Important notice
The course guide is provisional.
The PDF version of the course guide may take a few days to become available in the DDD.
Quantitative Methods
Code: 40094Credits: 15
| Degree programme | Type | Course |
|---|---|---|
| Economic Analysis | OB | 1 |
Contact lecturer
- Name :
- Pau Milán Solé
- Email :
- pau.milan@uab.cat
Teaching staff
- Jordi Caballe Vilella
- Fernando Payro Chew
Group languages
You can consult this information at the end of the document.
Prerequisites
There are no specific prerequisits.
Objectives
This module provides students advanced quantitative tools for economic analysis. The module covers optimization, probability and statistics.
The module is organized in two sections. The first one covers the foundations of optimization theory. The second section provides students
with the theoretical foundations of probability and statistics necessary for econometric and financial analysis.
Learning outcomes
- CA01 (Design analytical solutions for professional economic problems.) Design analytical solutions for professional economic problems.
- CA02 (Integrate a strategic decision question into a formal model for later resolution.) Integrate a strategic decision question into a formal model for later resolution.
- KA01 (Describe advanced mathematical tools for formalising multivariate models.) Describe advanced mathematical tools for formalising multivariate models.
- KA02 (List the key concepts of individual optimisation (metric spaces, convexity, differential equations) applied to economic analysis.) List the key concepts of individual optimisation (metric spaces, convexity, differential equations) applied to economic analysis.
- KA03 (Identify the probability and statistical foundations necessary for econometric inference.) Identify the probability and statistical foundations necessary for econometric inference.
- KA04 (Recognise the elements of game theory and balances used in multipersonal strategic decisions.) Recognise the elements of game theory and balances used in multipersonal strategic decisions.
- SA01 (Apply mathematical proof to derive results from economic theory.) Apply mathematical proof to derive results from economic theory.
- SA02 (Classify the relevant assumptions and variables to model a strategic interaction with two agents.) Classify the relevant assumptions and variables to model a strategic interaction with two agents.
- SA03 (Use algebra and differential calculus to solve economic problems in lab sessions.) Use algebra and differential calculus to solve economic problems in lab sessions.
- SA04 (Compare simulated datasets to determine the suitability of econometric techniques.) Compare simulated datasets to determine the suitability of econometric techniques.
Contents
I. Optimization
1. Sets and Metric Spaces:
2. Functions and Correspondences:
3. Linear Spaces and Linear Algebra:
4. Smooth functions, Optimization and Comparative Statics:
5. Difference and Differential Equations:
II. Probability and Statistics
1. Probability
2. Measure Theory
3. Random Variables and Distributions
4. Expectation
5. Special Distributions
6. Functions of Random Variables7. Stochastic Processes and Limiting Distributions
8. Sampling
9. Estimation
10. Hypothesis Testing
For a detailed description of the content of this module go to https://sites.google.com/view/idea-program/master-program
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Theory classes | 112.5 | 4.5 | |
| Personal study, study groups, textbook readings, article readings | 187.5 | 7.5 | |
| Problem solving and tutorials | 75 | 3 |
The course will consist of sessions where the instructor presents the material, and sessions specifically dedicated to problem solving. Students are encouraged to form study groups to discuss assignments and readings.
The proposed teaching methodology may undergo some modifications according to the restrictions imposed by the health authorities on on-campus courses.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Exam Part II | 40% | 0 | 0 | CA01, CA02, KA01, KA02, KA03, KA04, SA01, SA02, SA03, SA04 |
| Exam Part I | 40% | 0 | 0 | CA01, CA02, KA01, KA02, KA03, KA04, SA01, SA02, SA03, SA04 |
| Class Attendance and Problem sets and assignments | 20% | 0 | 0 | CA01, CA02, KA01, KA02, KA03, KA04, SA01, SA02, SA03, SA04 |
This modul does not contemplate an evaluation from a single comprehensive exam
| Exam Part I | 40% |
Exam Part II | 40% |
Problem sets and assignments + Class attendance and active participation | 20% |
The proposed evaluation activities may undergo some changes according to the restrictions imposed by the health authorities on on-campus courses.
In this course, the use of Artificial Intelligence (AI) technologies is not permitted in any of its phases. Any work that includes fragments generated with AI will be considered a breach of academic honesty and may result in a partial or total penalty to the activity's grade, or more severe sanctions in serious cases.
Bibliography
Optimization:
Axler, S.J., Linear algebra done right (Vol. 2). New York: Springer.
Carter, M., Foundations of mathematical economics. MIT Press.
Sydsæter, K., Hammond, P., Seierstad, A. and Strom, A., Further mathematics for economic analysis. Pearson education
Probability and Statistics:
Ash, R.B., Real Analysis and Probability, Academic Press.
Bierens, H.J., Introduction to the Mathematical and Statistical Foundations of Econometrics, Cambridge University Press.
Billingsley, P., Probability and Measure, Wiley.
DeGroot, M.H. and Schervish, M.J., Probability and Statistics, Pearson.
Hogg, R.V., McKean, J. and Craig, A.T., Introduction to Mathematical Statistics, Pearson.
Lindgren, B.V., Statistical Theory, Chapman and Hall/CRC.
Rice, J.A., Mathematical Statistics and Data Analysis, Cengage Learning.
Additional references will be provided during the course.
Software
- Matlab
- R
- Phyton
- Stata
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TEm) Theory (master) | 30 | English | first semester | morning-mixed |
| (PLABm) Practical laboratories (master) | 30 | English | first semester | morning-mixed |