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Basic Econometrics

Basic Econometrics. Course Leader Prof. Dr.Sc VuThieu. Basic Econometrics. Introduction : What is Econometrics?. Introduction What is Econometrics ?. Definition 1 : Economic Measurement

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Basic Econometrics

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  1. Basic Econometrics Course Leader Prof. Dr.Sc VuThieu Prof.VuThieu

  2. Basic Econometrics Introduction: What is Econometrics? Prof.VuThieu

  3. IntroductionWhat is Econometrics? Definition 1: Economic Measurement Definition 2: Application of the mathematical statistics to economic data in order to lend empirical support to the economic mathematical models and obtain numerical results(Gerhard Tintner, 1968) Prof.VuThieu

  4. IntroductionWhat is Econometrics? Definition 3: The quantitative analysis of actual economic phenomena based on concurrent development of theory and observation, related by appropriate methods of inference (P.A.Samuelson, T.C.Koopmans and J.R.N.Stone, 1954) Prof.VuThieu

  5. IntroductionWhat is Econometrics? Definition 4: The social science which applies economics, mathematics and statistical inference to the analysis of economic phenomena(By Arthur S. Goldberger, 1964) Definition 5: The empirical determination of economic laws(By H. Theil, 1971) Prof.VuThieu

  6. IntroductionWhat is Econometrics? Definition 6: A conjunction of economic theory and actual measurements, using the theory and technique of statistical inference as a bridge pier (By T.Haavelmo, 1944) And the others Prof.VuThieu

  7. Economic Theory Mathematical Economics Econometrics Economic Statistics Mathematic Statistics Prof.VuThieu

  8. IntroductionWhy a separate discipline? Economic theorymakes statements that are mostly qualitative in nature, while econometrics gives empirical content to most economic theory Mathematical economicsis to express economic theory in mathematical form without empirical verification of the theory, while econometrics is mainly interested in the later Prof.VuThieu

  9. IntroductionWhy a separate discipline? Economic Statisticsis mainly concerned with collecting, processing and presenting economic data. It does not being concerned with using the collected data to test economic theories Mathematical statisticsprovides many of tools for economic studies, but econometrics supplies the later with many special methods of quantitative analysis based on economic data Prof.VuThieu

  10. Economic Theory Mathematical Economics Econometrics Economic Statistics Mathematic Statistics Prof.VuThieu

  11. IntroductionMethodology of Econometrics Statement of theory or hypothesis: Keynes stated: ”Consumption increases as income increases, but not as much as the increase in income”. It means that “The marginal propensity to consume (MPC) for a unit change in income is grater than zero but less than unit” Prof.VuThieu

  12. IntroductionMethodology of Econometrics (2) Specification of the mathematical model of the theory Y = ß1+ ß2X ; 0 < ß2< 1 Y= consumption expenditure X= income ß1 andß2 are parameters; ß1 is intercept, and ß2 is slope coefficients Prof.VuThieu

  13. IntroductionMethodology of Econometrics (3) Specification of the econometric model of the theory Y = ß1+ ß2X + u ; 0 < ß2< 1; Y = consumption expenditure; X = income; ß1 andß2 are parameters; ß1is intercept and ß2 is slope coefficients; u is disturbance term or error term. It is a random or stochastic variable Prof.VuThieu

  14. IntroductionMethodology of Econometrics (4) Obtaining Data (See Table 1.1, page 6) Y= Personal consumption expenditure X= Gross Domestic Product all in Billion US Dollars Prof.VuThieu

  15. IntroductionMethodology of Econometrics (4) Obtaining Data Prof.VuThieu

  16. IntroductionMethodology of Econometrics (5) Estimating the Econometric Model Y^ = - 231.8 + 0.7194 X (1.3.3) MPC was about 0.72 and it means that for the sample period when real income increases 1 USD, led (on average) real consumption expenditure increases of about 72 cents Note: A hat symbol (^) above one variable will signify an estimator of the relevant population value Prof.VuThieu

  17. IntroductionMethodology of Econometrics (6) Hypothesis Testing Are the estimates accord with the expectations of the theory that is being tested? Is MPC < 1 statistically? If so, it may support Keynes’ theory. Confirmation or refutation of economic theories based on sample evidence is object of Statistical Inference (hypothesis testing) Prof.VuThieu

  18. IntroductionMethodology of Econometrics (7) Forecasting or Prediction With given future value(s) of X, what is the future value(s) of Y? GDP=$6000Bill in 1994, what is the forecast consumption expenditure? Y^= - 231.8+0.7196(6000) = 4084.6 Income Multiplier M = 1/(1 – MPC) (=3.57). decrease (increase) of $1 in investment will eventually lead to $3.57 decrease (increase) in income Prof.VuThieu

