Best practices for differentiated products demand estimation with PyBLP

Abstract

Differentiated products demand systems are a workhorse for understanding the price effects of mergers, the value of new goods, and the contribution of products to seller networks. Berry, Levinsohn, and Pakes (1995) provide a flexible random coefficients logit model which accounts for the endogeneity of prices. This article reviews and combines several recent advances related to the estimation of BLP-type problems and implements an extensible generic interface via the PyBLP package. Monte Carlo experiments and replications suggest different conclusions than the prior literature: multiple local optima appear to be rare in well-identified problems; good performance is possible even in small samples, particularly when "optimal instruments" are employed along with supply-side restrictions. If Python is installed on your computer, PyBLP can be installed with the following command: pip install pyblp.Up-to-date documentation for the package is available at https:// pyblp.readthedocs.io.

A BLP Demand Model of Product-Level Market Shares with Complementarity

“…This approach has been adopted in the literature. Conlon and Gortmaker (2020) tests performances of different Jacobian-based algorithms to implement the demand inverse in models demand for single products, and find supportive evidences for the numerical efficiency of Jacobian-based methods. A leading example is Newton-Raphson method:…”

“…In BLP models of single products, a suggested practice is to approximate the optimal instruments in the form of Amemiya (1977) and Chamberlain (1987) that achieve the semi-parametric efficiency bound. Reynaert and Verboven (2014) and Conlon and Gortmaker (2020) report significant gain when impelenting Berry et al (1995)'s GMM estimator using optimal instruments. However, the difficulty of approximating optimal instruments still remains in estimation procedure (10).…”

“…Conlon and Gortmaker (2020) provide a review of numerical methods for implementation of demand inverse in demand models of single products.32 For example, if the DGP is such that the sum of observed product-level market shares is larger than one, then any demand models of single products (Γ b = −∞ for any b) cannot rationalise the observed product-level market shares and hence the demand inverse is not feasible with Γ = −∞.…”

Taxation and market power in the legal marijuana industry

“…We implement the demand estimation using the pyblp package and following best practices as described by Conlon and Gortmaker (2019), which we find to converge rapidly and consistently.…”

“…We implement the demand estimation using the pyblp package and following best practices as described by Conlon and Gortmaker (2020), which we find to converge rapidly and consistently. This package makes it relatively straightforward to include approximations to the optimal IV in the sense of Chamberlain (1987) as described by Reynaert and Verboven (2014).…”