This paper estimates the rebound effect for motor vehicle using a time-varying cointegrating regression model. We consider U.S. national data for 1976-2015. Our models allow the rebound effect to evolve over time and especially the rebound effect is modeled as a smooth function of time. This approach is motivated by some recent studies that report some evidence of declined rebound effect. Our estimates for time-varying rebound effect have shown a significant downward trend for the sample period.