This paper makes two contributions in relation to the use of information criteria for inference on structural breaks when the coefficients of a linear model with endogenous regressors may experience multiple changes. First, we show that suitably defined information criteria yield consistent estimators of the number of breaks, when employed in the second stage of a two‐stage least squares (2SLS) procedure with breaks in the reduced form taken into account in the first stage. Second, a Monte Carlo analysis investigates the finite sample performance of a range of criteria based on Bayesian information criterion (BIC), Hannan–Quinn information criterion (HQIC) and Akaike information criterion (AIC) for equations estimated by 2SLS. Versions of the consistent criteria BIC and HQIC perform well overall when the penalty term weights estimation of each break point more heavily than estimation of each coefficient, while AIC is inconsistent and badly over‐estimates the number of true breaks.