The Second-order Asymptotic Properties of Asymmetric Least Squares Estimation

Tae Hwy Lee, Aman Ullah and He Wang ()
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He Wang: UCR

No 201910, Working Papers from University of California at Riverside, Department of Economics

Abstract: The higher-order asymptotic properties provide better approximation of the bias for a class of estimators. The first-order asymptotic properties of the asymmetric least squares (ALS) estimator have been investigated by Newey and Powell (1987). This paper develops the second-order asymptotic properties (bias and mean squared error) of the ALS estimator, extending the second-order asymptotic results for the symmetric least squares (LS) estimators of Rilstone, Srivastava and Ullah (1996). The LS gives the mean regression function while the ALS gives the "expectile" regression function, a generalization of the usual regression function. The second-order bias result enables an improved bias correction and thus an improved ALS estimation in finite sample. In particular, we show that the second-order bias is much larger as the asymmetry is stronger, and therefore the benefit of the second-order bias correction is greater when we are interested in extreme expectiles which are used as a risk measure in financial economics. The higher-order MSE result for the ALS estimation also enables us to better understand the sources of estimation uncertainty. The Monte Carlo simulation confirms the benefits of the second-order asymptotic theory and indicates that the second-order bias is larger at the extreme low and high expectiles.

Keywords: asymmetric least squares; expectile; delta function; second-order bias; Monte Carlo. (search for similar items in EconPapers)
JEL-codes: C13 C33 C52 (search for similar items in EconPapers)
Pages: 34 Pages
Date: 2018-12
New Economics Papers: this item is included in nep-ecm and nep-ore
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https://economics.ucr.edu/repec/ucr/wpaper/201910.pdf First version, 2018 (application/pdf)

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Journal Article: The Second-Order Asymptotic Properties of Asymmetric Least Squares Estimation (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:ucr:wpaper:201910

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