Estimating dynamic rational expectations models when the trend specification is uncertain

This paper explores various strategies for estimating rational expectations models when the trend specification is uncertain. One approach modified the likelihood function in order to reduce the influence of low-frequency dynamics. Hansen and Sargent (1993) conjectured that this would have little cost in correctly specified models and would improve estimated in mis-specified models. This paper confirms the first part of their conjecture but not the second. Contrary to intuition, the effects of trend-specification errors are spread across the entire frequency domain and are not confined to low-frequencies. Hence, deleting low-frequency dynamics does not remove the specification error. Another approach seeks a representation of the approximating model that does not condition on a specification of the trend, and it estimated parameters by GMM. This approach compares favorably with MLS when the trend is correctly specified and is superior when the trend is mis-specified.