This paper advances empirical demand analysis by integrating multimodal product representations derived from artificial intelligence (AI). Using a detailed dataset of toy cars on \textit{Amazon.com}, we combine text descriptions, images, and tabular covariates to represent each product using transformer-based embedding models. These embeddings capture nuanced attributes, such as quality, branding, and visual characteristics, that traditional methods often struggle to summarize. Moreover, we fine-tune these embeddings for causal inference tasks. We show that the resulting embeddings substantially improve the predictive accuracy of sales ranks and prices and that they lead to more credible causal estimates of price elasticity. Notably, we uncover strong heterogeneity in price elasticity driven by these product-specific features. Our findings illustrate that AI-driven representations can enrich and modernize empirical demand analysis. The insights generated may also prove valuable for applied causal inference more broadly.

This paper explores the use of unstructured, multimodal data, namely text and images, in causal inference and treatment effect estimation. We propose a neural network architecture that is adapted to the double machine learning (DML) framework, specifically the partially linear model. An additional contribution of our paper is a new method to generate a semi-synthetic dataset which can be used to evaluate the performance of causal effect estimation in the presence of text and images as confounders. The proposed methods and architectures are evaluated on the semi-synthetic dataset and compared to standard approaches, highlighting the potential benefit of using text and images directly in causal studies. Our findings have implications for researchers and practitioners in economics, marketing, finance, medicine and data science in general who are interested in estimating causal quantities using non-traditional data.

We provide uniform inference and confidence bands for kernel ridge regression (KRR), a widely-used non-parametric regression estimator for general data types including rankings, images, and graphs. Despite the prevalence of these data -- e.g., ranked preference lists in school assignment -- the inferential theory of KRR is not fully known, limiting its role in economics and other scientific domains. We construct sharp, uniform confidence sets for KRR, which shrink at nearly the minimax rate, for general regressors. To conduct inference, we develop an efficient bootstrap procedure that uses symmetrization to cancel bias and limit computational overhead. To justify the procedure, we derive finite-sample, uniform Gaussian and bootstrap couplings for partial sums in a reproducing kernel Hilbert space (RKHS). These imply strong approximation for empirical processes indexed by the RKHS unit ball with logarithmic dependence on the covering number. Simulations verify coverage. We use our procedure to construct a novel test for match effects in school assignment, an important question in education economics with consequences for school choice reforms.

Accurate, real-time measurements of price index changes using electronic records are essential for tracking inflation and productivity in today's economic environment. We develop empirical hedonic models that can process large amounts of unstructured product data (text, images, prices, quantities) and output accurate hedonic price estimates and derived indices. To accomplish this, we generate abstract product attributes, or ``features,'' from text descriptions and images using deep neural networks, and then use these attributes to estimate the hedonic price function. Specifically, we convert textual information about the product to numeric features using large language models based on transformers, trained or fine-tuned using product descriptions, and convert the product image to numeric features using a residual network model. To produce the estimated hedonic price function, we again use a multi-task neural network trained to predict a product's price in all time periods simultaneously. To demonstrate the performance of this approach, we apply the models to Amazon's data for first-party apparel sales and estimate hedonic prices. The resulting models have high predictive accuracy, with $R^2$ ranging from $80\%$ to $90\%$. Finally, we construct the AI-based hedonic Fisher price index, chained at the year-over-year frequency. We contrast the index with the CPI and other electronic indices.

We consider a setting with $N$ heterogeneous units and $p$ interventions. Our goal is to learn unit-specific potential outcomes for any combination of these $p$ interventions, i.e., $N \times 2^p$ causal parameters. Choosing combinations of interventions is a problem that naturally arises in many applications such as factorial design experiments, recommendation engines (e.g., showing a set of movies that maximizes engagement for users), combination therapies in medicine, selecting important features for ML models, etc. Running $N \times 2^p$ experiments to estimate the various parameters is infeasible as $N$ and $p$ grow. Further, with observational data there is likely confounding, i.e., whether or not a unit is seen under a combination is correlated with its potential outcome under that combination. To address these challenges, we propose a novel model that imposes latent structure across both units and combinations. We assume latent similarity across units (i.e., the potential outcomes matrix is rank $r$) and regularity in how combinations interact (i.e., the coefficients in the Fourier expansion of the potential outcomes is $s$ sparse). We establish identification for all causal parameters despite unobserved confounding. We propose an estimation procedure, Synthetic Combinations, and establish finite-sample consistency under precise conditions on the observation pattern. Our results imply Synthetic Combinations consistently estimates unit-specific potential outcomes given $\text{poly}(r) \times (N + s^2p)$ observations. In comparison, previous methods that do not exploit structure across both units and combinations have sample complexity scaling as $\min(N \times s^2p, \ \ r \times (N + 2^p))$. We use Synthetic Combinations to propose a data-efficient experimental design mechanism for combinatorial causal inference. We corroborate our theoretical findings with numerical simulations.

Offset Rademacher complexities have been shown to imply sharp, data-dependent upper bounds for the square loss in a broad class of problems including improper statistical learning and online learning. We show that in the statistical setting, the offset complexity upper bound can be generalized to any loss satisfying a certain uniform convexity condition. Amazingly, this condition is shown to also capture exponential concavity and self-concordance, uniting several apparently disparate results. By a unified geometric argument, these bounds translate directly to improper learning in a non-convex class using Audibert's "star algorithm." As applications, we recover the optimal rates for proper and improper learning with the $p$-loss, $1 < p < \infty$ and show that improper variants of empirical risk minimization can attain fast rates for logistic regression and other generalized linear models.