Advanced Econometrics

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 aim of the lecture and tutorials is to familiarize students with advanced econometric techniques, their properties and their most important applications.

• The lecture focuses on three areas of econometrics: time series models, panel data models and the use of Maximum Likelihood Method.

• During the lecture theory and empirical examples are presented. The aim of the tutorials is to familiarize students with the applications of econometric tools discussed during the lecture. Classes include solving tasks, computer laboratories and work on case studies including models estimated using time series and panel data and models for discrete variables.

• The lecture is intended for students of the second level of economic studies.

• The lecture uses concepts from the field of linear algebra, mathematical analysis, probability calculus, descriptive and mathematical statistics and basic econometrics.

• The lecture concerns three important areas of modern econometrics: models estimated on time series and panel data, and applications of Maximum Likelihood Method. During the lecture, the most important statistical models used in modern econometrics will be discussed. The lecture will be illustrated with simple empirical examples.

• Tutorials are used to familiarize students with the use of econometric tools discussed during the lecture and to check students' knowledge on an ongoing basis. It is not the purpose of the tutorials to repeat the lecture.

Subject of the lecture:

• Comparison of competing models.

• Problems related to sequential testing of hypotheses.

• General to specific method.

• Model selection: information criteria (AIC and BIC).

• Models based on time series:

• Seasonality definition.

• Definition of a stationary process.

• Testing the order of integration of variable - DF, ADF, KPSS test.

• Spurious regression problem.

• Definition of DL and ADL models.

• DL and ADL models: long- and short-term multipliers, average delay.

• Testing for Granger causality.

• ARIMA models.

• Cointegration and Error Correction Mechanism.

• Maximum Likelihood Method:

• Definition of the reliability function.

• Testing hypotheses in the context of Maximum Likelihood Method.

• Discrete dependent variables:

• Models for binary dependent variables (LMP, logit, probit).

• Model for discrete choice (ordered logit and ordered probit).

• Censored variables (tobit).

• Models estimated on panels:

• Properties of panel data and cross-sectional data.

• Individual effects.

• Definition of the Fixed and Random effects model.

• Hausmann test for the correctness of the variable effects model.

• Instrumental Variables Method (IV):

• Conditions that instruments must meet.

• Selection of instruments.

• A simple and generalized IV estimator.

• Hausman and Sargan test.

Mandatory literature

• Ekonometria, Jerzy Mycielski, 2010.

• Wooldridge, Introductory Econometrics.

• Greene, Econometric Analysis, Prentice Hall 2003 –5th edition .

Additional literature

• Charemza, Deadman, Nowa Ekonometria, PWE, 1997.

• Chow, Ekonometria, PWN 1995.

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

• 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.

A) Knowledge

The student has knowledge of advanced econometric tools.

• The student has knowledge about the selection of an appropriate set of explaining variables in the model based on statistical criteria.

• The student has knowledge about the construction of simple prognostic models estimated on time series data.

• The student has knowledge how to inquire about the causal relationships between variables.

• The student understands the quantitative assessment of the short and long-term impact of changes in explanatory variables on the explained variable.

• The student has knowledge how to inquire about stationarity.

• The student knows the methods for estimating long-term relationships between variables.

• The student has knowledge about model estimation in the case when dependent variables are binary / discrete.

• The student knows how to proceed in case of model estimation on panel data.

B) Skills

The student is able to use advanced econometric tools in his own research. The student knows how to prepare empirical material, formulate research hypotheses, estimate a model and interpret the obtained results.

• The student is able to design advanced econometric research.

• The student knows how to combine advanced econometric tools with the right data describing selected processes occurring in the economy.

• The student can estimate models based on time series.

• The student can estimate models based on panel data.

• The student can estimate models for discrete variables.

• The student can take into account the limitations of advanced analytical methods in his own study.

• The student has the ability to prepare an empirical data appropriate for the econometric methods learned.

• The student is able to carry out research including preliminary data analysis, model estimation and model diagnostics.

• The student is able to interpret the obtained results.

• The student is able to draw conclusions from his own analysis indicating the determinants of the studied phenomenon.

• The student has the ability to analyze the results obtained by other researchers using basic econometric tools.

C) Social competences

The student is aware that empirical verification of economic theory and analysis of economic processes is widely used in the modern world.

• The student can indicate important economic issues requiring quantitative research.

• The student understands the need for advanced econometric tools to analyze economic processes.

• The student is prepared to actively participate in groups pursuing social goals (political, economic, civic) based on econometric studies.

• The student is able to communicate results of his analyzes and analyzes of other people on a basic level, explain their basics and conclusions.

• The student can complement the acquired knowledge and skills.

• The student is aware of the importance of behaving in a professional and ethical manner in all situations where the basis for decisions are conclusions from econometric research.

SW01, SW02, SW03, SW04, SW05, SU01, SU02, SU03, SU04, SU05, SU06, SU07, SK01, SK02, SK03

• The final grade is issued as the weighted average of the exam grade and tutorials grade with 2/3 and 1/3 weights respectively.

• Only those student who have passed the tutorials will be admitted to the exam.

• The written exam lasts 90 minutes, consists of 4 theoretical questions and 3 tasks. Theoretical questions will be modified versions of the questions which can be found at the end of the sub-chapters in the textbook.