This paper introduces structural equations that do not satisfy the rank and/or order condition(s) for identification but still are identifiable. These equations are called seemingly unidentified structural equations. The key to the identifiability of these equations is that the right-hand-side endogenous variables undergo structural changes with respect to the exogenous and/or predetermined variables. To estimate the seemingly unidentified structural equations, this paper uses the classical minimum distance (MD) estimator and the principal components instrumental variables (PCIV) estimator. The PCIV estimator is different from conventional IV estimators for structural equations in that nonlinear functions of exogenous and/or predetermined variables are used as instruments. Simulation results comparing the estimator efficiency of the MD and PCIV estimators are reported in this paper. The results indicate that the MD and PCIV estimators are complementary to each other. The estimation methods proposed in this paper are applied to the Japanese export and GDP data to study the effect of export growth rate on that of GDP.