censorship
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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
• 56
• Class Exercises
• 28
• Preparation
• 98
• Exam
• 24
• English
• 206