Fuel efficiency and motor vehicle travel: the declining rebound effect
Summary (4 min read)
1. Introduction
- It has long been realized that improving energy efficiency releases an economic reaction that partially offsets the original energy saving.
- When vehicles are made more fuel-efficient, it costs less to drive a mile, so VMT increases if demand for it is downward-sloping.
- Just like income changes, changes in fuel prices affect the share of fuel costs in the total cost of driving, and so the authors also expect them to influence the rebound effect.
- Future values of the rebound effect depend on how those factors evolve.
- Section 3 presents their theoretical model and the econometric specification, and section 4 presents estimation results.
2. Background
- The rebound effect for motor vehicles is typically defined in terms of an exogenous change in fuel efficiency, E. Fuel consumption F and motor-vehicle travel M – the latter measured here as VMT per year – are related through the identity F=M/E.
- Most studies assume that that travel responds to fuel price PF and efficiency E with equal and opposite elasticities, as implied by the definition of the rebound effect based on the combined variable PM=PF/E. unimportant.
- Here, autocorrelation and the effects of a lagged dependent variable are measured with sufficient precision to distinguish them; they obtain a statistically significant coefficient on the lagged dependent variable, implying a substantial difference between long and short run.
- The authors attempt to remedy this in their empirical work.
- Disaggregate studies tend to produce a greater range of estimates; but those that exploit both cross-sectional and temporal variation are more consistent, finding a long-run rebound effect in the neighborhood of 20-25 percent.
3.1 System of Simultaneous Equations
- The authors empirical specification is based on a simple aggregate model that simultaneously determines VMT, vehicles, and fuel efficiency.
- Fuel efficiency is determined jointly by consumers and manufacturers accounting for the price of fuel, the regulatory environment, and their expected amount of driving; this process may include manufacturers’ adjustments of the relative prices of various models, consumers’ adjustments via purchases of various models (including light trucks), consumers’ decisions about vehicle scrappage, and driving habits.
- The standard definition of the rebound effect can be derived from a partially reduced form of (1), which is obtained by substituting the second equation into the first and solving for M. Denoting the solution by M̂ , this produces: ( )[ ] ( )VMVMMMVMV XXPPMXPXPPMVMM ,,,ˆ,,,,ˆˆ ≡= .
- (2) We call this equation a “partially reduced form” because V but not E has been eliminated (E being part of the definition of PM); thus the authors still must deal with the endogeneity of PM as a statistical issue.
- (3) Strictly speaking, the estimation of a statistical model proves associations, not causation.
3.2 Empirical Implementation
- While most studies reviewed in the previous section are implicitly based on (2), the authors estimate the full structural model based on system (1).
- Second, the authors allow for behavioral inertia by including the one-year lagged value of the dependent variable as a right-hand-side variable.
- Variable pf is the log of fuel price; hence log fuel cost per mile, pm, is equal to pf+fint.
- If variable pm were included only in the form shown in (4), the structural elasticity εM,PM would just be its coefficient in the usage equation, m 1β .
- Since the other terms in (6) are small, this means that m1β− is approximately the short-run rebound effect at those mean values.
3.3 Variables
- This section describes the main variables in (4) and their rationale.
- Next, this equation is interpreted as a partial adjustment model, so that the coefficient of lagged fuel intensity enables us to form a predicted desired fuel intensity for each state in each year, including years after 1977.
- For their preferred specification, the authors apply a correction assuming that the census counts are accurate and that the error in estimating population between them grows linearly over that ten-year time interval.
- The authors show them for the original rather than the logged version of variables; they also show the logged version after normalization for those variables that enter the specification through interactions.
4.1 Structural Equations
- Each table shows two different estimation methods: threestage least squares (3SLS) and ordinary least squares (OLS).
- In addition, the inclusion in their specification of pm^2 ≡ (pf+fint)2 requires including as instruments those combinations of variables that appear when fint is replaced by its regression equation and (pf+fint)2 is expanded.
- The negative effect of adults/road-mile can equivalently be viewed as confirmation that increasing road capacity produces some degree of induced demand, a result found by many other researchers.
- The results also suggest that CAFE regulation had a substantial effect of enhancing the fuel efficiency of vehicles – at its maximum value of 0.35 in 1984, the cafe variable increased long-run desired fuel efficiency by 21 percent.
4.2 Rebound Effects and Other Elasticities
- And some other elasticities implied by the structural models.
- Thus differences among OLS results in the literature, and differences between those results and ours, may be caused as much by differences in specification as by endogeneity bias.
- Thus the rebound effect decreased in magnitude over their sample period; their base specification attributes this decrease mostly to rising incomes but partly to falling fuel prices.
- 25 This scenario happens to put pm at its sample average, and thus enables us also to see the effect of rising income without falling fuel prices.
- Combining it with the elasticity of vehicle-miles traveled gives the total price-elasticity of fuel consumption, shown in the last panel of the table.
4.3 Estimates on separate time periods
- As noted, the authors find the rebound effect to be much smaller when computed for values of per capita income characterizing recent years than when computed for average values over the 36- year estimation period.
- Furthermore, the coefficient of lagged vma in the usage equation is considerably smaller (0.55 to 0.58) when estimated on these subsamples than when estimated on the full sample.
- Nevertheless, the summary results in Table 6 clearly show the hypothesized decline in the rebound effect as the authors move from the first two periods to the last period.
