The heterogeneity of household response to gasoline prices has key implications for the distributional impacts of gasoline taxation. However, this heterogeneity has mostly been assessed in a static framework, which ignores the dynamic nature of gasoline consumption. We contribute to this debate by developing a simple rational habits model of gasoline consumption, which allows to assess both rigidities on households' response to contemporaneous gasoline prices and forward-looking behavior vis-à-vis future gasoline prices. The parsimonious nature of this model makes it amenable to estimation on long-run household panel data, which allows the analysis of long-term responses. We estimate our model in the U.S. on the PSID panel dataset, using localized gasoline prices obtained from the Council for Community and Economic Research, for the period 1999-2015. We find that taking into account the dynamic features of gasoline demand yields a long-term price elasticity of -0.88, substantially larger than that reported from static models. Further, we find evidence that consumers are forward-looking in determining their gasoline consumption. Finally, after estimating the model by quintiles of income, we find evidence of significant heterogeneity in households long-term response across the income distribution, ranging from -1.44 to -0.7. Poorer households' gasoline consumption exhibits stronger habits, while richer households are more forward-looking. This implies that poorer households take longer to adjust their gasoline consumption to their long-term level. We finally combine these results to calculate the regressivity of a gasoline price increase corresponding to a $50/tCO2 carbon tax. We find suggestive evidence that as a consequence of dynamic heterogeneity, gasoline price increases are more regressive when occurring after a period of falling prices. These findings have important implications for the welfare impacts of policies fostering gasoline price increases, suggesting that they should be complemented with measures facilitating the adaptation of poorer households' gasoline demand.