Econometrics

obligatory courses

(in Polish) Wymagania formalne

Mnożenie macierzy, odwracanie macierzy, ślad macierzy i jego własności, liczenie pochodnych względem wektora parametrów, maksymalizacja funkcji wielu zmiennych – warunki konieczne

Wartość oczekiwana i jej własności, wariancja i jej własności. Pojęcie wektora losowego, pojęcie macierzy wariancji kowariancji, własności rozkładu normalnego.

Pojęcie estymatora, pojęcia nieobciążoności, zgodności oraz asymptotycznego rozkładu estymatora. Testowanie hipotez: hipoteza zerowa i alternatywna, poziom istotności, błąd I i II rodzaju, p-value.     

Założenia wstępne

algebra liniowa, analiza matematyczna, rachunek prawdopodobieństwa, statystyka matematyczna, mikroekonomia, makroekonomia

The aim of the lecture and tutorials is to familiarize students with econometric techniques, their properties and their most important applications. The main purpose of the lecture is to familiarize students with the theory of econometrics. Lectures are illustrated with simple empirical examples. More extensive empirical examples will be discussed during tutorials.

The lecture will discuss the problem of estimation in the Classical Linear Regression Model using Ordinary Least Squares Method. The first part of the course will be devoted to the presentation of the model, its assumptions and the method of estimation and interpretation. In the second part students will be introduced to the methods of hypothesis testing, model diagnostics and the consequences of not meeting particular assumptions. After the lecture, the students should be able to properly examine the relationships between variables in cross-sectional data and to interpret the results of a simple econometric research

The aim of the lecture and tutorials is to familiarize students with econometric techniques, their properties and their most important applications. The main purpose of the lecture is to familiarize students with the theory of econometrics. Lectures are illustrated with simple empirical examples. More extensive empirical examples will be discussed during tutorials.

The lecture will discuss the problem of estimation in the Classical Linear Regression Model using Ordinary Least Squares Method. The first part of the course will be devoted to the presentation of the model, its assumptions and the method of estimation and interpretation. In the second part students will be introduced to the methods of hypothesis testing, model diagnostics and the consequences of not meeting particular assumptions. After the lecture, the students should be able to properly examine the relationships between variables in cross-sectional data and to interpret the results of a simple econometric research.

The aim of the tutorials is to familiarize students with the applications of econometric tools discussed during the lecture and to check students' knowledge on an ongoing basis. It is not the aim of the tutorials to repeat the lecture. As part of the tutorials students should master the formulation of econometric models, their estimation using STATA or R or Python and the interpretation of the results.

Introduction

• The subject of econometrics.

• Types of statistical data.

• The concept of an econometric model.

The Least Squares Method (OLS)

• Discussion of the OLS estimator.

• Properties of the hyper-plane of regression, decomposition of the sum of residual squares, the measure of matching and their properties.

Interpretation of model parameters

• Discrete variables (including binary variables).

• Linear forms relative to transformed variables (logarithmic, translogarithmic, straight-line).

Classic Linear Regression Model (CLRM)

• Assumptions of the Classical Linear Regression Model.

• OLS estimator properties in CLRM: expected value and variance.

• Estimator of the linear function of parameters and its variance.

• The efficiency of the OLS estimator in CLRM: the Gauss-Markov theorem.

Statistical inference in CLRM

• Assumptions about the distribution of random error

• Distributions of OLS estimators in CLRM.

• Testing linear simple and complex hypotheses: t and F tests.

Basic problems of estimation with OLS

• Omitted variables: empirical example.

• Insignificant variables.

• Atypical observations and outliers - detection and conduct.

• Multicollinearity.

Diagnostic tests

• The role of diagnostic tests in model analysis. Testing CLRM assumptions.

Heteroscedasticity and autocorrelation

• Causes of heteroskedasticity and autocorrelation.

• Consequences of heteroscedasticity and autocorrelation.

• Generalized Least Squares Method (GLS).

• Transformation of the GLS model to OLS.

• Applicable GLS (Weighted OLS).

• Robust variance-covariance matrix estimators.

Mandatory literature:

Stock, Watson, Introduction to Econometrics, 2019

Additional literature:

Mycielski, Ekonometria, 2010

Wooldridge, Introductory Econometrics, 2002

Chow, Ekonometria, PWN, 1995

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

Greene, Econometric Analysis, Pearson, 2018 – 8th edition

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

A) Knowledge

The student has knowledge about the basic econometric tools used to verify research hypotheses.

1. The student has knowledge about the place of econometrics in the system of economic sciences.

2. The student understands the importance of quantitative research for business theory and practice.

3. The student knows the basic areas of application of econometrics.

4. The student knows the basic principles of statistical and empirical inference verification of hypotheses.

5. The student understands the role of the econometric model in statistical inference.

6. The student knows basic methods and tools that are used in econometrics.

7. The student knows and understands the limitations of basic methods used in econometrics.

8. The student knows the method thoroughly OLS methods and understands the need to use more advanced econometric techniques when OLS assumptions are not met.

9. The student knows the assumptions of the Classical Linear Regression Model and t methods of testing them.

10. The student knows the basic problems associated with failure to meet the assumptions of the Classical Linear Regression Model, omitted variables, insignificant variables, atypical observations, collinearity.

11. The student knows basic methods of action in case of failure to meet the assumptions of the Classical Linear Regression Model.

12. The student knows the methods of obtaining data and their limitations.

B) Skills

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

1. The student is able to design a basic econometric study.

2. The student knows how to connect basic econometric tools with the right data describing selected processes in the economy.

3. The student knows how to put forward simple research hypotheses that require the use of a model econometric.

4. The student is able to take into account the limitations of basic analytical methods in his own study.

5. The student has the ability to prepare empirical data suitable to known econometric methods.

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

7. The student can detect atypical and erroneous observations.

8. The student is able to diagnose the problem of collinearity in the model.

9. The student can test the assumptions of the Classical Linear Regression Model.

10. The student is able to interpret the obtained results.

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

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

C) Social competences

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

1. The student can indicate important economic issues that require quantitative research.

2. The student understands the need to use econometric tools for analysis economic processes.

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

4. The student can communicate results of his research and of other researchers at a basic level. He is able to explain their basics and conclusions.

5. The student is able to complement the acquired knowledge and skills.

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

KW01, KU01

The lecture ends with a written exam. The final grade consist of the exam grade with a weight of 2/3 and the grade from tutorials with a weight of 1/3.