Notes: These teaching resources correspond to the course "Statistique Mathématique" (in French) of the first year program of the Master ESA (Université of Orléans). Some of them have been also used for the course "Advanced Econometrics" (2013) of the first year of the Master of Science in Finance of HEC Lausanne.
Advanced econometrics
Introduction_ESA.pdfGeneral introduction
What is an econometrics?
Population and sample
Probability and random sampling
Cross-sectional data, time series data, and panel data
Parametric and semi-parametric models
Econometric model
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Chapter 1. Estimation Theory
What is an estimator?
Finite sample and large sample properties of an estimator
Convergence: almost sure, probability, mean square, distribution
Law of large numbers and Central Limit Theorem
Continous mapping theorem and delta method
Asymptotic distribution of an estimator
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Chapter1_Estimation_Theory_ESA.pdfChapter2_MLE_ESA.pdfChapter 2. Maximum Likelihood Estimation
Likelihood function
Maximum Likelihood Estimator
Score, Gradient, and Hessian
Fisher information matrix
Asymptotic properties of the maximum likelihood estimator
Applications :multiple linear regression, probit and logit models
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Chapter 3. The Multiple Linear Regression Model
The multiple linear regression model
Parametric and semi-parametric specifications
The Ordinary Least Squares (OLS) estimator
Statistical properties of the OLS
Finite and asymptotic sample properties of the OLS
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Chapter3_Linear_Model_ESA.pdfChapter4_Inference_ESA.pdfChapter 4. Statistical Hypothesis Testing
Statistical hypothesis testing and inference
Tests in the multiple linear regression model
The Student t-test and Fisher test
Maximum Likelihood Estimation (MLE) and Inference
The Likelihood Ratio (LR), Wald and Lagrange Multiplier (LM) tests
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Chapter 5. Heteroscedasticity
The generalized linear regression model
Generalized Least Squares (GLS)
Feasible Generalized Least Squares (FGLS)
Heteroscedasticity
White correction for heteroscedasticity
Testing for heteroscedasticity: Breusch-Pagan and White tests
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Chapter5_GLS_ESA.pdfChapter6_IV_ESA.pdfChapter 6. Endogeneity and Instrumental Variables
Definition and source of endogeneity
Endogeneity bias of the OLS estimator
Endogenity biais and smearing effect
Instrumental variable
Instrumental Variables (IV) estimator
Two-Stage Least Squares (2SLS)
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Chapter 7. Bayesian Econometrics
Prior and posterior distribution
Posterior distributions and inference
Application to Bayesian VAR
Numerical simulations
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Chapter7_Bayesian.pdfExercises
Exercises Chapter 1. Estimation Theory (slides)
MLE and Rayleigh distribution
CAPM and OLS regression
Exercises Chapter 2. Maximum Likelihood Estimation (slides)
MLE and Geometric distribution
MLE and AR(p) processes
Exercises Chapter 4. Statistical Hypothesis Testing (slides)
Parametric test and Neyman Pearson Lemma
The trilogy: LRT, Wald and LM tests
Exams
Mid-term exam 2013 - HEC Lausanne (statement) and (correction)
MLE and log-normal distribution
MLE and Probit model
Final exam 2014 - HEC Lausanne (statement) and (correction)
MLE and log-normal distribution
MLE and Logit model
Final exam 2014-2015 - Master ESA - Université d'Orléans (sujet)
MLE and log-normal distribution
MLE and Logit model
Mid-term exam 2015-2016 - Master ESA - Université d'Orléans (sujet) et (correction)
MLE and Gamma distribution
Wald test, LM test, LR test
Final exam 2020-2021 - Master ESA - Université d'Orléans (sujet) et (correction)
MLE and Logit model
Wald test, LM test, LR test
Mid-term exam 2021-2022 - Master ESA - Université d'Orléans (sujet) et (correction)
MLE and Weibull distribution
Wald test, LM test, LR test
Mid-term exam 2022-2023 - Master ESA - Université d'Orléans (sujet) et (correction)
AR model and maximum likelihood
z-tests in linear regression model
Wald test, LM test, LR test