Various identifying restrictions commonly used in small open economy structural vector autoregression (SVAR) models are tested against an SVAR model identified via Markov‐switching heteroskedasticity. The SVARs are estimated for three small open economies, Australia, Canada and New Zealand. The most supported model is the one that allows for simultaneity between monetary policy and the real exchange rate without restricting the long‐run response of the real exchange rate to a monetary policy shock. The impulse responses to a monetary policy shock and an exchange rate shock identified from such model are consistent with theoretical predictions.