Identification-robust simulation-based inference in joint discrete/continuous models for energy markets

In the analysis of energy use models, a common problem consists in correcting for endogenous discrete-choice variables. Indeed, energy demand equations often include endogenous dummies which reflect the underlying discrete-choice for e.g. energy equipment. The latter lead to discrete/continuous (D/C) statistical models where the discrete and continuous components are statistically dependent, so weak-identification problems may occur which stem from the "quality" of the first stage instrumental model. These problems are studied in the context of energy demand analysis. A wide mixed-logit-based class of models is considered which allow for dependent choices, heteroskedasticity and multi-dimensionality. The severity of weak-identification problems and relevance for empirical practice are documented, even with very large data sets. Tractable and reliable (in the sense of type I error control) solutions are proposed which combine generalized Anderson-Rubin (GAR) procedures and maximum simulated likelihood (MSL) methods for models commonly used in practice. Results are illustrated via Monte-Carlo examples and an empirical study on electricity demand.