(1) The paper does not look at the number of words, but at the importance of the content. The doctoral committee will review the quality of your thesis, and it is useless to spend money to publish it in an unknown magazine.

A good paper, such as the project you did with your tutor in your master's degree, can be uploaded through addtional paper word during the application process, even if it is not published, it will be a great bonus.

On the contrary, papers without nutrition, published, are useless. I have a classmate of EE who published a paper and thought it would have a great impact, but the result was rejected.

(2) The thesis is only a bonus. Even if there is no paper, the undergraduate mathematics score is very good and the economics score is very good, which is also very useful.

(3) The recommendation letter ranks first in the process of applying for a doctorate. Famous professors are a must.

(4) If you apply for the United States in China instead of the United States, it will be different. If you apply for a Ph.D. in the United States in China, the requirements for your background will be upgraded. Secondly, professors must be very famous.

(5) Finally, it depends on what school you apply for, which you can understand yourself.