EERC Methodological Seminars Series

 

ECONOMETRIC SEQUENCE

Estimation and Inference in Econometrics

 

Instructor: Stanislav Anatolyev, New Economic School, Moscow

 

 

This seminar is the first part of the econometric sequence. It serves as an introduction to principles of contemporary art of econometric estimation and inference, particularly when applied to cross-sectional analysis. Motivated by dissatisfañtion with exact inference, we will consider competing alternatives: asymptotic approximation and bootstrap. We will review estimation in a linear environment and then will turn to nonlinear models. Finally, we will study currently very popular Maximum Likelihood and Generalized Method of Moments estimators. Theoretical and empirical examples will be abundant throughout.

 

ORGANIZATION

 

Along with lectures, there will be separate computer sessions. The instructor will also be available during office hours. The students are encouraged to work in groups.

 

LITERATURE

 

Greene, William (1997) Econometric Analysis, 3rd edition

Lecture notes in Russian

 

SYLLABUS

 

I. Approximate Inference

1.      Three approaches to inference

        Three approaches to inference: exact, asymptotic, bootstrap.

        Problems with exact inference

2.      Asymptotic approach

        Convergence of sequences of random variables.

        Laws of Large Numbers. Central Limit Theorems.

        Continuous mapping theorems. Delta-method.

        Asymptotic confidence intervals

        Large sample hypothesis testing.

3.      Bootstrap approach

        Approximation by bootstrapping and approximation by simulation.

        Nonparametric bootstrap in a linear mean regression model.

        Bootstrap confidence intervals: percentile and percentile-t.

        Bootstrap hypothesis testing.

II. Linear Models: Estimation and Approximate Inference

1.      Estimation of a linear mean regression

        OLS estimator in linear mean regression models.

        Asymptotic properties of the OLS estimator.

        Efficiency and the GLS estimator.

2.      Instrumental variables in a linear model

        Endogeneity and instrumental variables.

        Simultaneity and errors in variables.

        IV and 2SLS estimators and their asymptotic properties.

III. Nonlinear Models: Estimation and Approximate Inference

1.      Estimation of a nonlinear mean regression

        Nonlinear Least Squares (NLLS) estimator.

        Asymptotic properties of NLLS estimators.

        Nonlinear optimization: the concentration method.

2.      The Maximum Likelihood (ML) estimator

        Likelihood function and likelihood principle. ML estimation.

        Asymptotic properties of ML estimators. Asymptotic efficiency.

        ML asymptotic tests: Wald, Likelihood Ratio, Lagrange Multiplier.

3.      Applications: limited dependent variables models

        Binary choice models. Probit and logit. ML and NLLS estimation.

        Censored data and sample selection. Tobit. Two step estimators.

        Count data. Poisson regression.

4.      The Generalized Method of Moments (GMM) estimator

        Just identifying moment conditions and the method of moments.

        Overidentifying moment conditions and the GMM problem.

        Asymptotic properties of GMM estimators

        Efficient GMM and feasible efficient GMM.

        The test of overidentifying restrictions (the J-test).