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

3 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

Keywords

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

ASJC Scopus subject areas

Finance
Economics and Econometrics

Access to Document

10.1016/j.econlet.2016.10.019

Fingerprint Dive into the research topics of 'Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation'. Together they form a unique fingerprint.

Cite this

Lee, J., & Seo, K. (2016). Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation. Economics Letters, 149, 67-70. https://doi.org/10.1016/j.econlet.2016.10.019

@article{7a575818e395466fbce3cf9bcf41991e,

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",

year = "2016",

month = dec,

day = "1",

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

language = "English",

volume = "149",

pages = "67--70",

journal = "Economics Letters",

issn = "0165-1765",

publisher = "Elsevier",

}

TY - JOUR

T1 - Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation

AU - Lee, Jinhyuk

AU - Seo, Kyoungwon

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

UR - http://www.scopus.com/inward/record.url?scp=84994012335&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994012335&partnerID=8YFLogxK

U2 - 10.1016/j.econlet.2016.10.019

DO - 10.1016/j.econlet.2016.10.019

M3 - Article

AN - SCOPUS:84994012335

VL - 149

SP - 67

EP - 70

JO - Economics Letters

JF - Economics Letters

SN - 0165-1765

ER -