The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Non-nested Hypotheses

  • M. Hashem Pesaran
  • M. Rodrigo Dupleich Ulloa
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_1835

Abstract

This article provides an overview of the literature on hypotheses testing when the hypotheses or models under consideration are non-nested. Two models are said to be non-nested if neither can be obtained from the other by some limiting process, including the imposition of equality and/or inequality constrains on one of the model’s parameters. Relevant concepts such as closeness measures and pseudo-true values are discussed and alternative approaches to testing non-nested hypotheses, including the Cox procedure, artificial nesting and the encompassing approach, are reviewed. The Vuong approach to model selection is also covered.

Keywords

Artificial nesting Cox’s test Encompassing test Hypothesis testing Kullback-Leibler information criteria Linear regression models Maximum likelihood estimation Model selection Non-nested hypotheses Pseudo-true values 

JEL Classifications

C1 C20 C52 
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Bibliography

  1. Ackello-Ogutu, C., Q. Paris, and W.A. Williams. 1985. Testing a von Liebig crop response function against polynomial specifications. American Journal of Agricultural Economics 67: 873–880.CrossRefGoogle Scholar
  2. Altissimo, F., and G.L. Violante. 2001. The nonlinear dynamics of output and unemployment in the US. Journal of Applied Econometrics 16: 461–486.CrossRefGoogle Scholar
  3. Atkinson, A. 1970. A method for discriminating between models. Journal of the Royal Statistical Society B 32: 323–353.Google Scholar
  4. Backus, D. 1984. Empirical models of the exchange rate: Separating the wheat from the chaff. Canadian Journal of Economics 17: 824–846.CrossRefGoogle Scholar
  5. Bera, A.K., and M.L. Higgins. 1997. ARCH and bilinearity as competing models for nonlinear dependence. Journal of Business and Economic Statistics 15: 43–50.Google Scholar
  6. Bleaney, M., and A. Nishiyama. 2002. Explaining growth: A contest between models. Journal of Economic Growth 7: 43–56.CrossRefGoogle Scholar
  7. Bresnahan, T.F. 1987. Competition and collusion in the American automobile market: The 1955 price war. Journal of Industrial Economics 35: 457–482.CrossRefGoogle Scholar
  8. Chen, Y.T., and C.M. Kuan. 2002. The pseudo-true score encompassing test for nonnested hypotheses. Journal of Econometrics 106: 271–295.CrossRefGoogle Scholar
  9. Clarke, K.A. 2001. Testing nonnested models of international relations: Reevaluating realism. American Journal of Political Science 45: 724–744.CrossRefGoogle Scholar
  10. Cox, D.R. 1961. Tests of separate families of hypothesis. Proceedings of the Forth Berkeley Symposium on Mathematical Statistics and Probability 1: 105–123.Google Scholar
  11. Cox, D.R. 1962. Further results on tests of separate families of hypothesis. Journal of the Royal Statistical Society B 24: 406–424.Google Scholar
  12. Dastoor, N.K. 1983. Some aspects of testing nonnested hypothesis. Journal of Econometrics 21: 213–228.CrossRefGoogle Scholar
  13. Davidson, R., and J.G. MacKinnon. 1981. Several tests for model specification in the presence of alternative hypothesis. Econometrica 49: 781–793.CrossRefGoogle Scholar
  14. Davidson, R., and J.G. MacKinnon. 2002. Bootstrap J tests of nonnested linear regression models. Journal of Econometrics 109: 167–193.CrossRefGoogle Scholar
  15. Davies, R.B. 1977. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64: 247–254.CrossRefGoogle Scholar
  16. Deaton, A.S. 1982. Model selection procedures, or, does the consumption function exist? In Evaluating the reliability of macro-economic models, ed. G.C. Chow and P. Corsi. New York: Wiley.Google Scholar
  17. Dowrick, S., and N. Gemmell. 1991. Industrialisation, catching up and economic growth: A comparative study across the world’s capitalist economies. Economic Journal 101: 263–275.CrossRefGoogle Scholar
  18. Dubin, R.A., and C.-H. Sung. 1990. Specification of hedonic regressions: Non-nested tests on measures of neighborhood quality. Journal of Urban Economics 27: 97–110.CrossRefGoogle Scholar
