Before revision:  Deep neural networks are well-suited to structured modeling of heterogeneity: we show how the network architecture can be designed to match the global structure of the economic model, giving novel methodology for deep learning as well as, more formally, improved rates of convergence. Our results on deep learning have consequences for other structured modeling environments and applications, such as for additive models. Our inference results are based on an influence function we derive, which we show to be flexible enough to to encompass all settings with a single, unified calculation, removing any requirement for case-by-case derivations. The usefulness of the methodology in economics is shown in two empirical applications: the response of 410(k) participation rates to firm matching and the impact of prices on subscription choices for an online service. Extensions to instrumental variables and multinomial choices are shown .
After revision:  We apply our methodology to a large scale advertising experiment for short-term loans. We show how economically meaningful estimates and inferences can be made that would be unavailable without our results .