Syllabus
EN
IT
Students are expected to have prior knowledge from the courses in Mathematics (8011190) and Statistics (8010848). A basic familiarity with Stata is also required.
Learning Objectives
LEARNING OUTCOMES: The Econometrics course aims to provide students with a solid theoretical and practical foundation for the quantitative analysis of economic phenomena. The program focuses on the linear regression model, robust statistical inference, the analysis of key specification problems (such as heteroskedasticity and endogeneity), and the use of advanced techniques including instrumental variables (IV) estimators and the generalized method of moments (GMM). Special emphasis is placed on the empirical application of the methods covered, through the use of the statistical software Stata for the analysis of real and simulated economic data. The course lays the groundwork for further studies in the quantitative area of the Economics degree and supports students in developing an empirical and critical approach to interpreting economic issues.
KNOWLEDGE AND UNDERSTANDING: Understand the core concepts of econometrics, especially the linear regression model and its properties (least squares, inference, model diagnostics). Identify common empirical modelling issues (e.g., heteroskedasticity, endogeneity) and appropriate econometric solutions (e.g., IV, GMM). Recognize the assumptions and limitations behind the estimation techniques.
APPLYING KNOWLEDGE AND UNDERSTANDING: Estimate and interpret regression models using Stata, selecting the most suitable technique for the empirical problem. Conduct hypothesis testing, assess model fit, and apply robust or corrective procedures when needed.
MAKING JUDGEMENTS: Choose independently the most appropriate estimation method for a given research question. Critically evaluate empirical results, considering potential violations of estimator assumptions, and propose suitable remedies where necessary.
COMMUNICATION SKILLS: Clearly and rigorously present the results of an econometric analysis, both orally and in writing. Produce concise reports including Stata-generated tables, highlighting key economic implications of the results.
LEARNING SKILLS: Develop an autonomous study method for advanced econometric topics (e.g., panel data, nonlinear models, causal inference). Understand the importance of mastering econometric tools for critically reading empirical literature and preparing for further studies (e.g., thesis, Ph.D., applied research).
KNOWLEDGE AND UNDERSTANDING: Understand the core concepts of econometrics, especially the linear regression model and its properties (least squares, inference, model diagnostics). Identify common empirical modelling issues (e.g., heteroskedasticity, endogeneity) and appropriate econometric solutions (e.g., IV, GMM). Recognize the assumptions and limitations behind the estimation techniques.
APPLYING KNOWLEDGE AND UNDERSTANDING: Estimate and interpret regression models using Stata, selecting the most suitable technique for the empirical problem. Conduct hypothesis testing, assess model fit, and apply robust or corrective procedures when needed.
MAKING JUDGEMENTS: Choose independently the most appropriate estimation method for a given research question. Critically evaluate empirical results, considering potential violations of estimator assumptions, and propose suitable remedies where necessary.
COMMUNICATION SKILLS: Clearly and rigorously present the results of an econometric analysis, both orally and in writing. Produce concise reports including Stata-generated tables, highlighting key economic implications of the results.
LEARNING SKILLS: Develop an autonomous study method for advanced econometric topics (e.g., panel data, nonlinear models, causal inference). Understand the importance of mastering econometric tools for critically reading empirical literature and preparing for further studies (e.g., thesis, Ph.D., applied research).
Prerequisites
Students are expected to have prior knowledge from the courses in Mathematics (8011190) and Statistics (8010848). A basic familiarity with Stata is also required.
Program
Module I
- Introduction (Lectures 1-3)
Econometric modelling and data structures
Ordinary least squares and the simple linear regression model
- Multiple Regression Analysis (Lectures 4-12)
Estimation, interpretation, and algebraic aspects of OLS
Finite sample properties of OLS
Qualitative information
The Gaussian linear model and exact statistical inference
Asymptotic properties and approximate inference
Robust inference
Heteroskedasticity tests and generalized least squares
- Endogeneity and the Instrumental Variables Approach (Lectures 13-18)
Key assumptions
IV and Wald estimators
Generalized Method of Moments and Two-Stage Least Squares
Tests for endogeneity, instrument relevance, and overidentifying restrictions
Module II
This course aims at providing a sound knowledge of the basic statistical tools for modelling
economic and financial time series.
Univariate Time Series
Stationary time series: Basic concepts. Stationarity, Total and partial autocorrelation,
Ergodicity, Linear stationary processes, ARMA models, Outliers, Forecasting.
Nonstationary time series: ARIMA models, The Beveridge-Nelson Trend-Cycle
decomposition, Seasonality,
Statistical inference: Estimation, Identification, Diagnostic checking.
