Abstract
The method of marginal likelihood is presented for the elimination of nuisance parameters from a model which represents a wide class of single equation distributed lag models. The technique relies on the ability to divide the information on the nuisance parameters given by the data into sufficient and ancillary statistics for the nuisance parameters. The marginal likelihood for the parameters of interest is obtained through the marginal distribution of the ancillary statistics. The marginal likelihood that is obtained is compared to the concentrated likelihood function obtained by substituting the solution of the likelihood equations of the nuisance parameters for their parameter values in the full likelihood. Three special cases of the general model are considered as examples: models with structural disturbances, lagged variables models, and a polynomial distributed lag model.
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