arXiv subjects

Sanjog Misra

Publications and source records attributed to Sanjog Misra.

7 recordsLinked to original sources

arXiv2026

Robust A/B Decisions

A/B tests are standard in firm decision making. In the standard pipeline, experimental data is converted to a deployment decision by applying a t-test of the difference in means (the lift) and deploying the treatment if lift is positive and statistically significant. This common workflow answers the wrong question. We argue that firms need a decision rule for economic payoffs in the future deployment environment, not a test of equality in the experimental sample. We develop an ambiguity-averse decision framework in which each arm is evaluated by its ambiguity-penalized value over distributions close to the experimental outcome distribution. The resulting rule has a simple closed form thanks to the Donsker-Varadhan representation and it requires only the outcome data from a standard A/B test plus one interpretable parameter governing trust in the experiment. Our rule is thus no more difficult to implement than a t-test. A mean-variance approximation shows how the rule penalizes variability, while a connection to utility maximization shows it to be a certainty equivalent. We are able to perform a real-world evaluation of our proposed rule in the context of digital marketing using an archive of 552 advertising experiments from an anonymous US-based online platform. The proposed rule substantially reduces regret relative to conventional hypothesis testing. The results show that economically conservative, distribution-aware deployment rules can outperform statistical-significance rules in digital experimentation.

econ.EM↗

arXiv2026

Deep Learning for Individual Heterogeneity

This paper integrates deep neural networks (DNNs) into structural models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic (or scientific or domain-restricted) structure and machine learning are complements in empirical modeling, not substitutes: DNNs provide the capacity to learn complex, nonlinear heterogeneity, while the structure ensures the estimates remain interpretable and suitable for decision-making and policy analysis. We start with a standard parametric structural model and then enrich its parameters into fully flexible functions, which are estimated using a DNN with the model structure built in. We illustrate our framework with an application to demand estimation in consumer choice. We show that by enriching a demand model we can capture rich heterogeneity exploit it to create personalized pricing. Optimization is not possible without structure, but cannot be heterogeneous without machine learning. The same lessons apply to precision dosing, adaptive treatment, educational testing, and other targeting settings. We provide theoretical justification for our proposed methodology: nonasymptotic bounds and a novel and general influence function for feasible inference via double machine learning, so that the latter can be easily applied in numerous new contexts. These results may be of interest in other contexts as they generalize prior work.

econ.EM↗

arXiv2025

Foundation Priors

Foundation models, and in particular large language models, can generate highly informative responses, prompting growing interest in using these ''synthetic'' outputs as data in empirical research and decision-making. This paper introduces the idea of a foundation prior, which shows that model-generated outputs are not as real observations, but draws from the foundation prior induced prior predictive distribution. As such synthetic data reflects both the model's learned patterns and the user's subjective priors, expectations, and biases. We model the subjectivity of the generative process by making explicit the dependence of synthetic outputs on the user's anticipated data distribution, the prompt-engineering process, and the trust placed in the foundation model. We derive the foundation prior as an exponential-tilted, generalized Bayesian update of the user's primitive prior, where a trust parameter governs the weight assigned to synthetic data. We then show how synthetic data and the associated foundation prior can be incorporated into standard statistical and econometric workflows, and discuss their use in applications such as refining complex models, informing latent constructs, guiding experimental design, and augmenting random-coefficient and partially linear specifications. By treating generative outputs as structured, explicitly subjective priors rather than as empirical observations, the framework offers a principled way to harness foundation models in empirical work while avoiding the conflation of synthetic ''facts'' with real data.

cs.AI↗

arXiv2025

Coarse Personalization

With advances in estimating heterogeneous treatment effects, firms can personalize and target individuals at a granular level. However, feasibility constraints limit full personalization. In practice, firms choose segments of individuals and assign a treatment to each segment to maximize profits: We call this the coarse personalization problem. We propose a two-step solution that simultaneously makes segmentation and targeting decisions. First, the firm personalizes by estimating conditional average treatment effects. Second, the firm discretizes using treatment effects to choose which treatments to offer and their segments. We show that a combination of available machine learning tools for estimating heterogeneous treatment effects and a novel application of optimal transport methods provides a viable and efficient solution. With data from a large-scale field experiment in promotions management, we find our methodology outperforms extant approaches that segment on consumer characteristics, consumer preferences, or those that only search over a prespecified grid. Using our procedure, the firm recoups over $99.5\%$ of its expected incremental profits under full personalization while offering only five segments. We conclude by discussing how coarse personalization arises in other domains.

econ.EM↗

arXiv2021

The Identity Fragmentation Bias

Consumers interact with firms across multiple devices, browsers, and machines; these interactions are often recorded with different identifiers for the same consumer. The failure to correctly match different identities leads to a fragmented view of exposures and behaviors. This paper studies the identity fragmentation bias, referring to the estimation bias resulted from using fragmented data. Using a formal framework, we decompose the contributing factors of the estimation bias caused by data fragmentation and discuss the direction of bias. Contrary to conventional wisdom, this bias cannot be signed or bounded under standard assumptions. Instead, upward biases and sign reversals can occur even in experimental settings. We then compare several corrective measures, and discuss their respective advantages and caveats.

econ.EM↗

arXiv2019

Deep Neural Networks for Estimation and Inference

We study deep neural networks and their use in semiparametric inference. We establish novel rates of convergence for deep feedforward neural nets. Our new rates are sufficiently fast (in some cases minimax optimal) to allow us to establish valid second-step inference after first-step estimation with deep learning, a result also new to the literature. Our estimation rates and semiparametric inference results handle the current standard architecture: fully connected feedforward neural networks (multi-layer perceptrons), with the now-common rectified linear unit activation function and a depth explicitly diverging with the sample size. We discuss other architectures as well, including fixed-width, very deep networks. We establish nonasymptotic bounds for these deep nets for a general class of nonparametric regression-type loss functions, which includes as special cases least squares, logistic regression, and other generalized linear models. We then apply our theory to develop semiparametric inference, focusing on causal parameters for concreteness, such as treatment effects, expected welfare, and decomposition effects. Inference in many other semiparametric contexts can be readily obtained. We demonstrate the effectiveness of deep learning with a Monte Carlo analysis and an empirical application to direct mail marketing.

econ.EM↗

arXiv2018

Targeted Undersmoothing

This paper proposes a post-model selection inference procedure, called targeted undersmoothing, designed to construct uniformly valid confidence sets for a broad class of functionals of sparse high-dimensional statistical models. These include dense functionals, which may potentially depend on all elements of an unknown high-dimensional parameter. The proposed confidence sets are based on an initially selected model and two additionally selected models, an upper model and a lower model, which enlarge the initially selected model. We illustrate application of the procedure in two empirical examples. The first example considers estimation of heterogeneous treatment effects using data from the Job Training Partnership Act of 1982, and the second example looks at estimating profitability from a mailing strategy based on estimated heterogeneous treatment effects in a direct mail marketing campaign. We also provide evidence on the finite sample performance of the proposed targeted undersmoothing procedure through a series of simulation experiments.

math.ST↗