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# Econometric Theory - ECO00033I

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• Department: Economics and Related Studies
• Module co-ordinator: Prof. Takashi Yamagata
• Credit value: 20 credits
• Credit level: I
• Academic year of delivery: 2023-24
• See module specification for other years: 2024-25

## Module summary

The module gives student a thorough introduction to the theoretical concepts underlying modern Econometrics.

## Related modules

### Prohibited combinations

• None

Prerequisite modules: Probability and Statistics, Mathematics for Economists

Co- requisite: Econometrics

## Module will run

Occurrence Teaching period
A Semester 2 2023-24

## Module aims

The module covers the following topics:

• Distribution Theory: Relations between normal, chi-square, F, and t distributions. Multivariate normal distributions, marginal and conditional normal distributions.

• Asymptotic theory: Limits, continuous functions, law of large numbers, convergence in probability, convergence in distribution and the central limit theorem.

• The Classical Linear Regression Model: Matrix algebra, Ordinary Least Squares (OLS) estimator, F and t tests

• Maximum Likelihood (ML) Estimation: ML estimator, Cramer-Rao lower bound, Neyman-Pearson lemma, likelihood ratio, Wald, and LM tests.

## Module learning outcomes

On successfully completing the module the student will be able to:

• apply key concepts and methods from statistical theory relevant for economic data analysis

choose statistical models and tests relevant for the analysis of small and large datasets

## Module content

Subject to changes:

1. Finite sample results: review matrix, least squares

2. gauss Markov theorem

3. F test

4. Finite sample results: MLE, Information, MVUE

5. Elements of Asymptotic theory: review sequence, limits, boundedness, lim sup

6. Convergence in distribution, Convergence in probability, Slutsky, cmt, WLLN, iidCLT (and inid/dependent data?

7. asymptotic properties of OLS estimator: consistency and asymptotic normality

8. 2sls estimator and its asymptotic properties.

9. asymptotic properties of MLE estimator: consistency and asymptotic normality

10. MLE of a parameter vector and Wald, LR and LM tests, with the regression example.

11. LM test for error serial correlation or intro to times-series analysis

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Econometric Theory
3 hours 100

None

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Econometric Theory
3 hours 100

## Module feedback

For the formative work students are set exercises prior to the seminars, and submit at least one piece of work to be marked which is returned within 25 working days of submission.

For the summative assessment a breakdown of marks by question will be provided also within 25 working days of the exam.

Bartle, R.G., Sherbert, D.R., Introduction to Real Analysis, Wiley.

Robert V. Hogg, R.V., McKean, J.W., Craig, A.T., 2019, Introduction to Mathematical Statistics, 8th ed., Pearson.

White, H., Asymptotic Theory for Econometricians, revised edition, Academic Press.

Abadir and Magnus, Matrix Algebra, CUP.

Johnston and Dinardo, Econometric Methods, McGrow-Hill.

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.