Quantitative Methods fo Economic Applications – Statistics

The aim of the course is to address statistical modelling and, in particular, introduce students to generalized linear models, which provide a unifying framework for many statistical techniques commonly adopted in economics and finance. At the end of the course, students will be able to model the relationship between a univariate response variable and a set of explanatory variables measured on various scales, to estimate the parameters of the model understanding their meaning and to check the adequacy of the model to data. Moreover, students will acquire the basic notion of the R software (R Core Team, 2019) to apply generalized linear models related techniques.

Recommended prerequisites

Basic knowledge of classical statistical principles and methods (estimation and hypothesis testing) and knowledge of basic matrix algebra and calculus.

 

Random variables, expected value, variance.  Random vectors, mean vector and variance-covariance matrix.
Parametric statistical model. Point estimators, finite sample properties (unbiasedness, mean squared error, efficiency) and large sample properties (asymptotic unbiasedness, consistency, asymptotic efficiency).
Likelihood function, maximum likelihood estimators and their properties. Score and Fisher information. Fisher scoring algorithm.
Confidence interval estimators, pivotal quantity, interval estimators based on the asymptotic properties of maximum likelihood estimators.
Testing hypotheses: test statistic, power function, type I and II errors, uniformly most powerful tests, consistency. P.value. Generalized likelihood ratio test, score test, Wald test.

Exponential family of distribution, properties of expectation and variance.

Generalized linear models, maximum likelihood estimation of model parameters, hypothesis testing for model parameters. Deviance, testing model goodness of fit.
Normal linear model (multiple linearregression, analysis of variance, general linear model).
Logistic regression, Poisson regression.
Generalized linear models will be fitted to dataset using the R-environment (R Core Team, 2019).

 

Textbook

Dobson, J. and Barnett, A.G. (2018) An Introduction to Generalized Linear Models, fourth ed., CRC Press.

Supplementary material

Supplementary material will be shared during the course.

Additional reading

Faraway, J.J. (2016) Extending the Linear Model with R, second ed., CRC Press.

 

The exam consists in a written and oral tests. The written test is composed by exercises on the inferential techniques introduced in the first part of the course, aiming to evaluate the theoretical knowledge of the methodologies, and by exercises on interpreting output obtained using R, aiming to assess the capability of interpreting the results of the analysis.
When the written test is satisfactory, the student will face an oral test, based on questions on the main course topics, aimed to evaluate the ability of applying the inferential techniques, and particularly the introduced models, in economic, business and financial contexts.
Two written midterms formed by exercises are scheduled. The topics of the first are the inferential techniques introduced in the first part of the course, the second midterm deals with interpreting R outputs.
If both midterms are satisfactory, the written test is passed.