Inverse product differentiation logit model: Holy grail or not?

Abstract

Random coefficient logit (RCL) is the workhorse model to estimate demand elasticities in markets with differentiated products using aggregated sales data. While the ability to represent flexible substitution patterns makes RCL preferable, its estimation is computationally challenging due to the numerical inversion of the demand function. The recently proposed inverse product differentiation logit (IPDL) addresses this computational issue by directly specifying the inverse demand function. In addition to computational gains, IPDL claims to maintain flexibility through non-hierarchical product segmentation across multiple characteristics. Thus, IPDL is an attractive alternative to RCL in theory, but its potential remains unexplored in empirical studies. We present the first application of IPDL in understanding the demand for passenger cars in China using province-level sales data. Our results show that IPDL is around 300 times faster than RCL, can capture complementarity patterns that cannot be captured by RCL, can identify substitution patterns as well as RCL, and outperforms RCL in goodness of fit measures.