# BLP Estimation Using Laplace Transformation and Overlapping Simulation Draws

42 Pages Posted: 31 May 2015 Last revised: 21 Oct 2019

See all articles by Han Hong

## Han Hong

Stanford University - Department of Economics

## Huiyu Li

Federal Reserve Banks - Federal Reserve Bank of San Francisco

## Jessie Li

University of California, Santa Cruz - Department of Economics

Date Written: May 29, 2015

### Abstract

We derive the asymptotic distribution of the parameters of the \citet{blp} (BLP) model in a many markets setting which takes into account simulation noise under the assumption of overlapping simulation draws. We show that as long as the number of simulation draws $R$ and the number of markets $T$ approach infinity, our estimator is $\sqrt{m}=\sqrt{min(R,T)}$ consistent and asymptotically normal. We do not impose any relationship between the rates at which $R$ and $T$ go to infinity, thus allowing for the case of $R\ll T$. We provide a consistent estimate of the asymptotic variance which can be used to form asymptotically valid confidence intervals. Instead of directly minimizing the BLP GMM objective function, we propose using Hamiltonian Markov Chain Monte Carlo methods to implement a Laplace-type estimator which is asymptotically equivalent to the GMM estimator.

Keywords: BLP model, Simulation estimator, Laplace-type estimator

JEL Classification: C10, C11, C13, C15

Suggested Citation

Hong, Han and Li, Huiyu and Li, Jessie, BLP Estimation Using Laplace Transformation and Overlapping Simulation Draws (May 29, 2015). Available at SSRN: https://ssrn.com/abstract=2612266 or http://dx.doi.org/10.2139/ssrn.2612266

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