  Statistical and structural modeling represent two distinct approaches to data
analysis. In this paper, we propose a set of novel methods for combining
statistical and structural models for improved prediction and causal inference.
Our first proposed estimator has the doubly robustness property in that it only
requires the correct specification of either the statistical or the structural
model. Our second proposed estimator is a weighted ensemble that has the
ability to outperform both models when they are both misspecified. Experiments
demonstrate the potential of our estimators in various settings, including
fist-price auctions, dynamic models of entry and exit, and demand estimation
with instrumental variables.
