Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation. (English) Zbl 1396.91392
Summary: This paper examines the numerical properties of the nested fixed-point algorithm (NFP) in the estimation of S. Berry et al. [Econometrica 63, No. 4, 841–890 (1995; Zbl 0836.90057)] random coefficient logit demand model. J.-P. Dubé et al. [Econometrica 80, No. 5, 2231–2267 (2012; Zbl 1274.91282)] 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.
MSC:
| 91B42 | Consumer behavior, demand theory |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 65D15 | Algorithms for approximation of functions |
Keywords:
random coefficients logit demand; numerical methods; nested fixed-point algorithm; Newton’s methodReferences:
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