Social Security and Old-Age Unemployment Risk with Efficient Wage Bargaining

I analyze a life-cycle economy with old age productivity risk where wages, employment and severance payments are set through efficient bargaining between risk averse unions and risk neutral firms. Allocations with limited union membership are second-best inefficient as they generate too little labor supply in young age, too much consumption before retirement, too little employment of older workers (early retirement) and too little insurance against old age unemployment. Providing public transfers to early retirees (disability benefits or early pensions) may help increasing the degree of risk sharing at the cost of a lower old age employment. Depending on absolute risk aversion being increasing or decreasing in consumption, these policies may or may not produce efficiency gains at equilibrium.