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This paper collects monthly data for the United States from January 2005 to April 2021 and develops a time-varying parameter vector autoregressive model with stochastic volatility (TVP-SV-VAR) model to investigate the time-varying relationship between climate policy uncertainty, oil prices, and renewable energy consumption. In addition, this paper discusses the dynamic impact of climate policy uncertainty on five types of renewable energy consumption. Our results show that the relationship between them is time-varying. In most periods, climate policy uncertainty positively affects oil prices in the short and medium term, and positively affects total renewable energy consumption in the short and long term. In addition, the impact of climate policy uncertainty on the consumption of the five types of renewable energy is heterogeneous. The results of the robustness tests indicate that our results are robust and our study has important implications for the development of relevant policies. [ABSTRACT FROM AUTHOR]