["Oxford Bulletin of Economics and Statistics, EarlyView. ", "\nABSTRACT\nThis paper formalizes how to test important economic and statistical hypotheses for the labor market in a cointegrated framework. That formalization offers substantive gains in understanding the labor market because that market can involve multiple cointegrating relationships. Those relationships include trend‐stationary gaps in labor force participation rates and in unemployment rates, added‐worker and discouraged‐worker effects in relationships between labor force participation rates and unemployment rates, and possible stationarity of variables. This paper then applies that framework to analyze the US labor market, finding several such long‐run relationships for data disaggregated by both age and gender, albeit with heterogeneity across age and gender. Forecasts from these models provide a benchmark from which to measure recovery from the covid‐19 pandemic.\n"]