Household Vehicle Type Holdings and Usage: An Application of the Multiple Discrete-Continuous Extreme Value (mdcev) Model Chandra R. Bhat and Sudeshna Sen



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ACKNOWLEDGEMENTS


The authors would like to thank Chuck Purvis of the Metropolitan Transportation Commissions (MTC) in Oakland for providing help with data related issues. The authors also appreciate the valuable comments of an anonymous reviewer on an earlier version of the paper.

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Table 1. Vehicle Type Distribution of One – Vehicle Households



Vehicle Type


Total number of households


Percentage of households


Mean Annual Mileage

(in miles)

Passenger Car


1298

72%

9299

Sports Utility Vehicle (SUV)

204

11%

10052

Pickup Truck

192

11%


9981

Minivan

89

5%

11193

Van

14

1%

10330




Table 2. Vehicle Type Distribution Among Two – Vehicle Households



Type of first vehicle


Type of second vehicle



Total number of households



Percentage total number of two-vehicle household


Mean Annual Mileage of vehicle type 1 (in miles)


Mean Annual Mileage of vehicle type 2 (in miles)


Passenger Car

Passenger Car

522

40.0%

19147*

19147*

Passenger Car

Pickup Truck

255

19.5%

10051

9591

Passenger Car

SUV

213

16.3%

9590

10736

Passenger Car

Minivan

151

11.6%

9841

10171

SUV

Pickup Truck

46

3.5%

9251

10502

Pickup Truck

Minivan

32

2.5%

10514

10524

Pickup Truck

Pickup Truck

21

1.6%

21587*

21587*

SUV

Minivan

17

1.3%

10993

11390

Passenger Car

Van

15

1.1%

7597

9549

SUV

SUV

13

1.0%

24481*

24481*

Minivan

Minivan

7

0.5%

25109*

25109*

SUV

Van

6

0.5%

9736

13564

Pickup Truck

Van

6

0.5%

15172

9509

Minivan

Van

1

0.1%

12014

9455

* These numbers represents the mean total annual miles across both vehicles. Note that the annual mileage is computed for each vehicle type; in case both vehicles are of the same type, the entries correspond to the total miles across both vehicles. The numbers are the same across the “Mean annual mileage of vehicle type 1” and “Mean annual mileage of vehicle type 2” for this reason.



Table 3. Empirical Results



Explanatory variables


Parameter


t-statistic


Household sociodemographics







Income greater than 115K







Pickup Truck

-0.6135

-4.683

Van

-0.8684

-1.517

Presence of children less than 4 years of age







SUV and Minivan

0.6010

3.926

Presence of children between 5 and 15 years of age







SUV

0.4090

3.836

Minivan

0.7099

4.611

Presence of children between 16 and 17 years of age







Minivan

0.8416

3.355

Household size







Minivan

0.5341

5.593

Presence of a mobility-challenged individual in the household







Minivan

0.3912

1.433

Van

2.1069

1.951

No. of employed persons in the household







Minivan

-0.3686

-3.775

No. of males







Pickup Truck

0.3257

4.207

Household location variables







Population Density







Pickup Truck and SUV

-0.0166

-4.143

Vehicle Operating cost(cents/mile) divided by household income







(in 000s)

-0.0314

-2.139

Baseline preference constants







Passenger Car (base)







SUV

-3.6514

-11.045

Pickup Truck

-3.1273

-9.199

Minivan

-5.5305

-10.592

Van

-12.5287

-4.584

Table 4a. Satiation Parameters


Vehicle Type

Parameter

t-statistic12

Passenger Car

0.4410

11.53

Sports Utility Vehicle (SUV)

0.9003

4.90

Pickup Truck

0.7293

6.55

Minivan

0.8480

4.04

Van

0.5124

2.34


Table 4b. Variance-Covariance Matrix


Vehicle Type

Vehicle Type

Passenger Car

SUV

Pickup Truck

Minivan

Van

Passenger Car


0


0


0


0


0


Sports Utility Vehicle (SUV)





2.32

(4.07)


2.24

(4.48)


1.51

(3.18)


0

Pickup Truck








3.35

(3.10)


1.46

(3.74)


0

Minivan











1.95

(1.98)


0

Van














28.94

(2.47)




Table 5. Impact of an increase in operating (fuel) cost from $1.40 per gallon to $2.00 per gallon



Vehicle Type



Percentage change in holdings of vehicle type



Percentage change in overall use of vehicle type

Passenger Car



- 0.1

+ 0.5

Sports Utility Vehicle (SUV)



- 5.9

- 3.0

Pickup Truck



- 2.1

- 6.2

Minivan


- 4.9

- 2.3

Van


- 3.4

- 6.5




1A number of earlier studies have also focused on vehicle ownership levels and use. These studies are not of immediate interest here since the focus of the current paper is on vehicle type holdings and use. For a comprehensive review of studies on vehicle ownership/use (with no vehicle type holdings analysis), the reader is referred to De Jong et al., 2004.

