 # Introduction to Econometric Theory

## Module description

Summary:

The aim of this module is to help you understand the basic principles of econometric theory. The skills and knowledge acquired through this module will help you understand the foundation of econometrics and derive the major analytical results in econometrics. This module provides essential analytical tools for those intending to attend the third year module Econometric Analysis. It is also useful for those who wish to have a more theoretical understanding of econometrics.

Internationalisation
Since mathematics is an international language the course content is relevant across the globe in theory and in practice.

Employability
Through the material mastered on this module, students learn numeracy skills and acquire advanced mathematical skills, which are highly valued by the majority of employers.

Sustainability
All of the resources for this module are available on the ELE (Exeter Learning Environment).

## Full module specification

Module title: Introduction to Econometric Theory BEE2020 2 2021/2 Dr Namhyun Kim - ConvenorProfessor Giuseppe Cavaliere - Lecturer 15 7.5 BEE1022 and BEE1023 BEE2006 or BEE2031 Duration (weeks) - term 2: 11

## Module aims

This module can be thought of as having two aims. The first is to complement the practical material taught in BEE1023 Introduction to Econometrics and BEE2031 Econometrics, for the benefit of more technically inclined and motivated students, by studying its underpinning in mathematics and statistical theory. The second aim is to provide an important preliminary coverage for those who will be taking Econometric Analysis (BEE3015) in year 3.
These are compulsory modules for those following the Economics with Econometrics degree. The module will focus largely on mastering matrix algebra, which is studied in the context of the multiple regression model and its ramifications. In parallel with this, the fundamentals of distribution theory are studied with a focus on the role of the normal distribution and the various distributions derived from it. These two topics come together and are integrated in the theory of statistical inference in the regression model.

## ILO: Module-specific skills

• 1. analyse problems in econometrics using mathematically advanced techniques
• 2. explain the role of distribution theory in solving problems in statistical inference, with the multiple regression model providing the framework of analysis

## ILO: Discipline-specific skills

• 3. demonstrate a clear understanding of the mathematical and statistical background of applied Economics

## ILO: Personal and key skills

• 4. demonstrate the appropriate use of relevant mathematical language and methods in economics

## Learning activities and teaching methods (given in hours of study time)

Scheduled Learning and Teaching ActivitiesGuided independent studyPlacement / study abroad
251250

## Details of learning activities and teaching methods

CategoryHours of study timeDescription
Scheduled learning and teaching activities20Lectures
Scheduled learning and teaching activities5Tutorials
Guided independent study125Reading, preparation for classes and assessments

## Formative assessment

Form of assessmentSize of the assessment (eg length / duration)ILOs assessedFeedback method
Homework assignmentsWeekly problem sets1,2In-class discussions

## Summative assessment (% of credit)

CourseworkWritten examsPractical exams
01000

## Details of summative assessment

Form of assessment% of creditSize of the assessment (eg length / duration)ILOs assessedFeedback method
Written examination702 hours1,2,3,4Written feedback
Mid term assessment302 hours1,2,3,4Written feedback

## Details of re-assessment (where required by referral or deferral)

Original form of assessmentForm of re-assessmentILOs re-assessedTimescale for re-assessment
Mid term assessment and written examination Written examination (100%)1, 2, 3, 4August Examination Period

## Syllabus plan

• Observations, variables and summary statistics; the two-variable regression model; the multiple regression model. Basic matrix concepts and properties
• Solving systems of equations; determinants and inverse matrices; linear dependence and rank. More on multiple regression
• Probability distributions; the normal (Gaussian) distribution and its properties; the multivariate normal distribution; discrete distributions; continuous distributions derived from the normal: chi-squared , t, and F. Conditional distributions
• Statistical inference in the classical regression model; properties of least squares; the projection matrices; residual variance estimation; efficiency and the Gauss Markov theorem. Generalized least squares
• Eigenvalues, eigenvectors and diagonalization; the distribution of quadratic forms; OLS confidence regions; the t test; tests of linear restrictions. Constrained least squares.
• The partitioned regression model. Frisch-Waugh Theorem, specification analysis
• Random regressors; conditional expectations; properties of OLS with random regressors; the Gauss Markov theorem with random regressors;
• Asymptotic theory (a non-technical introduction).
• Maximum likelihood estimation.

## Indicative learning resources - Basic reading

The textbook for the course is:

James Davidson (2018), Introduction to Econometric Theory, John Wiley & Sons.

This book contains all the course material, with additional background. The lectures will follow it closely.

There are a number of other textbooks that may be helpful for background reading.  These include:

Johnston, J. and DiNardo, J. (1997) Econometric Methods, 4th Edition, McGraw Hill Theil, H. (1971) Principles of Econometrics, Wiley

Judge, G. et al, (1998) The Theory and Practice of Econometrics, 2nd Edition, Wiley Greene, W. (2012) Econometric Analysis, 7th Edition, Pearson Education/Prentice Hall Davidson, J. (2000) Econometric Theory, Oxford: Blackwell

Davidson, R. and MacKinnon J. (2003) Econometric Theory and Methods, New York: OUP

Yes

01/09/2007

25/08/2020