Replacing rational expectations by recursive learning schemes complicates the dynamics of economic models. We show that when such models are used for structural inference, conventional asymptotic theory does not necessarily apply. In the context of two prototypical structural models with learning, we show that: (i) estimators of the structural parameters exhibit large biases and nonnormality; and (ii) t-statistics are nonpivotal, and t-tests are seriously size distorted. These features are attributable to a violation of ergodicity and to weak identification. We show that valid inference can be conducted using a generalized Anderson-Rubin statistic with appropriate choice of instruments. As an application we study a New Keynesian Phillips curve with learning
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