We use Twitter, Google mobility, and Oxford policy data to study the relationship between trust and compliance over the period March 2020 to January 2021 in ten, mostly European, countries. Trust has been shown to be an important correlate of compliance with COVID-19 containment policies. However, the previous findings depend upon two assumptions: first, that compliance is time invariant, and second, that compliance can be measured using self reports or mobility measures alone. We relax these assumptions by calculating a new time-varying measure of compliance as the association between containment policies and people's mobility behavior. Additionally, we develop measures of trust in others and national institutions by applying emotion analysis to Twitter data. Results from various panel estimation techniques demonstrate that compliance changes over time and that increasing (decreasing) trust in others predicts increasing (decreasing) compliance. This evidence indicates that compliance changes over time, and further confirms the importance of cultivating trust in others.