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    An almost ideal demand system model of household vehicle fuel expenditure allocation in the United States

    BY Gbadebo Oladosu
    01/01/2003

    The Energy Journal, Vol. 24, No. 1. Copyright 10 2003 by the IAEE. All rights reserved.
    The author acknowledges the help of Mark Schipper of the Energy Information Administration in locating and acquiring survey data. The paper also benefited from the comments of two anonymous referees. The author remains solely responsible for any errors or omissions.
    Assistant Professor of Environmental Policy, School of Environmental Science, Engineering and Policy, Drexel University, 600 Nesbitt Hall, 33rd and Market Street, Philadelphia, Pennsylvania 19104, USA. E-mail: gao22@drexel.edu

    HEADNOTE:
    In this study I model vehicle-fuel expenditure allocation in multi-vehicle households based on the Almost Ideal Demand System (AIDS). Using data from surveys conducted by the Energy Information Administration in 1988, 1991 and 1994, I estimate the AIDS model, augmented with a comprehensive set of household and vehicle characteristics for households owning 1 to 4 vehicles ordered by vehicle age. Results show that vehicle characteristics are the most significant factors in the expenditure allocation process. Mean and standard deviation of price, expenditure and Allen substitution elasticities are calculated across households. Own-price elasticities for all vehicles are close to 1. Allen substitution elasticities indicate that all vehicle pairs are substitutes, and only vehicle I is found to be expenditure inelastic. The approach taken in this study enables a disentangling of vehicle allocation/substitution effects from aggregate household vehicle use behavior. This will be useful in the analysis of efficiency and distributional effects of policies affecting household transportation.

    ABSTRACT:
    This study models vehicle-fuel expenditure allocation in multi-vehicle households based on the Almost Ideal Demand System (AIDS). The AIDS model is estimated using data from surveys conducted by the Energy Information Administration in 1988, 1991 and 1994, augmented with a comprehensive set of household and vehicle characteristics for households owning 1 to 4 vehicles ordered by vehicle age. Results show that vehicle characteristics are the most significant factors in the expenditure allocation process. Mean and standard deviation of price, expenditure and Allen substitution elasticities are calculated across households. Own-price elasticities for all vehicles are close to 1. Allen substitution elasticities indicate that all vehicle pairs are substitutes, and only vehicle I is found to be expenditure inelastic. The approach taken in this study enables a disentangling of vehicle allocation/substitution effects from aggregate household vehicle use behavior. This will be useful in the analysis of efficiency and distributional effects of policies affecting household transportation.

