We develop the first statistical matching micro approach reflecting the natural uncertainty of statistical matching arising from the identification problem in the context of categorical data. A complete synthetic file is obtained by imprecise imputation, replacing missing entries by
Additionally, we show how the results of imprecise imputation can be embedded into the theory of finite random sets, providing tight lower and upper bounds for probability statements. The results based on a newly developed simulation design–which is customised to the specific requirements for assessing the quality of a statistical matching procedure for categorical data–corroborate that the narrowness of these bounds is practically relevant and that these bounds almost always cover the true parameters.