Unemployment insurance (UI) helps workers smooth their consumption at job loss but can also affect their job search behavior due to moral hazard. We shed light on the effect of UI on job search behavior using new longitudinal data: we track job applications sent on a major online search platform for 500,000 French unemployed workers. We show that, in the year before their benefits exhaustion, unemployed workers increase their search intensity by 50% and decrease their target wage by 3.5%. After exhaustion, they keep a relatively high search intensity and low target wage. Prior evidence seemingly inconsistent with these findings can largely be explained by dynamic selection and duration dependence. Our structural estimation shows that the standard search model fits our reduced-form estimates very well. The behavioral reference-dependent search model provides an even better fit, but with a small degree of reference-dependence that only slightly affects search behavior. Overall, our findings suggest that the standard search model provides a good approximation of the dynamic impact of UI on search behavior.