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Some Non-Nested Hypothesis Tests and the Relations Among Them

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  • Russell Davidson
  • James G. Mackinnon

Abstract

In this paper we discuss several statistical techniques which may be used to test the validity of a possibly non-linear and multivariate regression model, using the information provided by estimating one or more alternative models on the same set of data. We first exposit, from a different perspective, the tests proposed by us in Davidson and MacKinnon (1981a), and discuss modified versions of these tests and extensions of them to the multivariate case. We then prove that all these tests, and also the tests previously proposed by Pesaran (1974) and Pesaran and Deaton (1978), based on the work of Cox (1961, 1962), are asymptotically equivalent under certain conditions. Finally, we present the results of a sampling experiment which shows that different tests can behave quite differently in small samples.

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  • Russell Davidson & James G. Mackinnon, 1982. "Some Non-Nested Hypothesis Tests and the Relations Among Them," Review of Economic Studies, Oxford University Press, vol. 49(4), pages 551-565.
  • Handle: RePEc:oup:restud:v:49:y:1982:i:4:p:551-565.
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    File URL: http://hdl.handle.net/10.2307/2297286
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    1. Pesaran, M H & Deaton, Angus S, 1978. "Testing Non-Nested Nonlinear Regression Models," Econometrica, Econometric Society, vol. 46(3), pages 677-694, May.
    2. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    3. M. H. Pesaran, 1974. "On the General Problem of Model Selection," Review of Economic Studies, Oxford University Press, vol. 41(2), pages 153-171.
    4. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-421, May.
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