2. 1.1 NVM ECONOMETRICS by N V M Rao BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI RAJASTHAN 2013

3. 1.2 NVM  Course No.: ECON C342/FIN C332/ MGTS C443  Course Title: ECONOMETRICS &  Course No.: ECON F241  Course Title: ECONOMETRIC METHODS  Instructor-in-charge: N.V.M. RAO  Room No.: 1222 A  E-mail: nvmrao@pilani.bits-pilani.ac.in  Course Mail id : nvmecotrix@gmail.com

4. 1.3 NVM Text Book: Christopher Dougherty, Introduction to Econometrics, Oxford, Fourth Edition, Indian Edition, 2011.

5. 1.4 NVM Reference Books: 1.Johnston J and John Dinardo, Econometric Methods, McGraw-Hill International, MGHISE, 4 th Edition, 1997 2.Damodar. N. Gujarati and Sangeetha, Basic Econometrics, Tata McGraw- Hill Publishing Company Limited, Fourth Edition, 2007 3.James H. Stock and Mark W. Watson, Introduction to Econometrics, Second Edition, Pearson Addison-Wesley, 2007 4.William H. Greene., Econometric Analysis, Pearson Education, Fifth Edition, 2007 5.Jeffrey M. Wooldridge, Introductory Econometrics: A Modern Approach, 4th Edition, Thomson, South-Western, 2009 6. R. S. Pindyck and D.L. Rubinfeld, Econometric Models and Economic Forecasts, Third Edition, McGraw-Hill: New York, 1991 7.H. Baltagi Badi, Econometrics, Springer, Delhi, Second Edition, 1999 8.Ramu Ramanathan, Introductory Econometrics With Applications, Thomson South-Western, Fifth Edition, 2002 9.Wonnacott & Wonnacott, Econometrics, Wiley, New York, 1970. 10.H. Theil, Econometrics, Wiley, New York, 1968. 11.A. S. Goldberger, Econometric Theory, Wiley, New York, 1964. 12.“Econometric Applications in India”, Edited by K L Krishna, Oxford, New Delhi, 1997.

6. 1.5 NVM Lecture Introduction to Econometrics Objectives What is econometrics? Introducing the simple econometric model The structure of economic data

7. 1.6 NVM Introduction to Econometrics What do I expect of you 1.Be serious in learning..be regular.. 2.before you come to class? See the slides and class material 3.Read the chapter(s), and as you read, write down on the slides any questions you have. Therefore, when you hear in the class, I do not expect it to be the first time you are hearing about a concept. If you don’t do this, it will seem like I am going really, really fast. If this approach to my teaching/your learning, which places high demand on your pre-class preparation, doesn’t suit you, I won’t be offended if you take course from someone else, next time.

8. 1.7 NVM Econometrics may be defined as the social science in which the tools of economic theory, mathematics & statistical inference are applied to the analysis of economic phenomena Econometrics attempts to quantify economic reality & to bridge the gap between economic theory & the real world. Econometrics consists of the development & application of statistical, mathematical & economic hypothesis that use empirical evidence for estimating the economic relationship, testing the validity of economic theories or evaluating government policy. What is Econometrics ?

9. 1.8 NVM Lot’s of definitions of econometrics. Nobel Prize Committee Paul Samuelson, et al. “Econometrics may be defined as quantitative analysis of actual economic phenomena.” Goldberger “... application of economic theory, mathematics and statistical inference to the analysis of economic phenomena.” 1. What is Econometrics ?

10. 1.9 NVM “Consists of the application of mathematical statistics to economic data to lend empirical support to the models constructed by mathematical economics and to obtain numerical results” (Gerhard 1968). “Econometrics may be defined as the social science in which the tools of economic theory, mathematics, and statistical inference are applied to the analysis of economic phenomena” (Goldberger 1964). “Econometrics is concerned with the empirical determination of economic laws” (Theil 1971). 1. What is Econometrics ?