  19. Elyasiani, E., and A. Nasseh. 1994. The appropriate scale variable in the U.S. money demand: An application of nonnested tests of consumption versus income measures. Journal of Business and Economic Statistics 12: 47–55.Google Scholar
  20. Ericsson, N. 1983. Asymptotic properties of instrumental variables statistics for testing nonnested hypothesis. Review of Economic Studies 50: 287–304.CrossRefGoogle Scholar
  21. Fisher, G.R., and M. McAleer. 1981. Alternative procedures and associated tests of significance for nonnested hypothesis. Journal of Econometrics 16: 103–119.CrossRefGoogle Scholar
  22. Frank, M.D., B.R. Beattie, and M.E. Embleton. 1990. A comparison of alternative crop response models. American Journal of Agricultural Economics 72: 597–603.CrossRefGoogle Scholar
  23. Gasmi, F., J.J. Laffont, and Q. Vuong. 1992. Econometric analysis of collusive behavior in a soft-drink market. Journal of Economics and Management Strategy 1: 277–311.CrossRefGoogle Scholar
  24. Ghysels, E., and A. Hall. 1990. Testing non-nested Euler conditions with quadrature based method approximation. Journal of Econometrics 46: 273–308.CrossRefGoogle Scholar
  25. Godfrey, L.G. 1998. Tests of non-nested regression models: Some results on small sample behaviour and the bootstrap. Journal of Econometrics 84: 59–74.CrossRefGoogle Scholar
  26. Goodman, A.C., and R.A. Dubin. 1991. Sample stratification with non-nested alternatives: Theory and a hedonic example. The Review of Economics and Statistics 72: 168–173.CrossRefGoogle Scholar
  27. Gourieroux, C., and A. Monfort. 1994. Testing nonnested hypothesis. In Handbook of econometrics, ed. R.F. Engle and D.L. McFadden, vol. 4. Amsterdam: North-Holland.Google Scholar
  28. Gourieroux, C., and A. Monfort. 1995. Testing, encompassing, and simulating dynamic econometric models. Econometric Theory 11: 195–228.CrossRefGoogle Scholar
  29. Gourieroux, C., A. Monfort, and A. Trognon. 1983. Testing nested and nonnested hypothesis. Journal of Econometrics 21: 83–115.CrossRefGoogle Scholar
  30. Halaby, C.N., and D.L. Weakliem. 1993. Ownership and authority in the earnings function: Nonnested tests of alternative specifications. American Sociological Review 58: 16–30.CrossRefGoogle Scholar
  31. Kim, S., N. Shephard, and S. Chib. 1998. Stochastic volatility: Likelihood inference and comparison with ARCH models. Review of Economic Studies 65: 361–393.CrossRefGoogle Scholar
  32. Kullback, S. 1959. Statistics and information theory. New York: Wiley.Google Scholar
  33. Lyon, C.C., and G.D. Thompson. 1993. Temporal and spatial aggregation: Alternative marketing margin models. American Journal of Agricultural Economics 75: 523–536.CrossRefGoogle Scholar
  34. McAleer, M., G. Fisher, and P. Volker. 1982. Separate misspecified regressions and the U.S. long run demand for money function. The Review of Economics and Statistics 64: 572–583.CrossRefGoogle Scholar
  35. McAleer, M., and S. Ling. 1998. A nonnested tests for GARCH and EGARCH models. Working paper, Department of Economics, University of Western Australia.Google Scholar
  36. McAleer, M., and M.H. Pesaran. 1986. Statistical inference in nonnested econometric models. Applied Mathematics and Computation 20: 271–311.CrossRefGoogle Scholar
  37. McAleer, M., M.H. Pesaran, and A.K. Bera. 1990. Alternative approaches to testing nonnested models with autocorrelated disturbances: An application to models of U.S. unemployment. Communications in Statistics A 19: 3619–3644.CrossRefGoogle Scholar
  38. Mizon, G., and J.F. Richard. 1986. The encompassing principle and its applications to testing nonnested hypothesis. Econometrica 3: 657–678.CrossRefGoogle Scholar
  39. Otsu, T., and Y.J. Whang. 2005. Testing for non-nested conditional moment restrictions via conditional empirical likelihood. Discussion Paper No. 1533, Cowles Foundation, Yale University.Google Scholar
  40. Pace, L., and A. Salvan. 1990. Best conditional tests for separate families of hypotheses. Journal of the Royal Statistical Society B 52: 125–134.Google Scholar
