Some currencies, like the U.S. dollar, are freely traded and the exchange rates are set by international markets. However, the exchange rate of the Chinese currency, the yuan, is partially controlled by the Chinese government. Each morning, the Chinese government sets a daily mid-point for the exchange rate and the free market allows the rate to move around this mid-point. Silvia Lang’s mathematics thesis researched if the Chinese yuan’s exchange rate can be modeled using the same model used for the U.S. dollar.

Existing research has found that the exchange rate between two freely traded currencies, like the U.S. dollar to the Japanese yen, can be modeled by a random walk, meaning the rate changes by a random positive or negative quantity at each observable timestamp. Lang looked to see if the exchange rate of the U.S. dollar to Chinese yuan from 2010 to 2016 could be modeled using the same models of random walks.

“My research, specifically unit root testing, found that there’s not enough evidence against modeling the exchange rate of U.S. dollar to Chinese yuan from 2010 to 2016 with the same model that’s used for the exchange rates of freely traded currencies, such as the U.S. dollar and the Japanese yen,” said Lang, a mathematics major with a statistics minor, political science minor, and scientific computing concentration.

In statistical hypothesis testing, researchers reject a null hypothesis if there is enough evidence against it, otherwise they fail to reject the null hypothesis. They do not accept a null hypothesis. Using a special hypothesis testing method called unit root testing, Lang failed to reject her hypothesis that the exchange rate between the U.S. dollar and the Chinese yuan could be modeled by random walk.

“So basically, we don’t have enough evidence against modeling the exchange rate of Chinese yuan with the same model that is used for freely traded currencies like the USD,” she said.

Her thesis work provides a new way to think about the Chinese yuan, especially as U.S. economists and policymakers worry that the Chinese government’s partial control over their exchange rate gives them an advantage in the international economy.

**What did you learn from working on your thesis?**

Through this year-long assignment, I learned how to divide a big project into smaller pieces and push each module from start to finish. I’ve also gotten better at asking for help when needed, including from my advisor, other professors, and my peers who have worked on related topics.

This project gave me the opportunity to use all of the skills I’ve learned at Haverford. My pure math background and stats minor enabled me to approach statistical problems from a mathematically rigorous perspective. The coding skills I’ve learned from my scientific computing concentration allowed me to simulate models that are essential to my thesis. Last but not least, my political science minor gives me the lens to examine the implications of my statistical analysis in the context of the international political economy.

**What are your plans for the future?**

I’m going to work as a data analyst at Ernst & Young with the Quantitative Economics and Statistics group . My job will involve conducting quantitative analysis on federal, state, and local tax policies. As I’ll probably encounter a lot of economic and time series data, I look forward to applying lessons from my thesis work to my professional career!

*“What They Learned”* *is a blog series exploring the thesis work of recent graduates.*