  19. IntroductionMethodology of Econometrics (8) Using model for control or policy purposes Y=4000= -231.8+0.7194 X  X  5882 MPC = 0.72, an income of $5882 Bill will produce an expenditure of $4000 Bill. By fiscal and monetary policy, Government can manipulate the control variable X to get the desired level of target variable Y Prof.VuThieu

  20. IntroductionMethodology of Econometrics Figure 1.4: Anatomy of economic modelling 1) Economic Theory 2) Mathematical Model of Theory 3) Econometric Model of Theory 4) Data 5) Estimation of Econometric Model 6) Hypothesis Testing 7) Forecasting or Prediction 8) Using the Model for control or policy purposes Prof.VuThieu

  21. Economic Theory Mathematic Model Econometric Model Data Collection Estimation Hypothesis Testing Application in control or policy studies Forecasting Prof.VuThieu

  22. Basic Econometrics Chapter 1: THE NATURE OF REGRESSION ANALYSIS Prof.VuThieu

  23. 1-1. Historical origin of the term “Regression” • The term REGRESSION was introduced by Francis Galton • Tendency for tall parents to have tall children and for short parents to have short children, but the average height of children born from parents of a given height tended to move (or regress) toward the average height in the population as a whole (F. Galton, “Family Likeness in Stature”) Prof.VuThieu

  24. 1-1. Historical origin of the term “Regression” • Galton’s Law was confirmed by Karl Pearson: The average height of sons of a group of tall fathers < their fathers’ height. And the average height of sons of a group of shortfathers > their fathers’ height. Thus “regressing” tall and short sons alike toward the average height of all men. (K. Pearson and A. Lee, “On the law of Inheritance”) • By the words of Galton, this was “Regression to mediocrity” Prof.VuThieu

  25. 1-2. Modern Interpretation of Regression Analysis • The modern way in interpretation of Regression: Regression Analysis is concerned with the study of the dependence of one variable (The Dependent Variable), on one or more other variable(s) (The Explanatory Variable), with a view to estimating and/or predicting the (population) mean or average value of the former in term of the known or fixed (in repeated sampling) values of the latter. • Examples: (pages 16-19) Prof.VuThieu

  26. Dependent Variable Y; Explanatory Variable Xs 1. Y = Son’s Height; X = Father’s Height 2. Y = Height of boys; X = Age of boys 3. Y = Personal Consumption Expenditure X = Personal Disposable Income 4. Y = Demand; X = Price 5. Y = Rate of Change of Wages X = Unemployment Rate 6. Y = Money/Income; X = Inflation Rate 7. Y = % Change in Demand; X = % Change in the advertising budget 8. Y = Crop yield; Xs = temperature, rainfall, sunshine, fertilizer Prof.VuThieu

  27. 1-3. Statistical vs.Deterministic Relationships • In regression analysis we are concerned with STATISTICAL DEPENDENCEamong variables (not Functional or Deterministic), we essentially deal with RANDOM or STOCHASTIC variables (with the probability distributions) Prof.VuThieu

  28. 1-4. Regression vs. Causation: Regression does not necessarily imply causation. A statistical relationship cannot logically imply causation. “A statistical relationship, however strong and however suggestive, can never establish causal connection: our ideas of causation must come from outside statistics, ultimately from some theory or other” (M.G. Kendal and A. Stuart, “The Advanced Theory of Statistics”) Prof.VuThieu

  29. 1-5. Regression vs. Correlation • Correlation Analysis: the primary objective is to measure the strength or degree of linear association between two variables (both are assumed to be random) • Regression Analysis: we try to estimate or predict the average value of one variable (dependent, and assumed to be stochastic) on the basis of the fixed values of other variables (independent, and non-stochastic) Prof.VuThieu

  30. Dependent Variable  Explained Variable  Predictand  Regressand  Response  Endogenous Explanatory Variable(s)  Independent Variable(s)  Predictor(s)  Regressor(s)  Stimulus or control variable(s)  Exogenous(es) 1-6. Terminology and Notation Prof.VuThieu

  31. 1-7. The Nature and Sources of Data for Econometric Analysis 1) Types of Data : • Time series data; • Cross-sectional data; • Pooled data 2) The Sources of Data 3) The Accuracy of Data Prof.VuThieu

  32. 1-8. Summary and Conclusions 1) The key idea behind regression analysis is the statistic dependence of one variable on one or more other variable(s) 2) The objective of regression analysis is to estimate and/or predict the mean or average value of the dependent variable on basis of known (or fixed) values of explanatory variable(s) Prof.VuThieu

  33. 1-8. Summary and Conclusions 3) The success of regression depends on the available and appropriate data 4) The researcher should clearly state the sources of the data used in the analysis, their definitions, their methods of collection, any gaps or omissions and any revisions in the data Prof.VuThieu

