Download Orthogonal Impulse Response - Econometric Modeling - Lecture Notes and more Study notes Econometrics and Mathematical Economics in PDF only on Docsity!
ORTHOGONAL IMPULSE RESPONSE
In the previous impulse response model we assumed that the error terms of the different equation
are uncorrelated. However, this assumption is quite restricted. A hypothetical shock in only one
equation does not respond a realistic adjustment process. To control for correlation between error
terms, we have to use the orthogonal impulse response sequences. The idea is to modify the
original moving-average construction in a way that the residuals are uncorrelated, i.e. the
residuals have to be orthogonal to each other
VARIANCE DECOMPOSITION
An alternative of impulse response, to receive a compact overview of the dynamic structures of a
VAR Model, are variance decomposition sequences. This method is also based on a vector
moving average model and orthogonal error terms. In contrast to impulse response, the task of
variance decomposition is to achieve information about the forecast ability. The idea is that even
a perfect model involves ambiguity about the realization of y, because the error terms associate
uncertainty. According to the interactions between the equations, the uncertainty is transformed
to all equations. The aim of the decomposition is to reduce the uncertainty in one equation to the
variance of error terms in all equations.
THE SAMPLE PROBLEM
Finance Development, Growth, and Stock Market Development in India; An Investigation
through VAR Model
Variables used under this study:
Broad money supply
Index of Industrial Production
Market capitalization
Data periods: 1994 to 2010 (monthly)
Solutions:
Unit Root Test
Cointegration
Granger Causality
Cointegration Results
Trace Test Maximum Eigenvalue Test ============================= ============================ Null Alternative λ- Tra CV Null Alternative λ- Max CV ======================================================================================= r = 0 r ≥ 0 32.72* 29.79 r = 0 r = 1 32.72* 21. r 1 r ≥ 1 6.678 15.49 r 1 r = 2 6.678 14. r 2 r > 2 1.446 3.841 r 20 r = 3 1.446 3. ======================================================================================= Note: r stands for the number of cointegrating vectors. The lag structure of VAR is determined by the highest values of the Akaike information criterion and Schwarz information criterion. The critical values are taken from Johansen and Juselius (1990). *: Indicates Statistical Significance at 5%. And other notations are defined earlier.
The Results of Granger Causality (VAR Format)
DV ∆EG ∆FD ∆SMD ECT Inferences
∆EG ------- 11.06* 7.279 -2.798* FD = > EG [0.00] [0.02] [0.00] SMD = > EG ∆FD 11.23* ------- 1.891 5.384* EG = > FD [0.00] [0.39] [0.00] ∆SMD 0.395 0.856 ------- -0. [0.82] [0.65] [0.33] Overall Conclusion: FD < = > EG SMD = > EG ======================================================================================= Note: ECT: Error Correction Term; *: Indicates Statistically Significant at 1%; and other notations are defined earlier.
REFERENCES FOR FURTHER READING:
Dhrymes, Phoebus J.: Introductory Econometrics, Springer‐Verlag, New York, 1978. Dielman, Terry E.: Applied Regression Analysis for Business and Economics, PWS‐Kent, Boston, 1991. Draper, N. R., and H. Smith: Applied Regression Analysis, 3d ed., John Wiley & Sons, New York, 1998. Dutta, M.: Econometric Methods, South‐Western Publishing Company, Cincinnati, 1975. Frank, C. R., Jr.: Statistics and Econometrics, Holt, Rinehart and Winston, New York, 1971. Goldberger, A. S.: A Course in Econometrics, Harvard University Press, Cambridge, Mass., 1991. Goldberger, A. S.: Topics in Regression Analysis, Macmillan, New York, 1968. Goldberger, Arthur S.: Introductory Econometrics, Harvard University Press, 1998. Greene, William H.: Econometric Analysis, 4th ed., Prentice Hall, Englewood Cliffs, N. J., 2000. Griffiths, William E., R. Carter Hill and George G. Judge: Learning and Practicing Econometrics, John Wiley & Sons, New York, 1993. Gujarati, Damodar N.: Essentials of Econometrics, 2d ed., McGraw‐Hill, New York, 1999. Hamilton, James D.: Time Series Analysis, Princeton University Press, Princeton, N. J., 1994. Harvey, A. C.: The Econometric Analysis of Time Series, 2d ed., MIT Press, Cambridge, Mass., 1990. Hayashi, Fumio: Econometrics, Princeton University Press, Princeton, N. J., 2000. Hill, Carter, William Griffiths, and George Judge: Undergraduate Econometrics, John Wiley & Sons, New York, 2001.
Hu, Teh‐Wei: Econometrics: An Introductory Analysis, University Park Press, Baltimore, 1973. Johnston, J.: Econometric Methods, 3d ed., McGraw‐Hill, New York, 1984. Judge, George G., Carter R. Hill, William E. Griffiths, Helmut Lütkepohl, and Tsoung‐Chao Lee: Theory and Practice of Econometrics, John Wiley & Sons, New York, 1980. Katz, David A.: Econometric Theory and Applications, Prentice Hall, Englewood Cliffs, N.J., 1982. Klein, Lawrence R.: A Textbook of Econometrics, 2d ed., Prentice Hall, Englewood Cliffs, N.J., 1974. Klein, Lawrence R.: An Introduction to Econometrics, Prentice Hall, Englewood Cliffs, N.J., 1962. Kmenta, Jan: Elements of Econometrics, 2d ed., Macmillan, New York, 1986. Koop, Gary: Analysis of Economic Data, John Wiley & Sons, New York, 2000. Madda, G. S., and Kim In‐Moo: Unit Roots, Cointegration, and Structural Change, Cambridge University Press, New York, 1998. Mills, T. C.: The Econometric Modelling of Financial Time Series, Cambridge University Press, 1993. Mills, T. C.: Time Series Techniques for Economists, Cambridge University Press, 1990. Mukherjee, Chandan, Howard White, and Marc Wuyts: Econometrics and Data Analysis for Developing Countries, Routledge, New York, 1998. Patterson, Kerry: An Introduction to Applied Econometrics: A Time Series Approach, St. Martin’s Press, New York, 2000. Rao, C. R.: Linear Statistical Inference and Its Applications, 2d ed., John Wiley & Sons, New York, 1975. Rao, Potluri, and Roger LeRoy Miller: Applied Econometrics, Wadsworth, Belmont, Calif., 1971.
SELF EVALUATION TESTS/ QUIZZES
1. ARIMA (1,2,3) means
a) The series has to be first differenced to make it stationary
b) The series has to be differenced twice to make it stationary
c) The series has to be differenced thrice to make it stationary
d) Can’t say about the stationary condition from the given information
2. Correlogram is
a) Test statistics used to test the chosen ARIMA model for goodness of fit
b) Plot of autocorrelation function and partial autocorrelation function against lag length
c) Plot of autocorrelation function and partial autocorrelation function against time
d) Plot of error term against time
3. Since the number of lags to be introduced in a VAR model can be a subjective question,
how does one decide how many lags to introduce in a concrete application
4. Let gMt be the annual growth in the money supply and let unemt be the unemployment
rate. Assuming that unemt follows a stable AR (1) process, explain in detail how you
would test whether gM Granger causes unem.
