The analysis of poverty persistence received considerable attention in recent years. In this paper we explore the role of the adopted poverty measure in the analysis of its persistence. Specifically, we consider three measures: the risk of poverty, the severe material deprivation and subjective poverty, motivated by the understanding of poverty as a complex phenomenon and for which no single measure can effectively capture its several dimensions. The empirical analysis is based on the 2013-2016 longitudinal sample of the EU-SILC survey. We focus on Italian households with dependent children. We apply a correlated random effects probit models with endogenous initial conditions to assess genuine state dependence after controlling for structural household characteristics and variables related to participation in the labour market. A strong state dependence emerges, regardless of the considered poverty measure thus providing evidence of poverty and social exclusion persistence. We also find evidence of relevance of initial conditions for all measures in focus. Nonetheless, structural household characteristics and household level economic variables play roles that are often different in the three parallel models; these differences are consistent with the aims and nature of the alternative measures.