This dissertation investigates several topics in state merit-based financial aid research. The main research content includes three separate studies, primarily using the administrative datasets from the Missouri Department of Higher Education. The first study is an empirical paper that examines the effects of the Missouri Bright Flight Scholarship (a merit-based financial aid) on producing STEM graduates in Missouri 4-year public institutions. The fuzzy regression discontinuity estimates indicate that this merit aid program has a negative but statistically insignificant effect on STEM/engineering initial major choice and degree completion. Particularly, the aid still has a negative impact on male students but may encourage female students to enter a STEM field. The second study is a technical note that addresses three ignored issues about regression discontinuity application in merit-based financial aid research: retaking and test score manipulation, rounding errors in the running variable, and misleading statistical inference. I re-examine the practices in recent related studies and provide recommendations for future financial aid research, particularly about dealing with test scores appropriately in regression discontinuity designs. The third study is a policy brief about the consequence of allowing test retaking in merit aid programs. Using the Missouri administrative data, I primarily compare the percentages of aid eligible students based on both the first-time and the highest ACT composite scores in different demographic groups. The empirical results indicate that underrepresented students are less likely to retake the ACT compared to their peers and the acceptance of the highest score brings more inequitable impacts on underrepresented students. The discussion may help policymakers to better understand the retaking behaviors so that they can make related policies to benefit underrepresented students with more effectiveness. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]