Rao, Surekha and Ghali, Moheb and Krieg, John
(2008):
*On the J-test for nonnested hypotheses and Bayesian extension.*

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## Abstract

Abstract Davidson and MacKinnon’s J-test was developed to test non-nested model specification. In empirical applications, however, when the alternate specifications fit the data well the J test may fail to distinguish between the true and false models: the J test will either reject, or fail to reject both specifications. In such cases we show that it is possible to use the information generated in the process of applying the J-test to implement a Bayesian approach that provides an unequivocal and acceptable solution. Jeffreys’ Bayes factors offer ways of obtaining the posterior probabilities of the competing models and relative ranking of the competing hypotheses. We further show that by using approximations of Schwarz Information Criterion and Bayesian Information Criterion we can use the classical estimates of the log of the maximum likelihood which are available from the estimation procedures used to implement the J test to obtain Bayesian posterior odds and posterior probabilities of the competing nested and non- nested specifications without having to specify prior distributions and going through the rigorous Bayesian computations.

Item Type: | MPRA Paper |
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Original Title: | On the J-test for nonnested hypotheses and Bayesian extension |

Language: | English |

Keywords: | specification testing, non-nested hypotheses, Bayes factor, Bayesian Information Criteria, Marginal likelihood |

Subjects: | C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General |

Item ID: | 14637 |

Depositing User: | surekha Rao |

Date Deposited: | 14 Apr 2009 00:38 |

Last Modified: | 27 Sep 2019 14:02 |

References: | BIBLIOGRAPHY 1. Balakrishnan, P, K. Surekha and B.P. Vani, 1994, The Determinants of Inflation in India, Bayesian and Classical Analyses, Journal of Quantitative Economics, vol. 10, no.3, 325-336. 2. Berger , J.O. and L. Pericchi, 2001, Objective Bayesian Methods for Model Selection: Introduction and Comaprison, in P. Lahiri ed. Institute of Mathematical Statistics Lecture Notes -- Monograph Series volume 38, Beachwood Ohio, 135--207. 3. Chib, S, ( 1995), Marginal Likelihood from the Gibbs Sampler, Journal of the American Statistical Association, 90, 1331-1350 4. Davidson, R and MacKinnon, J. G.. 1981, “Several Tests for Model Specification in the Presence of Alternative Hypotheses” Econometrica, vol. 49, pp. 781-793. 5. Davidson, R and MacKinnon, J. G., 1982, “Some Non-Nested Hypothesis Tests and the Relations Among Them,” The Review of Economic Studies, XLIX, 1982, pp. 551-565. 6. Davidson, Russell and MacKinnon, James G., 1993, Estimation and Inference in Econometrics, Oxford University Press. 7. Davidson, Russell and MacKinnon, James G., 2002, “Fast Double Bootstrap Tests of Non-nested Linear Regression Models,” Econometric Reviews, vol. 21, No. 4, pp. 419-429. 8. Davidson, Russell and MacKinnon, James G., 2004, Econometric Theory and Methods, Oxford University Press. 9. Eviews 5 User Guide, 2004, Quantitative Micro Software LLC, Irvine, California. 10. Faff, Robert and Gray, Philip, 2006, “On the Estimation and Comparison of Short-Rate Models Using the Generalized Method of Moments” Journal of Banking and Finance, Vol. 30, No. 11, pp. 3131-3146. 11. Gaver,K.M. and Geisel, M.S., 1974, “Discriminating among Alternative Models: Bayesian and Non-Bayesian Methods,” in Frontiers in Econometrics, P. Zarembka, ed., Academic Press, New York. 12. Gelfand, A., and Dey, D.K., Bayesian Model Choice: Asymptotics and Exact calculations, Journal of the Royal Statistical Society Series B, 56, 501-514. 