Identifying the Causal Effect of a Tax Rate Change When There are Multiple Tax Brackets

Abstract: Empirical researchers frequently obtain estimates of the behavioral response to a tax change by exploiting variation in the degree to which a tax reform affects different groups of individuals based on their individual characteristics and tax situations. This paper analyses the conditions under which it is possible to obtain a causal average treatment effect using pre-reform characteristics as instruments for the observed tax rate change, which I term the Fixed-Bracket Average Treatment Effect (FBATE). Previous literature has assumed that only one of these conditions is sufficient to identify a causal parameter. FBATE identifies the average treatment effect for individuals with no incentive to switch tax brackets in response to a tax reform or other shock that affects the bracket in which an individual is located. FBATE is the relevant parameter for welfare analysis if taxpayers whose response is identified by the FBATE estimate will have the same long-run response as the rest of the population. FBATE also highlights new trade-offs between different sources of identification; for example, an oft-touted source of identification|bracket creep|cannot yield a causal estimate. The paper also shows that using an alternative definition of treatment relative to what is usually employed in the literature obtains a causal average treatment effect for a larger subpopulation under weaker assumptions.