Pair copula constructions are highly flexible multivariate dependence models built from a cascade of bivariate copulas via iterative conditioning.A large number of estimation techniques for these models have been proposed,but almost all make the assumption that conditional pair copulas depend on the conditioning variables only through their conditional margins.This so-called simplifying assumption and its consequences remain the subject of current research.This talk will present a formal test of the simplifying assumption in trivariate pair copula constructions.The proposed test is based on the generalized likelihood ratio statistic,and uses a local likelihood estimator to specify the model under the alternative.The finite sample performance of the proposed test will be demonstrated using simulated and real data.The extension of the test procedure to higher dimensions faces some key challenges,including the generalization of the local likelihood methodology to accommodate multiple conditioning variables.These will be addressed in the talk,along with some recent developments.