Unit roots in economic and financial time series: Deterministic trends vs. random walks,
Unit-roots tests, Impulse response function and measures of persistence
Multivariate Time Series
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
Textbook:
Hamilton, J.D. (1994) "Time Series Analysis", Princeton University Press
- Introduction (Lectures 1-3)
Econometric modelling and data structures
Ordinary least squares and the simple linear regression model
- Multiple Regression Analysis (Lectures 4-12)
Estimation, interpretation, and algebraic aspects of OLS
Finite sample properties of OLS
Qualitative information
The Gaussian linear model and exact statistical inference
Asymptotic properties and approximate inference
Robust inference
Heteroskedasticity tests and generalized least squares
- Endogeneity and the Instrumental Variables Approach (Lectures 13-18)
Key assumptions
IV and Wald estimators
Generalized Method of Moments and Two-Stage Least Squares
Tests for endogeneity, instrument relevance, and overidentifying restrictions
Module II
This course aims at providing a sound knowledge of the basic statistical tools for modelling
economic and financial time series.
Univariate Time Series
Stationary time series: Basic concepts. Stationarity, Total and partial autocorrelation,
Ergodicity, Linear stationary processes, ARMA models, Outliers, Forecasting.
Nonstationary time series: ARIMA models, The Beveridge-Nelson Trend-Cycle
decomposition, Seasonality,
Statistical inference: Estimation, Identification, Diagnostic checking.
Unit roots in economic and financial time series: Deterministic trends vs. random walks,
Unit-roots tests, Impulse response function and measures of persistence
Multivariate Time Series
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
Textbook:
Hamilton, J.D. (1994) "Time Series Analysis", Princeton University Press
Books
Module I
The main reference is Wooldridge J.M., (2016), Introductory Econometrics: A Modern Approach, 6th ed., Cengage Learning.
For some topics, Wooldridge (2016) will be complemented by selected articles which will be made available on the material section of the course website and by some chapters from:
Greene W.H., Econometric Analysis, 8th ed., Pearson.
Module II
The suggested textbookis: Hamilton, J.D. (1994) "Time Series Analysis", Princeton
University Press. Further, lecture notes and slides will be distributed and they will consittute
the main reference.
The main reference is Wooldridge J.M., (2016), Introductory Econometrics: A Modern Approach, 6th ed., Cengage Learning.
For some topics, Wooldridge (2016) will be complemented by selected articles which will be made available on the material section of the course website and by some chapters from:
Greene W.H., Econometric Analysis, 8th ed., Pearson.
Module II
The suggested textbookis: Hamilton, J.D. (1994) "Time Series Analysis", Princeton
University Press. Further, lecture notes and slides will be distributed and they will consittute
the main reference.
Bibliography
Module I
For further study in econometrics, I suggest Peracchi (2001), Wooldridge (2010), Davidson and MacKinnon (2004) and references therein:
Peracchi F. (2001), Econometrics, Wiley, Chichester (UK).
Wooldridge J.M., (2010), Econometric Analysis of Cross-Section and Panel Data, 2nd ed., MIT Press, Cambridge (MA).
Davidson R. and MacKinnon J.G., Econometric Theory and Methods, New York, Oxford University Press, 2004.
Module II
Hamilton, J.D. (1994) "Time Series Analysis", Princeton University Press.
For further study in econometrics, I suggest Peracchi (2001), Wooldridge (2010), Davidson and MacKinnon (2004) and references therein:
Peracchi F. (2001), Econometrics, Wiley, Chichester (UK).
Wooldridge J.M., (2010), Econometric Analysis of Cross-Section and Panel Data, 2nd ed., MIT Press, Cambridge (MA).
Davidson R. and MacKinnon J.G., Econometric Theory and Methods, New York, Oxford University Press, 2004.
Module II
Hamilton, J.D. (1994) "Time Series Analysis", Princeton University Press.
Teaching methods
The course is delivered through face-to-face lectures and guided empirical exercises, using a blended theoretical and practical approach. It includes 48 hours of instruction, according to the schedule published on the course website before the beginning of the semester.
Lectures cover the theoretical and methodological foundations of econometrics, with a focus on regression models, statistical inference, and the identification of empirical issues such as heteroskedasticity and endogeneity. Theory is constantly integrated with practice through empirical examples, simulations, and interpretation of Stata output, helping students develop analytical skills and apply tools to real-world problems.
Students are actively encouraged to ask questions, express doubts, and formulate critical insights during lectures and exercises, drawing on the concepts and techniques acquired. This interactive approach supports the development of cross-disciplinary skills such as critical reasoning, quantitative problem solving, empirical interpretation, and evidence-based decision-making.
Given the applied and interactive nature of the course, regular and active attendance is strongly recommended.
