Title: Estimating Nesting Structures (with Ali Hortacsu, Jonas Lieber and Julien Monardo)
Abstract:
We build on a recent generalization of differentiated product demand models: the Inverse Product Differentiation Logit (IPDL). Like the nested logit and its variations, which the IPDL generalises, the model relies on a nesting structure for contemplated alternatives. We propose a method to estimate nest parameters. Because the number of potential nests is exponential in the number of groups, there is a dimensionality issue. Building on insights from the estimation of high-dimensional models with non-negativity constraints, we show theoretically and in simulations that non-negativity conditions coming from economic theory are sufficient for regularization. In particular, the researcher does not have to choose a second stage tuning parameter for the non-negative IV estimator. Our method can be implemented efficiently by solving a sequence of convex programs, which can be highly parallelized.