# 15-138/III (2015-12-24)

Author(s)
Drew Creal, The University of Chicago Booth School of Business, United States; Siem Jan Koopman, VU University Amsterdam, the Netherlands; André Lucas, VU University Amsterdam, the Netherlands; Marcin Zamojski, VU University Amsterdam, the Netherlands
Keywords:
dynamic models, time-varying parameters, generalized method of moments, non-linearity
JEL codes:
C10, C22, C32, C51

We introduce a new estimation framework which extends the Generalized Method of Moments (GMM) to settings where a subset of the parameters vary over time with unknown dynamics. To filter out the dynamic path of the time-varying parameter, we approximate the dynamics by an autoregressive process driven by the score of the local GMM criterion function. Our approach is completely observation driven, rendering estimation and inference straightforward. It provides a unified framework for modeling parameter instability in a context where the model and its parameters are only specified through (conditional) moment conditions, thus generalizing approaches built on fully specified parametric models. We provide examples of increasing complexity to highlight the advantages of our method.