Predicting the click-through rate (CTR) in online ad auctions is essential for calculating bid amounts and forming rankings. However, predicting CTR from historical data faces some difficulties, one of which is the cold-start problem. Our research uses the instrumental variables (IVs) framework to address the cold-start problem and selection bias, validating robust CTR prediction in online advertising auctions. Although generally identifying IVs in wide applications is notably challenging, their potential use is not limited to CTR prediction; they can potentially be used to address practical issues and research questions in advertising auctions in general. We put forth bid amounts as IVs, discussing their validity as IVs and testing the robustness of predictions using IVs in both simulations and real data scenarios. Moreover, we enhanced our methodology by integrating explicit interactions between bid amounts and other features, demonstrating that accounting for heterogeneity in IVs significantly improves prediction accuracy in actual data. Our proposal on IVs and its refined CTR prediction approach enriches the research fields on causal inference robustness and invariant prediction.