Based on US state-level data for the period 1982-2016, two reduced-form versions of New Keynesian wage Phillips curves are examined. These are based on either sticky nominal wages or real-wage rigidity. The endogeneity of unemployment is taken into account by instrumentation and the use of common correlated effects (CCE) and mean group (MG) methods. This is the first time that this methodology has been applied in this context. These are important issues, as ignoring them may lead to substantial biases. The results show that while the aggregate data do not provide estimates that are consistent with either of the theoretical models examined, the panel methods do. Moreover, use of an appropriate MG CCE estimator leads to economically significant changes in parameters (primarily a steeper Phillips curve) relative to those from inappropriate but widely used panel methods. In the real-wage rigidity case, this is required to deliver results that have a theoretically admissible interpretation.