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.
- 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 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
- 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 Autoregressions 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.
Lessons and classes, using the econometric software STATA.
Textbook: "Introduction to Econometrics" by J.H. Stock e M.W. Watson.