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    An Almost Ideal Demand System model of household vehicle fuel expenditure allocation in the United States

    BY Oladosu, Gbadebo
    01/01/2003
    by Oladosu, Gbadebo on 1/1/03.

    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. A lien substitution elasticities indicate that all vehicle pairs are substitutes, and only vehicle 1 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.
    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 (1) 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 rebou nd 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 endogen ous 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. (2) We employ an Almost Ideal Demand System (AIDS) model of vehicle-fuel 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
    We assume a two-stage budgeting model of household consumption decisions in which vehicle-fuel expenditure is weakly separable from all other goods in the household's budget. Vehicle-fuel expenditure in the lower stage is specified using the Almost Ideal Demand System (AIDS) of Deaton and Muellbauer (1980). For a household, h, having x = 1.. .i household characteristics and owning v or z = 1...j vehicles each described by r = 1...k vehicle characteristics, we define the following notations:
    [e.sub.h] is total fuel expenditure on vehicle holdings;
    [u.sub.h] is household utility from vehicle holdings use;
    [p.sub.v] is the fuel price for vehicle v;
    [y.sub.s, h] is the dummy for household h's characteristic x;
    [C.sub.r, v, h] is the dummy for characteristic r of vehicle v in household h;
    [m.sub.v,h] is the efficiency rating of vehicle v in household h;
    [g.sub.v,h] is a value function derived from vehicle v's k characteristics in household h;
    P, [Y.sub.h], [C.sub.v,h], [M.sub.h], [G.sub.h] are vectors/matrices of [p.sub.v], [y.sub.x,h], [c.sub.r,v,h], [m.sub.v,h] and [g.sub.v,h], respectively;
    [[alpha].sub.0], [[alpha].sub.v], [[gamma].sub.v,z], [[phi].sub.v,x], [[mu].sub.v,z] [[theta].sub.v,z], [[beta].sub.0], [[beta].sub.v] are parameters of the model;
    [beta], [alpha], [gamma], [phi], [mu] and [theta] are vectors/matrices of [[beta].sub.v], [[alpha].sub.v], [[gamma].sub.v,z], [[phi].sub.v,x], [[mu].sub.v,z] and [[theta].sub.v,z], respectively.
    The complete AIDS expenditure system, augmented with household and vehicle characteristics, is: (3)
    ln [e.sub.h] ([u.sub.h], P, [Y.sub.h], [G.sub.h]) = ln a(P, [Y.sub.h], [G.sub.h]) + [u.sub.h] ln b(P) (1)
    where
    ln a(P, [Y.sub.h], [G.sub.h]) = [[alpha].sub.0] + [summation over (v)] [[alpha].sub.v]ln[p.sub.v] + 1/2 [summation over (v,z)] [[gamma].sub.v,z] l[np.sub.v] l[np.sub.z] + [summation over (v,z)] [[micro].sub.v,z] l[np.sub.v] l[nm.sub.z,h] + [summation over (v,x)] [[phi].sub.v,x] l[np.sub.v][y.sub.x,h] [summation over (v,z)] [[theta].sub.v,z] l[np.sub.v][g.sub.z,h] (2)
    lnb(P) = [[beta].sub.0] [[PI].sub.v][p.sup.[beta]v.sub.v] (3)
    [g.sub.v,h] = f([C.sub.v,h]) (4)
    f(*) is a functional transformation of vehicle characteristics.
    Fuel expenditure share for each vehicle, [w.sub.v,h], is derived by applying Shepard's Lemma to equation 1: (4)
    [w.sub.v,h] = [[alpha].sub.v] + [summation over (z)] [[gamma].sub.v,z]ln[p.sub.z] + [summation over (z)] [[micro].sub.v,z]ln[m.sub.z,h] + [summation over (x)] [[phi].sub.v,x][y.sub.x,h]
    + [summation over (z)] [[theta].sub.v,z][g.sub.z,h] + [[beta].sub.v]ln([e.sub.h]/[Q.sub.h]) (5)
    where [Q.sub.h] is a household price index given by
    ln[Q.sub.h] = [[alpha].sub.0] + [summation over (v)] [[alpha].sub.v]ln[p.sub.v] + 1/2 [summation over (v,z)] [[gamma].sub.v,z]ln[p.sub.v]log[p.sub.z] + [summation over (v,z)] [[mu].sub.v,z]ln[p.sub.v][m.sub.z,h]
    + [summation over (v,x)] [[phi].sub.v,x]ln[p.sub.v][y.sub.x,h] + [summation over (v,z)] [[theta].sub.v,z]ln[p.sub.v][g.sub.z,h] (6)
    and
    [[gamma].sub.v,z] = ([[gamma].sup.*.sub.v,z] + [[gamma].sup.*.sub.z,v])/2 (6)
    Since the AIDS does not satisfy the conditions for household utility maximization automatically, the conditions are usually imposed in empirical estimation. However, it is impossible to impose monotonicity and non-negativity conditions globally. We impose adding-up, symmetry and homogeneity on the system, leading to the following restrictions on parameters: (5)
    Adding up: [summation over (v)] [[alpha].sub.v] = 1; [summation over (v)] [[gamma].sub.v,z] = 0; [summation over (v)] [[beta].sub.v] = 0; [summation over (v)] [[mu].sub.v,z] = 1; [summation over (v)] [[phi].sub.v,x] = 0; [summation over (v)] [[theta].sub.v,z] = 0 (7)
    Symmetry: [[gamma].sub.v,z] = [[gamma].sub.z,v] (8)
    Homogeneity: [summation over (z)] [[gamma].sub.v,z] = 0; (9)
    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 follo w 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.
    Dependent and independent variables for the model are derived from the database as follows. Fuel expenditures shares are based on real expenditures. We use the consumer price index (base 1994) to calculate real expenditures ([10.sup.3]$ ) and real prices ($ /gallon) from nominal values. Fuel efficiency rating ([10.sup.1] miles-per-gallon) is the [MPG.sub.EPA55/45] data. Each household and vehicle characteristic category shown in Table 1 is converted into a dummy variable. We include data for households with 1-4 vehicles since the number of observations for more than four vehicles is small. As explained in section 2, vehicle characteristics enter the model through the value function, [g.sub.v,h], which we specify as:
    [g.sub.v,h] = [vo.sub.v,h] x exp([summation over (r)] [[lambda].sub.r,v] [c.sub.r,v,h]) (10)
    where [vo.sub.v,h], is a dummy variable equal to 1 if a household owns the [v.sup.th] vehicle, and zero otherwise. Parameter [[lambda].sub.r,v], captures the effect of vehicle characteristics [c.sub.r,v,h] in an exponential manner. This transformation follows the practice in vehicle choice studies where logit or multinomial models use the exponential function to derive latent vehicle values from characteristics (see Kayser, 2000; Mannering and Winston, 1985; and Henscher et al. 1989). Given this specification, vehicle effects in our model are captured through parameters [[theta].sub.v,z] and [[lambda].sub.r,v]. We refer to these as vehicle-ownership and vehicle-characteristics effects, respectively. To simplify the AIDS model, the price index, [Q.sub.h], is usually approximated using the Stone's index. We adopt this practice here, so that [Q.sub.h] is calculated from the data as
