The result that UI is welfare improving is also related to the implicit contract literature developed by Azariadis (1975), Bailey (1974), and Gordon (1974). In this literature, firms provide insurance to risk-averse workers by increasing employment above the first-best level. Introducing UI would make workers more willing to take the job loss risk and improve welfare. There are, however, important differences between this story and our’s further.
First, endogenous job composition (capital-labor ratios) and free entry play key a role in our model, and imply that UI not only increases ex ante welfare but also raises the level of output and improves the composition of jobs. In the standard implicit contract model, UI reduces output, and there are no implications about job composition. Second, our result is derived in a general equilibrium search model, which has two advantages: (i) the source of the inefficiencies are fully specified, and we show that when frictions disappear, the economy is efficient and there is no room for UI; (ii) firms cannot improve upon the decentralized equilibrium, which contrasts with the implicit contract setting where firms can increase their profits by introducing severance payments.
Analyses of optimal UI in the presence of asymmetric information, e.g. Shavell and Weiss (1979), Hansen and Imrohoroglu (1992), Atkeson and Lucas (1995) and Hopenhayn and Nicolini (1997), and partial equilibrium analyses of UI such as Mortensen (1977) also relate to our work. But because they treat the distribution of jobs and wage offers as exogenous, they do not share our result that UI may increase output.
We start in the next section with a static model that illustrates most of our main points. To highlight our main innovations, we also abstract from conventional moral hazard. In Section 3, we analyze the output implications of risk-aversion and UI. In Section 4, we characterize the optimal level of UI. Section 5 extends our analysis to a dynamic setup and introduces conventional moral hazard. Section 6 discusses extensions and empirical implications of our analysis. Section 7 concludes. Appendix A contains the important proofs, while the remaining proofs are available upon request.