11th Meetup: Estimating aggregate random co-eff logit w/ Bayesian techniques

Our first meetup of 2018!

Schedule:

• 18:30: Arrive
• 19:00: Presentation
• 20:00: Off to the pub

Talk:

Estimating aggregate random coefficients logit with Bayesian techniques

Jim Savage (Lendable) and Shoshana Vasserman (Harvard)

(Jim presenting) Aggregate random coefficients logit is a workhorse model in marketing and industrial organization. Yet the typical method of estimating its parameters, the BLP algorithm and its descendants, have some shortcomings. They do not explicitly model measurement error, making inference in small markets difficult. The function that maps parameters to choice probabilities is highly non-linear, making optimization uncomfortably dependent on algorithm choice and starting values. And GMM does not estimate posterior densities for unknowns, making formal decision-theoretic analysis of policy changes impossible. We propose a simple generative framework for aggregate random coefficients logit, which takes a latent factor approach to modeling the unobserved demand shock. This is conceptually similar to earlier work by Allenby, Chen and Yang (2003), albeit in an aggregate context. The advantages are that we get precise, probabilistic inference in small markets, don't have numerical difficulties, and, because we get a full posterior over all unknowns, can integrate any loss function over uncertain estimates. The main cost is that identification of the unobserved demand shocks depends on the researcher specifying the "correct" price-setting model. We explore this issue.

Applications are given to a general election from 1970s Tanzania, and the for-profit retirement savings industry in Australia. Jim is the Head of Data Science at Lendable, a NYC-based wholesale lender operating in Sub-Saharan Africa. Before that he was an economist at Australian think-tank the Grattan Institute, a DSSG fellow at the University of Chicago, and an economist at the Australian Treasury. He writes a blog on Bayesian modelling at modernstatisticalworkflow.blogspot.com.