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Kevin Drum recently set off a round of debate in the blogosphere lately with a post about the price elasticity of oil and carbon taxes. He cited an IMF study that showed a long-run price elasticity of oil demand of -0.035. What this means is if oil prices go up 10%, then the long-run demand for oil goes down 0.35%. The implication he draws is that any reasonably priced carbon tax isn’t going to have much of an impact on demand, and so it’s not going to be an effective policy for reducing carbon emissions. There’s obviously some problems with this, some of which has already been covered by Ryan Avent, Megan McArdle, and Kevin Drum himself, with Jim Manzi and Kevin Drum, again, on the other side. Importantly, as Alex Tabarrok pointed out, this is but one estimate of the price elasticity of demand for oil, and it’s smaller than what you find in the literature. The following table from a James Hamilton paper, also linked to by Alex, reports the results of several literature reviews of oil and gasoline price elasticities:

As you can see, all of these elasticities are significantly above the IMF estimate. However, there have been several recent studies, including the Hamilton study, that argue that the price elasticity of demand has decreased in the past decade. Hamilton, in fact, argues that markets were surprised by how low the global price elasticity of demand was, and the unresponsiveness of demand explains the high gas prices of 2007-2008.

Another recent studyby Hughes, Knittel, and Sperling,  found short-run gas price elasticities of -0.034 to -0.077 for 2001-2006 compared to the much larger elasticities for 1975-1980, which range from -0.21 to -0.34. While these numbers are larger than the IMF numbers, they are never the less low and indicate that the average elasticities found in past studies may be too big.

However there are important caveats to these estimates that suggest the real current elasticity is higher. First, the evidence has indicated that the response of demand to price changes is asymmetric: price increases cause a larger response to demand than price decreases. This is because price increases are more likely to cause shifts to newer, more energy efficient technologies than price decreases are to undo such shifts. Any estimate of the average price elasicity then will be a downward biased estimate for the likely response to a price increase.

recent paper by Davis and Killian The Journal of Applied Economics covers some other econometric issues in the literature. For instance, we know price and quantity demanded are jointly determined, which means that there will be a correlation between the price variable and the errors such that single equation or panel data methods, like those used in the reported IMF estimates,  will bias estimates towards zero.  Some studies attempt to use exogeneous oil shocks as instrumental variables. This approach is used in the appendix to the IMF study. But this requires the assumption that consumers will respond the same to these shocks as to normal real price appreciation. If consumers expect shocks to be more temporary than a demand led increase in price, this is a questionable assumption.

As Killian and Davis point out, another serious problem with these estimates is that they estimate the price elasticity of demand, and not the tax elasticity of demand. They argue:

“…the response of gasoline consumption to a change in tax is likely to differ from its response to an average change in  price. Price changes induced by tax changes are more persistent than other price changes and thus may induce larger behavioral changes. In addition, gasoline tax increases are often accompanied  by media coverage that may have an effect of its own.”

To overcome these issues, they look at U.S. state level demand for gasoline. Their results shed some interesting light on how the econometric mispecifications affect elasticity estimates. Using a single equation model they estimate an elasticity of -0.10. Using a panel data method, as done in the IMF study, the elasticity increases to -0.19. And finally using changes in state level gas taxes as an instrument they find an elasticity of -0.46, which more than four times larger than the single equation model.

 They conclude with an important caveat about the literature:

Overall, our results indicate that gasoline consumption is more sensitive to gasoline taxes than  would be implied by recent estimates of the gasoline price elasticity. Even under the largest plausible estimates, however, gasoline tax increases of the magnitude that have been discussed  would have only a moderate short-run impact on total US gasoline consumption and carbon  emissions based on our estimates. A natural conjecture is that the long-run elasticities will be larger,  but standard econometric models based on historical data do not allow the prediction of such long-run effects.

The International Handbook on the Economics of Energy also puts these estimates in the correct context:

Whatever their scope and origin, estimates of price elasticities should be treated with caution. Aside from the difficulties of estimation, behavioural responses are contingent upon technical, institutional, policy and demographic factors that vary widely between different groups and over time. Demand reponses are known to vary with the level of prices, the origin of the price changes (for example, exogenous versus policy induced), expectations of future prices, government fiscal policy (for example, recycling of carbon tax revenues), saturation effects, and other factors (Sorrel and Dimitropoulos, 2007). The past is not necessarily a good guide to the future in this area, and it is possible that the very long-run response to price changes may exceed those found in empirical studies that from relatively short time periods.

The evidence certainly seems to suggest that more recent estimates are better than earlier ones, but for a variety of reasons these will underestimate the long-run elasticities.

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