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Exact Permutation Tests for Non-nested Non-linear Regression Models

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  • Richard Luger

Abstract

This paper proposes exact distribution-free permutation tests for the specification of a non-linear regression model against one or more possibly non-nested alternatives. The new tests may be validly applied to a wide class of models, including models with endogenous regressors and lag structures. These tests build on the well-known J test developed by Davidson and MacKinnon (1981) and their exactness holds under broader assumptions than those underlying the conventional J test. The J-type test statistics are used with a randomization or Monte Carlo resampling technique which yields an exact and computationally inexpensive inference procedure. A simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions. The test procedure developed is illustrated by an application to inflation dynamics.

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Paper provided by Department of Economics, Emory University (Atlanta) in its series Emory Economics with number 0419.

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Date of creation: Nov 2004
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Handle: RePEc:emo:wp2003:0419

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  1. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
  2. Gali, Jordi & Gertler, Mark, 1999. "Inflation dynamics: A structural econometric analysis," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 195-222, October.
  3. James M. Nason & Gregor W. Smith, 2005. "Identifying the New Keynesian Phillips Curve," Working Papers 1026, Queen's University, Department of Economics.
  4. Godfrey, L. G. & Pesaran, M. H., 1983. "Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence," Journal of Econometrics, Elsevier, vol. 21(1), pages 133-154, January.
  5. DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 2005-03, Universite de Montreal, Departement de sciences economiques.
  6. Kennedy, P., 1993. "Randomization Tests in Econometrics," Discussion Papers dp93-08, Department of Economics, Simon Fraser University.
  7. Godfrey, Leslie G, 1983. "Testing Non-Nested Models after Estimation by Instrumental Variables or Least Squares," Econometrica, Econometric Society, vol. 51(2), pages 355-65, March.
  8. Fisher, Gordon R. & McAleer, Michael, 1981. "Alternative procedures and associated tests of significance for non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 16(1), pages 103-119, May.
  9. Dufour, J.M. & Roy, R., 1984. "Some Robust Exact Results on Sample Autocorrelations and Tests of Randomness," Cahiers de recherche 8412, Universite de Montreal, Departement de sciences economiques.
  10. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-93, May.
  11. Davidson, R. & Mackinnon, J.G., 1997. "Bootstrap Tests of Nonnested Linear Regression Models," ASSET - Instituto De Economia Publica 170, ASSET (Association of Southern European Economic Theorists).
  12. Godfrey, L. G., 1998. "Tests of non-nested regression models some results on small sample behaviour and the bootstrap," Journal of Econometrics, Elsevier, vol. 84(1), pages 59-74, May.
  13. McCabe, B. P. M., 1989. "Misspecification tests in econometrics based on ranks," Journal of Econometrics, Elsevier, vol. 40(2), pages 261-278, February.
  14. Kurmann, Andre, 2005. "Quantifying the uncertainty about the fit of a new Keynesian pricing model," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1119-1134, September.
  15. Yanqin Fan & Qi Li, 1995. "Bootstrapping J-type tests for non-nested regression models," Economics Letters, Elsevier, vol. 48(2), pages 107-112, May.
  16. Ma, Adrian, 2002. "GMM estimation of the new Phillips curve," Economics Letters, Elsevier, vol. 76(3), pages 411-417, August.
  17. Michelis, Leo, 1999. "The distributions of the J and Cox non-nested tests in regression models with weakly correlated regressors," Journal of Econometrics, Elsevier, vol. 93(2), pages 369-401, December.
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Cited by:
  1. Achim Zeileis & Torsten Hothorn, 2013. "A toolbox of permutation tests for structural change," Statistical Papers, Springer, vol. 54(4), pages 931-954, November.

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