11. 1.10 NVM the subject deserves to be studied in its own right for the following reasons: Economic theory makes statements or hypotheses that are mostly qualitative in nature (the law of demand), the law does not provide any numerical measure of the relationship. This is the job of the econometrician. The main concern of mathematical economics is to express economic theory in mathematical form without regard to measurability or empirical verification of the theory. Econometrics is mainly interested in the empirical verification of economic theory. Economic statistics is mainly concerned with collecting, processing, and presenting economic data in the form of charts and tables. It does not go any further. The one who does that is the econometrician. Why Econometrics a Separate Discipline?

12. 1.11 NVM Broadly speaking, traditional econometric methodology proceeds along the following lines: 1. Statement of theory or hypothesis. 2. Specification of the mathematical model of the theory 3. Specification of the statistical, or econometric, model 4. Collecting the data 5. Estimation of the parameters of the econometric model 6. Hypothesis testing 7. Forecasting or prediction 8. Using the model for control or policy purposes. Methodology of Econometrics

13. 1.12 NVM Describing economic reality Testing hypothesis about economic theory Forecasting future economic activity Major Uses of Econometrics

14. 1.13 NVM Consumption theory 1. Economics Theory : Consumption theory “ Keynes postulated a positive relationship between consumption and incomes”, i.e., people’s income 4. Econometric (–Regression) Model (Based on past data) C t =  0 +  1 Y t + u t => dC/dY =  1  estimate (or measure) the relationship between C & Y 3. Statistics: YearC Y 19802447.1 3776.3 19812476.9 3841.1 ….…. …. 20004651.8 5991.7 Data & Find the mean, variance, standard deviation, correlation correlation, etc. 2. Mathematical Expression: Consumption = f(Income) => C = f(Y) => MPC = dC/dY = f’(Y) > 0 ; assume 0 < MPC < 1

15. 1.14 NVM Economic Relationships: government budget trade deficit Wage inflation Stock Market Index capital gains tax crime rate unemployment exchange Rate Properties Market rent control laws Interest rate Money supply GDP Growth

16. 1.15 NVM measurementquantitative Provide measurement and quantitative analysis analysis of actual economic phenomena or economic relationship based on 1. Economic theory 2. Economic data 3. Methods of model constructed The Role of Econometrics

17. 1.16 NVM economic theory economic data } economic decisions To use information effectively : Economic Decisions *Econometrics* helps us combine economic theory and economic data to find the answers. When the price of goods increases one rupee, what will be the change of the quantity demanded?

18. 1.17 NVM Consumption, C, is some function of income (Inc) : C = f (Inc) For applied econometric analysis this consumption function must be specified more precisely. The Consumption Function

19. 1.18 NVM Demand, q d, for an individual commodity: q d = f ( p, p c, p s, Inc) p = own price; p c = price of complements; p s = price of substitutes; Y = income demand Supply, q s, of an individual commodity: q s = f ( p, p c, p f, p s ) p = own price; p c = price of complement products; p s = price of substitutes; p f = price of factor inputs supply

20. 1.19 NVM Q d = f (P, P s, Y d ) Q d Dependent variable: Q d PP s Y d Independent variables: P, P s, Y d From the theory of consumption,  P   Q d  (Law of demand)  P s   Q d  (Definition of substitutes)  Y d   Q d  (For normal goods)

21. 1.20 NVM Listing the variables in an economic relationship is not enough. For effective policy we must know the amount of change needed for a policy instrument to bring about the desired effect: By how much should the Reserve Bank raise (cut) interest rates to prevent inflation (recession)? By how much can the price of PROFSHOW Tickets be increased and still fill the BITS CENTRAL AUDITORIUM? By how much can the price of Cricket Tickets be increased and still fill the stadium? How much ?

22. 1.21 NVM How Much? Answering the question of How Much? Need to estimate parameters that are both: 1. unknown and 2. unobservable

23. 1.22 NVM Average or systematic behaviour over many individuals or many firms. Not a single individual or single firm. Economists are concerned with the unemployment rate and not whether a particular individual gets a job. The Statistical Model

24. 1.23 NVM The Statistical Model Systematic part provides prediction, f (Inc), but actual will miss by random error, u. Consumption, c, is function of income, Inc, with error, u: C = f (Inc) + u Actual vs. Predicted Consumption: Actual = systematic part + random error

