This dissertation consists of two chapters studying problems faced by youths in two contexts that could be pivotal to their future: admissions to higher education and the juvenile criminal justice system. The underrepresentation of women in science, technology, engineering, and mathematics (STEM) fields has been studied extensively, and there have been calls for improving the gender balance in STEM fields through admission policies in higher education. In the first chapter, I estimate preferences for both applicants and programs using data from the centralized post-secondary admission system in Taiwan and explore how the preferences relate to the gender gap in STEM fields. To account for applicants’ and programs’ decision timing, I introduce a modified version of the truth-telling assumption for estimating preferences under a deferred-acceptance mechanism. On the program side, I find substantial heterogeneity across programs in gender preferences, reflected in their ranking of applicants. On the applicants’ side, the largest difference between gender lies in male applicants’ preference for programs where students are strong in math, and the preference is higher for those with lower math scores. Female applicants’ emphasis on math is weaker and show less heterogeneity. To examine the potential impact of implementing minority reserves within STEM programs on gender balance, I conduct simulations of a counterfactual policy reserving seats for women in admissions to STEM programs. I find that while minority reserves could yield improvements in female representation within STEM programs, the magnitude of these changes are modest. The results also suggest that the limited efficacy of such policies may stem from the concentration of female applicants’ preferences towards similar programs. In the second chapter (co-authored with Diego Amador), I study the effects of short-term detention on youths when they are arrested for the first time. Many youths accused of delinquent conduct are detained as their cases get processed by juvenile courts. Using a decade of detailed administrative data for all initial detention decisions made in Harris County, we find that these short-term detentions of low-risk youths lead to a sizeable increase in the likelihood of rearrest. We also find that these effects are concentrated on youths arrested for non-violent, less serious offenses and are unrelated to the actual amount of time spent in detention. To obtain our estimates, we implement the double/debiased machine learning estimator for matching, which relies on selection on observables as the key assumption. We go beyond traditional robustness checks by directly gauging the vulnerability of our results to violations of selection on observables, and sensitivity tests show that our estimates are robust to plausible levels of violations of this assumption.