ECONOMETRICS

The course aims to handle some aspects of the econometric methods with respect to the regression models, both uni- and multi-equational like the models of simultaneous equations and the vector autoregressive models (VAR). Consequently, the purpose is to prepare the student to use the basic econometric tools for the measurement, interpretation and forecast of the economic and financial phenomena. The course is well equipped with econometric practice.

At the end of the course the students are able to know the relevant part of the econometric theory that is essential for the interpretation of the results produced by an econometric software. In particular, they will acquire skills in the treatment of macroeconomic and financial data for the specification, estimation and forecasting with regression models. The preparation is completed with the analysis of current aspects of the real and financial economy, using time series downloaded from available databases.

Elementary matrix algebra, Random variable theory, Elementary Statistical inference: Point estimation and testing.

Introduction to the linear regression model
- Specification of single equation bivariate and multivariate model
- Ordinary Least Square (OLS): algebraic approach to calculate the unknown parameters
- Probabilistic interpretation of the regression
- Properties of the estimators: examples
- Regression with linear constraints
- Insights on hypothesis testing: tests on linear constraints
Model validation: Residuals analysis
- Autocorrelation and heteroscedasticity tests
- Normality test
Asymptotic properties of estimators
- Stochastic convergences
- Useful limit theorems for asymptotic analysis
- Asymptotic properties of the OLS estimator
- Properties of OLS estimators in finite sample
Univariate and multivariate stationary stochastic processes
- Univariate and multivariate stochastic processes, frequently used processes
Univariate and multivariate stationary stochastic processes
- Univariate and multivariate stochastic processes, frequently used processes
- Wold decomposition theorem and Linear Genral Processes
- Dynamic properties: long-term coefficients and impulsive response functions
Stochastic non-stationary processes
- Unit root processes and spurious regression
- Stationary trend processes (TS) and stationary in difference (DS)
- Some examples of estimation of non-stationary economic series
Specification of the regression model
- Inclusion of irrelevant variables and exclusion of relevant variables
- Specification strategies
- Selection of regressors
Specification strategies with integrated processes
- Cointegration and Error Correction Model representation
- Generalizations of the representation of an ECM model
- Specification strategies in the presence of regressors I (1) and I (0)
- Simulation of an ECM model
Multiple equation models
- Parametric identification in simultaneous equations model
- Limited Information and Full Information estimation methods
Identification and Information
- Sufficiency and ancillarity of a statistic and a parameter
Exogeneity and incomplete equation systems
- Strict econometric exogeneity
- Weak, strong and super-exogeneity
- Admissibile operations as consequence of the different concepts of exogeneity
- Exogeneity testing
Overview of Bayesian inference
Outline of decision theory
Forecasting
- Ex-ante and ex-post forecast
- Static and Dynamic forecast

References:
A) Hamilton J.(1995), Econometria delle serie storiche, Trad. B. Sitzia, Monduzzi, Milano
B) Cappuccio N. e R. Orsi (2005), Econometria, Il Mulino
C) Peracchi F. (1995), Econometria, McGraw-Hill Libri Italia
D) Verbeck M. (2006), Econometria, Zanichelli

The exam is individual and consists in:
a) presentation of a uniequational multivariate regression model on current data of the real or financial economy;
b) exposition and discussion of some topics of econometric theory

Lectures, tutorial exercises, practical application on economic and/or financial data using econometric software

Italian

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