Advanced Econometrics - HEC Lausanne Christophe Hurlin · Pelgrin, F. (2010), Lecture notes Advanced Econometrics, HEC Lausanne (a special thank) Ruud P., (2000) An introduction to

IntroductionAdvanced Econometrics - HEC Lausanne

Christophe Hurlin

University of Orléans

October 2013

Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October 2013 1 / 27

Instructor Christophe Hurlin

Contact [email protected]

Teaching assistant Sara Cavalli

Personal websitehttps://hec.unil.ch/docs/index.php/churlin/cours/512/session_1461Personal websitehttp://www.univ-orleans.fr/deg/masters/ESA/CH/churlin_E.htm


Introduction

What is econometrics? Not an easy question!

Main objective of this course is to de�ne this term!

Econometrics can be de�ned as the statistical analysis of economic(�nancial) phenomena.

"Econometrics is the quantitative analysis of actual economicphenomena based on the concurrent development of theory andobservation, related by appropriate methods of inference", P. A.Samuelson, T. C. Koopmans, and J. R. N. Stone (1954)


Introduction

Econometrics is fundamentally based on four elements:

1 A sample of data

2 An econometric model

3 An estimation method

4 Some inference methods


Introduction

Question: Why using a sample?

Let us assume that we want to study a characteristic / property xof the individuals of a population.

The individuals (unit) of the population are not necessarily somepersons: it can be �rms, assets, countries, time index etc..

The characteristic x may be quantitative (salary, weight, total asset,GDP etc.) or qualitative (social status, genre etc.)

The characteristic x may be stochastic or deterministic (weight,size etc..).


Introduction

Adam and Eve, Titian (1490-1576)

In the case of a population oftwo individuals, inference,econometrics, etc (and thiscourse.).. are useless.

Let us imagine that Adamweighs 80 kg and Eve 50 kg...


Introduction

When the population is largeor in�nite, sampling is theonly mean to study the weight


Introduction

De�nition (Population)A population can be de�ned as including all people or items with thecharacteristic one wishes to understand.

1 In most of cases, it is impossible to observe the entire statisticalpopulation, due to cost constraints, time constraints, constraints ofgeographical accessibility.

2 A researcher would instead observe a statistical sample from thepopulation in order to attempt to learn something about thepopulation as a whole.


Introduction

In most of cases, the sample is random:

De�nition (Probability sampling)A probability sampling is a sampling method in which every unit in thepopulation has a chance (greater than zero) of being selected in thesample.

Consequence: a sample is a collection of random variables even thecharacteristic x is deterministic.

sample: fX1,X2, ...,XNg


Introduction

Example (random sample)

Let us consider a population of four persons and denote by ex the weight(assumed to be non stochastic) of the individual with:

exA = 80 exB = 50 exC = 40 exD = 90Consider a random sample of N = 2 individuals denoted by8<: X1|{z}

Weight of the �rst indi. selected in the sample

,X2

9=;So we can obtain a realisation

fx1, x2g = f50, 80g or fx1, x2g = f90, 40g or fx1, x2g = f90, 90g etc.


Introduction

FactWhatever the assumption made on the characteristic X (deterministic orstochastic) the result of the probability sampling is a random sample, i.e.a collection of random variables X1, X2, ..,XN .

FactGiven the sampling probability method used, we can assume that theserandom variables are independent and identically distributed (i.i.d.).


Introduction

FactIn general, in economics and �nance, only one realisation of the sampleis available: this is your data set!

fx1, x2, .., xNg


Introduction

The challenge of econometrics and mathematical statistic is to drawconclusions about a population (or the true DGP) after observing only onerealisation fx1, ..xNg of a random sample (your data set..).


Introduction

In econometrics, data come from one of the two sources: experiments andnon experimental observations

1 Experimental data are based on (randomized controlled)experiments designed to evaluate a treatment or policy or toinvestigate a causal e¤ect.

2 Data obtained outside an experimental setting are calledobservational data (issued from survey, administrative records etc...)

All of this lecture is devoted to methods for handling real-worldobservational data


Introduction

Whether the data is experimental or observational, data sets can be mainlydistinguished in three types:

1 Cross-sectional data

2 Time series data

3 Panel data


Introduction

Cross-sectional data:

Data for di¤erent entities: workers, households, �rms, cities,countries, and so forth.

No time dimension (even if date of data collection varies somewhatacross units, it is ignored).

