# Objectif

The main objective of this course is to present modern econometric methods in a unified way. An asymptotic approach, particularly relevant in a context of big data, is adopted.The central statistical theory is that of extremal estimators and of the derived   theories of hypothesis testing and confidence regions. This general theory is applied to maximal likelihood methods, to pseudo-maximum likelihood methods (of order one, two and four),to non-linear least squares methods , to least absolute deviations methods , to quantile regressions, to the general method of moments (GMM), and to the asymptotic least squares methods (including minimum distance, chi-square and Berkson’s methods) . The simulated versions of these methods are also considered as well as indirect inference methods. The usefulness of all these methods in the context of big data is discussed. Applications to many kinds models are proposed: parametric or semi-parametric models, static or dynamic models, quantitative or qualitative models.

After this course the students should be able to master the implementation and the theoretical properties of the statistical methods used in static or dynamic econometric models.

# Plan

ECONOMETRIC MODELING.
Statistical models
Statistical problems
Sample models
Conditional Static Models (CSM)
Dynamic models
Steps of econometric modeling
Econometrics and big data
Econometrics and computer power
INFORMATION.
Kullback Information
Fisher Information
Fisher Information in dynamic models
STATISTICAL METHODS BASED ON EXTREMAL ESTIMATORS.
Extremal estimators
Hypothesis testing
Confidence regions
M-Estimators
Quasi-Generalized M-Estimators
Dynamic models
PARAMETRIC AND SEMI-PARAMETRIC ASYMPTOTIC BOUNDS.
Parametric Bounds
Semi-Parametric Bounds
NON-LINEAR LEAST SQUARES, LEAST ABSOLUTE DEVIATION METHODS, QUANTILE REGRESSIONS.
Nonlinear Least Square estimators (NLS)
Tests and confidence regions based on the NLS.
Extensions to multivariate and dynamics models
Least absolute deviations and quantile regressions methods
Asymptotic efficiency
Applications of NLS and quantile regressions to various domains
Applications of NLS and quantile regressions to financial econometrics
PSEUDO AND COMPOSITE MAXIMUM LIKELIHOOD METHODS.
Pseudo Maximum Likelihood Methods of Order 1(PML1)
Linear exponential families
Asymptotic properties of the PML1
Quasi Generalized PML1 (QGPML1) Methods
Pseudo Maximum Methods of Order 2
Pseudo maximum Likelihood Method of Order 4
Application of PML1 and QGPML1 to Heterogeneous Poisson Models
Application of PML2 and PML4 Methods to ARMA-GARCH Models
Composite PML methods and big data.
GENERALIZED METHODS OF MOMENTS (GMM).
Context, static case
Definition and properties of the GMM. method
Special case of a constraint based on conditional moments
Dynamic case
Examples: Two stage least squares (2SLS),Nonlinear two stage least squares
Tests and confidence regions
Applications to Keynesian models, Dynamic panel models
Applications to  CCAPM, Absence of Arbitrage Opportunity
ASYMPTOTIC LEAST SQUARES.
Definition of the Asymptotic Least Squares (ALS) methods
Example: Explicit constraints on the auxiliary parameter, Affine constraints on the parameter of Interest
Asymptotic properties
Important particular cases : Minimum Distance Method, Minimal Chi-square Method, Berkson’s Method
Test of mixed hypotheses
ALS methods and big data
Applications to the Asset Pricing Theory (APT)
SIMULATION BASED METHODS FOR DYNAMIC MODELS
Dynamic modeling
Dynamic models with latent variables and big data
State space models
Simulation based methods
Examples
INDIRECT INFERENCE
General principles of indirect inference (II)
An exercise
Asymptotic properties
Asymptotically equivalent methods(Score based methods)
Composite Indirect Inference and big data
Applications: Stochastic volatility models, Diffusions
Simulated Method of Moments (SMM)

# 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.