Back to square one: identification issues in DSGE models

We investigate identifiability issues in DSGE models and their consequences for parameter estimation and model evaluation when the objective function measures the distance between estimated and model impulse responses. Observational equivalence, partial and weak identification problems are widespread and they lead to biased estimates, unreliable t-statistics and may induce investigators to select false models. We examine whether different objective functions affect identification and study how small samples interact with parameters and shock identification. We provide diagnostics and tests to detect identification failures and apply them to a state-of-the-art model.