Identification of structural parameters in models with adaptive learning can be weak, causing standard inference procedures to become unreliable. Learning also induces persistent dynamics, and this makes the distribution of estimators and test statistics non-standard. Valid inference can be conducted using the Anderson-Rubin statistic with appropriate choice of instruments. Application of this method to a typical new Keynesian sticky-price model with perpetual learning demonstrates its usefulness in practice.
CHEVILLON, G., MASSMANN, M. et MAVROEIDIS, S. (2010). Inference in Models with Adaptive Learning. Journal of Monetary Economics, 57(3), pp. 341-351.