Sylvain Leduc, Kevin Moran, and Robert J. Vigfusson in the FRBSF Economic Letter:
Why has consumption not responded more to cheap oil? Clearly, the U.S. economy was buffeted by headwinds over the past year, like weak foreign growth and the substantial appreciation of the dollar, that may have masked the positive effects of cheaper oil. Moreover, the decline in gas prices has been more muted than the drop in the price of oil. However, another possible reason is that the impact of changes in oil prices on the economy depends not only on the magnitude of the change, but also on its perceived persistence. Consumer spending is more likely to rise if people believe the decline in oil prices will last for a while; by contrast, if consumers think lower oil prices are not here to stay, they may simply decide to save what they don’t spend at the pump.
Figure 4: Estimated share of permanence in oil price movements