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Quantitative Foundations for Econometrics (ETS-620)

Prerequisites For this Course:

None

Text Book(s):

  • David Diez, Mine Cetinkaya-Rundel, Christopher D. Barr. Edition (2019), OpenIntro Statistics, 4th
  • Freedman, D., Pisani, R., and Purves, R. (2007), Statistics (4th Edition).
  • Spanos, Aris. (1986), Statistical Foundations of Econometric Modelling, Cambridge University Press.
  • Hogg, R. V., and A. T. Craig (2005), Introduction to Mathematical Statistics, 5th Ed., Macmillan.
  • Mittelhammer, Ron C. (2001), The Mathematical Statistics for Economics and Business, Springer.

Reference Book(s):

  • Herman J. Bierens (2004), Introduction to the Mathematical and Statistical Foundations of Econometrics, Cambridge University Press.
  • Orley Ashenfelter, Levine, and Zimmerman (2006), Statistics and Econometrics: Methods and Applications, Wiley.
  • Davidson, R., and Mackinnon, J. (1993), Estimation and Inference in Econometrics, Oxford University Press.
  • Griliches, Z., and Intriligator, M. (1983, 1984), Handbook of Econometrics, Vols. 1 and 2, North Holland.
  • Mills, Terence C., and Markellos, Raphael N. (2008), The Econometric Modelling of Financial Time Series, Cambridge University Press.
  • Stock, J.H. & Watson, M.W. (2015), Introduction to Econometrics, Pearson (3rd Edition).
  • Introduction to Statistics: An Islamic Approach: Part 1: Descriptive Statistics (https://sites.google.com/site/introstatspart1/)
  • Introduction to Statistics: An Islamic Approach: Part 2: Probability and Statistics. (https://sites.google.com/site/i2sia2ps/home)

Course Description

Statistics attempts to make evaluations concerned with uncertainty and numerical conjectures about perplexing questions. The focus of the course is upon understanding real-life statistical problems. The course Quantitative Foundations of Econometrics is all about how to deal with some interesting problems statistically, why these methods work, and what to watch out for when others use them. This course develops a foundational understanding of the quantitative tools essential for econometric analysis. It begins with descriptive statistical methods, probability theory, and progresses to random variables, distributions, and statistical inference. The course then transitions into econometric modeling frameworks, including linear regression, multivariate models, dynamic models, and simultaneous equation systems. The approach emphasizes real-world applications, data visualization, and critical interpretation of statistical results with statistical reasoning.

This course provides the essential mathematical and statistical foundations necessary for the study of econometrics. It is designed to prepare students for more advanced knowledge in econometric theory and applied empirical analysis. This unique course offers a deep learning experience to students who make an effort. It requires a lot of practical work from the students. More than teaching about manipulation of numbers, this course is meant to teach students how to construct arguments, and how to avoid being deceived by data. Therefore, practical examples from economics are extensively used throughout to illustrate key concepts.

Course Objectives

In this course students are supposed to develop proficiency in fundamental techniques relevant to econometrics. They should be able to understand core concepts of descriptive data analysis, probability and random variables and get familiarity with distribution theory and the properties of estimators.

  • 1.Understand fundamental statistical methods and their applications in economics.
  • Interpret and visualize data through descriptive and inferential statistical techniques.
  • Grasp concepts of probability, random variables, distributions, and expectations.
  • Apply statistical inference methods including estimation, hypothesis testing, and confidence intervals.
  • Understand econometric model structures including the Gauss Linear Model, dynamic and simultaneous equation models.
  • Develop a critical understanding of the assumptions and limitations of econometric techniques.

Learning Outcomes

Upon completion of this course, students will:

  • Demonstrate a comprehensive understanding of quantitative skills needed for econometrics.
  • Capability to apply probability theory in solving econometric problems.
  • Apply descriptive data analysis techniques.
  • Ability to analyze and interpret economic data using statistical methods and create arguments.
  • Learn important techniques of probability and probability distributions.
  • Proficiency in estimation and hypothesis testing in econometric contexts.
  • Understanding of the construction and estimation of linear and multivariate regression models.
  • Develop the analytical skills necessary to contribute to academic research or policy analysis in the field of econometrics.
  • Ability to critically assess empirical econometric studies.

 

Lecture Plan

  Session  Topic  Readings Activities  Instructor
Module # 1: Descriptive Study of Data
1 Introduction to Econometric Modeling Sorting, ranking and percentiles Classroom lecture, book chapter reading. Video lecture from online course: lec 2c-8c  

 

Home task

Dr. Amena Urooj

& Dr. Nadia

Hassan

2 Measures of central tendency & their rhetorical

usage

Classroom lecture, book chapter reading. Video

lecture from online course:

8H-10c

 

 

Assignment 1

Dr. Nadia Hassan
3 Measures of dispersion Classroom lecture, book

chapter reading. Video lecture from online course:

10H-11H

 

 

Quiz 1

Dr. Nadia Hassan
4 Data visualization importance and power of visualizing data Classroom lecture, book chapter reading.  

