Basic Econometrics

1. Basic Econometrics

2. Basic Econometrics Introduction: What is Econometrics?

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)

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)

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)

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

7. Economic Theory Mathematical Economics Econometrics Economic Statistics Mathematic Statistics

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

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

10. Economic Theory Mathematical Economics Econometrics Economic Statistics Mathematic Statistics

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”

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

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

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

15. IntroductionMethodology of Econometrics (4) Obtaining Data

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

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)

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

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

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

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

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

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”)

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”

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)

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

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)

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”)

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)

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

31. THE NATURE OF THE VARIABLE • Ratio Scale: • Ratio of two variables, distance between two variables, and ordering of variables are meaningful • Interval Scale: • Distance and ordering between two variables meaningful, but not ratio • Ordinal Scale: • Ordering of two variables meaningful (not ratio or distance) • Nominal Scale: • Categorical or dummy variables, qualitative in nature

32. 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

33. 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)

34. 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

35. Basic Econometrics Chapter 2: TWO-VARIABLE REGRESSION ANALYSIS: Some basic Ideas

36. 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)

37. 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 )

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

39. 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)

40. 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

41. 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

42. 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

43. 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:

44. 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

45. 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)

46. Weekly Consumption Expenditure (Y) SRF1 SRF2 Weekly Income (X)

47. 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)

48. 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

49. 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

50. 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.