Stay-at-home orders were essential policy measures to mitigate the spread of COVID-19 in the absence of effective vaccines. However, the effectiveness of the orders was highly dependent on compliance. We use mobile devices' mobility data and the staggered implementation of stay-at-home orders and their extensions to estimate compliance responses to these policies. Treating the first announced end dates of the stay-at-home orders as the reference points for the general public, we find that the duration of extension beyond the reference points is negatively associated with the level of compliance. This result suggests that the government officials need to consider the behavioral consequences of their policy delivery and manage public expectations to ensure the effectiveness of the stay-at-home orders.