**Econometrics**

**Doctoral school in Economics**

**Department of Economics and Social Sciences, Marche Polytechnic University**

**Course Description: **

The **Econometrics** course will be organized in three blocks. The first block (24 hours) will present an advanced treatment of econometric theory and principles of estimation and inference in linear regression models, focusing also on maximum likelihood estimation, generalized methods of moments, and heteroskedasticity. In the second block (17 hours), students will study the estimation of nonlinear regression models, notably limited dependent variable models. The third block (21 hours) will present models for time series data. Further 25 hours of computer tutorials will be aimed at developing analytical skills using Gretl (http://gretl.sourceforge.net).

**Learning Outcomes:**

- Development of analytical skills so that students can evaluate critically the econometric outputs in the economic literature and correctly interpret them.
- Development of analytical and technical skills so that students can design proper econometric model to answer their research questions.
- Development of computer programming skills so that students can estimate sophisticated and state-of-art econometric models.

**Prerequisites: **

Students should have knowledge, at least at undergraduate level, of the following topics:

- Scope of Econometrics, the structure of economic data;
- Causality and the notion of
*ceteris paribus*in econometrics; - Definition of the simple linear regression model and its interpretation;
- Ordinary Least Squares (OLS) estimates and OLS properties;
- Interpretation of OLS estimates;
- Multiple regression analysis: many independent variables in the linear regression model;
- OLS estimates and their interpretation with multiple regressors;
- Inference in multiple regression analysis;
- The Gauss-Markov theorem;
- Testing hypothesis about a single parameter;
- Testing hypothesis about multiple linear restrictions;
- OLS asymptotics;
- Goodness-of-fit measures;
- Linear models (in the parameters) with quadratics and/or logarithms of the regressors;
- Linear models with interaction terms;
- Linear models with qualitative independent variables;
- Heteroskedasticity: testing and robust inference;
- Misspecification: functional form misspecification, omitted variables, measurement error;
- Instrumental variables estimation.

These topics are in chapters 1 to 9 and 15 of “Introductory Econometrics: A Modern Approach” (Wooldridge, 7^{th} edition, 2015). Alternatively, they can be found in chapters 1-9 and 12 of “Introduction to Econometrics” (Stock and Watson, 3^{rd} edition, 2015). These textbooks are for undergraduate economics students who have taken a course of introductory probability and statistics.

**Syllabus:**

Block 1:

- Asymptotic theory.
- Maximum Likelihood: Estimation.
- Maximum Likelihood: Testing.
- Generalized Method of Moments.
- Linear Model and Ordinary Least Squares.
- Instrumental Variables estimation.
- Robust inference.

Block 2:

- Binary response models.
- Multinomial response models.
- Ordered response models.
- Count response models.
- Heteroskedasticity and endogenous regressors in nonlinear models.
- Tobit model.
- Sample selection issues.

Block 3:

- Dynamic models
- Time series and stochastic processes.
- ARMA models.
- Nonstationary processes and unit roots tests.
- VAR and SVAR models.
- Cointegration.

**Exam:**

At the end of the course, students will be assigned a take-home exam on the second and the third blocks (60% of the final grade) with deadline on 6 January 2020 and there will be an open-book written exam on the first block (40% of the final grade) on Tuesday 14 January 2020. On Thursday 16 January, students will be asked to orally explain what they did in the take home exam and why.

Students that will not pass the exam will resit it later in the year: the resit will be an open-book written exams on all the blocks.

**Lecturers:**

- Lecturer of 1st block: Riccardo Lucchetti
- Lecturer of 2nd block: Matteo Picchio
- Lecturer of 3rd block: Giulio Palomba
- Lecturers of computer tutorials: Luca Pedini e Francesco Valentini

**Reading list:**

- Cameron A.C. and Trivedi P.K. (2005), Microeconometrics: Methods and Applications, Cambridge University Press.
- Cochrane J.H. (2005), Time Series for Macroeconomics and Finance, http://econ.lse.ac.uk/staff/wdenhaan/teach/cochrane.pdf.
- Davidson R. and Mackinnon J.G. “Econometric Theory and Methods”, Oxford University Press.
- Hansen B.E. “Econometrics” http://www.ssc.wisc.edu/~bhansen/econometrics/.
- Wooldridge J.M. (2010), Econometric Analysis of Cross Sections and Panel Data, MIT Press.
- Lütkepohl H. and Krätzig M. (2004), Applied Time Series Econometrics, CUP.

A detailed list of chapters of these textbooks will be provided during the course.

**Software for computer tutorials:**

- Gretl, freely downloadable at http://gretl.sourceforge.net.