Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation

Jinhyuk Lee; Kyoungwon Seo

doi:10.1016/j.econlet.2016.10.019

Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation

Jinhyuk Lee, Kyoungwon Seo

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

This paper examines the numerical properties of the nested fixed-point algorithm (NFP) in the estimation of Berry et al. (1995) random coefficient logit demand model. Dubé et al. (2012) find the bound on the errors of the NFP estimates computed by contraction mappings (NFP/CTR) has the order of the square root of the inner loop tolerance. Under our assumptions, we theoretically derive an upper bound on the numerical bias in the NFP/CTR, which has the same order of the inner loop tolerance. We also discuss that, compared with NFP/CTR, NFP using Newton's method has a smaller bound on the estimate error.

Original language	English
Pages (from-to)	67-70
Number of pages	4
Journal	Economics Letters
Volume	149
DOIs	https://doi.org/10.1016/j.econlet.2016.10.019
Publication status	Published - 2016 Dec 1

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government NRF-2014S1A5A8018374 (Seo) and Korea University Grant K1520071 (Lee). We thank Kyoo il Kim, Daniel Ackerberg and in particular Jeremy Fox for very helpful discussions.

Publisher Copyright:
© 2016 Elsevier B.V.

Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

Keywords

Nested fixed-point algorithm
Newton's method
Numerical methods
Random coefficients logit demand

ASJC Scopus subject areas

Finance
Economics and Econometrics

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10.1016/j.econlet.2016.10.019

Cite this

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title = "Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation",

abstract = "This paper examines the numerical properties of the nested fixed-point algorithm (NFP) in the estimation of Berry et al. (1995) random coefficient logit demand model. Dub{\'e} et al. (2012) find the bound on the errors of the NFP estimates computed by contraction mappings (NFP/CTR) has the order of the square root of the inner loop tolerance. Under our assumptions, we theoretically derive an upper bound on the numerical bias in the NFP/CTR, which has the same order of the inner loop tolerance. We also discuss that, compared with NFP/CTR, NFP using Newton's method has a smaller bound on the estimate error.",

keywords = "Nested fixed-point algorithm, Newton's method, Numerical methods, Random coefficients logit demand",

author = "Jinhyuk Lee and Kyoungwon Seo",

note = "Funding Information: This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government NRF-2014S1A5A8018374 (Seo) and Korea University Grant K1520071 (Lee). We thank Kyoo il Kim, Daniel Ackerberg and in particular Jeremy Fox for very helpful discussions. Publisher Copyright: {\textcopyright} 2016 Elsevier B.V. Copyright: Copyright 2016 Elsevier B.V., All rights reserved.",

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doi = "10.1016/j.econlet.2016.10.019",

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PY - 2016/12/1

Y1 - 2016/12/1

N2 - This paper examines the numerical properties of the nested fixed-point algorithm (NFP) in the estimation of Berry et al. (1995) random coefficient logit demand model. Dubé et al. (2012) find the bound on the errors of the NFP estimates computed by contraction mappings (NFP/CTR) has the order of the square root of the inner loop tolerance. Under our assumptions, we theoretically derive an upper bound on the numerical bias in the NFP/CTR, which has the same order of the inner loop tolerance. We also discuss that, compared with NFP/CTR, NFP using Newton's method has a smaller bound on the estimate error.

AB - This paper examines the numerical properties of the nested fixed-point algorithm (NFP) in the estimation of Berry et al. (1995) random coefficient logit demand model. Dubé et al. (2012) find the bound on the errors of the NFP estimates computed by contraction mappings (NFP/CTR) has the order of the square root of the inner loop tolerance. Under our assumptions, we theoretically derive an upper bound on the numerical bias in the NFP/CTR, which has the same order of the inner loop tolerance. We also discuss that, compared with NFP/CTR, NFP using Newton's method has a smaller bound on the estimate error.

KW - Nested fixed-point algorithm

KW - Newton's method

KW - Numerical methods

KW - Random coefficients logit demand

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VL - 149

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EP - 70

JO - Economics Letters

JF - Economics Letters

ER -

Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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