Shapes as Product Differentiation︎︎︎


with Eric Schulman, Kristen Grauman, Santhosh Ramakrishnan


arxiv︎︎︎  slides︎︎︎

Nov 2022,
Revise & Resubmit,
RAND Journal of Economics

Many differentiated products have key attributes that are high-dimensional (e.g., design, text). We consider one of the simplest design products, fonts, and quantify their shapes by constructing neural network embeddings. Using the embeddings and data from the world's largest online market place for fonts, we study the causal effect of a merger on the merging firm's creative decisions of product differentiation.

*This project is featured in a typography magazine ︎︎︎ and included in the MIT graduate machine learning course ︎︎︎.



Nov 2024

Finding IVs is a heuristic and creative process, and justifying exclusion restrictions is largely rhetorical. We propose using large language models (LLMs) to systematically search for new IVs through narratives and counterfactual reasoning.



Sep 2024

Most work on treatment choice and policy learning focuses on utilitarian welfare (i.e., average welfare), which can be sensitive to skewed heterogeneity. We propose a robust policy learning framework that enables the policymaker to act with prudence/negligence and to be influenced by vote shares.



Mar 2024


new draft coming soon

We identify average and quantile treatment effects for binary, ordered and continuous treatments with only binary IV under local copula invariance. The resulting semiparametric estimation procedures are very easy to implement.


Feb 2024


new draft coming soon


The classic control function approach requires invertibility, which limits its applicability (e.g., discrete treatments). We allow the control function to be set-valued and derive sharp bounds on structural parameters.


© Sukjin Han