 # Statistical Methods of Econometrics

#### MONFORT Alain

Département : Finance

### Objectif

The objectives of this course are as follows. First, the key issues of mathematical modelling of economic phenomena will be highlighted. Second, it will be proposed a general framework providing a toolbox allowing to address these issues. Third, it will be checked that the classic econometric methods are particular cases of this framework. Fourth, advanced methods derived from this general approach will be presented and illustrated by various applications (in economics, finance, insurance).

EXAM : it will be based on a homework consisting in summarizing, evaluating and, if possible, extending a piece of literature centered on a research article.

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

### Plan

INTRODUCTION : KEY ISSUES
Deterministic vs probabilistic modelling, Postulated vs data driven models,
Agnostic vs structural approach, Data mining or data snooping, Model risk and
misspecified models, Efficiency vs robustness, Statistical vs numerical algorithms,
Econometrics and big data, Econometrics and simulations, Econometrics and machine
learning.
PART I : A UNIFYING TOOLBOX
Information, Extremal estimators, The Sandwich formula, Meta test and
confidence region theory, Efficiency parametric and semi-parametric bounds.
PART II : CLASSIC METHODS
Classic inference methods for static or dynamic models as straightforward
particular cases of the general approach proposed in part I : Maximum Likelihood (ML)
method, Nonlinear Least Squares, Absolute Deviation Method, Quantile Regression,
Generalized Method of Moments (GMM), 2 Stage Least Squares…
PART III : ADVANCED METHODS AND APPLICATIONS

•  Pseudo-Maximum Likelihood (PML) methods of order 1, 2, 4, applications to Non Gaussian ARMA-GARCH models in finance, rating in insurance.
•  Composite Maximum Likelihood (CML) methods, CML and big data, application to corporate risks with a systemic component.
•  Asymptotic Least Squares (ALS), inference on deep or structural parameters, tests of mixed hypotheses, Berkson method, applications to risk premia, simultaneous equations, aggregated Markov chains.
• Typology of simulation based econometric methods, the basic combinatorial problem of dynamic models with latent variables, the Kalman and Kitagawa-Hamilton filters, simulations based on observable or latent variables, Metropolis-Hastings algorithm, Bayesian approach.
• Indirect inference, instrumental model, pseudo-true value, binding function, simulated observations and two step Sandwich formula, Composite Indirect Inference (CII) and big data, Simulated Method of Moments (SMM) as particular case, applications to stochastic volatility models and continuous time stochastic processes.

### Références

REFERENCES : Gouriéroux C. and Monfort A. : « Statistics and Econometric
Models » (2 volumes) Cambridge University Press ;
Gouriéroux C. and Monfort A. : « Simulation Based Econometric Methods », Oxford
University Press.