efficiency

We propose a likelihood-based estimator for random coefficients discrete choice demand models that is applicable in a broad range of data settings. Intuitively, it combines the likelihoods of two mixed logit estimators—one for consumer level data, and one for product level data—with product level exogeneity restrictions. Our estimator is both efficient and conformant: its rates of convergence will be the fastest possible given the variation available in the data. The researcher does not need to pre-test or adjust the estimator and the inference procedure is valid across a wide variety of scenarios. Moreover, it can be tractably applied to large datasets. We illustrate the features of our estimator by comparing it to alternatives in the literature.

In this paper I propose three new estimators of nonparametric regression functions subject to weak separability (WS). The use of WS reduces the curse of dimensionality. WS nests other separability concepts such as (generalized) additive separability ((G)AS). The advantage of WS over (G)AS is that WS allows for interactions between regressors whereas (G)AS does not permit any interactions. The estimators use marginal integration and are shown to have a limiting normal distribution and a convergence rate which is the same as that of an unconstrained nonparametric estimator of a regression function of lower dimension. An attractive and unusual feature of two of my estimators is that regressors can have arbitrary convex support and that the integration regions can depend on the values of the remaining variables. The estimators can be iterated and I show that under strong assumptions further asymptotic efficiency improvements are possible. The computation of the estimators is simple. The performance of one of the estimators is studied in a simulation study.