Statistical matching is a technique for integrating two or more data sets when information available for matching records for individual participants across data sets is incomplete. Statistical matching can be viewed as a missing data problem where a researcher wants to perform a joint analysis of variables that are never jointly observed. A conditional independence assumption is often used to create imputed data for statistical matching. We consider a general approach to statistical matching using parametric fractional imputation of Kim (2011) to create imputed data under the assumption that the specified model is fully identified. The proposed method does not have a convergent expectation-maximisation (EM) sequence if the model is not identified. We also present variance estimators appropriate for the imputation procedure. We explain how the method applies directly to the analysis of data from split questionnaire designs and measurement error models.