This paper documents a novel finding indicating that re-employment wages are elastic to the level of unemployment insurance (i.e., a binding reservation wage) and adapts the IV estimator for duration dependence in Schmieder et al. (2016) to account for this fact. Using administrative data from Spain, we find that unemployed workers lower their re-employment wages by 3 percent immediately after the exhaustion of unemployment insurance (UI) benefits. Workers’ characteristics and permanent unobserved heterogeneity cannot explain this. To estimate duration dependence, we extend the IV framework proposed by Schmieder et al. (2016), whose estimator of duration dependence is proportional to the response of wages to an extension of the potential duration of UI, to account for the response of reservation wages. We find that while extending the potential duration of UI has an insignificant effect on re-employment wages, duration dependence is strongly negative. We estimate that the degree of duration dependence in Spain is approximately 0.8 percent per month in daily wages. Workers’ inability to find full-time jobs as the duration of non-employment increases is an important mechanism behind this effect, since the duration dependence of hourly wages is 0.25 percent per month. Failing to account for the fact that reservation wages are binding would underestimate the magnitude of duration dependence by 15 to 20 percent.
This paper argues that the value of unemployment insurance (UI) can be decomposed into a liquidity component and an insurance component. While the liquidity component captures the value of relieving the cost to access liquidity during unemployment, the insurance component captures the value of protecting the worker against a potential permanent future income loss. We develop a novel sufficient statistics method to identify each component that requires only the labor supply responses to changes in the potential duration of UI and severance payment and implement it using Spanish administrative data. We find that the liquidity component represents half of the value of UI, while the insurance component captures the remaining half. However, the relevance of each component is highly heterogeneous across different groups of workers. Poorer and wealthier workers are both similarly liquidity-constrained, but poorer workers place a higher value on UI because the insurance component is significantly more important for them. On the other hand, wealthier workers and workers with more cash-on-hand value additional UI equally, but the wealthier value its liquidity, while those with more liquidity care about its insurance value. Finally, from a welfare perspective, we show that extending the potential duration of Spain’s UI would increase welfare. However, in our counterfactual case where UI is complemented with the provision of liquidity, the optimal potential duration of Spain's UI should be lower than its current level.
