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Facoltà di Scienze Agrarie e Alimentari Università degli Studi di Milano
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Statistics and econometrics - unit 3
Codice: K0704C
Docente:  Giacomo Aletti
Anno di corso: 
Articolazione dei CFU: Lezioni frontali: 1,5
Esercitazioni in aula: 0,5
Obiettivi formativi:  Part 1: The aim of this part of the course is to give students the preliminary elements of probability and statistics. This part concentrates on the linear regression model, with particular attention to the OLS estimation procedure and related properties, finite and asymptotic, of the estimators.

Parts 2: The aim of these parts of the course is to provide students with the basic principles of the econometric analysis. All the theoretical aspects of the econometric modelling will be treated jointly with interesting and modern empirical applications in order to motivate students and try to respond to real-world questions with specific numerical answers.
Competenze acquisite:  At the end of the course the students should be able to formalize autonomously a statistical or econometric empirical problem and perform the related data analysis.
Sintesi del programma: 
Programma:  • Economic Questions and Data
- Economic Questions We Examine
- Causal Effects and Idealized Experiments
- Data: Sources and Types

• Review of Probability: Basic Notions

• Review of Statistics
- Estimation of the Population Mean
- Hypothesis Tests Concerning the Population Mean
- Confidence Intervals for the Population Mean
- Comparing Means from Different Populations
- Differences-of-Means Estimation of Causal Effects Using Experimental Data
- Using the t-Statistic When the Sample Size Is Small
- Scatterplot, the Sample Covariance, and the Sample Correlation

• Linear Regression with One Regressor
- The Linear Regression Model
- Estimating the Coefficients of the Linear Regression Model
- Measures of Fit
- The Least Squares Assumptions
- Appendix 2: Derivation of the OLS Estimators
- Sampling Distribution of the OLS Estimator

• Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals
- Testing Hypothesis about one of the Regression Coefficients
- Confidence Intervals for a Regression Coefficient
- Regression when X Is a Binary Variable
- Heteroskedasticity and Homoskedasticity
- The Theoretical Foundation of Ordinary Least Squares
- Using the t-Statistic in Regression When the Sample Size Is Small
- Appendix 1: Formulas for OLS Standard Errors

• 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
- Multicollinearity

• 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

• 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
- Autoregressions
- Time Series Regression with Additional Predictors and ADL Model
- Lag Length Selection Using Information Criteria

• 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 (to read only)
- 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

Readings: Reference book: Introduction to Econometrics - J.H. Stock and M.W. Watson
Materiale didattico: 
Modalità d'esame e altre info: 
Programma di Statistics and econometrics - unit 3 (versione in pdf)
Università degli Studi di Milano