Advanced Econometrics I

obligatory courses

(in Polish) Wymagania wstępne

• Analiza matematyczna

• Algebra liniowa

• Rachunek p-stwa

• Statystyka opisowa

• Statystyka matematyczna

• Ekonometria

Wymagania formalne:

• Analiza matematyczna: liczenie pochodnych funkcji wielu zmiennych, maksymalizacja funkcji wielu zmiennych – warunki konieczne

• Algebra liniowa: mnożenie macierzy, odwracanie macierzy, liniowa zależność, określoność macierzy•

• Rachunek p-stwa: Wartość oczekiwana i jej własności, wariancja i jej własności,. Pojęcie wektora losowego, pojęcie macierzy wariancji kowariancji, własności rozkładu Bernoulliego, chi kwadrat i normalnego.

• Statystyka opisowa: Średnia z próby, wariancja z próby, odchylenie standardowe z próby, kowariancja empiryczna, współczynnik korelacji empirycznej, histogram, częstość empiryczna, tablica krzyżowa.

• Statystyka matematyczna: Pojęcie estymatora, nieobciążoność estymatora, pojęcie zgodności estymatora i asymptotycznego rozkładu estymatora. Testowanie hipotez: hipoteza zerowa i alternatywna, poziom istotności, błąd I i II rodzaju, p-value. Własności MNW (dla skalarów), pojęcie funkcji wiarygodności, test LR

• Ekonometria: Własności Estymatora Metody Najmniejszych Kwadratów (MNK), własności statystki R2, testy diagnostyczne, efekty cząstkowe (krańcowe), dyskretne zmienne objaśniające, zmienne nieistotne i pominięte, testowanie hipotez prostych i złożonych, endogeniczność zmiennych objaśniających, współliniowość zmiennych, heteroskedastyczność i autokorelacja błędu losowego, odporne estymatory macierzy wariancji i kowariancji, Uogólniona Metoda Najmniejszych Kwadratów (UMNK).

• The objective of this course is to acquaint students with advanced econometric techniques, its properties and the most important applications.

• Lecture is concentrated on tree 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

• Lecture presents the theory and some empirical examples. Problem sessions are to teach econometric tools presented on the lecture. Problem sessions consist of solving some exercises, computer lab sessions and dicussions on student papers which are expected to contain empirical analysis based on models covered on the lecture.

• Lecture uses the material from the lectors on linear algebra, mathematical analysis, mathematical statistics and on basic econometrics

• Final grading is based on grades from problem sessions and written exam.

• 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.

Obligatory literature

• Zbiór zdań z ekonometrii, Jerzy Mycielski, 2009

• Ekonometrii, Jerzy Mycielski, WNE 2009

• Materiały do nauki STAT’y, K.Kuhl, M. Kurcewicz, G. Ogonek, P. Strawiński, J. Tyrowicz, 2005

Additional literature

• Charemza, Deadman, Nowa Ekonometria, PWE, 1997

• Chow, Ekonometria, PWN 1995

• Davidson, McKinnon, Estimation and Inference in Econometrics, OUP, 1993

• Greene, Econometric Analysis, Prentice Hall 2003 – wydanie 5-te

• Goldberger, Teoria Ekonometrii, PWE, 1972

• Maddala, Limited Dependent and Qualitative Variables in Econometrics, OUP 19837.

• Steward, Econometrics, Philip Allan 1991

• Theil, Zasady ekonometrii, PWN, 1979

• Wooldridge, Econometric Analysis of Cross Section and Panel Data, MIT Press, 2002

Student should be able to choose econometric model and the method of estimation which is suited to reaserch proble he/she is dealing with. In particular students should have following skills:

• choice of the set of the expanatory variables on the basis of statistical criterions

• understandig the way the ML models are defined

• estimation of the models with binary, descre or truncated dependent variables

• knowledge of the methods used in the case of nonrandom selection

• formulation of the models estimated on panel data

• understanding of the way GMM models are fomulated

• understanding of endogeneity problem and of the way the potential instruments are choosen

• understanding the difference between the structural and reduced forms and between structural parameters and multipliers

• understanding the difference between limited and full information estimation methods

• estimation of SEM models

Lectures are suplemented with problem sessions which are taking place in computer labs. On the problem seasions students arer learning how to use STATA to estimate models covered on the lecture.

• Final grade is a weighted average of the grades from written exam and problem sessions with weights 2/3 and 1/3 respectively. Students who failed the problem sessions are not permitted to take the exam.

• Written exam takes 90 min and consists of 4 theoretical questions, 2 modified exercises similar to the problems in the problem set, and 1 exercise not included in problem set. Theoretical questions are modified versions of the questions given at the end of each lecture. In order to pass the exam student has to solve at least one exercise and answer 2 theoretical questions..