Introduction. Advanced Econometrics - HEC Lausanne. Christophe Hurlin. University of Orléans. October 2013

Transcription

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

2 Instructor Contact Teaching assistant Christophe Hurlin Sara Cavalli Personal website Personal website Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

3 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 economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference", P. A. Samuelson, T. C. Koopmans, and J. R. N. Stone (1954) Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

4 Econometrics is fundamentally based on four elements: 1 A sample of data 2 An econometric model 3 An estimation method 4 Some inference methods Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

5 Question: Why using a sample? Let us assume that we want to study a characteristic / property x of the individuals of a population. The individuals (unit) of the population are not necessarily some persons: 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..). Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

6 In the case of a population of two individuals, inference, econometrics, etc (and this course.).. are useless. Let us imagine that Adam weighs 80 kg and Eve 50 kg... Adam and Eve, Titian ( ) Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

7 When the population is large or in nite, sampling is the only mean to study the weight Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

8 De nition (Population) A population can be de ned as including all people or items with the characteristic one wishes to understand. 1 In most of cases, it is impossible to observe the entire statistical population, due to cost constraints, time constraints, constraints of geographical accessibility. 2 A researcher would instead observe a statistical sample from the population in order to attempt to learn something about the population as a whole. Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

9 In most of cases, the sample is random: De nition (Probability sampling) A probability sampling is a sampling method in which every unit in the population has a chance (greater than zero) of being selected in the sample. Consequence: a sample is a collection of random variables even the characteristic x is deterministic. sample: fx 1, X 2,..., X N g Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

10 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: ex A = 80 ex B = 50 ex C = 40 ex D = 90 Consider a random sample of N = 2 individuals denoted by 8 < : X {z} 1 9 =, X 2 ; So we can obtain a realisation Weight of the rst indi. selected in the sample fx 1, x 2 g = f50, 80g or fx 1, x 2 g = f90, 40g or fx 1, x 2 g = f90, 90g etc. Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

11 Fact Whatever the assumption made on the characteristic X (deterministic or stochastic) the result of the probability sampling is a random sample, i.e. a collection of random variables X 1, X 2,.., X N. Fact Given the sampling probability method used, we can assume that these random variables are independent and identically distributed (i.i.d.). Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

12 Fact In general, in economics and nance, only one realisation of the sample is available: this is your data set! fx 1, x 2,.., x N g Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

13 The challenge of econometrics and mathematical statistic is to draw conclusions about a population (or the true DGP) after observing only one realisation fx 1,..x N g of a random sample (your data set..). Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

14 In econometrics, data come from one of the two sources: experiments and non experimental observations 1 Experimental data are based on (randomized controlled) experiments designed to evaluate a treatment or policy or to investigate a causal e ect. 2 Data obtained outside an experimental setting are called observational data (issued from survey, administrative records etc...) All of this lecture is devoted to methods for handling real-world observational data Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

15 Whether the data is experimental or observational, data sets can be mainly distinguished in three types: 1 Cross-sectional data 2 Time series data 3 Panel data Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

16 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 somewhat across units, it is ignored). Order of data does not matter! Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

17 Time series data: Data for a single entity (person, rm, country) collected at multiple time 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 Data Generating Process (DGP). Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

18 Panel data or longitudinal data: Data for multiple entities (individuals, rms, countries) in which outcomes and characteristics of each entity are observed at multiple points in time. Combine cross-sectional and time series issues. Present several advantages with respect to cross-sectional and time series data (depending on the question of interest!). Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

19 De nition (Econometric model) An econometric model speci es the statistical relationship that is believed to hold between the various economic quantities pertaining to a particular economic phenomenon under study. An econometric model can be derived from a deterministic economic model by allowing for uncertainty, or from an economic model which itself is stochastic. However, it is also possible to use econometric models that are not tied to any speci c economic theory. Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

20 We can distinguish: 1 Parametric model: the relationship (joint probability distribution) between the dependent variable /vector Y and the explicative variables 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 function can not be described using a nite number of parameters. The link function is assumed to be unknown and has to be estimated. Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

21 The general approach of econometrics is the following: 1 Step 1: Model speci cation 2 Step 2: Estimation of the parameters 3 Step 3: Validation 1 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 of the model, etc.) Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

22 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 c econometric courses of the Masters. Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

23 References Amemiya T. (1985), Advanced Econometrics. Harvard University Press. Greene W. (2007), Econometric Analysis, sixth edition, Pearson - Prentice Hil (recommended) Johnson J., Econometric Methods, 3rd edition, MacGraw-Hill Pelgrin, F. (2010), Lecture notes Advanced Econometrics, HEC Lausanne (a special thank) Ruud P., (2000) An introduction to Classical Econometric Theory, Oxford University Press. Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

24 Course outline Chapter 1: Estimation theory Chapter 2: Maximum Likelihood Estimation (MLE) Chapter 3: The multiple linear regression model: the Ordinary Least Squares (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) Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

25 End of the general introduction Christophe Hurlin (University of Orléans) Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

26 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 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 simply based on the make-up exam grade - the mid-term exam no longer counts. Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27

27 Course rules 1 The nal exam and the retake exams cover the entire course (including the exercises). The mid-term exam covers the parts indicated 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. The solution approach has to be clear to the grader. In particular, (numerical) results without analytical derivations receive no grade. Christophe Hurlin (University of Orléans) Advanced Econometrics - HEC Lausanne October / 27