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Global and Partial Non-Nested Hypotheses and Asymptotic Local Power

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  • Pesaran, M. Hashem

Abstract

This paper addresses two related issues in the literature of non-nested hypotheses testing. Firstly, by means of a measure of “closeness” of probability density functions, it shows how any two hypotheses can be placed into the nested and the non-nested categories with the latter category being subdivided further into “globally” and “partially” non-nested hypotheses. Secondly, by emphasizing the distinction between a “local null” and a “local alternative,” the paper shows that only in the case of partially non-nested hypotheses is it possible to specify local alternatives. In this case the paper derives the asymptotic distribution of the Cox test statistic under local alternatives and shows that it is distributed as a normal variate with a mean which is directly related to the measure of “closeness” of the alternative to the null hypothesis.

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  • Pesaran, M. Hashem, 1987. "Global and Partial Non-Nested Hypotheses and Asymptotic Local Power," Econometric Theory, Cambridge University Press, vol. 3(1), pages 69-97, February.
    • Handle: RePEc:cup:etheor:v:3:y:1987:i:01:p:69-97_00
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    Cited by:

    1. Heinz König & Michael Lechner, 1994. "Some Recent Developments in Microeconometrics - A Survey," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 130(III), pages 299-331, September.
    2. TengTeng Xu, 2012. "The Role of Credit in International Business Cycles," Staff Working Papers 12-36, Bank of Canada.
    3. Pieroni, Luca & Ricciarelli, Matteo, 2008. "Modelling dynamic storage function in commodity markets: Theory and evidence," Economic Modelling, Elsevier, vol. 25(5), pages 1080-1092, September.
    4. Zhongjun Qu & Denis Tkachenko, 2023. "Using arbitrary precision arithmetic to sharpen identification analysis for DSGE models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 644-667, June.
    5. McAleer, Michael, 1995. "The significance of testing empirical non-nested models," Journal of Econometrics, Elsevier, vol. 67(1), pages 149-171, May.
    6. Michael P. Leung, 2022. "Dependence‐robust inference using resampled statistics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 270-285, March.
    7. Monique Reid & Pierre Siklos, 2023. "Rationality and biases insights from disaggregated firm level inflation expectations data," Working Papers 11050, South African Reserve Bank.
    8. McAleer, Michael, 1994. "Sherlock Holmes and the Search for Truth: A Diagnostic Tale," Journal of Economic Surveys, Wiley Blackwell, vol. 8(4), pages 317-370, December.
    9. Neil R. Ericsson, 1987. "Monte Carlo methodology and the finite sample properties of statistics for testing nested and non-nested hypotheses," International Finance Discussion Papers 317, Board of Governors of the Federal Reserve System (U.S.).
    10. Mishra, Ankita & Moosa, Imad A. & Tawadros, George B. & Mishra, Vinod, 2023. "The effect of political and bureaucratic regime changes on Australia's real interest rate," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 124-136.
    11. Andrew B. Whitford, 2007. "Competing Explanations for Bureaucratic Preferences," Journal of Theoretical Politics, , vol. 19(3), pages 219-247, July.
    12. Duo Qin, 2022. "Redirect the Probability Approach in Econometrics Towards PAC Learning," Working Papers 249, Department of Economics, SOAS University of London, UK.
    13. Pons Novell, Jordi, 1997. "Selección de modelos no anidados. Un estudio de Monte Carlo," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 7, pages 131-139, Junio.

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