13. Ghali, M., 1987, “Seasonality, Aggregation and the Testing of the Production Smoothing Hypothesis,” The American Economic Review, vol. 77, no. 3, pp. 464-469. 14. Ghali, M., 2005, “Measuring the Convexity of the Cost Function”, International Journal of Production Economics, vol. 93-94, Elsevier, Amsterdam. 15. Ghali, M., 2007, “Comparison of Two Empirical Cost Functions,” International Journal of Production Economics, 108, pp. 15-21 16. Godfrey, L.G., and Pesaran, M.H., 1983, “ Tests of Non-Nested Regression Models: Small Sample Adjustments and Monte Carlo Evidence,” Journal of Econometrics, vol. 21, pp. 133-154. 17. Goldberger, A.S., 1968, Topics in Regression Analysis, Macmillan, London. 18. Gourieroux, C. and Monfort, A, 1994, “Testing Non-Nested Hypotheses,” Chapter 44 in Handbook of Econometrics, R.F. Engle and D.L. McFadden eds., Elsevier Science. 19. Greene, William, 2003, Econometric Analysis, 5th edition, Prentice Hall, New Jersey. 20. Jeffreys, H. (1935), Some Tests Of Significance, Treated by the Theory of Probability, Proceedings of the Cambrdige Philosophical Society, 31 , 203-222. 21. Jeffreys, H., 1961, “ Theory of Probability”, 3rd edition, Oxford University Press, Oxford, UK. 22. Kass R. and A.E. Raftery, (1995),” Bayes Factors”, Journal of the American Statistocal Association, Vol 90, no 430, 773-795 23. Krane, Spencer, and Steven Braun, (1991), “Production Smoothing Evidence from Physical-Product Data,” Journal of Political Economy, vol. 99,no 3, pp. 558-581. 24. Koop, Gary, 2003, Bayesian Econometrics, John Wiley and Sons, England. 25. Lai, Kon S., 1991, “Aggregation and Testing of the Production Smoothing Hypothesis,” International Economic Review, vol.32, no. 2, pp.391- 403. 26. Lovell, Michael C., 1963, “Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis,” Journal of the American Statistical Association, vol. 58, pp. 993-1010. 27. Leamer, E.E., 1978, Specification Searches, Ad Hoc Inference with Non –experimental data, John Wiley, New York. 28. Malinvaud, E., 1966, Statistical Methods of Econometrics, Rand McNally & Co., Chicago. 29. McAleer, Michael, 1995, “The significance of testing empirical non-nested models,” Journal of Econometrics, vol. 67, pp. 149-171. 30. Pesaran, M.H, and Weeks, M., 2001, “Non-nested Hypotheses Testing: An Overview,” chapter 13 in Theoretical Econometrics, Baltagi, B.H. ed., Blackwell Publishers, Oxford. 31. Pesaran, M.H., 1983, “Comment,” Econometric Reviews, vol. 2, no. 1, pp. 145-9. Marcel Dekker, Inc. 32. Pesaran, M.H., and Deaton, A.S, 1978, “Testing Non-nested Nonlinear Regression Models,” Econometrica, Vol. 46, N0. 3, pp. 677-94. 33. Ramey, Valerie A., and Kenneth D. West, 1999 “Inventories,” in Handbook of Macroeconomics, Volume 1B, John B. Taylor and Michael Woodford eds., Elsevier Science, pp. 863-923. 34. Singh, Tarlok, 2004, “Optimising and Non-optimising Balance of Trade Models: A Comparative Evidence from India,” International Review of Applied Economics, Vol. 18, No. 3, pp. 349-368. 35. Surekha, K. and W.E. Griffiths, 1990, “Comparison of Some Bayesian Heteroscedastic Error Models”, Statistica, anno l, n. 1 pp. 109 -117 36. Surekha K. and M. Ghali, 2001, “Speed of Adjustment and Production Smoothing: Bayesian Estimation”, International Journal of Production Economics, vol. 71, no. 3, pp.55-65 37. Schwarz, G, 1978, “Estimating the Dimensions of a Model, The Annals of Statistics, Vol. 6, no 2, pp. 461-464. 38. West, Kenneth, 1986 “A Variance Bounds Test of the Linear Quadratic Inventory Model,” Journal of Political Economy, vol.94, no.2, pp. 347-401. 39. Zellner, A. 1971, An Introduction to Bayesian Inference in Econometrics, John Wiley, New York 40. Zellner, A. 1984, Basic Issues in Econometrics, University of Chicago Press, Chicago. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/14637 |