### 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 |
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Pages (from-to) | 67-70 |

Number of pages | 4 |

Journal | Economics Letters |

Volume | 149 |

DOIs | |

Publication status | Published - 2016 Dec 1 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Finance
- Economics and Econometrics

### Cite this

**Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation.** / Lee, Jinhyuk; Seo, Kyoungwon.

Research output: Contribution to journal › Article

*Economics Letters*, vol. 149, pp. 67-70. https://doi.org/10.1016/j.econlet.2016.10.019

}

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 -