    BODY:
    INTRODUCTION
    The United States transportation sector has important energy, environmental, and policy implications. With a quarter of total national energy use, about 95 percent of which are petroleum products, the sector is deeply affected by energy security issues such as dwindling domestic oil reserves, fluctuating world oil prices, and tightening refining capacity. Light trucks and cars, which are mostly driven by households, consume about two-thirds of total transportation energy use in the United States (EIA, 2001). This contributes to several serious environmental problems including ground-level ozone, carbon monoxide poisoning, particulate emissions, and greenhouse gas emissions.
    Although fuel prices in the US are among the lowest of the OECD economies, transportation energy policies remain a highly sensitive subject as demonstrated by the Clinton energy tax proposal of 1993 (Yohe, 1993; Burns, 2000). On the one hand, the ubiquity of transportation in social and economic activities means that effects of such price-based policies are rapidly transmitted throughout the economy. On the other hand, the effectiveness of price as a means of intervention in the transport market is subject to numerous externalities and price distortions (DeCiccio and Mark, 1998) .
    Given this, policy makers tend to shy away from price-based policies for resolving energy and environmental issues in the transportation sector. Instead, less visible measures, such as technology and emission standards, are employed. This is exemplified by the Corporate Average Fuel Efficiency (CAFE) standards. Established in 1975, CAFE standards led to a "doubling of passenger car economy and more than a 50 percent increase in light-truck MPG' from 1975 to 1984" (Greene, 1998). A host of other state and federal regulations, including provisions in the 1990 Clean Air Act, also address environmental problems emanating from the transportation sector. These programs, not unlike price-based policies, are sources of controversy. Some analysts argue the success of CAFE in reducing US transportation energy use, while others object on several grounds. Among the arguments that recently swayed the US Senate towards rejecting increases in the CAFE standards are safety and cost issues. The extent of take-back or rebound effects of the CAFE standards is another matter of debate. In addition, the US Environmental Protection Agency (EPA) contends that increases in households driving are offsetting ozone control achieved through clean-car regulations (EPA, 1993).
    Studies on transportation energy issues increased tremendously after the energy crunch of the 1970s. The majority of studies examine the effect of price changes, as well as income changes, on household transportation fuel use (see Espey 1998 for a meta-analysis). Others deal with the effectiveness of policies such as the CAFE standards (Greene, 1998; Greene et al., 1999; Goldberg, 1996). Most of these studies employ aggregate econometric models, sometimes modified by adding a vehicle choice model to correct for selectivity bias. However, aggregate models cannot capture the effects of many structural factors that are important determinants of household vehicle use. Golob et al. (1996) and Greene et al. (1999) pursue innovative approaches aimed at addressing this issue. Golob et al. (1996) employ a structural equations model of vehicle miles traveled (VMT) in two-vehicle households as a function of household and vehicle characteristics. The model was used to examine the direct and total effects of other endogenous variables (driver age, gender and employment) and exogenous variables on VMT for each vehicle. Starting from a household production function framework, Greene et al. (1999) specify a transportation model for five groups of 1-, 2-, 3-, 4- and 5-vehicle households. Each group's model consists of three simultaneous log-linear equations for vehicle use (miles), fuel economy (miles per gallon), and price ($/mile). Independent variables include household and vehicle characteristics. The model was used to calculate price elasticities and examine the size of the rebound effect.
    The current study follows the Golob and Greene path in developing a model of vehicle use in multi-vehicle households taking vehicle holdings as given.' We employ an Almost Ideal Demand System (AIDS) model of vehiclefuel expenditure, and include households with 1-4 vehicles. Our focus is on fuel expenditure allocation among vehicles rather than aggregate vehicle holdings use. Such a model enables an examination of price and income effects for individual vehicles. In addition, by capturing household, vehicle and market factors a comprehensive evaluation of the effectiveness, efficiency, and equity effects of current and proposed household transportation policies and technologies can be performed. The model is described in the next section, and the database used for its estimation is summarized in section 3. In the fourth section, estimation results and various elasticity calculations are discussed. The paper ends with a concluding section.
    II. MODEL DESCRIPTION
    III. DATA AND ESTIMATION
    Estimation of the above system is based on data from the 1988, 1991 and 1994 residential transportation energy surveys (RTECS) conducted by the Energy End Use and Statistics Division of the Energy Information Administration. Each of the surveys collected private transportation data from a sub-sample of respondents to the preceding year's residential energy consumption survey (RECS). Data collected include household characteristics, vehicle characteristics and use, and fuel prices. The EIA has tabulated these databases in considerable detail (EIA, 1990; EIA, 1993; EIA, 1997).
    Table 1 summarizes household and vehicle variables from the 1994 database. Distribution of area type, region, household size, age, race and gender in the sample matches those in the 1994 Statistical Abstract of the United States closely (US Census Bureau, 1995). The data show that about 87 percent of surveyed households own at least one vehicle, and almost 60 percent own at least two vehicles. However, less than 3 percent of households own more than four vehicles. There were 5,414 vehicles in the 1994 database, giving an average of about two vehicles per household. Numbering of vehicles in the survey was done by individual households, and can be expected to reflect both household and vehicle characteristics.6 Body type is composed mainly of Cars, with between 57 percent for the third vehicle and 68 percent for the first vehicle. Pickup Trucks come second with between 14 percent for the first vehicle and 27 percent for the third vehicle. Sport Utility vehicles, Minivans, Station Wagons, and Large Vans follow in that order accounting for between 2-7 percent.
    The remaining vehicle characteristics shown in Table 1; age, engine size, number of cylinders, fuel system, transmission type, and drive type affect vehicle performance and household driving pleasure. These will in turn affect allocation and fuel economy of vehicle use. Categorization of household and vehicle attributes for inclusion in the model is based on the need to separate out different effects, and available data. Table 2 is a summary of vehicle fuel use and expenditure data from the three RTEC surveys. Mean fuel efficiency rating for each vehicle is between 21-26 miles/gallon with a standard deviation of between 6-7 miles/gallon. Fuel price has a mean of about $1/gallon and a standard deviation of around 10 percent in each survey. Considerable variation in vehicle use across households can be observed with a standard deviation of about 50 percent for each vehicle and total miles driven. Mean use across vehicles is between 6,000-11,000 miles, while total mileage is around 18,000 miles.
