A.Y. 2021/2022
Overall hours
Learning objectives
The aim of the course is to provide students with the basic principles of econometrics. All the aspects of econometric models treated during the course will be investigated through modern empirical applications in order to motivate students and respond to important problems coming from the real world with appropriate and specific numerical answers. Specifically, the first aim of the course is to extend the simple linear regression model, already thought in the course of Statistics, in different directions: extend the number of regressors, consider potential departures from the standard assumptions of the model, develop a theoretical framework for making inference on the parameters of the model, both for small sample and asymptotically. The second specific aim, concerns the introduction to non-linear regression models like models for binary dependent variables or non-linear specifications among the regressors.
Expected learning outcomes
At the end of the course students will have received the introductory notions of econometrics. In particular, they will be able to specify a linear regression model, estimate the coefficients and perform tests of hypothesis on them. Moreover, students will be able to read and critically comment on the results of econometric analyses based on linear regression models or on regression models presenting some nonlinearities, like logit and probit ones. These expected outcomes should help students in understanding empirical analysis introduced in different courses, as well as provide them with quantitative tools for the development of the final thesis.
Course syllabus and organization

Single session

Lesson period
Second trimester
Course syllabus
- Economic questions and economic data
quantitative economic questions
causal effects and ideal experiments
data: sources and types

- Basic notions of probability
stochastic variables and probability distributions
expected value and variance
bivariate distributions: independence, covariance and correlation
Normal, chi-squared, Student-t and F distributions
law of large numbers and central limit theorem

- Basic notions of statistics
estimation of the mean of a population
hypothesis testing about the mean of a population
confidence intervals for the mean of a population
scatterplot, sample covariance and correlation

- Linear regression model with one single regressor
the linear regression model
estimation of the coefficients of the linear regression model
goodness of fit
assumptions of the linear regression model
OLS estimator and its sample distributions
California test score dateset (Appendix)
derivation of the OLS estimator (Appendix)
sample distribution of the OLS estimator (Appendix)
Formulas for the standard errors of the OLS estimator (Appendix)

- Linear Regression with Multiple Regressors
Omitted Variable Bias
The Multiple Regression Model
The OLS Estimator in Multiple Regression
Measure of Fit in Multiple Regression
The Least Squares Assumptions in Multiple Regression
The Distribution of the OLS Estimators in Multiple Regression

- Hypothesis Tests and Confidence Intervals in Multiple Regression
Hypothesis Tests and Confidence Intervals for a Single Coefficient
Tests of Joint Hypotheses
Testing Single Restrictions Involving Multiple Coefficients
Model Specification for Multiple Regression
Analysis of the Test Score Data Set

- Nonlinear Regression Functions
A General Strategy for Modeling Nonlinear Regression Functions
Nonlinear Functions of a Single Independent Variable
Interactions Between Independent Variables
Nonlinear Effects on Test Scores of Student-Teacher Ratio

- Assessing Studies Based on Multiple Regression (to read only)
Internal and External Validity
Threats to Internal Validity of Multiple Regression Analysis
Internal and External Validity when the Regression is Used for Forecasting
Example: Test Scores and Class Size

- Regression with a Binary Dependent Variable
Binary Dependent Variables and the Linear Probability Model
Probit and Logit Regression
Estimation and Inference in the Logit and Probit Models
Some applications

- Instrumental Variable Regression
The IV Estimator with a Single Regressor and a Single Instrument
The General IV Regression Model
Checking Instrument Validity
Where Do Valid Instruments Come From?
Appendix 2: Derivation of the Formula for the TSLS Estimator
Appendix 3: Large-Sample Distribution of the TSLS Estimator

- Introduction to Time Series Regression and Forecasting
Using Regression Model for Forecasting
Introduction to Time Series Data and Serial Correlation
Time Series Regression with Additional Predictors and ADL Model
Lag Length Selection Using Information Criteria
Nonstationarity: Trends
Detecting Stochastic Trends: Testing for a Unit AR root (to read only)

- Estimation of Dynamic Causal Effects
Dynamic Causal Effects
Estimation of Dynamic Causal Effects with Exogenous Regressors
Dynamic Multipliers (to read only)

- The Theory of Linear Regression with One Regressor (to read only)
The Extended Least Squares Assumptions and the OLS Estimator
Fundamentals of Asymptotic Distribution Theory (basic notions only)
Asymptotic Distribution of the OLS Estimator and t-Statistic
Exact Sampling Distributions When the Errors Are Normally Distributed
Weighted Least Squares (basic notions only)

- The Theory of Multiple Regression
The Linear Multiple Regression Model and the OLS Estimator in Matrix Form
Asymptotic Distribution of the OLS Estimator and t-Statistic
Test of Joint Hypotheses
Prerequisites for admission
Basic course of Statistics, including notions of inferential statistics. Basic notions of calculus and matrix algebra.
Teaching methods
Lessons and classes, using the econometric software STATA.
Teaching Resources
Textbook: "Introduction to Econometrics" by J.H. Stock e M.W. Watson.
Assessment methods and Criteria
Written exam.
SECS-P/05 - ECONOMETRICS - University credits: 6
Lessons: 40 hours
Wednesday: 13:30-16:30 (by appointment)