Teacher(s)
Language
English
Prerequisites
Mathematics and Statistics for Economists
Main themes
The course must cover the basic most important topics of econometric theory at an advanced level.
These themes concern econometric model formulation, estimation and testing.
Teaching is at an advanced level. Proofs of important results are covered, though not systematically. Applications are also used so that students learn how to carry applications in their own research.
Contents
These themes concern econometric model formulation, estimation and testing.
Teaching is at an advanced level. Proofs of important results are covered, though not systematically. Applications are also used so that students learn how to carry applications in their own research.
Contents
- Linear regression : exact finite sample theory of ordinary and generalized least squares
- Large-sample theory: convergence concepts, stochastic processes (stationarity and ergodicitys, IID and white noise, martingales, martingale difference sequences) and limit theorems for IID and MDS). Application to large sample theory of least-squares estimation.
- GMM and the method of instrumental variables
- The method of maximum likelihood: (estimation and testing) and its application to linear regression and non-linear regression models.
- Empirical applications. Use of an econometric and simulation/computational software.
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 |
The purpose is that students acquire the basic tools of econometric research which are of general use in more specialized fields of research and which are covered in subsequent courses (Microeconometrics and Econometrics of Time-Series). An example of such a tool is the method of estimation by maximum likelihood. |
Content
1 Linear regression
1.1 Before modeling
1.2 Modeling by regression
1.2.1 Conditional distribution
1.2.2 Exogeneity
1.2.3 Regression
1.2.4 Linear regression
1.2.5 Identification
1.3 Statistical model
1.3.1 What is a statistical model?
1.3.2 Marginal-Conditional decomposition
1.4 Ordinary Least Squares
1.4.1 Definitions
1.4.2 Geometry of Least Squares
1.4.3 Gauss-Markov Theorem
1.4.4 Testing
1.5 Regression with instrumental variables
1.5.1 Statistical model with instrumental variables
1.5.2 Identification
1.5.3 Estimation by projection
2 Convergence results in linear regression
2.1 Asymptotic properties of Projection estimators
2.1.1 Introduction
2.1.2 Consistency
2.1.3 Asymptotic Normality
2.2 Inference under heteroskedasticity
2.3 Generalized Method of Moments (GMM)
2.3.1 Optimal GMM
2.3.2 Testing for overidentifying restrictions
3 Likelihood
3.1 Extremum estimators
3.1.1 Consistency
3.1.2 Asymptotic Normality
3.2 Maximum likelihood estimation
3.2.1 Definition and consistency
3.2.2 Asymptotic distribution of MLE
3.2.3 Cramer-Rao inequality and asymptotic efficiency
1.1 Before modeling
1.2 Modeling by regression
1.2.1 Conditional distribution
1.2.2 Exogeneity
1.2.3 Regression
1.2.4 Linear regression
1.2.5 Identification
1.3 Statistical model
1.3.1 What is a statistical model?
1.3.2 Marginal-Conditional decomposition
1.4 Ordinary Least Squares
1.4.1 Definitions
1.4.2 Geometry of Least Squares
1.4.3 Gauss-Markov Theorem
1.4.4 Testing
1.5 Regression with instrumental variables
1.5.1 Statistical model with instrumental variables
1.5.2 Identification
1.5.3 Estimation by projection
2 Convergence results in linear regression
2.1 Asymptotic properties of Projection estimators
2.1.1 Introduction
2.1.2 Consistency
2.1.3 Asymptotic Normality
2.2 Inference under heteroskedasticity
2.3 Generalized Method of Moments (GMM)
2.3.1 Optimal GMM
2.3.2 Testing for overidentifying restrictions
3 Likelihood
3.1 Extremum estimators
3.1.1 Consistency
3.1.2 Asymptotic Normality
3.2 Maximum likelihood estimation
3.2.1 Definition and consistency
3.2.2 Asymptotic distribution of MLE
3.2.3 Cramer-Rao inequality and asymptotic efficiency
Teaching methods
Lectures
Evaluation methods
A written exam and an oral exam
Other information
Support: lecture notes(in pdf) by S. Van Bellegem
Bibliography
Faculty or entity