Home task

Dr. Nadia Hassan
5 Data visualization: Boxplot, Histograms, Data Density Classroom lecture, book chapter reading. Video

lecture from online course:

12c-12H, 13c-13H, 14c-

14H

 

 

 

Assignment 2

Dr. Nadia Hassan
6 Data visualization: Bivariate Relations Classroom lecture, book

chapter reading.

Quiz 2 Dr. Amena Urooj
7 Moments, Moment

Generating Function

Classroom lecture, book

chapter reading. Video lecture from online course:

  Dr. Nadia Hassan
8 Moments, Moment Generating Function for various distributions, Cumulant Generating Function Classroom lecture, book chapter reading. Home task Dr. Nadia Hassan
Module # 2: Foundations of Statistics and Probability
9 Probabilities, the sample space, and random variables Classroom lecture, book

chapter reading. Video lecture from online course: L1.1, L1.2, L1.3

 

 

Home task

Dr. Nadia Hassan
10 Probability distribution of a discrete random variable Classroom lecture, book

chapter reading. Video lecture from online course: L2

 

Home task

Dr. Amena Urooj

 

         
11 Probability distribution of a discrete random variable Classroom lecture, book chapter reading. Video lecture from online course:

L3

 

 

Assignment 3

Dr. Amena Urooj
12 Probability distribution of a continuous random variable (Normal Distribution) Classroom lecture, book chapter reading. Video

lecture from online course:

L4, L6

 

 

Home task

Dr. Nadia Hassan
13 Expected values, mean, and variance Classroom lecture, book

chapter reading. Video lecture from online course: L5

 

 

Quiz 3

Dr. Amena Urooj
14 Other measures of the shape of a distribution Classroom lecture, book chapter reading. Video lecture from online course: L7   Dr. Amena Urooj
 

 

15

Two random variables, Joint and marginal distributions Classroom lecture, book chapter reading. Video

lecture from online course:

L6

 

Home task

Dr. Nadia Hassan
 

16

MID TERM EXAM  
Module # 3: Statistical Inference and Sampling
 

 

 

17

Random sampling, importance of random sampling, The

distribution of the sample average

Classroom lecture, book chapter reading. Video

lecture from online course:

L1.4, L1.5

 

 

 

Home task

Dr. Amena Urooj
 

 

18

 

Large sample approximations to sampling distributions

Classroom lecture, book

chapter reading. Video lecture from online course: L6

 

 

Home task

Dr. Nadia Hassan
 

 

19

The law of large numbers, The central limit theorem and consistency Classroom lecture, book chapter reading. Video lecture from online course: L6  

 

Assignment 4

Dr. Nadia Hassan
 

 

20

Student’s t distribution Classroom lecture, book chapter reading. Video

lecture from online course:

L6

 

 

Home task

Dr. Nadia Hassan
 

 

21

F distribution Classroom lecture, book chapter reading. Video

lecture from online course:

L6

 

 

Assignment 5

Dr. Nadia Hassan
 

 

22

Estimation Methods and

Properties of Estimators

Classroom lecture, book

chapter reading. Video

 

 

Quiz 4

Dr. Amena Urooj
 

23

Hypothesis tests concerning the population mean, Means from different populations Classroom lecture, book chapter reading.  

Home task

Dr. Nadia Hassan

 

 

 

         
 

 

 

24

The p-value, confidence intervals for the population mean, Means from different populations Classroom lecture, book

chapter reading.

 

 

 

Home task

Dr. Amena Urooj
 

25

t-Statistics and Small

Sample Inference

Classroom lecture, book chapter reading.  

Quiz 5

Dr. Amena Urooj
Module # 4: Econometric Modeling Frameworks
 

 

 

 

26

Introduction to Econometric Models, Specification of the Gauss Linear Model,

Linear Regression Model – Assumptions &

Diagnostics

Classroom lecture, book chapter reading.  

 

 

 

Home task

Dr. Nadia Hassan
 

 

27

Multivariate Linear Regression Models specification, Assumptions, Diagnostics and Interpretations Classroom lecture, book chapter reading.  

 

Home task

Dr. Amena Urooj
 

28

Dynamic Linear

Regression Models, Estimation and Inference

Classroom lecture, book chapter reading.  

Home task

Dr. Nadia Hassan
 

29

Simultaneous Equation

Models

Classroom lecture, book

chapter reading.

 

Home task

Dr. Nadia Hassan
 

30

Multivariate Normal Distribution & Applications Classroom lecture, book chapter reading.  

Home task

Dr. Amena Urooj
 

31

Applications in Financial

Time Series Modeling

Classroom lecture, book chapter reading.  

Assignment 6

Dr. Amena Urooj
 

32

Final Exam