    ln [Q.sub.h] = [summation over (v)] [w.sub.v,h] ln[p.sub.v] (11)
    A stochastic term is added to each share equation in the system. We assume that these error terms sum to zero across vehicles for each household; but are not independently distributed. We also assume that the error terms have the same covariance matrix for each household (Jorgenson et al. 1982). Dropping the household subscript, the estimated system of equations is:
    [w.sub.v] = [[alpha].sub.v] + [summation over (z)] [[gamma].sub.v,z] ln[p.sub.z] + [summation over (z)] [[micro].sub.v,z] ln[m.sub.z] + [summation over (x)] [[phi].sub.v,x][y.sub.x]
    + [summation over (z)] [[theta].sub.v,z][[vo.sub.z] exp ([summation over (r)] [[lambda].sub.r,z][c.sub.r,z])] + [[beta].sub.v]ln(e/Q) + [[epsilon].sub.v] (12)
    where [[epsilon].sub.v] is the random error term. This is a simultaneous 4-equation model with a singular covariance matrix. By assuming that [[epsilon].sub.v] is normally distributed, we can use a maximum likelihood (ML) estimator to estimate parameters of three of these equations and calculate those of the fourth equation using equations (7) to (9). The ML estimator is invariant to which equation is dropped. In addition, the first category of each household and vehicle characteristic in Table 1 is dropped from the model. Therefore, the reference household for the model has (i) the dropped household characteristics, and (ii) ownes 1-4 vehicles, each of which is described by the dropped vehicle characteristics. Based on the above, 7,272 of the 9,033 observations in the database are suitable for model estimation. The equations are estimated using the Full Information Maximum Likelihood (FIML) facility of the Time Series Processor (TSP) econometric software.
    Parameter estimates are used to calculate price elasticities, expenditure elasticities, and substitution elasticities for each household and vehicle in the sample. Elasticity calculations are based on the following equations:
    Uncompensated Price Elasticity, [[epsilon].sub.v,z]:
    [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
    Expenditure Elasticity, [[eta].sub.v]:
    [eta].sub.v] = 1 + [[beta].sub.v]/[w.sub.v] (14)
    Compensated Price Elasticity, [U.sub.v,z]
    [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)
    Elasticity of Substitution, [[sigma].sub.v,z]:
    [[sigma].sub.v,z] = 1 + [[gamma].sub.v,z]/[w.sub.v][w.sub.z] for v [not equal to] z and [[sigma].sub.v,z] = [[epsilon].sub.v,z]/[w.sub.v] for v = z (16)
    IV. RESULTS
    Several versions of the above system of equations are estimated as summarized in Table 3. The model specification in section 2 is the "unconstrained" or null model (Model 1). Homotheticity and non-positivity of diagonal elements of the price coefficients matrix, [gamma], are then imposed on the system (Models 2-4). Models 2-4 are compared against Model 1 based on goodness-of-fit criteria ([R.sup.2] and Likelihood-Ratio tests), mean own-price elasticities, mean expenditure elasticities, and mean own-Allen elasticities. Non-positive own-price elasticities and Allen elasticities are necessary but insufficient conditions for regularity of the household expenditure function.
    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, [R.sup.2] 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 non-homothetic 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
    The constant term is significant for vehicles 2 and 3, with estimates of 0.78 and 0.16, respectively. The calculated value for vehicle 4 is 0.07. Interpretation of the constant term as the intercept is not strictly applicable in this model. When all variables take a value of zero (corresponding to the reference household, a price level of $ 1/gallon, total real fuel expenditure of $ 1000, and vehicle fuel efficiency rating of 10 mpg), the vehicle value function, [g.sup.v,h], takes a value of unity. Thus the product of dummy variable, [vo.sub.v,h], and the vehicle-ownership parameter, [[theta].sub.v,z], become constant terms in the share equations. For a 4-vehicle reference household, the resulting values are the column sums of the constant terms and elements of the vehicle-ownership parameter matrix. These values are 0.23, 0.19, 0.28, and 0.30 for vehicles 1, 2, 3, and 4, respectively. For a 1-vehicle reference household only vehicle 1's share equation is relevant, and the resulting value is 1.12. Of course, th e share value for any 1-vehicle household is necessarily unity.
    All elements of the price parameter matrix ([gamma]) are insignificant and close to zero. Given the direct relationship between fuel economy and use, Table 4 shows that only three of the sixteen efficiency parameters are insignificant. All diagonal elements are negative, while all off-diagonal elements, except [[micro].sub.3,1], are positive. This implies that efficiency increases will have negative own-vehicle effects and positive cross-vehicle effects on expenditure allocation. One area of discussion in the literature is the symmetry of price and fuel economy effects on household fuel use. Greene et al. (1999) found that symmetry of price and efficiency effects is not rejected for most of the samples in their study.
    Symmetry in the current model requires price and efficiency coefficients to have the same magnitude, but opposite signs. Since this is not the case in Model 3, we impose these conditions and re-estimate the model. The 2xLR for the two model variants is 230. Therefore Model 3 (non-symmetry of price and efficiency effects) cannot be rejected. (7)
    Expenditure
