Variation in the price of steel is an important factor to take into consideration when discussing cost control and management decisions in the construction industry. We employ various conventional and advanced econometrics methods to examine the interrelationships of steel prices in three related markets during the time period June 2002 to May 2010: Mainland China (CH), Taiwan (TW), and the United States (US). We adopt the Gregory and Hansen (GH) test and regime-switching (RS) model for cointegration, both of which accommodate endogenous structural break(s), to produce a more accurate analysis of a period in the presence of structural change(s). The empirical result of the RS cointegration test with respect to multiple structural breaks suggests a long-run equilibrium relationship among the three variables considered. This finding differs from the result of the GH test but confirms the result of the conventional Johansen test. Furthermore, the results of the Granger causality test indicate that both CH and US steel prices have great influence on the TW steel price; the Taiwanese steel market is closely linked with China and US steel markets in the long run.