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 bootstrap


B. Time Series Econometrics

B.1 Stochastic Processes
B.2 Asymptotic Theory
B.3 Stationary ARMA processes
B.4 Stationary Vector Processes
B.5 Non-stationary Processes
B.6 Cointegration
B.7 State-space Models

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 course is organized into two modules. The exam is passed if the average of both modules is larger than or equal to 18.

The exam consists of a number of mainly theoretical questions, for example, asking to demonstrate some theoretical results or to define a suitable testing strategy to validate some specific economic problem. To each answer is assigned a score (from 0 to 10 points, depending on the number of questions in the exam). The evaluation is completed by analyzing the paper as a whole.

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