    Coefficients of the log of "real" expenditure are significant for vehicles 1, 2, and 3. According to Deaton and Muellbauer (1980), these coefficients should be negative for necessities and positive for luxuries. Interestingly, the estimate for vehicle 1 is negative, while those for the remaining vehicles are positive. These estimates are consistent with simultaneous shifting of some transportation load away from the first vehicle, and increasing total expenditure. The size of the coefficient estimates suggest that the shifting effect is largely restricted to vehicles 1 and 2.
    Household Characteristics
    Only a few household characteristic parameters prove to be significant. Income categories 3 and 5 are significant and negative for vehicle 3. None of the area type dummies is significant, and only the West is barely significant among regional dummies. Among member and driver size dummies, household size category 3 for vehicle 4 and driver size category 3 for vehicle 3 are significant. Education category 2 is significant for vehicles 1 and 4, while category 3 is significant for vehicle 2.
    Vehicle Characteristics
    All elements of the vehicle-ownership parameter matrix are significant at the 1 % level. This suggests that vehicle interaction is an important factor in household fuel expenditure allocation. Among vehicle characteristics, vehicle type, age and cylinder size are significant for most vehicles, while engine size, fuel system, transmission type and drive type are less so.
    The effect of a change in characteristic r of vehicle z on vehicle v's expenditure share, [[DELTA].sub.r,z] [w.sub.v], can be stated as:
    [[DELTA].sub.r,z] [w.sub.v] = [[theta].sub.v,z] [vo.sub.z][ exp ([[lambda].sub.r,z]) - 1 ] (17)
    When [vo.sub.z] is equal to 1, vehicle-characteristics effects (captured by the term in square brackets) will be negative, zero, or positive depending on whether [[lambda].sub.r,z] is negative, zero, or positive, respectively. These effects are weighted by vehicle-ownership parameters, [[theta].sub.v,z], to determine the ultimate sign and magnitude of vehicle effects on expenditure shares.
    Discussion of vehicle effects can be simplified by observing the following. All diagonal elements of the vehicle-ownership parameter matrix are positive, while all off-diagonal elements are negative. Apart from matching our expectations, this observation implies that own- and cross-vehicle-ownership effects will change expenditure shares in opposite directions. Thus, the sign of a characteristic's own-vehicle effects will be the same as that carried by its estimated coefficient, and opposite for cross-vehicle effects. Given this, the discussion below focuses on vehicle 1's own-characteristic effects.
    The own-vehicle-ownership parameter for vehicle 1 is 1.12. This is consistent with the fact that all households in the database own at least one vehicle (vehicle 1). Body type coefficients are all positive for vehicle 1. Thus, compared to Cars, other body types will increase vehicle 1's expenditure allocation, holding all other variables constant. Large Vans have the largest effect followed by Minivans, Station Wagons and Sport Utility Vehicles. The effect of vehicle age on vehicle 1 is positive for the 3-5 year age category, but negative for other categories. The positive coefficient is insignificant and small. Thus, one may conclude that vehicle 1 is used less as it gets older. Relative values of the coefficients for Vehicles 2-4 lead to the same conclusion for each vehicle. Coefficients for number of cylinders in vehicle 1 are all positive, while that for engine size, are all negative. However, those for cylinders are significant while those for engine size are not. Rear wheel drive has a negative and sign ificant coefficient, while 4-wheel drive has a positive but insignificant coefficient for vehicle 1. Expenditure allocation also favors fuel injection vehicles over diesel systems for vehicle 1. Given that transmission type is likely to be more of a driving convenience feature, the coefficient estimate for manual transmission can be expected to be zero or negative. It is negative for all vehicles.
    Elasticity Calculations
    Table 6 contains mean and standard deviations of calculated elasticities across households. Lack of symmetry in the price elasticities matrix mean that only own-price estimates can be given any consistent interpretation. Since price term coefficients are close to zero, equation 13 implies that price elasticities are dependent on the expenditure coefficients, [beta], and initial expenditure shares. (8) Accordingly, we observe that uncompensated own-price elasticities are all close to unity, with vehicles 1 and 4 being slightly inelastic, and vehicles 2 and 3 being slightly elastic. Expenditure coefficients do not enter the compensated price elasticities calculation. Consequently, compensated own-price elasticities are smaller in magnitude than uncompensated counterparts ranging from -0.36 for vehicle 1 to -0.70 for vehicle 3. Mean expenditure elasticity estimates for all vehicles, except vehicle 1, suggest that fuel use is slightly expenditure elastic. The highest estimate is only 1.05 for vehicle 2. The stand ard deviation of expenditure elasticities is less than half the mean for all vehicles.
    The matrix of Allen elasticities of substitution is symmetric. Therefore it provides a more consistent explanation of price-induced substitution effects than price elasticities. As seen from Table 6, all vehicle pairs are substitutes. Most of the elasticities are close to 1, but those between vehicle 4 and vehicles 1 and 3 are around 0.6. We note that the own-Allen elasticity for vehicle 4 is positive. Thus, the expenditure function violates regularity conditions for some observations in our database.
    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 [R.sup.2] 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 disent angled 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 o f different ways including, disposing its vehicle, replacing and/or adding to vehicle holdings, and changing the pattern of vehicle(s) 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 ex plore 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.
    Table 1