Lectures cover the theoretical and methodological foundations of econometrics, with a focus on regression models, statistical inference, and the identification of empirical issues such as heteroskedasticity and endogeneity. Theory is constantly integrated with practice through empirical examples, simulations, and interpretation of Stata output, helping students develop analytical skills and apply tools to real-world problems.
Students are actively encouraged to ask questions, express doubts, and formulate critical insights during lectures and exercises, drawing on the concepts and techniques acquired. This interactive approach supports the development of cross-disciplinary skills such as critical reasoning, quantitative problem solving, empirical interpretation, and evidence-based decision-making.
Given the applied and interactive nature of the course, regular and active attendance is strongly recommended.
Exam Rules
Module I
The final exam consists of a written test lasting 90 minutes, made up of three exercises. Two exercises are more theoretical in nature, requiring discussion and proof of results and/or theorems covered in class, as well as analysis of the assumptions and statistical properties of the discussed estimation approaches. The third exercise is more applied and involves interpreting output produced using Stata, reporting estimation results and hypothesis testing evidence.
To pass the exam, students must score at least 18 on at least two of the exercises. The final grade is calculated as the arithmetic mean of the three scores. Each exercise is graded on a 0–33 scale, allowing a final mark of 30 to be achieved even without scoring 30 on all three exercises.
Students must register for the final exam through the portal: https://delphi.uniroma2.it. Those who fail or withdraw may retake the exam during the same session.
Grading Scale
Fail: Major gaps and/or inaccuracies in the understanding of basic econometric concepts (e.g., model specification, estimation assumptions); weak grasp of inference methods; limited ability to interpret empirical results; vague or unfounded arguments.
18-20: Barely sufficient knowledge of key topics; weak understanding of assumptions; basic analytical and reasoning skills with some uncertainty; sufficient autonomy of judgment.
21-23: Operational knowledge of estimation methods; able to apply and discuss basic models; correct analysis and logically coherent arguments, though not in depth.
24-26: Good understanding of theoretical and applied content; statistically sound interpretations; rigorous methodological reasoning.
27-29: Full and confident knowledge of tools, including advanced topics (e.g., GLS, GMM, robust inference); strong analytical and critical thinking; independent evaluation of results.
30-30L (cum laude): Excellent command of econometric methods, even in complex contexts; outstanding analytical and reasoning skills; original problem-solving ability; strong autonomy and capacity to connect theory with empirical evidence.
Module II
The evalaution consists of a written exam that involves theoretical exercises and questions
about the topics of the course. The average mark of the homework (if taken) will be
weighted for 20% of the overall mark.
The student should demonstrate to have learned the theory and the advanced skills
required for the econometric analysis of empirical phenomenons over time.
Students who withdraw or fail an exam, can re-take the exam in the same session.
The final exam consists of a written test lasting 90 minutes, made up of three exercises. Two exercises are more theoretical in nature, requiring discussion and proof of results and/or theorems covered in class, as well as analysis of the assumptions and statistical properties of the discussed estimation approaches. The third exercise is more applied and involves interpreting output produced using Stata, reporting estimation results and hypothesis testing evidence.
To pass the exam, students must score at least 18 on at least two of the exercises. The final grade is calculated as the arithmetic mean of the three scores. Each exercise is graded on a 0–33 scale, allowing a final mark of 30 to be achieved even without scoring 30 on all three exercises.
Students must register for the final exam through the portal: https://delphi.uniroma2.it. Those who fail or withdraw may retake the exam during the same session.
Grading Scale
Fail: Major gaps and/or inaccuracies in the understanding of basic econometric concepts (e.g., model specification, estimation assumptions); weak grasp of inference methods; limited ability to interpret empirical results; vague or unfounded arguments.
18-20: Barely sufficient knowledge of key topics; weak understanding of assumptions; basic analytical and reasoning skills with some uncertainty; sufficient autonomy of judgment.
21-23: Operational knowledge of estimation methods; able to apply and discuss basic models; correct analysis and logically coherent arguments, though not in depth.
24-26: Good understanding of theoretical and applied content; statistically sound interpretations; rigorous methodological reasoning.
27-29: Full and confident knowledge of tools, including advanced topics (e.g., GLS, GMM, robust inference); strong analytical and critical thinking; independent evaluation of results.
30-30L (cum laude): Excellent command of econometric methods, even in complex contexts; outstanding analytical and reasoning skills; original problem-solving ability; strong autonomy and capacity to connect theory with empirical evidence.
Module II
The evalaution consists of a written exam that involves theoretical exercises and questions
about the topics of the course. The average mark of the homework (if taken) will be
weighted for 20% of the overall mark.
The student should demonstrate to have learned the theory and the advanced skills
required for the econometric analysis of empirical phenomenons over time.
Students who withdraw or fail an exam, can re-take the exam in the same session.