Shapes as Product Differentiation︎︎︎
with Eric Schulman, Kristen Grauman, Santhosh Ramakrishnan
arxiv︎︎︎ slides︎︎︎
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 ︎︎︎.
![](https://freight.cargo.site/t/original/i/05371e7389269b09e39334ef63f6a2389ec4d752ae2068a929f6ff55640a4088/tsne_sample400_perp70_exg30_edited.png)
![](https://freight.cargo.site/t/original/i/785d78957a2398185b59aec583a0ab914f42f76271e94561b4c1dd95c77938f6/Supply_side_Mean_Distances_Time_Plot_02252020.png)
Jan 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.
![](https://freight.cargo.site/t/original/i/045fb856c4350392c5811d270eddc69c5ecd8d615ab033b5b26d86a6fb3cbb0a/pi1_median_rhc.png)
![](https://freight.cargo.site/t/original/i/8f3e907d012c72a786d4ed60056b0b6c4c085af46f4ce2b7274c11678af94215/pi1_3rd_quantile_rhc.png)
On Quantile Treatment Effects, Rank Similarity, and the Variation of IVs︎︎︎
with Haiqing Xu
arxiv︎︎︎ slides︎︎︎
Aug 2023
We provide a novel interpretation for rank similarity, which motivates us to relax it in a way that is useful to bound the QTEs using multi-valued IVs. The bounds are easy to calculate in practice and are shown to be informative.
Semiparametric Models for Dynamic Treatment Effects and Mediation Analyses with Observational Data︎︎︎
with Sungwon Lee
slides︎︎︎
Aug 2023
We propose a class of semiparametric models using copula to point identify and efficiently estimate dynamic treatment effects and dynamic mediator effects under treatment endogeneity.
Feb 2024
We develop a test of information ordering to examine if the true information structure is at least as informative as a proposed baseline. We utilize the notion of Bayes Correlated Equilibrium (BCE).
![](https://freight.cargo.site/t/original/i/a597fbceba068da2bf380e9ce54c730cd0f4e01433765a7c6510559a7b475022/BCE_fig1-copy.jpg)
![](https://freight.cargo.site/t/original/i/5d842b6b475924a35e99418f273c64d07e45863d7c2da0fb33837966fda3857d/BCE_fig2-copy.jpg)