Research

Working papers

"Uniformly Valid Model Selection with the Bootstrap"

This paper explores how bootstrapping can improve inference for the Vuong test. I suggest a bootstrap test with a test statistic similar to that of Shi (2015). I establish that the new bootstrap test has uniformly valid asymptotic size control in the case of both non-overlapping and overlapping models. I also show that the new test achieves an asymptotic refinement for non-overlapping models. Implementing the new test is very similar to the standard bootstrap. When compared with other Vuong tests in Monte Carlo simulations, the proposed test controls size equally well and achieves higher power. Finally, I illustrate the new test with four stylized empirical examples from multiple fields of economics. The new test selects a model at higher confidence levels in all examples. 

github 1 (implementation and monte carlo), github 2 (empirical examples) 

"Shapes as Product Differentiation: Neural Network Embedding in the Analysis of Markets for Fonts" with Sukjin Han, Kristen Grauman, and Santhosh Ramakrishnan

Many differentiated products have key attributes that are high-dimensional (e.g., design, text). Quantifying these attributes is important for economic analyses. This paper considers one of the simplest design products, fonts, and quantifies their shapes by constructing embeddings using a modern convolutional neural network. The embedding maps a font's shape onto a low-dimensional vector. Importantly, we verify the resulting embedding is economically meaningful by showing that the mutual information is large between the embedding and descriptions assigned to each font by font designers and consumers. This paper then conducts two economic analyses of the font market. We first illustrate the usefulness of the embeddings by a simple trend analysis of font style. We then study the causal effect of a merger on the merging firm's creative product differentiation decisions by using the embeddings in a synthetic control method. We find that the merger causes the merging firm temporarily to increase the visual variety of font design.

github 1  (neural net), github 2 (synthetic control)

Included in the MIT graduate machine learning course.

"Beliefs and Timing in Healthcare Bargaining" with David S. Sibley

Recent empirical work using Nash-in-Nash bargaining models finds that insurer competition may lower bargaining leverage with providers increasing premiums. In this paper, we explore theoretical circumstances where insurer competition increases premiums under alternative assumptions about beliefs and timing in a Nash-in-Nash bargaining model with one provider and two insurers. We show that a merger can decrease premiums; our results are robust to assumptions about beliefs, including the common passive beliefs assumption. Additionally, we show the provider benefits from insurer competition and can raise reimbursements by bargaining sequentially – one insurer before the other in a setting similar to Horn and Wolinsky (1988).

github (numerical examples)

Works in progress

• "Comparing the Effects of Current Pay and Defined Benefit Pensions on Employee Retention" with Justin Falk and Nadia Karamcheva

• "Heterogeneous enrollment responses in Medicare Advantage"