25. 1.24 NVM Then the statistical model becomes: C =  0 +  1 Inc + u Need to define f (Inc) in some way to make consumption, C, a linear function of income, Inc : f (Inc) =  0 +  1 Inc C = f (Inc) + u The Consumption Function

26. 1.25 NVM X Wage = f (X) + u The Wage Function X Where X can represent a group of variables such “education”, “experience”, and “training”, etc. f(X) =  0 +  1 educ +  2 experi +  3 training The statistical estimation model then becomes: Wage =  0 +  1 educ +  2 experi +  3 training + u

27. 1.26 NVM Dependent variable, Y, is the focus of study (predict or explain changes in dependent variable). Explanatory variable(s), X or others, help us explain observed changes in the dependent variable. Y =  0 +  1 X + u The Econometric Model or Regression Model Parameters :  0 and  1 Intercept (Constant) :  0 Slope (Coefficient of X) :  1 The source of changes of Y is from the variation in X.

28. 1.27 NVM Left hand-side Variable: Regressand Dependent Explained Response Endogenous Terminology and Notation Y =  0 +  1 X + u Right hand-side Variable: Regressor Independent Explanatory Stimulus or control Exogenous  0,  1 : Coefficient  0 : Interceptor constant  1 :slope u : Random error

29. 1.28 NVM Further … Statistical Models Controlled (experimental) vs. Uncontrolled (observational) Uncontrolled experiment (econometrics) explaining consump- tion, Y: price, X 1, and income, X 2, vary at the same time. Controlled experiment (“pure” science) explaining mass, Y : pressure, X 1, held constant when varying temperature, X 2, and vice versa.

30. 1.29 NVM Econometric model economic model economic variables and parameters. statistical model sampling process with its parameters. data observed values of the variables.

31. 1.30 NVM Y =  0 +  1 X Interpretations When X = 0, Y =  0 When X = 1, Y =  0 +  1 When X = 5, Y =  0 + 5  1 When X = x’, Y =  0 +  1 x’ When X is raised by one unit, Y is expected to increase by  1 units

32. 1.31 NVM The Stochastic Linear Model Weekly Food Expenditures vs. weekly income

33. 1.32 NVM......................................... X Y 0 Observed points Theoretical relation

34. 1.33 NVM The simple linear regression model u Y =  0 +  1 X + u u u : The stochastic error term (random error term / disturbance) Deterministic component of Y E(Y|X) =  0 +  1 X Stochastic component of Y u uu u 2. Econometric Models

35. 1.34 NVM E(Y|X) =  0 +  1 X Expected value of Y given X. Rules of the expectation operator: Let a 1 and a 2 be two constants and X 1 and X 2 be two independent random variables. E(a 1 ) = a 1 E(a 1 X 1 ) = a 1 E(X 1 ) E(X 1  X 2 ) = E(X 1 )  E(X 2 ) E[(X 1 – E(X 1 )) 2 ] = var(X 1 ) 2. Econometric Models

36. 1.35 NVM u Sources of “u” Y ≠  0 +  1 X Omitted variables: Omission of less influential variables Ignorance of theory Unavailability of data 2. Econometric Models

37. 1.36 NVM u Sources of “u” Y ≠  0 +  1 X Bad quality of data: Poor proxy variables Immeasurable theoretical concepts Concise theoretical concepts Measurement errors 2. Econometric Models

38. 1.37 NVM u Sources of “ u ” Y ≠  0 +  1 X Wrong functional form Example: Linear versus nonlinear, double log versus quadratic Purely random human behavior 2. Econometric Models

39. 1.38 NVM Notations Data set: (X 1, Y 1 ), (X 2, Y 2 ), …, (X N, Y N ) For the 1 st observation: Y 1 =  0 +  1 X 1 + u 1 2 nd observation: Y 2 =  0 +  1 X 2 + u 2  N th observation: Y N =  0 +  1 X N + u N 2. Econometric Models

40. 1.39 NVM General form, Y i =  0 +  1 X i + u i (i = 1, 2, …, N). 2. Econometric Models conditional expected value The conditional expected value of Y i : E(Y i |X i ) =  0 +  1 X i Or Y t =  0 +  1 X t + u t (t = 1, 2, …, N). For time point