    Distribution of Household and Vehicle Characteristics in the Database
    (percent)

    Household Characteristics

    Area Type
    In-Metro 45.6
    Out-Metro 20.1
    Non-Metro 16.9

    Region
    Northeast 19.8
    Midwest 24.8
    South 36.1
    West 19.4

    Income Category
    [less than or equal to]$ 13,999 27.5
    $ 14-000$ 34,999 33.4
    $ 35,000-$ 49,999 17.3
    $ 50000-$ 74999 13.2
    >$ 75000 8.6

    Household Size
    [less than or equal to]2 57.4
    [greater than or equal to]&[less 39.5
    than or equal to]5
    >5 3.0

    Number of Drivers
    [greater than or equal to]&[less 11.5
    than or equal to]5
    >5 0.1

    Education of Head
    Up to 8th grade 8.7
    9-l2th grade 45.5
    College-Graduate 45.8

    Age of Head
    [less than or equal to]24 6.0
    24-35 23.6
    36-55 37.5
    56-65 11.8
    >65 21.2

    Race of Head
    White 83.5
    Non-White 16.5

    Gender of Head
    Female 46.6
    Male 53.4

    Number of Vehicles
    1 87.6
    2 58.8
    3 24.9
    4 9.0
    >4 2.7

    Vehicle Characteristics

    Vehicle 1 Vehicle 2 Vehicle 3 Vehicle 4

    Body Type

    Car 67.8 62.9 57.3 60.8
    Station Wagon 3.5 4.4 5.1 3.0
    Large Van 1.6 2.4 2.8 3.0
    Mini Van 6.7 4.6 2.7 2.6
    Pickup Truck 14.1 19.9 27.1 24.2
    Sport Utility 6.3 5.7 5.0 6.4

    Vehicle Age (years)

    0-2 23.7 34.6 68.5 88.3
    3-5 19.6 7.8 2.1 0.4
    6-10 22.9 21.1 9.0 2.9
    >10 33.8 36.5 20.4 8.3

    Engine Size (litres)

    [less than or equal to]2 18.9 12.6 4.9 1.8
    >2&[less than or equal to]4 45.6 26.2 9.2 2.9
    >4&[less than or equal to]5 13.7 10.6 4.7 1.8
    >5&[less than or equal to]7 7.9 7.5 4.1 1.4
    >7 14 43 77 92

    Number of Cyclinder

    3 or 4 40.4 40.3 38.8 35.8
    5 or 6 38.6 31.5 25.3 25.5
    8 21.0 28.2 36.0 38.7

    Fuel System

    Carburetor 46.7 52.3 51.3 49.1
    Fuel Injection 52.1 46.5 47.0 48.0
    Diesel 1.2 1.2 1.7 3.0

