This paper introduces a computational framework to analyze global identification of linearized DSGE models. A formal identification condition is established that relies on the restrictions linking the observationally equivalent state space representations and on the inherent constraints imposed by the model solution on the deep parameters. This condition is next used to develop an algorithm that checks global identification by searching for observationally equivalent model parametrizations. The algorithm is efficient as the identification conditions it employs shrink considerably the space of candidate deep parameter points and the model does not need to be solved at each of these points. The working of the algorithm is demonstrated with two examples.