In view of the lack of harmonised EU statistics covering the distributional aspects of households' income, consumption and wealth in a single data set, an alternative commonly used to estimate that joint distribution is statistical matching. A main problem in statistical matching is that the relationship between income, consumption and wealth can be estimated only indirectly, relying on a strong assumption: the Conditional Independence Assumption (CIA), which might not hold and it is difficult to test. This work presents the tools to overcome the CIA, making it a justifiable hypothesis and testing it with the help of auxiliary information.