Deep Learning for Individual Heterogeneity: An Automatic Inference Framework

Abstract

We propose a methodology for effectively modeling individual heterogeneity using deep learning while still retaining the interpretability and economic discipline of classical models. We pair a transparent, interpretable modeling structure with rich data environments and machine learning methods to estimate heterogeneous parameters based on potentially high dimensional or complex observable characteristics. Our framework is widely-applicable, covering numerous settings of economic interest. We recover, as special cases, well-known examples such as average treatment effects and parametric components of partially linear models. However, we also seamlessly deliver new results for diverse examples such as price elasticities, willingness-to-pay, and surplus measures in choice models, average marginal and partial effects of continuous treatment variables, fractional outcome models, count data, heterogeneous production function components, and more. Deep neural networks are particularly well-suited to structured modeling of heterogeneity in economics: we show how the network architecture can be easily 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 or other varying coefficient 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: we study the response of 410(k) participation rates to firm matching and the impact of prices on subscription choices for an online service. Extensions of the main ideas to instrumental variables and multinomial choices are shown.

The macroeconomy as a random forest

“…This paper is the first to exploit the link between this strand of work and the sempiternal search for the "true" state dependence in empirical macroeconomic models. In contemporaneous work, Farrell et al (2020) highlight the potential for interpretability of partially linear neural networks in a heterogeneous treatment effect context.…”

Empowering a Sustainable Future: Fostering Sustainable Behavior with Targeted Interventions

“…In contrast to standard policies, our approach accounts for response heterogeneity across consumers and simultaneous treatment with multiple interventions. Deep learning can efficiently capture such heterogeneity, model non-linearities, and jointly process various data types in their raw form without effortful data transformations (LeCun et al, 2015;Goodfellow et al, 2015;Farrell et al, 2020;Gabel et al, 2019). This contributes to automation and scalability.…”

Essays on estimating dynamic discrete choice models: methods and applications

“…recent studies have developed on the intersection between machine learning (in particular deep learning) and structural estimation, see the summary byIskhakov et al (2020) andIgami (2020) Farrell et al (2021). provide theoretical justification of using DNN as the approximation structure andFarrell et al (2020) discuss possible applications of DNN Semenova (2018). applies machine learning to estimation of DDCM under the Conditional Choice Probability (CCP) framework.…”