Lecture25: Simultaneous Equation Modeling(Contd.)

Transcription

1 P age Modle 8: Simltaneos Eqation Modeling Lectre5: Simltaneos Eqation Modeling(Contd.) Rdra P. Pradhan Vinod Gpta School of Management Indian Institte of Technolog Kharagpr, India

2 P age ADVANTAGES ASSOCIATED WITH IDENTIFICATION PROBLEM It solves mlticolinearit It gives an indication of varios alternatives to solve simltaneos eqation sstem It gives a strctre of strctral modelling vs. redced from of the modelling

3 P age PROBLEMS OF ESTIMATION In the simltaneos eqation sstems, OLS cannot be sed directl to have the estimate the parameters and se the model for prediction and forecasting. On the contrar, we have several alternatives methods to solve the simltaneos eqations sstem. These inclde:. Indirect Least Sqares (ILS). Two Stages Least Sqares Method (SLS). Three Stages Least Sqares Method ( SLS) 4. Limited Information Maimm Likelihood Method (LIMLM) 5. Fll Information Maimm Likelihood Method (FIMLM) THE SAMPLE PROBLEMS

4 P age Eqation : Order Condition: K=6; M=4; G= (K M) = 6 4= (G ) = = Eactl identified Rank condition: As this is non zero, eqation is eactl identified. Eqation : Order Condition: K=6; M=; G= (K M) = 6 = (G ) = = Over identified

5 4 P age 4 Rank condition: As this is non zero, eqation is eactl identified. Eqation : Order Condition: K=6; M=4; G= (K M) = 6 4= (G ) = = Eactl identified Rank condition:

6 5 P age 5 As this is zero, eqation is not identified. ESTABLISING IDENTIFICATION FROM THE REDUCED FORM Order condition: G M K Rank condition G* = nmber of endogenos variables contained in a particlar eqation. An eqation containing G* endogenos variables is identified if it is possible to constrct at least one non zero determinant of order (G* ) from the redced form coefficients of the eogenos variables eclded from that particlar eqation. The redced form for this model is: 4 Eqation : Order Condition: K=6;M=4;G= (K M) = 6 4= (G ) = = Eactl identified

7 6 P age Rank condition: Eclded endogenos: Inclded eogenos:, 4 G*=, (G* )= As both and are non zero, eqation is eactl identified. Eqation : Order Condition: K=6; M=; G= (K M) = 6 = (G ) = = Over identified Rank condition: Eclded endogenos: Inclded eogenos: 4 6

8 7 P age G*=, (G* )= As both and are non zero, eqation is over identified. Eqation : Order Condition: K=6; M=4; G= (K M) = 6 4= (G ) = = Eactl identified Rank condition: Eclded endogenos: None Inclded eogenos: 4 4 G*=, (G* )= 4 Eqation is not identified. 7

9 8 P age REFERENCES FOR FURTHER READING: Montgomer, D. C., Peck, E. A., and G. G. Vining: Introdction to Linear Regression Analsis, Wile India, New York, 6. Dielman, Terr E.: Applied Regression Analsis for Bsiness and Economics, PWS-Kent, Boston, 99. Draper, N. R., and H. Smith: Applied Regression Analsis, d ed., John Wile & Sons, New York, 998. Frank, C. R., Jr.: Statistics and Econometrics, Holt, Rinehart and Winston, New York, 97. Goldberger, Arthr S.: Introdctor Econometrics, Harvard Universit Press, 998. Grabill, F. A.: An Introdction to Linear Statistical Models, vol., McGraw- Hill, New York, 96. Greene, William H.: Econometric Analsis, 4th ed., Prentice Hall, Englewood Cliffs, N. J.,. Griffiths, William E., R. Carter Hill and George G. Jdge: Learning and Practicing Econometrics, John Wile & Sons, New York, 99. Gjarati, Damodar N.: Essentials of Econometrics, d ed., McGraw-Hill, New York, 999. Hill, Carter, William Griffiths, and George Jdge: Undergradate Econometrics, John Wile & Sons, New York,. Johnston, J.: Econometric Methods, d ed., McGraw-Hill, New York,

10 9 P age Katz, David A.: Econometric Theor and Applications, Prentice Hall, Englewood Cliffs, N.J., 98. Koop, Gar: Analsis of Economic Data, John Wile & Sons, New York,. Kotsoiannis, A.: Theor of Econometrics, Harper & Row, New York, 97. Maddala, G. S.: Introdction to Econometrics, John Wile & Sons, d ed., New York,. Mills, T. C.: The Econometric Modelling of Financial Time Series, Cambridge Universit Press, 99. Mittelhammer, Ron C., George G. Jdge, and Doglas J. Miller: Econometric Fondations, Cambridge Universit Press, New York,. Mkherjee, Chandan, Howard White, and Marc Wts: Econometrics and Data Analsis for Developing Contries, Rotledge, New York, 998. Pindck, R. S., and D. L. Rbinfeld: Econometric Models and Econometric Forecasts, 4th ed., McGraw-Hill, New York, 99. Verbeek, Marno: A Gide to Modern Econometrics, John Wile & Sons, New York,. Wooldridge, Jeffre M.: Introdctor Econometrics, Soth-Western College Pblishing,. 9

11 P age FAQS (FREQUENTLY ASKED QUESTIONS):. For simltaneos eqation models a) There mst be more than on endogenos variables b) There mst be more than on eogenos variables c) There mst be more than on parameter to be estimated d) There mst be more than on endogenos and eogenos variables. Appling OLS to simltaneos eqation reslts in the parameter being a) Inefficient b) Inconsistent c) With minimm variance d) Inefficient and inconsistent. The simltaneos eqation bias a) Refer to bias of the researcher towards sing this model b) In the bias in the estimated parameter that disappears when sample size becomes large c) In the bias in the estimated parameter that does not disappears even when sample size becomes large d) Means the error terms are biased positivel in small samples 4. In simltaneos eqation model the nmber eqation to be estimated are a) One more than the nmber of endogenos variables b) Eqal to the nmber of endogenos variables c) Depends on the nderling economic theor d) Eqal to the nmber endogenos and eogenos variables

12 P age SELF EVALUATION TESTS/ QUIZZES. State whether each of the following statements is tre or false: a) The method of OLS is not applicable to estimate a strctral eqation in a simltaneos-eqation model. b) In case an eqation is not identified, SLS is not applicable. c) The problem of simltaneit does not arise in a recrsive simltaneos-eqation model. d) The problems of simltaneit and eogeneit mean the same thing. e) The SLS and other methods of estimating strctral eqations have desirable statistical properties onl in large samples. f) There is no sch thing as an R for the simltaneos-eqation model as a whole. g) If an eqation is eactl identified, ILS and SLS give identical reslts.. Eplains following methods briefl: a) Ordinar least sqares(ols) b) Indirect least sqares(ils) c) Two Stage least sqares(sls). Consider the following modified Kenesian model of income determination: C t = β + β Y t + t I t = β + β Y t + β Y t + t

13 P age Y t = C t + I t + G t Where C = consmption ependitre I = investment ependitre Y = income G = government ependitre G t and Y t are assmed predetermined a) Obtain the redced-form eqations and determine which of the preceding eqations are identified (either jst or over). b) Which method will o se to estimate the parameters of the overidentified eqation and of the eactl identified eqation? Jstif or answer. 4. Wh is it nnecessar to appl the two-stage least-sqares method to eactl identified eqations?