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

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 after Berry, Levinsohn & Pakes (1995). The estimation is conducted through a Bayesian estimation similar to Jiang et al. (2009). But in difference to them here the time intensive contraction mapping for assessing the mean utility in every iteration step of the estimation procedure is omitted. This is because the likelihood function is computed via a special case of the control function method (Park & Gupta (2009) and Petrin & Train (2002)) and hence a full random walk MCMC algorithm is applied. In difference to Park & Gupta (2009) the uncorrelated error, which is explicitly introduced through the control function procedure, is not integrated out, but sampled with a random walk MCMC. Thus the suggested simple proceeding enables (i) to use the whole information from the data set about the market share in the estimation in difference to Park & Gupta (2009), (ii) accelerates the Bayesian estimation in difference to Jiang et al. (2009) though omitting the contraction mapping and (iii) additionally in difference to both cited methods allows the demand shock be estimated without a distributional assumption if wanted.