  34. Basic Econometrics Chapter 2: TWO-VARIABLE REGRESSION ANALYSIS: Some basic Ideas Prof.VuThieu

  35. 2-1. A Hypothetical Example • Total population: 60 families • Y=Weekly family consumption expenditure • X=Weekly disposable family income • 60 families were divided into 10 groups of approximately the same income level (80, 100, 120, 140, 160, 180, 200, 220, 240, 260) Prof.VuThieu

  36. 2-1. A Hypothetical Example • Table 2-1 gives the conditional distribution of Y on the given values of X • Table 2-2 gives the conditional probabilities of Y: p(YX) • Conditional Mean (or Expectation): E(YX=Xi ) Prof.VuThieu

  37. Table 2-2: Weekly family income X ($), and consumption Y ($) Prof.VuThieu

  38. 2-1. A Hypothetical Example • Figure 2-1 shows the population regression line (curve). It is the regression of Y on X • Population regression curve is the locus of the conditional means or expectations of the dependent variable for the fixed values of the explanatory variable X (Fig.2-2) Prof.VuThieu

  39. 2-2. The concepts of population regression function (PRF) • E(YX=Xi ) = f(Xi) is Population Regression Function (PRF) or Population Regression (PR) • In the case of linear function we have linear population regression function (or equation or model) E(YX=Xi ) = f(Xi) = ß1 + ß2Xi Prof.VuThieu

  40. 2-2. The concepts of population regression function (PRF) E(YX=Xi ) = f(Xi) = ß1 + ß2Xi • ß1 and ß2 are regression coefficients, ß1is intercept and ß2 is slope coefficient • Linearity in the Variables • Linearity in the Parameters Prof.VuThieu

  41. 2-4. Stochastic Specification of PRF • Ui = Y - E(YX=Xi ) or Yi = E(YX=Xi ) + Ui • Ui = Stochastic disturbance or stochastic error term. It is nonsystematic component • Component E(YX=Xi ) is systematic or deterministic. It is the mean consumption expenditure of all the families with the same level of income • The assumption that the regression line passes through the conditional means of Y implies that E(UiXi ) = 0 Prof.VuThieu

  42. 2-5. The Significance of the Stochastic Disturbance Term • Ui = Stochastic Disturbance Term is a surrogate for all variables that are omitted from the model but they collectively affect Y • Many reasons why not include such variables into the model as follows: Prof.VuThieu

  43. 2-5. The Significance of the Stochastic Disturbance Term Why not include as many as variable into the model (or the reasons for using ui) + Vagueness of theory + Unavailability of Data + Core Variables vs. Peripheral Variables + Intrinsic randomness in human behavior + Poor proxy variables + Principle of parsimony + Wrong functional form Prof.VuThieu

  44. Table 2-4: A random sample from the population Y X ------------------ 70 80 65 100 90 120 95 140 110 160 115 180 120 200 140 220 155 240 150 260 ------------------ Table 2-5: Another random sample from the population Y X ------------------- 55 80 88 100 90 120 80 140 118 160 120 180 145 200 135 220 145 240 175 260 -------------------- 2-6. The Sample Regression Function (SRF) Prof.VuThieu

  45. Weekly Consumption Expenditure (Y) SRF1 SRF2 Weekly Income (X) Prof.VuThieu

  46. 2-6. The Sample Regression Function (SRF) • Fig.2-3: SRF1 and SRF 2 • Y^i = ^1 + ^2Xi (2.6.1) • Y^i = estimator of E(YXi) • ^1 = estimator of 1 • ^2 = estimator of 2 • Estimate = A particular numerical value obtained by the estimator in an application • SRF in stochastic form: Yi= ^1 + ^2Xi + u^i or Yi= Y^i + u^i(2.6.3) Prof.VuThieu

  47. 2-6. The Sample Regression Function (SRF) • Primary objective in regression analysis is to estimate the PRF Yi= 1 + 2Xi + ui on the basis of the SRF Yi= ^1 + ^2Xi + ei and how to construct SRF so that ^1 close to 1 and ^2 close to 2 as much as possible Prof.VuThieu

  48. 2-6. The Sample Regression Function (SRF) • Population Regression Function PRF • Linearity in the parameters • Stochastic PRF • Stochastic Disturbance Term ui plays a critical role in estimating the PRF • Sample of observations from population • Stochastic Sample Regression Function SRF used to estimate the PRF Prof.VuThieu

  49. 2-7. Summary and Conclusions • The key concept underlying regression analysis is the concept of the population regression function (PRF). • This book deals with linear PRFs: linear in the unknown parameters. They may or may not linear in the variables. Prof.VuThieu

  50. 2-7. Summary and Conclusions • For empirical purposes, it is the stochastic PRF that matters. The stochastic disturbance term ui plays a critical role in estimating the PRF. • The PRF is an idealized concept, since in practice one rarely has access to the entire population of interest. Generally, one has a sample of observations from population and use the stochastic sample regression (SRF) to estimate the PRF. Prof.VuThieu

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