Updating the PPP puzzle: should we use nonlinear models?

We investigate the empirical support to the Purchasing Power Parity hypothesis in sixteen real exchange rates for the decade 1999-2009 by implementing Cointegrated VAR analysis, panel cointegration and nonlinear models. The theory is ejected and both the puzzles remain unsolved if considering linear models, while a nonlinear scenario seems to allow for a partial solution to the puzzle if adopting a modified General-to-Specific modelling strategy. The parameters restrictions commonly used in literature and the automatic use of symmetric transitions between different regimes when estimating the conditional mean are criticized and shown being two plausible candidates for explaining the puzzle.