Research

We document six facts about the structure and dynamics of the LLM market using API usage data from OpenRouter and Microsoft Azure. First, we show rapid growth in the number of models, creators, and inference providers, driven by open-source entrants. Second, we show price declines and persistent price heterogeneity across and within intelligence tiers, with open-source models being 90% cheaper than comparable closed-source models of the same intelligence. Third, we document market dynamism, with frequent turnover among leading models and creators. Fourth, we present evidence of horizontal and vertical differentiation, with no single model dominating across use cases, and demand for intelligence varying widely across applications. Fifth, we estimate preliminary short-run price elasticities just above one, suggesting limited scope for Jevons-paradox effects. Finally, we show that although the share of firms using multiple models increased over time, most firms concentrate their use on a single model, consistent with experimentation rather than persistent reliance on multiple models.

This paper explores the individual-level dynamics of learning by doing using a uniquely detailed dataset from a freight forwarding firm. In contrast to work that primarily examines learning and productivity at the firm level, I use high-frequency data on employee interactions with an internal web application to estimate learning trajectories, information depreciation, and the effects of collaboration. For specific roles, new employees reach productivity levels comparable to experienced workers within weeks, while information depreciation is substantial, with only 10% to 30% retained after one month. These results suggest that in some knowledge-intensive settings, the costs of retraining new employees may be lower than commonly assumed.

We describe the emerging business-to-business market for large language model (LLM) inference and document key empirical patterns in its supply, pricing, and dynamics, using data from OpenRouter. First, supply has expanded rapidly: the number of commercially available models, model creators, and inference providers has grown sharply, driven heavily by open-source entrants. Second, the price of intelligence has fallen roughly a thousandfold, and open-source models now cost about 90 percent less than comparable closed-source ones. Third, the market is highly dynamic, with frequent turnover among leading models and creators. Fourth, we document substantial horizontal and vertical differentiation: no single model dominates across use cases, and demand for intelligence varies widely across applications. We place these patterns in historical perspective alongside earlier general-purpose technologies.

We develop a matching mechanism designed to reduce congestion in the Gale-Shapley deferred-acceptance algorithm. Simulations demonstrate that the modified mechanism can reduce the congestion problem by orders of magnitude. We are developing a theoretical framework that establishes these results without relying on simulation alone.

This project examines dynamic bidding strategies in auctions with common- and private-value components, where bidders accumulate information through experience and develop asymmetric beliefs about the common value. The model incorporates learning by bidding, with the precision of private information improving through repeated participation. I establish nonparametric identification of the asymmetric conditionally independent private information model in static and dynamic settings and plan to apply the framework to first-price sealed-bid real-estate auctions.

We extend the double/debiased machine learning framework with a method for estimating marginal treatment effects without requiring a prespecified functional form for the treatment-outcome relationship. Drawing on sieve estimation and generalized cross-validation, the approach adaptively tunes this mapping while maintaining valid inference. The framework is designed for continuous or complex treatments with high-dimensional confounders.