Inverse Product Differentiation Logit Model : Holy Grail or Not?

Since the seminal work by Berry-Levinsohn-Pakes (BLP), random coefficient logit (RCL) has become 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 a preferable model, its estimation is computationally challenging due to the numerical inversion of the demand function. Recently proposed inverse product differentiation logit (IPDL) claims to address these computational challenges by directly specifying the inverse demand function and representing flexible substitution patterns through non-hierarchical product segmentation in multiple dimensions. Unlike the two-stage simulation-based estimation of RCL, IPDL requires estimating a traditional linear instrumental variable regression model. In theory, IPDL appears to be an attractive alternative to RCL, but its potential has not yet been explored 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 indicate that demand elasticity estimates of IPDL and RCL are not statistically different, i.e., IPDL could capture substitution patterns similar to RCL. The estimation of IPDL takes less than a second on a regular computer (i.e., over 500 times faster than RCL). Overall, the flexibility and computational efficiency of IPDL could make it a workhorse model for demand estimation using market-level aggregated sales data