ECONOMETRICS

This course is one of the core teaching activities of the PhD program in "Economics" and of the course "Economia e Finanza - QEM". In line with the educational objectives of the course, this activity aims to present the main mathematical and statistical tools necessary for the analysis of economic phenomena; particular attention will be devoted to the use of formal language and methodological rigor. More specifically, the course aims to complete students preparation in Econometrics by being able to deal with advanced econometric models and methods. Moreover, it will provide students with the main econometric methods, with special reference to the analytical derivation of the estimators and to inference procedures.

Knowledge and competencies:
- sound knowledge of the theoretical foundations of econometric methods
- specification and formal derivation of econometric models based on economic models
- investigate, understand and interpret economic and financial phenomena, by means of up-to-data econometric tools

Application of acquired knowledge and skills:
- ability to exploit up-to-date analytical tools and formal derivations to gain insights on relevant economic relationships
- interpretation and management of economic dynamics, through the use of advanced analytical tools

Judgement and interpretation skills:
- evaluate strengths and weaknesses of the methodologies analyzed and of their empirical application
- being able to critically interpret the outcomes of empirical analyses

Mathematical Tools:
- Matrix Algebra
- Differential Calculus

Statistical Tools:
- Random Variables and Distribution Theory
- Point and Interval Estimation
- Hypothesis Testing
- Least Squares and Standard Linear Model

A. Classic Econometric Models

A.1 Regression Models
A.2 The classical hypothesis
A.3 The Statistical Properties of Ordinary Least Squares
A.4 The Frisch-Waugh-Lowell theorem
A.5 Hypothesis Testing in Linear Regression Models
A.6 Asymptotic results
A.7 Generalized Least Squares and Related Topics
A.8 A primer on instrumental variables
A.9 A primer on likelihood methods


B. Time Series Econometrics

B.1. Univariate time series processes Intro
B.2. ARMA processes
B.3. Covariance stationarity and the Wold representation theorem
B.4. Martingales and martingale differences
B.5. WLLNs for covariance stationary processes, Martingale convergence theorem
B.6. Martingale Central Limit Theorem: Conditions and Applications
B.7. Estimation and inference in Stationary models
B.8. Estimation and inference with Explosive processes
B.9. Functional CLT, Estimation and inference with Unit root processes
B.10. Spurious regression and univariate cointegration regression
B.11. Multivariate time series modelsL Estimation and inference with covariance stationary vector processes

First Part
F. Hayashi, Econometrics, Princeton University Press, 2000.

Second Part
J.D. Hamilton, Time Series Analysis, Princeton University Press, 1994.

Additional references:
- Lectures slides and additional material will be made available on Moodle during the course

The exam consists in a written exam that is evaluated on a 30-point basis.

Homeworks and assignments provided during the course are intended to verify the progress in the learning activity and the abilities to go deep autonomously to the heart of the topics of the course. They are not graded.

Overall course grade
The exam is considered passed with the achievement of 18 total points out of 30.

written and oral

The instructor is responsible for ensuring the authenticity and originality of all examinations and coursework. In cases of suspected academic misconduct, an additional on-site assessment may be required during the exams, which may differ from the standard format.

The course is organized into two modules. The exam is considered passed if the average grade across the two modules is greater than or equal to 18.

The exam consists of a number of mainly theoretical questions, for example requiring students to prove certain theoretical results or to define appropriate statistical strategies for addressing specific economic problems.
Each answer is assigned a score (from 0 to 10 points, depending on the number of questions in the exam). The final grade is determined by evaluating the exam as a whole.

Specifically,
A. Grades in the 18–22 range will be awarded when the following criteria are met:

- sufficient knowledge and theoretical and applied understanding of the course content;
- limited ability to interpret empirical and/or theoretical results;
- sufficient communication skills, particularly with regard to the use of subject-specific terminology.

B. Grades in the 23–26 range will be awarded when the following criteria are met:

- satisfactory knowledge and theoretical and applied understanding of the course content;
- satisfactory ability to interpret empirical and/or theoretical results;
- satisfactory communication skills, particularly with regard to the use of subject-specific terminology.

C. Grades in the 27–30 with honours range will be awarded when the following criteria are met:

- good or excellent knowledge and theoretical and applied understanding of the course content;
- good or excellent ability to interpret empirical and/or theoretical results;
- fully appropriate communication skills, particularly with regard to the use of subject-specific terminology.

Lectures, classes and homework. Students will be encouraged to solve and to hand in some pieces of homework throughout the course and to work in groups