    Transmission Type

    Automatic 78.9 73.6 68.9 69.4
    Manual 21.1 26.4 31.1 30.6

    Drive Type

    Front-Wheel 54.9 46.5 34.9 28.0
    Rear-Wheel 34.1 42.3 53.3 60.5
    4-Wheel 11.1 11.2 11.8 11.4

    Table 2

    Summary of Annual Vehicle Energy Use and Expenditure Data

    1988

    1 2 3 4 All

    Fuel Efficiency
    (miles/gallon)
    Mean 25.59 23.83 22.50 21.42 -
    Standard Deviation 6.61 7.28 7.26 7.32 -

    Fuel Price ($ /gallon)
    Mean 1.00 0.98 0.97 0.95 -
    Standard Deviation 0.08 0.07 0.07 0.07 -

    Vehicle Use
    ([10.sup.3] miles)
    Mean 9.77 8.53 7.13 6.01 17.56
    Standard Deviation 6.30 5.94 5.60 5.34 12.67

    Fuel Use
    ([10.sup.3] gallons)
    Mean 0.49 0.48 0.44 0.40 0.95
    Standard Deviation 0.32 0.35 0.35 0.35 0.70

    Expenditure
    ([10.sup.3] $ )
    Mean 0.48 0.47 0.42 0.38 0.94
    Standard Deviation 0.32 0.34 0.34 0.34 0.68

    1991

    1 2 3 4 All

    Fuel Efficiency
    (miles/gallon)
    Mean 25.95 24.44 23.42 22.63 -
    Standard Deviation 6.31 6.79 7.10 6.97 -

    Fuel Price ($ /gallon)
    Mean 1.19 1.19 1.18 1.18 -
    Standard Deviation 0.09 0.08 0.08 0.08 -

    Vehicle Use
    ([10.sup.3] miles)
    Mean 10.21 8.85 7.75 6.29 17.96
    Standard Deviation 6.41 5.97 5.91 5.40 12.92

    Fuel Use
    ([10.sup.3] gallons)
    Mean 0.50 0.47 0.45 0.39 0.93
    Standard Deviation 0.32 0.33 0.36 0.32 0.69

    Expenditure
    ([10.sup.3] $ )
    Mean 0.59 0.56 0.53 0.45 1.11
    Standard Deviation 0.38 0.39 0.42 0.37 0.82

    1994

    1 2 3 4 All

    Fuel Efficiency
    (miles/gallon)
    Mean 25.86 25.04 23.80 23.76 -
    Standard Deviation 5.93 6.31 6.98 6.35 -

    Fuel Price ($ /gallon)
    Mean 1.16 1.15 1.14 1.14 -
    Standard Deviation 0.09 0.09 0.09 0.09 -

    Vehicle Use
    ([10.sup.3] miles)
    Mean 11.02 9.85 8.64 7.96 18.31
    Standard Deviation 6.30 6.06 6.09 6.30 13.97

    Fuel Use
    ([10.sup.3] gallons)
    Mean 0.53 0.51 0.49 0.44 0.92
    Standard Deviation 0.31 0.34 0.38 0.36 0.73

    Expenditure
    ([10.sup.3] $ )
    Mean 0.61 0.58 0.56 0.51 1.07
    Standard Deviation 0.37 0.40 0.44 0.41 0.84

    Note:

    Fuel efficiency numbers correspond to the EPA composite (highway/city)
    dynamometer test procedure on pre-production prototype vehicles
    (designated [MPG.sub.EPA 55/45]). Fuel prices are averages based on
    monthly prices assigned to individual households using BLS Pump Survey
    (for gasoline) and Lundberg Survey (for diesel) data. Vehicle miles
    traveled (VMT) were determined for most vehicles in the survey using
    odometer readings or responses from the earlier RECS survey data. For a
    small proportion of vehicles data were based solely on a multiple linear
    regression model using household characteristics as independent
    variables. Fuel use was calculated by dividing household VMT by an
    annualized fuel economy value. The annualized MPG adjusts the
    [MPG.sub.EPA 55/45] for seasonal and in-use conditions (see EPA, 1997
    for details). Expenditure is the product of fuel use and fuel price.

    Table 3

    Comparison of Four Versions of the Model

    Unconstrained
    Elements of [gamma]

    Non-
    Homothetic Homothetic

    Model 1 Model 2

    Number of Observations * 7,272 7,272
    Log-likelihood value 24,749 24,738
    2 x Log-likehood ratio ** 0 22
    Degree of freedom - 3

    Share equation [R.sup.2]

    Vehicle 1 0.78 0.78
    Vehicle 2 0.68 0.68
    Vehicle 3 0.72 0.72

    Mean Own-Price Elasticities

    Vehicle 1 -0.78 -0.69
    Vehicle 2 -0.36 -0.64
    Vehicle 3 -0.62 -0.86
    Vehicle 4 -0.79 -0.91

    Mean Expenditure Elasticities

    Vehicle 1 0.95 1
    Vehicle 2 1.05 1
    Vehicle 3 1.03 1
    Vehicle 4 1.03 1

    Mean Own Allen Elasticities

    Vehicle 1 8.35 7.86
    Vehicle 2 132.95 132.43
    Vehicle 3 51.40 50.70
    Vehicle 4 28.98 27.67

