Asymptotic theory for differentiated products demand models with many markets

Freyberger, Joachim

doi:10.1016/j.jeconom.2014.10.009

Cited by 34 publications

(19 citation statements)

References 27 publications

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“…11 If inf c t I ct grows fast enough with n × T , this estimator is uniformly consistent, that is, sup c sup t S ct − E(Y ict |η c ) → p 0. Section 3.2 of Freyberger's (2015) arguments (using Bernstein's Inequality) implies that the above convergence holds if log(n × T )/ min c t I ct → 0.…”

mentioning

confidence: 98%

Estimating Semi-Parametric Panel Multinomial Choice Models Using Cyclic Monotonicity

Shi¹,

Shum²,

Song³

2018

Econometrica

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This paper proposes a new semi-parametric identification and estimation approach to multinomial choice models in a panel data setting with individual fixed effects. Our approach is based on cyclic monotonicity, which is a defining convex-analytic feature of the random utility framework underlying multinomial choice models. From the cyclic monotonicity property, we derive identifying inequalities without requiring any shape restrictions for the distribution of the random utility shocks. These inequalities point identify model parameters under straightforward assumptions on the covariates. We propose a consistent estimator based on these inequalities.

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confidence: 98%

Estimating Semi-Parametric Panel Multinomial Choice Models Using Cyclic Monotonicity

Shi¹,

Shum²,

Song³

2018

Econometrica

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“…Freyberger develops asymptotic theory in differentiated product demand systems according to a small number of products and a large number of markets [17]. However, few of the above literatures deal with the strategic customers.…”

Section: Literature Reviewmentioning

confidence: 99%

Strategic Customer Behavior and Pricing Strategy Based on the Horizontal Differentiation of Products

Zhao

Yue

et al. 2020

Mathematical Problems in Engineering

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Manufacturers produce products with horizontal differences to meet different needs of customers. This paper compares the influence of three different sales channels on strategic customers’ choice and the pricing strategy of products with horizontal differentiation. The results show that the strategic customers whose willingness to pay (WTP) is close to 1 will buy high-performance products and whose WTP is close to 0 will not purchase any kind of products in the two dual-channel models. If the manufacturers adopt dual channel to sell products with horizontal differences, the retailers agree that the manufacturers sell high-performance products in the traditional channel and sell low-performance products in the electronic channel. In dual-channel supply chain model I, the higher the satisfaction of high-performance products and the lower the satisfaction of low-performance products, the more conducive to the retailers.

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“…We ignore the simulation error in the following. See Berry, Linton, and Pakes () and Freyberger () for dealing with the simulation error. Define

\frac{d^{2} f ((), θ)}{d θ^{2}}

, the second derivative of a vector‐valued function f , by

\frac{d^{2} f (θ)}{d θ^{2}} \equiv (\begin{matrix} \frac{d^{2} f (θ)}{d θ_{1}^{2}} & \dots & \frac{d^{2} f (θ)}{d θ_{1} d θ_{K}} \\ ⋮ & ⋱ & ⋮ \\ \frac{d^{2} f (θ)}{d θ_{K} d θ_{1}} & \dots & \frac{d^{2} f (θ)}{d θ_{K} d θ_{K}} \end{matrix}),

where

\frac{d^{2} f ((), θ)}{d θ_{k} d θ_{k^{'}}}

is a column vector.…”

Section: The Ablp Estimationmentioning

confidence: 99%

A computationally fast estimator for random coefficients logit demand models using aggregate data

Lee

Seo

2015

The RAND J of Economics

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This article proposes a computationally fast estimator for random coefficients logit demand models using aggregate data that Berry, Levinsohn, and Pakes (1995; hereinafter, BLP) suggest. Our method, which we call approximate BLP (ABLP), is based on a linear approximation of market share functions. The computational advantages of ABLP include (i) the linear approximation enables us to adopt an analytic inversion of the market share equations instead of a numerical inversion that BLP propose, (ii) ABLP solves the market share equations only at the optimum, and (iii) it minimizes over a typically small dimensional parameter space. We show that the ABLP estimator is equivalent to the BLP estimator in large data sets. Our Monte Carlo experiments illustrate that ABLP is faster than other approaches, especially for large data sets.

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Asymptotic theory for differentiated products demand models with many markets

Cited by 34 publications

References 27 publications

Estimating Semi-Parametric Panel Multinomial Choice Models Using Cyclic Monotonicity

Estimating Semi-Parametric Panel Multinomial Choice Models Using Cyclic Monotonicity

Strategic Customer Behavior and Pricing Strategy Based on the Horizontal Differentiation of Products

A computationally fast estimator for random coefficients logit demand models using aggregate data

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