This paper proposes a new method to identify and estimate structural parameters in infinitely repeated games with public monitoring. Our approach does not rely on equilibrium selection assumptions or require a complete specification of monitoring informativeness or agents' patience. Instead, leveraging the results in Awaya and Krishna (2019), we construct the identified set by imposing coarse correlated ε-equilibrium (ε-CCE) restrictions for the underlying stage game. The resulting approach to estimation is computationally tractable and useful to recover bounds on payoff parameters, a common discount factor, and the informativeness of the monitoring structure. We illustrate the method in simulations.