This paper is about measuring state dependence in dynamic discrete outcomes. I develop a nonparametric dynamic potential outcomes (DPO) model and propose an array of parameters and identifying assumptions that can be considered in this model. I show how to construct sharp identified sets under combinations of identifying assumptions by using a flexible linear programming procedure. I apply the analysis to study state dependence in unemployment for working age high school educated men using an extract from the 2008 Survey of Income and Program Participation (SIPP). Using only nonparametric assumptions, I estimate that state dependence accounts for at least 30–40% of the four‐month persistence in unemployment among high school educated men.