    Non-positive Constrainson
    Diagonal Elements of[gamma]

    Non-
    Homothetic Homothetic

    Model 3 Model 4

    Number of Observations * 7,272 7,272
    Log-likelihood value 24,723 24,712
    2 x Log-likehood ratio ** 52 74
    Degree of freedom 3 6

    Share equation [R.sup.2]

    Vehicle 1 0.78 0.78
    Vehicle 2 0.68 0.68
    Vehicle 3 0.72 0.72

    Mean Own-Price Elasticities

    Vehicle 1 -0.99 -1
    Vehicle 2 -1.01 -1
    Vehicle 3 -1.00 -1
    Vehicle 4 -0.93 -1

    Mean Expenditure Elasticities

    Vehicle 1 0.95
    Vehicle 2 1.06 1
    Vehicle 3 1.04 1
    Vehicle 4 1.02 1

    Mean Own Allen Elasticities

    Vehicle 1 -3.50 -3.55
    Vehicle 2 -6.25 -6.20
    Vehicle 3 -8.70 -8.67
    Vehicle 4 7.34 6.40

    * Number of observations used in calculating elasticities varies with
    vehicle ownership.

    ** The probability that the chi-square value is less than or equal to
    11.34 (3 degrees of freedom), or 16.81 (6 degrees of freedom) is 99
    percent.

    Table 4

    Estimation Results: Constant, Price, Efficiency and Household
    Characteristics Coefficients *

    Parameter Estimates

    Vehicle 1 Vehicle 2

    Constant 0.001 0.776 (1)
    Price Vehicle 1 0.000
    Vehicle 2 0.000 0.000
    Vehicle 3 0.004 0.000
    Vehicle 4 -0.004 0.000
    Efficiency Vehicle 1 -0.127 (1) 0.1021 (1)
    Vehicle 2 0.087 (1) -0.122 (1)
    Vehicle 3 -0.005 0.063 (1)
    Vehicle 4 0.021 0.029
    Area Type Out-Metro 0.003 -0.005
    Non-Metro 0.006 -0.006
    Region Midwest -0.004 0.003
    South -0.007 0.004
    West -0.008 0.004
    Gender of Head Male -0.002 0.002
    Age of Head 24-35 0.001 0.001
    36-55 0.000 -0.003
    56-65 -0.002 0.004
    >65 0.002 0.000
    Education of Head 9-12th grade -0.010 (1) 0.005
    College -0.007 0.009 (3)
    Race of Head Non-White 0.000 0.000
    Number of Drivers [greater than 0.006 -0.010
    or equal to]3&
    [less than or
    equal to]5
    >5 -0.058 -0.016
    Household Size [greater than -0.004 0.003
    or equal to]3&
    [less than or
    equal to]5
    >5 -0.011 0.005
    Income Category $ 14,000-$ 34,999 0.005 -0.004
    $ 35,000-$ 49,999 0.008 -0.010
    $ 50000-$ 74999 0.009 -0.008
    [greater than 0.005 0.005
    or equal to]
    $ 75000
    Log of Real Expenditure -0.014 (1) 0.008 (1)

    Parameter Estimates

    Vehicle 3 Vehicle 4

    Constant 0.156 (1) 0.067
    Price Vehicle 1
    Vehicle 2
    Vehicle 3 0.000
    Vehicle 4 -0.004 0.008
    Efficiency Vehicle 1 0.021 (1) 0.005 (3)
    Vehicle 2 0.027 (1) 0.008 (1)
    Vehicle 3 -0.075 (1) 0.017 (1)
    Vehicle 4 0.046 (1) -0.095 (1)
    Area Type Out-Metro 0.003 -0.001
    Non-Metro 0.001 -0.001
    Region Midwest 0.004 -0.010
    South 0.004 -0.012
    West 0.006 -0.014 (3)
    Gender of Head Male -0.001 0.001
    Age of Head 24-35 0.001 -0.003
    36-55 0.005 (3) -0.001
    56-65 0.001 -0.002
    >65 -0.002 0.001
    Education of Head 9-12th grade 0.005 0.000
    College -0.002 0.001
    Race of Head Non-White -0.001 0.000
    Number of Drivers [greater than 0.003 0.001
    or equal to]3&
    [less than or
    equal to]5
    >5 0.072 (2) 0.002
    Household Size [greater than 0.003 -0.001
    or equal to]3&
    [less than or
    equal to]5
    >5 -0.003 0.009 (1)
    Income Category $ 14,000-$ 34,999 0.001 -0.001
    $ 35,000-$ 49,999 -0.001 (3) 0.002
    $ 50000-$ 74999 0.000 -0.001
    [greater than -0.008 (2) -0.002
    or equal to]
    $ 75000
    Log of Real Expenditure 0.003 (3) 0.002 (1)

