This paper presents a model of the labor market in which unemployed workers are uncertain about their relative ability to find a job. Unsuccessful search induces individuals to revise their beliefs downwards. Once self-confidence is sufficiently low, workers become discouraged and give up on search. This non-stationarity gives rise to structural flows from unemployment to non-participation in equilibrium. In contrast, existing models typically maintain stationarity and appeal to exogenous stochastic shocks to generate transitions from unemployment to non-participation. Our model is based on relaxing a single assumption in a standard matching framework workers are uncertain about their job finding probability and yet the model generates a variety of important implications. Our alternative assumption is supported by experimental evidence. The first implication of the model is a declining hazard from unemployment to employment, arising due to erosion of self-confidence in search. Second, because search outcomes are only a noisy signal about ability, some individuals can become overly discouraged and stop search too early due to wrong beliefs. Finally, workers with greater unemployment duration are less confident, and thus have a worse threat point in wage bargaining. Consequentially, they earn lower starting wages even if they are identical in terms of objective productivity. We discuss how the model provides a new, unifying explanation for a variety of important facts from field evidence.