    Based on the LR test alone, we cannot reject Model 1 for any of the alternative models. However, all models have very good, almost identical, RZ values for each share equation in the system. Own-price elasticities for all models lie between -0.36 and -1.01, with Models 3 and 4 having larger absolute values than Models 1 and 2. Models 1 and 2 have high and positive values for three of four mean own-Allen elasticities, whereas three of four in Models 3 and 4 have negative signs. Expenditure elasticities for the nonhomothetic models (Models 1 and 3) are virtually the same and close to unity. We report the results for Model 3 in this paper since it preserves non-- homotheticity of the system, while having non-positive mean own-price elasticities.
    A. Parameter Estimates
    Tables 4 and 5 contain parameter estimates (and standard errors) for the model. Statistically significant parameters are identified with super-script numbers in the table. We provide a discussion of these estimates below.
    Constant, Price and Efficiency Rating
    CONCLUSION
    Building on previous efforts, a household vehicle-fuel expenditure allocation model based on the Almost Ideal Demand System of Deaton and Muellbauer (1980) has been presented. This approach fits into both the multi-- budget and household production function frameworks, and incorporates a comprehensive set of household and vehicle characteristics. Parameters of the system of expenditure share equations are estimated using cross-sectional data for 7,272 United States households from the 1988, 1991 and 1994 RTECS. The model is a good fit to the data with RZ of around 0.7 for all equations. The most significant factors in the fuel expenditure allocation process are vehicle characteristics. All vehicles are substitutes for one another, but to different degrees. Vehicle 1 is expenditure inelastic, while all other vehicles are expenditure elastic.
    These results provide some useful insights into household vehicle use behavior. First, use of a flexible functional form allows elasticities to vary across households allowing for more detailed analysis of price and income effects. Thus, the standard deviation of calculated elasticities, especially expenditure and compensated price, are non-negligible. Second, price elasticities are not trivial although price coefficients are close to zero (see footnote 8). This is because elasticities derived from the AIDS involve both price and expenditure coefficients that capture the effect of price changes on real expenditure. The significant differences between compensated and uncompensated price elasticities in Table 6 emphasize this point. Another evidence on this effect is Kayser (2000). In that study, a positive price term coefficient was offset by a negative price-income interaction coefficient to produce a low, but negative, price elasticity. Third, this approach allows substitution/allocation effects to be disentangled from aggregate effects in household transportation decisions. Our findings on the importance of vehicle characteristics in household vehicle usage are in accordance with those of Green et al. (1999). The latter is the only other study to incorporate characteristics other than body type and fuel economy in a vehicle utilization model. The current approach also addresses a difficulty in multi-vehicle household modeling pointed out by Greene et al. (1999) that "including the characteristics, as well as the use of every other vehicle in each vehicle's own use equation leads to an unwieldy (and possibly unestimable) system of equations." By partitioning vehicle effects into vehicle-ownership and vehicle-characteristic effects, the model parsimoniously captures 304 own- and cross- vehicle effects by 92 parameters.
    What are the implications of these results for policy? Although the elasticities calculated in this study are for individual vehicles (ordered by vehicle age - see footnote 6), and therefore not directly comparable to those from most previous studies, it is safe to conclude that the corresponding aggregate household elasticities are likely to vary considerably across households. This implies that reliance on aggregate elasticities that are averages over household groups for policy formulation or simulation could be misleading. Groups on either side of such averages may respond differently from policy intentions, with consequences for fairness and overall effectiveness. The importance of vehicle attributes mean that policies affecting vehicle choice may be useful in changing vehicle use behavior. Although this lends some support to CAFE standards-type policies, the results also suggest that policy designs require careful evaluation. A policy may induce a single-vehicle household to respond in a number or mix of different ways including, disposing its vehicle, replacing and/or adding to vehicle holdings, and changing the pattern of vehicles) use. Policy responses in multi-vehicle households will be even more complex. The current model begins to capture some of these effects. Efficiency parameter estimates, for example, show that own-efficiency improvements in multi-vehicle households decrease expenditure allocation to that vehicle, but lead to increased allocation to other vehicles. This means that efficiency effects on total fuel use may be a net decrease or increase depending on the efficiency mix of vehicle holdings, fuel prices, and effects on real expenditures. The flexibility engendered by household substitution of vehicles is essential to measuring policy effects.
    The main limitations of the current exercise are related to issues of selectivity bias and violations of theoretical regularity conditions. Selectivity bias can be corrected by jointly estimating a vehicle choice model with the allocation model. Moreover, a vehicle choice model and an aggregate transportation demand model will be needed to complement the model in this study for policy analysis purposes. Violation of regularity conditions is an inherent problem of the AIDS and other flexible functional forms. This can be resolved, on the one hand, by imposing the corresponding conditions locally and examining the range of regularity around the point of interest. If the function remains regular over the practical region of interest the model would be useful for policy analysis. On the other hand, similar but more regular functional forms can be tested against the AIDS. Although the model based on our choice of vehicle ordering performs quite well as indicated by Table 3, it will be an interesting exercise to explore the effect of alternative orderings. In addition, alternative data types, such as panel data that traces households over time, will be needed to examine the dynamics of household vehicle use behavior. These and other extensions are reserved for future research.

