Econometric Methods - Uni Trier · Econometric Methods Introduction Dr. Matthias Op nger Lehrstuhl für Finanzwissenschaft WS 2015/16 Dr. Matthias Op nger Econometric Methods …

Econometric Methods

Introduction

Dr. Matthias Op�nger

Lehrstuhl für Finanzwissenschaft

WS 2015/16

Dr. Matthias Op�nger Econometric Methods WS 2015/16 1 / 24

Overview

Moving on to ...

1 Overview

2 Introduction

3 Introduction to Ordinary Least Squares Regression

4 Quality of the Estimation Procedure


Overview

Time and Location

Lectures:

Wednesdays: 8:15 - 9:45 in HS 1

Tutorials:

Thursdays: 10:15 - 11:45 in C 106d


Overview

Contact Information

Dr. Matthias Op�nger

Room: C 504

E-Mail: op�[email protected]

O�ce hours: upon appointment


Overview

Literature and Grading

Lecture:

Ludwig von Auer (2013): Ökonometrie, 6. Au�age

Je�rey M. Wooldrigde (2008): Introductory Econometrics: A ModernApproach, 4th Edition

Stock and Watson (2006/2011): Introduction to Econometrics, 3rd

Edition

Tutorial:

Ulrich Köhler & Frauke Kreuter (2008): Datenanalyse mit Stata, 3.Au�age

Christopher F. Baum (2006): An Introduction to ModernEconometrics Using Stata

Grading:

Final Exam: 100%


Overview

Course Outline:

1 Introduction: The Simple Regression Model2 Multiple Regression Analysis: Speci�cation of the Estimation

Equations3 Multiple Regression Analysis: Estimation4 Hypothesis Testing5 Violation of the Assumption A1: Inaccurate Choice of Exogenous

Variables6 Violation of the Assumption A2: Nonlinear Relationship7 Violation of the Assumption A3: Variable Parameter Values8 Violation of the Assumptions B1 and B2: Nonzero Mean of the

Disturbances and Heteroskedasticity9 Violation of the Assumption B3: Autocorrelation10 Panel Data Models11 Further Topics


Introduction

Moving on to ...

1 Overview

2 Introduction




Introduction

Introduction

Econometrics serve to detect and quantify the causal relationships

Veri�cation of the economic theory through the economic reality bymeans of measurement

The most important method is the ordinary least squares (OLS)regression


Introduction

IntroductionFour Functions of Econometrics

Economic Model⇓

Speci�cation⇓

Econometric Model⇓

Estimation⇓

Estimated Model⇓ ⇓

Hypothesis Testing Prognoses


Introduction

IntroductionAn Example: Waiter's tip

Economic Model:

y = f (x)

Econometric Model:

yt = βxt + ut

Estimated Model:

yt = βxt + ut

yt = βxt


Introduction

IntroductionAn Example: Waiter's tip

Two guests are observed.xt denotes the amount invoiced in euro and yt denotes the tip in euro:

Guest 1 : (x1 = 10, y1 = 2)

Guest 2 : (x2 = 30, y2 = 3)

We assume an econometric model for the determination of the amount oftip: yt = βxt + ut . Say, both guests have the same value for β. Diddisturbances occur in the case of two guests?Possible solution:

β = 0, 15


Introduction

IntroductionData Set

There are basically three types of data sets:

Time Series Data

Cross Section Data

Panel Data

Guest 1 Guest 2 Guest 31st Evening (x1, y1) = (10, 2) (x2, y2) = (20, 2) (x3, y3) = (25, 4)2nd Evening (x4, y4) = (30, 3) (x5, y5) = (35, 3) (x6, y6) = (41, 6)3rd Evening (x7, y7) = (50, 7) (x8, y8) = (14, 2) (x9, y9) = (17, 2)


Introduction to Ordinary Least Squares Regression

Moving on to ...

1 Overview

2 Introduction





Introduction to Least Squares RegressionBasic idea

There is one true and linear relationship between the amount of tipand the amount of the invoice

yt = α+ βxt + ut

The aim is to estimate parameters α and β

Minimize the deviation between yt and yt , and hence ut



Introduction to Least Squares RegressionAn Example: Data

The tip amounts of 20 guests are observed. The corresponding data is asfollows:

t xt yt t xt yt1 10,00 2,00 11 60,00 7,002 30,00 3,00 12 47,50 5,50...

......

......

...10 12,50 1,00 20 20,00 2,50



Introduction to Least Squares RegressionThe true relationship

Figure : The true relationship between the invoiced amount x and the tip value y .



Introduction to Least Squares RegressionThe true relationship and the sample

Figure : The relationship between the observed value yt and the disturbance ut and

α+ βxt .



Introduction to Least Squares RegressionResidual Squares

Figure : Minimizing the estimated error terms, ut .



Introduction to Least Squares RegressionResult: OLS Regression

Method of least squares: minimize the sum of squared residuals, Suu:

Suu =T∑t=1

(yt − α− βxt)2 → min

Method: Take partial derivatives (compare von Auer 2011, pp. 57).Result:

β = Sxy/Sxx

α = y − βxwhere Syy is the variation of endogenous variable, Sxx is the variation

of exogenous variable and Sxy is the covariation.

Syy ≡∑

(yt − y)2 ; Sxx ≡∑

(xt − x)2 ; Sxy ≡∑

(xt − x) (yt − y)


Quality of the Estimation Procedure

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1 Overview

2 Introduction





Quality of the Estimation ProcedureUnbiasedness

The estimator βA is unbiased, if mean of the repeated sample values βA

corresponds to the real value of β. In other words, if E (βA) = β.

Figure : Comparison of estimators βA and βB .



Quality of the Estimation ProcedureE�ciency

An unbiased estimator βA is e�cient, if it has the smallest variancevar(βA) among the class of unbiased estimators.

Figure : A further comparison of estimators βA and βB .



Quality of the Estimation ProcedureOrdinary Least Squares Estimator I

It can be proved that under certain assumptions (A-, B- andC-Assumptions):

E (α) = α and E (β) = β

The OLS-Estimator α and β are linear estimators. One can show thattheir variances are the smallest among the class of unbiased estimators.

Under certain assumptions, the OLS-Estimators α and β are e�cientin the class of unbiased linear estimators (BLUE) - excluding thenonlinear estimators.

Under certain assumptions, the OLS-Estimators α and β are e�cientin the class of unbiased estimators including the nonlinear estimators(BUE).



Quality of the Estimation ProcedureOrdinary Least Squares Estimator II

Figure : A variance is compatible with various distributions.


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Econometric Methods - Uni Trier · Econometric Methods Introduction Dr. Matthias Op nger Lehrstuhl für Finanzwissenschaft WS 2015/16 Dr. Matthias Op nger Econometric Methods …