  41. Pagan, A.R., A.D. Hall, and P.K. Trivedi. 1983. Assessing the variability of inflation. Review of Economic Studies 50: 585–596.CrossRefGoogle Scholar
  42. Pesaran, M.H. 1974. On the general problem of model selection. Review of Economic Studies 41: 153–171.CrossRefGoogle Scholar
  43. Pesaran, M.H. 1981. Pitfalls of testing nonnested hypotheses by the Lagrange multiplier method. Journal of Econometrics 17: 323–331.CrossRefGoogle Scholar
  44. Pesaran, M.H. 1982a. A critique of the proposed tests of the natural rate-rational expectations hypothesis. Economic Journal 92: 529–554.CrossRefGoogle Scholar
  45. Pesaran, M.H. 1982b. Comparison of local power of alternative tests of nonnested regression models. Econometrica 50: 1287–1305.CrossRefGoogle Scholar
  46. Pesaran, M.H. 1982c. On the comprehensive method of testing nonnested regression models. Journal of Econometrics 18: 263–274.CrossRefGoogle Scholar
  47. Pesaran, M.H. 1987. Global and partial nonnested hypothesis and asymptotic local power. Econometric Theory 3: 69–97.CrossRefGoogle Scholar
  48. Pesaran, M.H., and A.S. Deaton. 1978. Testing nonnested nonlinear regression models. Econometrica 46: 677–694.CrossRefGoogle Scholar
  49. Pesaran, M.H., and B. Pesaran. 1993. A simulation approach to the problem of computing Cox’s statistic for testing nonnested models. Journal of Econometrics 57: 377–392.CrossRefGoogle Scholar
  50. Pesaran, M.H., and B. Pesaran. 1997. Working with Microfit 4.0. Oxford: Oxford University Press.Google Scholar
  51. Pesaran, M.H., and S. Potter. 1997. A floor and ceiling model of US output. Journal of Economic Dynamics and Control 21: 661–696.CrossRefGoogle Scholar
  52. Pesaran, M.H., and M. Weeks. 2001. Nonnested hypothesis testing: An overview. In Companion to theoretical econometrics, ed. B.H. Baltagi. Oxford: Basil Blackwell.Google Scholar
  53. Poterba, J.M., and L.H. Summers. 1983. Dividend taxes, corporate investments, and ‘Q’. Journal of Public Economics 22: 135–167.CrossRefGoogle Scholar
  54. Quandt, R.E. 1974. A comparison of methods for testing nonnested hypothesis. The Review of Economics and Statistics 56: 92–99.CrossRefGoogle Scholar
  55. Ram, R. 1986. Government size and economic growth: A new framework and some evidence from cross-section and time-series data. American Economic Review 76: 191–203.Google Scholar
  56. Ramalho, J.J.S., and R.J. Smith. 2002. Generalized empirical likelihood nonnested tests. Journal of Econometrics 107: 99–125.CrossRefGoogle Scholar
  57. Rivers, D., and Q. Vuong. 2002. Model selection tests for nonlinear dynamic models. The Econometrics Journal 5: 1–39.CrossRefGoogle Scholar
  58. Royston, P., and S.G. Thompson. 1995. Comparing non-nested regression models. Biometrics 51: 114–127.CrossRefGoogle Scholar
  59. Sandler, T., and J.C. Murdoch. 1990. Nash–Cournot or Lindahl behavior?: An empirical test for the NATO allies. Quarterly Journal of Economics 105: 875–894.CrossRefGoogle Scholar
  60. Santos Silva, J.M.C. 2001. A score test for non-nested hypothesis with applications to discrete data models. Journal of Applied Econometrics 16: 577–597.CrossRefGoogle Scholar
  61. Smith, R.J. 1992. Nonnested for competing models estimated by generalized method of moments. Econometrica 4: 973–980.CrossRefGoogle Scholar
  62. Vannetelbosch, V.J. 1996. Testing between alternative wage-employment bargaining models using Belgian aggregate data. Labour Economics 3: 43–64.CrossRefGoogle Scholar
  63. Victoria-Feser, M.-P. 1997. A robust tests for non-nested hypothesis. Journal of the Royal Statistical Society B 59: 715–727.CrossRefGoogle Scholar
  64. Vuong, Q.H. 1989. Likelihood ratio tests for model selection and nonnested hypothesis. Econometrica 57: 307–333.CrossRefGoogle Scholar
  65. Walker, A.M. 1967. Some tests of separate families of hypothesis in time series analysis. Biometrika 54: 39–68.CrossRefGoogle Scholar
  66. White, H. 1982. Regularity conditions for Cox’s test of nonnested hypothesis. Journal of Econometrics 19: 301–318.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • M. Hashem Pesaran
    • 1
  • M. Rodrigo Dupleich Ulloa
    • 1
  1. 1.