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Regressions with asymptotically collinear regressors

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  • Kairat T. Mynbaev

Abstract

We investigate the asymptotic behavior of the OLS estimator for regressions with two slowly varying regressors. It is shown that the asymptotic distribution is normal one-dimensional and may belong to one of four types depending on the relative rates of growth of the regressors. The analysis establishes, in particular, a new link between slow variation and $L_p$-approximability. A revised version of this paper has been published in Econometrics Journal (2011), volume 14, pp. 304--320.
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Suggested Citation

  • Kairat T. Mynbaev, 2011. "Regressions with asymptotically collinear regressors," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 304-320, July.
  • Handle: RePEc:ect:emjrnl:v:14:y:2011:i:2:p:304-320
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    References listed on IDEAS

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    1. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    2. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(04), pages 557-614, August.
    3. Mynbaev, Kairat T., 2009. "Central Limit Theorems For Weighted Sums Of Linear Processes: Lp -Approximability Versus Brownian Motion," Econometric Theory, Cambridge University Press, vol. 25(03), pages 748-763, June.
    4. Mynbaev, Kairat, 2000. "$L_p$-Approximable sequences of vectors and limit distribution of quadratic forms of random variables," MPRA Paper 18447, University Library of Munich, Germany, revised 2001.
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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