E c o n o m e t r i c s

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1 H:/Lehre/Econometrics Master/Lecture slides/chap 0.tex (October 7, 2015) E c o n o m e t r i c s This course 1

2 People Instructor: Professor Dr. Roman Liesenfeld SSC-Gebäude, Universitätsstr. 22, Room Tutorials: Tobias Eckernkemper SSC-Gebäude, Universitätsstr. 22, Room This course 2

3 Goals and Prerequisites The goal of this course is to get familiar with a wide range of topics in modern econometrics, focusing on what is important for doing and understanding empirical work. It covers econometric techniques used for cross-sectional analysis as well as time series analysis. The econometric methods are illustrated using applications from fields like labor economics, finance, international economics, consumer behavior, macro economics. Background knowledge in statistics (Statistik A and Statistik B) and Mathematics are absolutely necessary. Having taken a course in econometrics at the bachelor level would be a great advantage, but is not necessary. This course 4

4 Organization The course will follow the structure of the book A Guide to Modern Econometrics by Marno Verbeek. Lecture slides and exercises will be available via the system ILIAS. Computer exercises applying the econometric techniques discussed during the lecture to real data will be performed using the (open source) programm gretl. An introduction to gretl will be given. This course 5

5 Exam There will be a written exam of 60 min for students under the old Master PO 2013 and of 120 min for students under the new Master PO Master PO 2015 students are allowed to use two A4 pages (two sided) of hand-written notes and Master PO 2013 students one A4 page. There will be no formula sheet. The questions will rather aim at you understanding of the material and your ability to interpret regression output. This course 6

6 Contents 1 Elements of Matrix Algebra and Statistical Theory 2 Linear Regression Model 2.1 Ordinary Least Squares (OLS) as an Algebraic Instrument 2.2 The Linear Regression Model and its Assumptions 2.3 The OLS Estimator and its small-sample Properties 2.4 Goodness-of-fit 2.5 Hypothesis Testing: t- and F-Tests 2.6 Multicollinearity 2.7 Predictions 2.8 Example: The Capital Asset Pricing Model This course 7

7 Contents 3 Asymptotic Properties of the OLS Estimator 3.1 Principles of Asymptotic Theory 3.2 Weak Law of Large Numbers 3.3 Central Limit Theorems 3.4 Consistency of the OLS Estimator 3.5 Asymptotic Normality of the OLS Estimator 3.6 Asymptotic Tests 4 Interpreting and Selecting Regression Models 4.1 The Regression Function and its Interpretation 4.2 Selecting the Regressors 4.3 Specifying the Functional Form of the Regression Function 4.4 Examples: Explaining House Prices, Individual Wages This course 8

8 5 Heteroskedastic Errors Contents 5.1 Empirical Illustrations Involving Heteroskedasticity 5.2 What is Heteroskedasticity? 5.3 Consequences of Heteroskedasticity for the OLS Estimator 5.4 The Generalized Least Squares (GLS) and the Feasible GLS Estimator 5.5 Heteroskedasticity-consistent Standard Errors for OLS 5.6 Testing for Heteroskedasticity: Testing Equality of two Unknown Variances, Breusch-Pagan Test, White Test 6 Autocorrelated Errors 6.1 What is Autocorrelation? 6.2 First-order Autocorrelation and the (F)GLS Estimator 6.3 Testing for First-order Autocorrelation 6.4 Higher-order Autocorrelation and Moving Average Errors 6.5 Heteroskedasticity-and-autocorrelation-consistent Standard Errors for OLS This course 9

9 Contents 7 Endogenous Regressors and Instrumental Variables 7.1 A Review of the Properties of the OLS Estimator 7.2 Situations Where the OLS is not Applicable: Autocorrelation with Lagged Dependent Variable, Measurement Errors, Endogeneity and Omitted Variables, Simultaneity and Reverse Causality 7.3 Instrumental Variable (IV) Estimation 7.4 Example: Returns to Schooling 7.5 Generalized IV Estimator 7.6 Specification Tests This course 10

10 Contents 8 Generalized Method of Moments 8.1 Basic Principle of Moment Estimators 8.2 The Method of Moment Estimator 8.3 The Generalized Method of Moment Estimator 8.4 Example: Consumption Based Capital Asset Pricing Model 9 Maximum Likelihood 9.1 Maximum Likelihood (ML) Estimation 9.2 Asymptotic Properties of the ML estimator 9.3 ML Estimator for the Parameters of the Linear Regression Model 9.4 Hypotheses Testing This course 11

11 Contents 10 Models with Limited Dependent Variables 10.1 Binary Choice Models (Probit/Logit) 10.2 Ordered Multiresponse Models (Ordered Probit) 10.3 Models for Censored Data (Standard Tobit) 11 Time Series Models 11.1 Time Series Data 11.2 Autoregressive-Moving-Average (ARMA) Models 11.3 Estimation of the Parameters of ARMA Models 11.4 Model Selection 11.5 Forecasting with ARMA Models 11.6 Stationarity and Unit Roots This course 12

12 Literature Main textbook Verbeek, M.: A Guide to Modern Econometrics, 4th edition, John Wiley & Sons Ltd, Chichester, Additional recommended books Greene, W.: Econometric Analysis. 7th Edition, Boston, Hayashi, F.: Econometrics. Princeton, Books at an introductory level Wooldridge, J.M.: Introductory Econometrics, 5th edition, Mason/Ohio, Stock, J.H., Watson, M.W.: Introduction to Econometrics. 2nd Edition, Boston, Assenmacher, W.: Einführung in die München, Ökonometrie. 6. Auflage, This course 13

A Guide to Modern Econometric:

A Guide to Modern Econometric: 4th edition Marno Verbeek Rotterdam School of Management, Erasmus University, Rotterdam B 379887 )WILEY A John Wiley & Sons, Ltd., Publication Contents Preface xiii 1 Introduction