Identification schemes are of essential importance in structural analysis. This paper focuses on testing a commonly used long-run structural parameter identification scheme claiming to identify fundamental and non-fundamental shocks to stock prices. Five related widely used structural models on assessing stock price determinants are considered. All models are either specified in vector error correction (VEC) or in vector autoregressive (VAR) form. A Markov switching in heteroskedasticity model is used to test the identifying restrictions. It is found that for two of the models considered, the longrun identification scheme appropriately classifies shocks as being either fundamental or non-fundamental. A small empirical exercise finds that the models with properly identified structural shocks deliver realistic conclusions, similar as in the literature. On the other hand, models with identification schemes not supported by the data yield dubious conclusions on the importance of fundamentals 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 are properly captured, it is important to test the structural identification scheme.