Order of data does not matter!


Introduction

Time series data:

Data for a single entity (person, �rm, country) collected at multipletime periods. Repeated observations of the same variables (GDP,prices).

Order of data is important!

Observations are typically not independent over time;

In this case the notion of population corresponds to the DataGenerating Process (DGP).


Introduction

Panel data or longitudinal data:

Data for multiple entities (individuals, �rms, countries) in whichoutcomes and characteristics of each entity are observed at multiplepoints in time.

Combine cross-sectional and time series issues.

Present several advantages with respect to cross-sectional and timeseries data (depending on the question of interest!).


Introduction

De�nition (Econometric model)An econometric model speci�es the statistical relationship that is believedto hold between the various economic quantities pertaining to a particulareconomic phenomenon under study.

An econometric model can be derived from a deterministic economicmodel by allowing for uncertainty, or from an economic model whichitself is stochastic.

However, it is also possible to use econometric models that are nottied to any speci�c economic theory.


Introduction

We can distinguish:

1 Parametric model: the relationship (joint probability distribution)between the dependent variable /vector Y and the explicativevariables X is fully characterised by a set of parameters θ

Y = f (X ; θ) + ε

where link function f (.) is assumed to be known.

2 Non parametric and semi-parametric models: the link functioncan not be described using a �nite number of parameters. The linkfunction is assumed to be unknown and has to be estimated.


Introduction

The general approach of econometrics is the following:

1 Step 1: Model speci�cation

2 Step 2: Estimation of the parameters

3 Step 3: Validation1 Signi�cance tests;2 Speci�cation tests;3 Backtesting (forecasting performances);4 Etc.

4 Step 4: Use of the model (forecasting, feedback on the building ofthe model, etc.)


Introduction

Objectives of the course

The objective of this course are mainly related to the steps 2 (Estimation)and 3 (Validation)

More speci�cally:

1 To provide a global understanding of modern econometric methods;

2 To give a critical assessment of the presented methods;

3 To constitute an introduction and a basis for the more speci�ceconometric courses of the Masters.


Introduction

References

Amemiya T. (1985), Advanced Econometrics. Harvard University Press.

Greene W. (2007), Econometric Analysis, sixth edition, Pearson - PrenticeHil (recommended)

Johnson J., Econometric Methods, 3rd edition, MacGraw-Hill

Pelgrin, F. (2010), Lecture notes Advanced Econometrics, HEC Lausanne (aspecial thank)

Ruud P., (2000) An introduction to Classical Econometric Theory, OxfordUniversity Press.


Introduction

Course outline

Chapter 1: Estimation theory

Chapter 2: Maximum Likelihood Estimation (MLE)

Chapter 3: The multiple linear regression model: the Ordinary LeastSquares (OLS) estimator

Chapter 4: Inference and statistical hypothesis testing

Chapter 5: The Generalized Least Squares (GLS) estimator

Chapter 6: Endogeneity, error-in-variables and the Instrumental Variables(IV) estimator

Chapter 7: The Generalized Method of Moments (GMM)


End of the general introduction

Christophe Hurlin (University of Orléans)


Course rules

Your grade will be determined based on the following criteria:

Final Exam (F) (compulsory)

Mid-term (MT) (optional)

Retake exam (RE) (compulsory if necessary).

Two cases:

1 Without retake exam, the �nal grade is given by:

GRADE = 0.7 � F + 0.3 �max(MT ,F )

2 With a retake exam, the �nal grade is given by

GRADE = 1 � RE

In other words, if you need to redo the exam, then the grade will be simplybased on the make-up exam grade - the mid-term exam no longer counts.


Course rules

1 The �nal exam and the retake exams cover the entire course(including the exercises). The mid-term exam covers the partsindicated by the instructor.

2 All exams (mid-term, �nal, and retake exams) are closed book.

3 All type of calculator is authorized for all the exam.

4 The duration of the �nal exam and the retake exam is 180 minutes.The midterm is 120 minutes.

5 Careful and clear justi�cation of your answers will be rewarded. Thesolution approach has to be clear to the grader. In particular,(numerical) results without analytical derivations receive no grade.


Documents

Advanced Econometrics - HEC Lausanne Christophe Hurlin · Pelgrin, F. (2010), Lecture notes Advanced Econometrics, HEC Lausanne (a special thank) Ruud P., (2000) An introduction to