Advanced Econometrics I 2400-M1IiEZEKO

• Lecture is concentrated on tree important areas of econometrics: models estimated on panel data, properties and applications of Maximum Likelihood (ML) estimators and properties and applications of Generalized Method of Moments (GMM) estimators. On the lecture the most important statistical models and estimation methods used in contemporary econometrics will be presented. Lecture is ilustrated with simple empirical examples.
• Problem sessions are intended to teach students how to use econometric tools and verify their up to day progress. Problem sessions are not to repeat the material covered on lectures. On the problem sessions students should learn how to choose and formulate econometric model well suited to research problem, the estimation of this model with STATA package and the interpretation of the results obtained.
• An important part of part of problem session is the work on final paper consisting of the econometric analysis of same economic problem.
Topics covered:
Specification search and data mining
• Simple and joint hypotheses, Lovel bias
• Nested and nonnested hypotheses
• General to specific methods
• Specification search: information criteria (AIC i BIC)
Maximum Likelihood Method (ML)
• Definition of likelihood function
• Assumptions of ML
• Properties of ML (consistency, efficiency, asymptotic distributions)
• Variance estimation of ML estimators
• Example: Ordinary Least Squares (OLS) estimator and Nonlinear Least Squares (NLOLS) estimator
• Hypothesis testing for ML
• Comparison of Likalihood Ratio (LR), Wald (W) and Lagrange Multipliers (LM) tests
Application of ML: dicrete dependent variables
• Binary dependet variables (logit, probit)
• Decrete choice models (ordered logit and probit models, polynomial logit, conditional logit)
• Count data models (Poissona model)
• Intepretation of parameters, marginal effects and odds ratios for dscrete dependent variables models
Applications of ML: truncated and censored data models, nonrandom selection models
• Truncated and censored data models: truncated regresion model, tobit
• Nonrandom selection: Heckman model
Panel data models
• Properties panel data
• Notion of the individual effect
• Random effect (RE) and fixed effect (FE) models, assumtions and estimation
• Comparison of RE and FE models
• Hausman test for validity of RE model
M Estimation
• Assumptions
• Sketches of proofs of consistency and asymptotic normality
• Variance estimation of M estimators
• Example: pseudo-ML estimation
Generalized Method of Moments
• Conditional and unconditional moments, law of iterated expectations
• Sample moments and moment restrictions, notion of the intrumental variable
• Identification problem, models with underidentified, exactly identfied and overidetified parameters
• Optimal instruments, optimal weighting metrix, two-stage GMM estimator
• Variance estimation of ML estimators
• Hypothesis testing and test of the validity of instruments
Applications of GMM: Instrumental Variable Estimator (IV)
• Good instruments, conditions
• Choice of instruments
• Simple and generalized IV estimator
• Hausmana and Sargana tests
Simultaneus Equations Models (SEM)
• Notation
• Exogeneity of variables: definitions
• Haavelmo bias: simultaneity
• Hausmana-Wu exogeneity test
• Identyfication problem in SEM: necessary and sufficient conditions
• SEM estimation (2SLS, 3SLS)

Estimated number of hours needed for obtaining the declared learning outcome:
Lecture + problem sessions = 60 godz.
Individual reading (2 hours. Each week) = 30 godz.
Writng the model = 30 hours
Solving exercises and preparation to exam 30 godz.
Razem 150 hours.