Essays on model selection




Schulman, Eric H.

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This dissertation discusses model selection and evaluation in economics from a variety of perspectives, and techniques.

Chapter 1 approaches model selection from the perspective of non-nested hypothesis testing. I explore how bootstrapping can improve inference for the Vuong test. I establish that the suggested bootstrap 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. The suggested test is easy to implement and similar to bootstrapping the standard Vuong test. When compared with other existing Vuong tests in Monte Carlo simulations, the suggested test controls size equally well and achieves higher power. Finally, I illustrate selecting models with the bootstrap in four stylized empirical examples from various fields of economics. The new test selects a model at lower significance levels in all examples.

Chapter 2 is joint work with Sukjin Han, Kristen Grauman and Santosh Ramakrishnan. This chapter focuses on model evaluation in the presence of high-dimensional unstructured data on product attributes (e.g., design, text). Quantifying these attributes is important for economic analyses. We consider one of the simplest design products, fonts, and quantify 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.

Chapter 3 is joint work with David Sibley. This chapter considers model selection in the context of Nash-in-Nash bargaining model with one hospital, two competing insurers, and linear demand. We find an externality related to the entry of a second insurer. This externality is directly proportional to the hospital's profit in the event of a disagreement with an insurer. We explore how different assumptions about the hospital's disagreement profit, such as passive beliefs, influence the extent of this externality thereby increasing prices and premiums. Additionally, we explore how the hospital can benefit from the externality associated with the entry of another insurer by bargaining sequentially -- one insurer before the other. We show the hospital has higher profit in a sequential negotiation. Sequential bargaining creates a second mover advantage among the insurers compared to simultaneous bargaining. Lastly, we derive empirical implications of beliefs and timing in our model, to help evaluate whether insurer competition may increase prices in practice.



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