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

- We study the nested fixed-point algorithm (NFP).
- We theoretically derive an upper bound on the errors of the NFP estimates.
- We show the bound is smaller than that of Dube et al. (2012).
- We show the bound is smaller with Newton's method than contraction mappings.

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.