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Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 21

Chapter 21 Optimal Unemployment Insurance 21.1. History-dependent UI schemes This chapter applies the recursive contract machinery studied in chapters 19, 20, and 22 in contexts that are simple enough that we can go a long way toward computing the optimal contracts by hand. | Chapter 21 Optimal Unemployment Insurance 21.1. History-dependent UI schemes This chapter applies the recursive contract machinery studied in chapters 19 20 and 22 in contexts that are simple enough that we can go a long way toward computing the optimal contracts by hand. The contracts encode history dependence by mapping an initial value and a random time t observation into a time t consumption allocation and a continuation value to bring into next period. We use recursive contracts to study good ways of insuring unemployment when incentive problems come from the insurance authority s inability to observe the effort that an unemployed person exerts searching for a job. We begin by studying a setup of Shavell and Weiss 1979 and Hopenhayn and Nicolini 1997 that focuses on a single isolated spell of unemployment followed by a single spell of employment. Later we take up settings of Wang and Williamson 1996 and Zhao 2001 with alternating spells of employment and unemployment in which the planner has limited information about a worker s effort while he is on the job in addition to not observing his search effort while he is unemployed. Here history-dependence manifests itself in an optimal contract with intertemporal tie-ins across these spells. Zhao uses her model to offer a rationale for a replacement ratio in unemployment compensation programs. - 746 - A one-spell model 747 21.2. A one-spell model This section describes a model of optimal unemployment compensation along the lines of Shavell and Weiss 1979 and Hopenhayn and Nicolini 1997 . We shall use the techniques of Hopenhayn and Nicolini to analyze a model closer to Shavell and Weiss s. An unemployed worker orders stochastic processes of consumption and search effort ct at ft 0 according to E ftf u c at 21.2.1 t 0 where ft G 0 1 and u c is strictly increasing twice differentiable and strictly concave. We assume that u 0 is well defined. We require that ct 0 and at 0. All jobs are alike and pay wage w 0 units of