    Standard Errors

    Vehicle 1 Vehicle 2

    Constant 0.001 0.048
    Price Vehicle 1 0.000
    Vehicle 2 0.003 0.000
    Vehicle 3 0.005 0.004
    Vehicle 4 0.000 0.000
    Efficiency Vehicle 1 0.016 0.014
    Vehicle 2 0.015 0.015
    Vehicle 3 0.012 0.012
    Vehicle 4 0.020 0.019
    Area Type Out-Metro 0.005 0.004
    Non-Metro 0.005 0.005
    Region Midwest 0.006 0.005
    South 0.005 0.005
    West 0.006 0.006
    Gender of Head Male 0.004 0.004
    Age of Head 24-35 0.008 0.008
    36-55 0.008 0.008
    56-65 0.009 0.009
    >65 0.009 0.009
    Education of Head 9-12th grade 0.005 0.005
    College 0.005 0.005
    Race of Head Non-White 0.005 0.005
    Number of Drivers [greater than 0.007 0.007
    or equal to]3&
    [less than or
    equal to]5
    >5 0.055 0.053
    Household Size [greater than 0.005 0.005
    or equal to]3&
    [less than or
    equal to]5
    >5 0.011 0.011
    Income Category $ 14,000-$ 34,999 0.005 0.005
    $ 35,000-$ 49,999 0.006 0.006
    $ 50000-$ 74999 0.006 0.006
    [greater than 0.008 0.007
    or equal to]
    $ 75000
    Log of Real Expenditure 0.003 0.003

    Standard Errors

    Vehicle 3 Vehicle 4

    Constant 0.046 0.000
    Price Vehicle 1
    Vehicle 2
    Vehicle 3 0.000
    Vehicle 4 0.000 0.000
    Efficiency Vehicle 1 0.005 0.002
    Vehicle 2 0.004 0.002
    Vehicle 3 0.013 0.003
    Vehicle 4 0.011 0.011
    Area Type Out-Metro 0.002 0.001
    Non-Metro 0.003 0.001
    Region Midwest 0.003 0.011
    South 0.003 0.010
    West 0.003 0.012
    Gender of Head Male 0.002 0.001
    Age of Head 24-35 0.005 0.002
    36-55 0.004 0.002
    56-65 0.005 0.002
    >65 0.005 0.002
    Education of Head 9-12th grade 0.003 0.001
    College 0.003 0.001
    Race of Head Non-White 0.003 0.001
    Number of Drivers [greater than 0.004 0.002
    or equal to]3&
    [less than or
    equal to]5
    >5 0.031 0.015
    Household Size [greater than 0.003 0.001
    or equal to]3&
    [less than or
    equal to]5
    >5 0.006 0.003
    Income Category $ 14,000-$ 34,999 0.003 0.001
    $ 35,000-$ 49,999 0.003 0.002
    $ 50000-$ 74999 0.003 0.002
    [greater than 0.004 0.002
    or equal to]
    $ 75000
    Log of Real Expenditure 0.002 0.001

    * Superscript numbers are

    (a)1 implies significance at the 0.01 level

    (b)2 implies significance at the 0.05 level

    (c)3 implies significance at the 0.10 level

    Table 5

    Estimation Results: Vehicle-Ownership and Vehicle-Characteristics
    Coefficients *

    Parameter Estimates

    Vehicle 1 Vehicle 2

    Vehicle Ownership Vehicle 1 1.124 (1) -0.875 (1)
    Vehicle 2 -0.578 (1) 0.612 (1)
    Vehicle 3 -0.202 (1) -0.219 (1)
    Vehicle 4 -0.120 (1) -0.103 (1)
    Body Type Station Wagon -0.010 (3) 0.008
    Large Van 0.034 (1) 0.031
    Mini Van 0.016 (1) 0.063 (1)
    Pickup Truck 0.000 -0.003
    Sport Utility 0.008 0.016
    Vehicle Age (years) 3-5 0.006 -0.027
    6-10 -0.022 (1) -0.100 (1)
    >10 -0.041 (1) -0.149 (1)
    Engine Size (litres) >2&[less than -0.006 (1) 0.010
    or equal to]4
    >4&[less than -0.008 0.002
    or equal to]5
    >5&[less than -0.016 (2) 0.014
    or equal to]7
    >7 -0.061 (1) 0.132 (1)
    Number of Cylinders 5 or 6 0.014 (1) 0.050 (1)
    8 0.016 (2) 0.069 (1)
    Fuel System Fuel Injection 0.009 (1) -0.001
    Diesel 0.002 -0.007
    Transmission Type Manual -0.002 -0.019 (3)
    Drive Type Rear-Wheel -0.007 (1) -0.008
    4-Wheel 0.006 0.018

