Transitioning to renewable energies has become undeniably important in recent decades, especially for the United States. Oil price shocks are prominent determinants of renewable energy. Hence, this study examines the impacts of oil supply, aggregate demand, and oil-specific demand shocks on renewable energy consumption from 1973:01 to 2021:05 using Structural VAR and Time-Varying Parameter VAR models. Based on the results, oil supply shocks generally have a negligible effect on renewable energy, except those that originate from sharp changes in Saudi Arabian oil production and the U.S. recession-induced oil supply deficit. Aggregate demand shocks, such as those caused by the Persian Gulf War and the Asian financial crisis, negatively affect renewable energy by reducing investments and making oil more affordable. Conversely, oil-specific demand shocks, such as the 1979 Iranian Revolution and the 2008 financial crisis, initially reduce renewable energy attractiveness but ultimately lead to increased renewable energy consumption due to soaring oil prices. This study’s unique approach of separately examining global oil market shocks provides new insights, complementing and extending previous research on the relationship between oil prices and renewable energy consumption. Eventually, policy implications for strengthening incentive policies and adding punitive policies to seeking investment in renewable energy are proposed.