Tim Christensen

We consider the problem of estimating personalized treatment policies that are "externally valid" or "generalizable": they perform well in target populations that differ from the experimental (or training) population from which the data are sampled. We first show that welfare-maximizing policies for the experimental population are robust to a certain class of shifts in the distribution of potential outcomes between the experimental and target populations (holding characteristics fixed). We then develop methods for estimating policies that are robust to shifts in the joint distribution of outcomes and characteristics. In doing so, we highlight how treatment effect heterogeneity within the experimental population shapes external validity.

Researchers routinely use AI or other machine learning methods to estimate latent variables, then plug-in the estimates as covariates in a regression. We show both theoretically and empirically that naively treating AI/ML-generated variables as "data" leads to biased estimates and invalid inference. To restore valid inference, we propose two methods: (1) an explicit bias correction with bias-corrected confidence intervals, and (2) joint estimation of the regression parameters and latent variables. We illustrate these ideas through applications involving label imputation, dimensionality reduction, and index construction via classification and aggregation.

Empirical models of demand for differentiated products rely on low-dimensional product representations to capture substitution patterns. These representations are increasingly proxied by applying ML methods to high-dimensional, unstructured data, including product descriptions and images. When proxies fail to capture the true dimensions of differentiation that drive substitution, standard workflows will deliver biased counterfactuals and invalid inference. We develop a practical toolkit that corrects this bias and ensures valid inference for a broad class of counterfactuals. Our approach applies to market-level and/or individual data, requires minimal additional computation, is efficient, delivers simple formulas for standard errors, and accommodates data-dependent proxies, including embeddings from fine-tuned ML models. It can also be used with standard quantitative attributes when mismeasurement is a concern. In addition, we propose diagnostics to assess the adequacy of the proxy construction and dimension. The approach yields meaningful improvements in predicting counterfactual substitution in both simulations and an empirical application.

We propose a method to select and estimate the best low-dimensional linear factor model from a high-dimensional set of factors. This method selects the best subset of factors and estimates their loadings by mixed-integer optimization. The approach is based on a sound theoretical criterion, is supported by statistical guarantees, precludes unreasonably high rewards-for-risk, and enforces positive SDFs. Portfolios based on factors selected with our method yield superior out-of-sample alphas relative to standard benchmarks.

We derive optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter θ and the decision maker can use a point-identified parameter μ to deduce restrictions on θ. Examples include treatment choice under partial identification and pricing with rich unobserved heterogeneity. We discuss implementation of optimal decision rules in both parametric and semiparametric models via the bootstrap and Bayesian methods. We provide detailed applications to treatment choice and optimal pricing. Our approach is well suited for realistic empirical settings in which the derivation of finite-sample optimal rules is intractable.