    Parameter Estimates Standard
    Errors

    Vehicle 3 Vehicle 4 Vehicle 1

    Vehicle Ownership Vehicle 1 -0.183 (1) -0.067 (1) 0.023
    Vehicle 2 -0.026 (1) -0.008 (1) 0.021
    Vehicle 3 0.436 (1) -0.016 (1) 0.015
    Vehicle 4 -0.104 (1) 0.327 (1) 0.022
    Body Type Station Wagon 0.059 (1) 0.000 0.005
    Large Van 0.095 (1) -0.042 (3) 0.009
    Mini Van -0.025 -0.404 (3) 0.005
    Pickup Truck 0.095 (1) -0.017 0.004
    Sport Utility 0.124 (1) -0.062 0.008
    Vehicle Age (years) 3-5 -0.166 (1) 0.026 0.004
    6-10 -0.243 (1) -0.049 0.004
    >10 -0.289 (1) -0.085 0.006
    Engine Size (litres) >2&[less than 0.029 0.040 (3) 0.003
    or equal to]4
    >4&[less than -0.002 0.060 (3) 0.006
    or equal to]5
    >5&[less than 0.029 0.019 0.008
    or equal to]7
    >7 0.111 (2) -0.279 (1) 0.018
    Number of Cylinders 5 or 6 0.055 (1) 0.066 (1) 0.004
    8 0.086 (1) 0.077 (2) 0.007
    Fuel System Fuel Injection 0.024 (3) -0.067 (1) 0.003
    Diesel -0.028 0.088 (1) 0.008
    Transmission Type Manual -0.028 (2) -0.021 0.003
    Drive Type Rear-Wheel 0.009 -0.079 (1) 0.003
    4-Wheel -0.066 (1) -0.020 0.005

    Standard Errors

    Vehicle 2 Vehicle 3 Vehicle 4

    Vehicle Ownership Vehicle 1 0.050 0.047 0.023
    Vehicle 2 0.022 0.004 0.002
    Vehicle 3 0.015 0.024 0.003
    Vehicle 4 0.020 0.014 0.032
    Body Type Station Wagon 0.017 0.024 0.027
    Large Van 0.022 0.030 0.025
    Mini Van 0.023 0.043 0.065
    Pickup Truck 0.013 0.017 0.018
    Sport Utility 0.030 0.043 0.044
    Vehicle Age (years) 3-5 0.017 0.037 0.091
    6-10 0.017 0.036 0.090
    >10 0.020 0.036 0.091
    Engine Size (litres) >2&[less than 0.013 0.020 0.023
    or equal to]4
    >4&[less than 0.022 0.031 0.033
    or equal to]5
    >5&[less than 0.027 0.038 0.039
    or equal to]7
    >7 0.039 0.052 0.077
    Number of Cylinders 5 or 6 0.013 0.020 0.023
    8 0.022 0.032 0.032
    Fuel System Fuel Injection 0.009 0.014 0.016
    Diesel 0.035 0.038 0.036
    Transmission Type Manual 0.011 0.015 0.016
    Drive Type Rear-Wheel 0.010 0.015 0.016
    4-Wheel 0.019 0.026 0.030

    * Superscript numbers are:

    (a)(1)Implies significance at the 0.01 level

    (b)(2)Implies significance at the 0.05 level

    (c)(3)Implies significance at the 0.10 level.

    Table 6

    Mean and Standard Deviation of Calculated Elasticities

    Mean

    Vehicle 1 Vehicle 2 Vehicle 3 Vehicle 4

    Uncompensated
    Price Elasticities

    Vehicle 1 -0.99 -0.01 0.00 -0.05
    Vehicle 2 0.00 -1.01 0.00 0.00
    Vehicle 3 0.03 -0.01 -1.00 -0.06
    Vehicle 4 0.00 -0.01 -0.04 0.90

    Comensated
    Price Elasticities

    Vehicle 1 -0.36 0.41 0.33 0.19
    Vehicle 2 0.64 -0.59 0.30 0.24
    Vehicle 3 0.65 0.41 -0.70 0.18
    Vehicle 4 0.62 0.41 0.26 -0.66

    Substitution
    Elasticities

    Vehicle 1 -3.50
    Vehicle 2 1.00 -6.25
    Vehicle 3 1.19 1.01 -8.70
    Vehicle 4 0.62 0.99 0.61 7.34

    Expenditure
    Elasticities
    0.95 1.05 1.03 1.03

    Standard Deviation

    Vehicle 1 Vehicle 2 Vehicle 3 Vehicle 4

    Uncompensated
    Price Elasticities

    Vehicle 1 0.00 0.01 0.14 0.19
    Vehicle 2 0.00 0.00 0.01 0.00
    Vehicle 3 0.05 0.01 0.00 0.20
    Vehicle 4 0.05 0.00 0.15 0.39

    Comensated
    Price Elasticities

    Vehicle 1 0.32 0.21 0.19 0.27
    Vehicle 2 0.32 0.21 0.17 0.15
    Vehicle 3 0.31 0.21 0.17 0.28
    Vehicle 4 0.34 0.21 0.26 0.38

    Substitution
    Elasticities

    Vehicle 1 13.48
    Vehicle 2 0.03 36.22
    Vehicle 3 1.15 0.08 36.13
    Vehicle 4 1.48 0.04 1.63 325.25

    Expenditure
    Elasticities
    0.19 0.29 0.12 0.11
    (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.sub.h], instead of [e.sub.h]. This will mean replacing [u.sub.h], with [q.sub.h] (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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    Gbadebo Oladosu *
    * 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
    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.

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