# Objective

The aim of this course is to present modern econometric methods in a unified form. The central statistical theory will be the theory of extreme estimators and the consequent theory of test methods and confidence regions. This general theory will be applied to the non-linear least squares method, the maximum likelihood and pseudo-maximum likelihood methods and the generalised moments method, as well as the asymptotic least squares method. Applications to a variety of models will be considered.

# Planning

1. Statistical modelling and information. Parametric and semi-parametric models. Sampling models, static and dynamic conditionals. Statistical problems. Kullback information. Fisher information.
2. Extreme estimators.Definitions. Convergence. Asymptotic normality. Tests. Confidence regions. M-estimators. Quasi-generalised m-estimators.
3. Asymptotic efficiency bounds. Parametric bound. Semi-parametric bound.
4. Non-linear least squares. Definitions. Examples: index models, splines, neural networks. Asymptotic properties. Robust estimator of the asymptotic variance-covariance matrix. Case of conditional homoscedasticity. Applications.
5. Pseudo-maximum likelihood (PML) methods.First-order PML methods (PML1). Linear exponential family. Quasi-generalised PML1 method. Semi-parametric optimality. Second-order PML method (PML2). Quadratic exponential family. Introduction to higher-order PML methods. Applications.
6. Generalised moments method (GMM). Simple moments method. Definition and properties of the GMM. Optimal metric. Case of the definition of the parameter by a conditional expected value. Semi-parametric optimality. Optimal instruments. Linear and non-linear two-stage least squares methods. Applications.
7. Asymptotic least squares method (ALS). Parameter of interest, auxiliary parameter. Definition and properties of the ALS. Optimal method. Mixed hypotheses test. Applications.
8. Extensions. Dynamic models. Introduction to methods based on simulations.

# Références

Gourieroux C. and A.Monfort : “Statistics and Econometric Models”,(2 volumes) Cambridge University Press ,1995.
Gourieroux C. and A.Monfort :”Simultation Based Econometric Methods”,Oxford University Press, 1996.