We explore the long-run relationship between the unemployment rate and the labor force participation rates for U.S. over the period of 1976-2015. We use U.S. state level data and panel cointegration techniques that are robust to cross-sectional heterogeneity, cross-sectional dependency, omitted variable bias and endogeniety issues. We find evidence that on average these two variables are cointegrated and are inversely related. Similar to studies that employ U.S. country level data, this study further questions the empirical relevance of the unemployment invariant hypothesis for the case of the U.S.