    FOOTNOTE
    1. MPG = miles per gallon.
    2. A qualification to Golob et al. (1996) on the presence of selectivity bias applies to the current study. Selectivity bias results because vehicle holdings are considered exogenous, whereas travel requirements would be expected to influence vehicle choice. This source of bias also applies to Greene et al. (1999).
    3. See Jorgenson et al. (1982) and Filippini (1995) for similar incorporation of non-price variables in demand systems.
    4. As pointed out by Filippini (1995), use of the AIDS in the second stage of the two-stage household budgeting model is consistent with a one-stage framework. Further, as Kayser (2000) noted, the underlying model best derives gasoline consumption from a household production of transportation services. The above two-stage formulation is similar to the household production function formulation. For a strict household production function system, the AIDS can be used to specify a cost function, c,, , instead of e, . This will mean replacing u,, , with q, (a measure of aggregate production of transportation services), but the share equations will be otherwise identical to those derived here.
    5. See Jorgensen et al. (1982) on monotonicity and non-negativity in the Translog demand system (a flexible functional form similar to the AIDS). In the current model, we examine the mean elasticities of substitution matrix for regularity of the system at that point.
    6. In using the data for our analysis vehicle holdings for each household have been ordered from newest to oldest. As a reviewer noted, this is better than the alternative of random ordering although it imposes some structure on the data, Parameter estimates based on random ordering will be meaningless since vehicle ordering is inconsistent across households. This issue has not arisen in most previous uses of household vehicle data because individual vehicle effects are not usually considered. Golob et al. (1999) model household vehicle use in a manner similar to this study, and ordered vehicle holdings by age. The implication is that one must keep in mind that Vehicle 1 is the newest vehicle, Vehicle 2 is the second newest vehicle, and so on when interpreting the results.
    7. Note that definitions of the efficiency variable in these two models are different. The Greene et al. (1999) variable captures the effect of in-use conditions, while our variable is simply the efficiency rating. In use-conditions are captured in our model by household and vehicle factors that are explicitly incorporated.
    8. We call the reader's attention to the following caveat regarding price elasticity calculations. Survey data for 1988, 1991 and 1994 were used to estimate our model to account for lack of price variation in single-year cross-sectional data. However, it should be noted that this introduced a temporal variation of only + 1-5 percent to the price data, although there is some geographical price variation as well. As noted by a referee, this level of variation in the price data may have contributed to our insignificant price coefficient estimates.

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    LOAD-DATE: April 19, 2003

    by Gbadebo Oladosu on 1/1/03.