ESSAYSIN MARKETING,ECONOMICS,ANDOPTIMIZATION

a dissertation submitted to the department of management science and engineering and the committee on graduate studies of stanford university in partial fulfillment of the requirements for the degree of doctor of philosophy

ding ma november 2018

© 2018 by Ding Ma. All Rights Reserved. Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/xp256qm9828

ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Wesley Hartmann, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Michael Saunders, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Kenneth Judd

Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost for Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.

iii iv ABSTRACT

This thesis includes four self-contained essays on marketing, economics, and opti- mization, all sharing a common theme: creating numerical models and algorithms to tackle computationally challenging optimization problems. The first essay considers geographic sub-branding via manufacture location in marketing. Manufacture location, as part of geographic product identity, is be- coming a significant differential factor among a variety of products and a sub- branding element in various markets, but there is little empirical research on how manufacture location influences consumer preference and purchase choices. The first barrier comes naturally from the market. Most of the time, manufacture loca- tion is completely correlated with product characteristics. I was fortunately able to acquire both data and a whole year research grant from Ford Motor Com- pany. New car buyer data in the Chinese automobile market makes possible the analysis of manufacture location as a geographic sub-branding element. Hedo- nic price analysis gives us a quick and intuitive view of how much consumers are willing to pay for geographic sub-branding products, and also motivates our new brand and sub-brand definition for a BLP-type random coefficient discrete choice model. However, using General Method of Moments (GMM) to estimate the variance-covariance matrix of consumer brand taste coefficients poses another challenge for all existing optimization solvers. To prevent indefinite unknown variance-covariance matrices in the constraints of the optimization problem from terminating the solver, I reformulate the optimization program and successfully solve the problem. If the computation becomes more difficult, we can also apply our new algorithm NCL, which is described in details in the third essay. Our re- sults reveal the strong substitution patterns in the market and confirm our defini- tion and framework of brand and geographic identity. Furthermore, our method can be helpful in the analysis of branding and sub-branding in other empirical settings. The second essay studies optimal income taxation with multidimensional tax- payer types in economics. This engendered the subject of the third essay: stabilized optimization via an NCL algorithm in numerical optimization. The income taxa- tion literature has generally focused on economies where individuals differ only in their productivity, i.e., income. In reality, people diffe