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A Note on 'Bayesian analysis of the random coefficient model using aggregate data', an alternative approach

Zenetti, German (2010): A Note on 'Bayesian analysis of the random coefficient model using aggregate data', an alternative approach.

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Abstract

In this note on the paper from Jiang, Manchanda & Rossi (2009), I want to discuss a simple alternative estimation method of the multinomial logit model for aggregated data with random coefficients - the so-called BLP model, named for Berry, Levinsohn & Pakes (1995). The estimation is conducted through a Bayesian estimation similar to Jiang et al. (2009). However in contrast to Jiang et al. (2009) I omit the time-intensive contraction mapping for assessing the mean utility in every iteration step of the estimation procedure. The likelihood function is computed through a special case of the control function method (Park & Gupta (2009) and Petrin & Train (2002)). A full random walk MCMC approach is applied, that uses two random walk MCMC chains - one to draw the parameters of the model, and a second one to sampled an explicitly introduced uncorrelated error term. In total, the suggested simple procedure (i) permits the use of the full information from the data set, in contrast to Park & Gupta (2009), (ii) accelerates the Bayesian estimation by omitting the contraction mapping, in contrast to Jiang et al. (2009), and (iii) in contrast to both cited methods, allows the demand shock to be estimated without a distributional assumption, if desired.

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