Identification schemes are of essential importance in structural analysis. This paper focuseson testing a commonly used long-run structural parameter identification scheme claiming to identifyfundamental and non-fundamental shocks to stock prices. Five related widely used structural modelson assessing stock price determinants are considered. All models are either specified in vector errorcorrection (VEC) or in vector autoregressive (VAR) form. A Markov switching in heteroskedasticitymodel is used to test the identifying restrictions. It is found that for two of the models considered,the long-run identification scheme appropriately classifies shocks as being either fundamental or nonfundamental.A small empirical exercise finds that the models with properly identified structuralshocks deliver realistic conclusions, similar as in some of the literature. On the other hand, modelswith identification schemes not supported by the data yield dubious conclusions on the importance offundamentals for real stock prices. This is because their structural shocks are not properly identified,making any shock labelling ambiguous. Hence, in order to ensure that economic shocks of interest areproperly captured, it is important to test the structural identification scheme.