The Equilibrium Worker-Firm Allocation and the Deadweight Losses of Taxation


We analyze how taxes distort the allocation of workers across jobs. We construct a rich model of two-sided search, in which workers search to enter and then climb the job ladder, and firms with vacancies search to find employees. Workers differ in their productive abilities. Jobs differ in terms of productivities as well as amenities that come with them. In competitive search equilibrium, the allocation is efficient in the sense that it maximizes aggregate utility net of taxes. A planner levies proportional taxes on labour income to finance lump-sum transfers to all workers and benefits to unemployed workers. Since the equilibrium allocation is efficient, the dead-weight losses from taxes are determined by the effects of the behavioral responses on the tax base and on aggregate unemployment benefits. A higher proportional tax on labor income gives rise to distortions along three dimensions: First, it influences the workers' incentives to do costly on- and off the job search. Second, it distorts the workers' ranking of jobs, as it makes high-amenity, low-productive jobs relatively more attractive. Finally, it distorts job creation. The direction of the distortions depend crucially on the relative growth of amenities and productivities when climbing the job ladder. We calibrate the model using Danish matched employer-employee data and use the calibrated model for three purposes. First, we compared it to a laissez-faire economy without taxes and transfers in order to illustrate the effects of taxes and transfers on the three distortionary channels. Second, we calculate the deadweight loss elasticity at the current tax level and analyze it's roots. Finally, we derive optimal tax policies as a function of the planner's equity preferences.