41. 1.40 NVM The Estimated Regression Model Estimating this model by econometric techniques fitted : The estimated (fitted) value of Y i u i Y i =  0 +  1 X i + u i (i = 1, 2, …, N). 2. Econometric Models “hat”

42. 1.41 NVM stochastic error The stochastic error (or random error) term is a theoretical value & is unobserved u u i = Y i – E(Y i |X i ). 2. Econometric Models residual The residual is an empirical value & is observed e u e i = Y i – Y i or u i = Y i – Y i

43. 1.42 NVM Example 1.1: Which of the following expressions are correct? a.Y i =  0 +  1 X i b.Y i =  0 +  1 X i + u i c.Y i =  0 +  1 X i d.Y i =  0 +  1 X i + e i e.Y i =  0 +  1 X i + e i. 2. Econometric Models

44. 1.43 NVM 3. The Data Structure Cross-sectional data ============================= Name Sex Age Height Weight (inches) (pounds) ------------------------------------------------- Anand M 14 69 112 Aruna F 13 56 84 Bandan F 14 62 102 Hari M 15 67 135 John M 16 70 165 Saila F 16 63 120 =============================

45. 1.44 NVM Time series data (million Rs. at current mkt prices) ========================= Year GDP Consumption ------------------------------------------ 1991 668512 391098 1992 779335 451670 1993 897463 514239 1994 1010885 592665 1995 1084570 652875 1996 1195315 718779 ========================= 3. The Data Structure

46. 1.45 NVM Panel data Company Quarter Closing Volume HSBC 1997.3 233 228831.6 HSBC 1997.4 259 298602.1 HSBC 1998.1 191 521680.5 HSBC 1998.2 231 409539.9 BEA 1997.3 32.3 236392.1 BEA 1997.4 28.9 225633.6 BEA 1998.1 18.15 319408.4 BEA 1998.2 15.85 188125.7 3. The Data Structure

47. 1.46 NVM Causality vs. Correlation Causality: The relationship between cause and effect Correlation: The strength of linear association between two variables Consider the relation between weight and height. What is the direction of causality?

48. 1.47 NVM Regression: Tests the strength and direction of the quantitative relations involved. Three possibilities of a statistical relation between events A and B: 1. A  B; 2. B  A; 3. C  A and C  B; 4. By chance. 4. Causality vs. Correlation

49. 1.48 NVM Example: Predicting Weights Suppose you think that weight = f (height). Econometric model: Y i = f(X i ) +  i =  o +  1 X i +  i Y i : The weight (in pounds) of the i th person X i : The height (in inches above 5 feet) of the i th person  i : The value of the stochastic error term for the i th person

50. 1.49 NVM ObsX YObsX Y ----------------------------------------------------------- 514011170 1 51401111170 91579162 2 915712 9162 1320510165 3 132051310165 1219812180 4 121981412180 101628160 5 1016215 8160 111749155 6 1117416 9155 815010165 7 81501710165 916515190 8 91651815190 1017013185 9 101701913185 1218011155 10 121802011155 Table 1.1: Heights and Weights 5. Example

51. 1.50 NVM = 103.40 + 6.38X i

52. 1.51 NVM 00 11 ^ ^

53. 1.52 NVM The method of least squares gives the results, = 103.40 + 6.38X i Interpretations: When the height is 5 feet, i.e., X=5, the weight is 103.4+6.38*5 = 135.3 pounds. When the height increases, the weight will increase. When the height increases “one inch”, the weight is expected to increase “6.38 pounds”. 5. Example

54. 1.53 NVM Statement of theory or hypothesis Specification of the mathematical model of the theory Specification of the econometric model of the theory Obtaining data for the analysis. Estimation with statistical properties. Hypothesis testing Analyze and evaluate implications of the results Forecasting or prediction Using the model for control or policy purpose The Practice of Econometrics

55. 1.54 NVM Economic Empirical Study Economic Theory; Past Experience, studies Formulating a model: Cause - effect C = f(Y) ==> C t =  0 +  1 Y t + u t Gathering data:Statistics monthly, quarterly, yearly data Estimating the model:Simple OLS method or other advances Testing the hypothesis: H 0 :  1 >0, positive relationship or not If not true Interpreting the results: Forecasting Policy implication and decisions