According to rational bubble theory, housing prices are composed of economic fundamentals such as rent and the bubble component. While it is clear that non-causality between housing prices and rents serves as evidence of housing bubbles, within-city spillovers can be found in the causal relations. In other words, the causality test covers the detection of the housing bubbles or within-city spillovers underlying overheated housing markets. The purpose of this study is to propose a time-varying version of the Granger-causality test introduced by Shi et al. (J Financial Econom 18:158–180, 2020) in order to trace the status of housing markets across four first-tier cities in China. The empirical results indicate that there are various causal relationships, namely, within-city spillovers over time in Shanghai, Guangzhou and Shenzhen, while exuberant behavior with a housing bubble are especially noteworthy in the case of Beijing.