We study time-varying price leadership between international stock markets using a Markov switching causality model. We demonstrate variations in the causality pattern over time, with the US being the dominant country in causing other markets. We examine the factors which determine a country’s role in the causal relationship. For country-specific factors, we show that trades openness increases price leadership. We also find that the lead–lag relationship between the stock markets is weaker during crisis periods, confirming the “wake-up call” hypothesis, with markets and investors focusing substantially more on idiosyncratic, country-specific characteristics during the crisis