This paper sets out some tools for understanding the performance of the value added tax (VAT). Applying a decomposition of VAT revenues (as a share of GDP) to the universe of VATs over the last 20 years shows that developments have been driven much less by changes in standard rates than by changes in "C-efficiency" (an indicator of the departure of the VAT from a perfectly enforced tax levied at a uniform rate on all consumption). Decomposing C-efficiency for EU members into a "policy gap" (in turn divided into effects of rate differentiation and exemption) and a "compliance gap" (reflecting imperfect implementation) suggests that the former are in almost all cases far larger than the latter, with rate differentiation and exemptions playing roles that differ quite widely across countries.
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Michael Keen (2013) studied this question.