- Except for the first period, the long-run estimates agree closely with these full-model predictions.
4.4 Other Specifications and Estimation Methods
- As the authors have seen, fuel prices are potentially important for the rebound effect; but their influence depends on a coefficient (that of pm^2) whose estimate is statistically imprecise.
- The authors also show some 2SLS results for both the full model and this reduced model, in order to examine more carefully whether specification error in the model could be adversely affecting the 3SLS estimates.
- Third, with 3SLS, the simplified specification is somewhat more conservative than the full specification in predicting how much the rebound effect has declined during the period; but it is more radical in the predicted effect of income because this simplified specification does not use fuel prices to help explain the decline.
- The third pair of columns in Table 7 shows the results of using a Generalized Method of Moments (GMM) estimator that allows the residuals to be correlated arbitrarily over time and for their variances to vary over time.
- This results in total fuel consumption responding more sensitively to changes in fuel prices or in the stringency of cafe standards.
4.5 Caveats
- The authors call attention to three limitations.
- The posited sources of measurement error are mostly unrelated to their independent variables; and even if they were, their use of fixed effects eliminates the spurious effect of any cross-state relationship that is consistent over time.
- One might worry that errors in measuring fuel consumption by state could appear in both VMT data (in those states where the VMT estimate is based on fuel consumption) and in fuel efficiency.
- 33 Second, their estimates, like those of most previous studies, rely on the theoretical restriction that people react to changes in cost per mile in the same way whether those changes arise from variations in fuel prices or in fuel efficiency.
- It appears that the time-series properties of the usage equation are poorly identified when pf and fint are allowed to have separate effects.
5. Conclusion
- The authors study supports many earlier findings that the long-run rebound effect, i.e. the elasticity by which changes in fuel efficiency affect the amount of driving, was 20-25% in the U.S. over the last third of the 20th century.
- The rebound effect is likely to diminish still further as rising incomes reduce the significance of fuel costs in decisions about travel, although this may be offset to some extent by increases in fuel prices.
- The authors model as estimated can be used to forecast the dynamic adjustment path resulting from specific policies.
- In urbanized areas, traffic congestion is an endogenous part of the system explaining reactions to changes in fuel efficiency.
- The degree to which the CAFE regulations have affected fleet fuel efficiency remains uncertain.
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Frequently Asked Questions (15)
Q2. What future works have the authors mentioned in the paper "Fuel efficiency and motor vehicle travel: the declining rebound effect" ?
The question of CAFE ’ s effects remains an interesting area for future research, and the authors believe their approach offers a better chance of resolving it than previous attempts. To make further progress probably requires estimating models that disaggregate the passenger-vehicle fleet into the two categories, cars and light trucks, that are regulated differently under CAFE.
Q3. What is the importance of obtaining reliable measures of it?
Obtaining reliable measures of it is important because it helps determine the effectiveness of measures intended to reduce fuel consumption and because increased driving exacerbates congestion and air pollution.
Q4. How do the authors eliminate spurious effects of such correlations?
In their work, the authors eliminate the spurious effects of such crosssectional correlations by using fixed-effects specification, i.e. by including a dummy variable for each state.
Q5. What is the reason why Goldberg estimates the rebound effect?
Goldberg (1998) estimates the rebound effect using the Consumer Expenditure Survey for the years 1984-1990, as part of a larger equation system that also predicts automobile sales and prices.
Q6. What makes the simplified specification a suitable estimator?
the stability of the simplified specification lends support to the view that the model is well specified, making 3SLS a suitable estimator.
Q7. What is the reason why the recent studies use micro data?
Two recent studies use micro data covering several different years, thereby takingadvantage of additional variation in fuel price and other variables.
Q8. Why does their model have a dynamic component?
Because their model has a dynamic component, it could predict the year-by-year response to such a policy while taking into account projected changes in income and fuel prices — although the reliability of doing so diminishes if projected values lie outside the ranges observed in their data.
Q9. What is the estimate of the rebound effect for the US?
Their best estimates of the rebound effect for the US as a whole, over the period 1966-2001, are 4.5% for the short run and 22.2% for the long run.
Q10. What is the significance of the aggregate studies?
These aggregate studies highlight the possible importance of lagged dependent variables(inertia) for sorting out short-run and long-run effects.
Q11. What is the elasticity of the VMT with respect to lane miles?
22 Their implied long-run elasticity of VMT with respect to road-miles is 0.020//(1-0.7907)≈0.1, considerably smaller than the long-run elasticities with respect to lane-miles of 0.8 found by Goodwin (1996, p. 51) and Cervero and Hansen (2002, p. 484).
Q12. What is the conservative approach to explain the rebound effect?
In terms of policy, the full specification with 3SLS also happens to be the most conservative approach in explaining their main result, which is that the rebound effect declines with income.
Q13. How much is the rebound effect in the long run?
Thus the average rebound effect in this sample is estimated to be approximately 4.5% in the short run, and 22.2% in the long run.respectively.
Q14. What is the reason why the richer specification is unreliable?
the authors believe that this richer specification is unreliable because it over-fits the data: coefficients on a variable and its lag are in several instances large and opposite in sign, and the predicted desired fuel intensity show implausible oscillations over time.
Q15. What is the suitable base specification for the study?
the authors believe their base specification is the most suitable one given the short time period over which the authors can observe pre-CAFE behavior.