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 multi-product demand rely on low-dimensional product representations to capture
substitution patterns, increasingly using proxies built from unstructured data. When proxies are
imperfect, standard workflows yield biased counterfactuals and invalid inference. We develop a practical
toolkit to address these issues. Our methods apply to market-level and/or individual data, require
minimal additional computation, provide simple standard-error formulas, and accommodate proxies from
fine-tuned models. Further, we propose diagnostics to assess proxy quality. Our methods yield meaningful
improvements in predicting substitution in empirically calibrated simulations and in an application
where we assess counterfactual prediction performance against a ground truth.
AI/ML methods are increasingly used in economics to generate binary variables (or labels) via
classification algorithms. When these generated variables are included as covariates in regressions,
even small misclassification errors can induce large biases in OLS estimators and invalidate standard
inference. We study whether the bootstrap can correct this bias and deliver valid inference. We first
show that a seemingly natural fixed-label bootstrap, which generates data using estimated labels but
relies on a corrupted version in estimation, is generally invalid unless a strong independence condition
between the latent true labels and other covariates holds. We then propose a coupled-label bootstrap
that jointly resamples the true and imputed labels, and show it is valid without this condition. Two
finite-sample adjustments further improve coverage: a variance correction for uncertainty in estimated
misclassification rates and a Hessian rotation for near-singular designs. We illustrate the methods in
simulations and apply them to investigate the relationship between wages and remote work status.
We consider linear regression when some covariates are endogenous, a variable sufficient to control for
endogeneity exists but is latent, and the practitioner can generate many proxies for the latent control.
For instance, one could cheaply but imperfectly impute the latent control using different AI/ML methods,
each generating a different proxy. There are several options the practitioner might consider in this
scenario: including all proxies or factors computed from the proxies as controls, instrumental variables
estimation, and some nonlinear variants thereof. We use a transparent model to derive the implicit
estimand each approach targets, determine when these estimands recover the parameter of interest, and
provide some practical recommendations. We show that with a sufficiently rich set of generated controls,
practitioners can consistently estimate the parameter of interest without relying on validation data.
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.