Dynamic Causal Forests, with an Application to Payroll Tax Incidence in Norway

Abstract

This paper develops a machine-learning method that allows researchers to estimate heterogeneous treatment effects with panel data in a setting with many covariates. Our method, which we name the dynamic causal forest (DCF) method, extends the causal-forest method of Wager and Athey (2018) by allowing for the estimation of dynamic treatment effects in a difference-in-difference setting. Regular causal forests require conditional independence to consistently estimate heterogeneous treatment effects. In contrast, DCFs provide a consistent estimate for heterogeneous treatment effects under the weaker assumption of parallel trends. DCFs can be used to create event-study plots which aid in the inspection of pre-trends and treatment effect dynamics. We provide an empirical application, where DCFs are applied to estimate the incidence of payroll tax on wages paid to employees. We consider treatment effect heterogeneity associated with personal- and firm-level variables. We find that on average the incidence of the tax is shifted onto workers through incidental payments, rather than contracted wages. Heterogeneity is mainly explained by firm-and workforce-level variables. Firms with a large and heterogeneous workforce are most effective in passing on the incidence of the tax to workers.