Recent papers identify the effects of unemployment insurance and potential benefit duration (PBD) on unemployment duration and reemployment wages using quasi-experiments. To make known problems of heterogeneity in quasi-experiments tractable, they often use models of job search, but we argue that letting the data speak without restrictions remains surprisingly informative. We focus on two broad questions: How informative are the local average effects quasi-experiments identify and what can we learn about causes and mechanisms from quasi-experiments in the presence of heterogeneous treatment effects? We first line out a framework for treatment effect heterogeneity with two interdependent outcomes, such as duration and wages, and then re-examine the effects of longer PBD in Schmieder, von Wachter and Bender (2016). Local average effects become more informative when amended with other parameters identified by (quasi-)randomization: Duration effects of PBD almost exclusively prolong few long spells, which helps to explain differences between studies. Dynamic selection into reemployment timing is non-monotonic, but does not change with PBD at short durations so dynamic treatment effects are identified at short durations. For wage effects of PBD, we find neither evidence of positive effects nor meaningful heterogeneity. Even though key structural parameters are not identified because LATE confounds average effects with the covariance of first and second stage effects, the data remain informative about causes and mechanisms. A wage decomposition shows that wage loss operates through the firm fixed effect, which speaks against individual-based causes such as skill depreciation or bargaining. Using dynamic treatment effects and mediation analyses, we find PBD to affect wages even for workers who do not change unemployment duration, i.e. directly. The negative direct effect we find casts doubt on key assumptions of common models of job search.