2 Some studies, such as Train (1986), use the logarithm of vehicle use as the dependent variable. However, the basic functional relationship between the dependent and independent variables takes a linear regression form.

3Standard discrete choice models assume no satiation effects because they use a linear utility specification. That is, the marginal utility of any vehicle type is independent of vehicle usage. The reader is referred to Bhat, 2005 for further details.

4 The MMDCEV model used here is a static vehicle type holdings and use model, similar to the studies listed earlier in this section. Such static models predict holdings at any particular period without regard to the vehicle holdings in the earlier period. The application of such static models at different and closely-spaced time points can lead to the unrealistic situation of a household holding very different vehicle portfolios between the two time points. However, such static models may be reasonable over longer time periods, as indicated by De Jong et al. (2004). Another formulation that seeks to more consistently reflect the actual household vehicle holdings decision process is the dynamic vehicle transaction approach, in which households decide on disposing, adding, replacing, or maintaining the status quo of their current vehicles over time as well as the attributes of any new vehicles entering their household vehicle fleet (see, for example, Hocherman et al., 1983; Gilbert, 1992; HCG, 1995; De Jong, 1996; Bunch et al., 1996). The dynamic approach is particularly appealing for short-to-medium term forecasts. However, such transaction models require a “significant ongoing commitment to collecting panel data” (see Bunch, 2000) and can be relatively cumbersome to apply. Besides, the theoretical linkage between usage and vehicle type holdings is rather tenuous in most dynamic models to date.



5 This is only because we do not have adequate information from the survey to construct a mileage value for use of non-motorized modes of travel. If this information were available, we can add another “vehicle type” category corresponding to non-motorized modes. This category can be considered as an “outside good” which is always “consumed”, since households will use non-motorized modes for some amount of their travel (if at least for walking to the personal vehicle). In this instance, M would correspond to the total annual motorized and non-motorized travel mileage, and the annual motorized mileage would be endogenous to the model. The total annual motorized and non-motorized travel mileage would need to be modeled in an earlier step in this case.

6 The MDCEV model formulation also represents a multiple discrete-continuous extension of the single discrete-continuous model formulations of Hausman (1980), Dubin and McFadden (1984), Hanemann (1984), Mannering and Winston (1985), Train (1986), Chiang (1991), Chintagunta (1993), and Arora et al. (1998). In the single discrete-continuous models, the discrete alternatives are assumed to be perfect substitutes so that, in the context of the current application, only a single vehicle type is chosen. This may be viewed as a special two alternative case within the multiple discrete-continuous formulation, with one alternative (say the first) always being consumed. This first alternative may be labeled as “non-motorized travel mode”, an “outside good” which is always “consumed”, since households will use non-motorized modes for some amount of their travel (if at least for walking to the personal vehicle). The second alternative would be a composite of all motorized vehicle types, the baseline utility for which corresponds to the maximum utility across all motorized vehicle types j. This maximum utility is essentially a log-sum parameter from the standard discrete choice model for vehicle type. With this simplification, the MDCEV model is applicable to the single discrete-continuous case of a single vehicle type choice and corresponding usage. Of course, if the problem at hand is truly a single discrete-continuous one, the customized formulations of Hausman, Dubin and McFadden, Hanemann, and others listed above have the advantage of elegance and simplicity originating from the application of Roy’s identity to an indirect utility function that links the discrete and continuous choices.


7 The vehicle type classification used here is oriented toward transportation infrastructure planning and emissions modeling, and hence the detailed make/model of vehicles is not considered. Some earlier studies have used a finer definition of vehicle types to include vehicle makes and models (see Bunch, 2000 for a review).

8 The sample size of 3500 was based on run-time considerations as well as the judgment that 3500 observations were adequate for accurate and reliable model estimation.

9 As per the fuel economy statistics, passenger cars are considered the most fuel efficient vehicles, while pickup trucks and vans are considered the least fuel efficient.

10 An increase in vehicle operating costs would likely also impact other travel choices, such as travel mode and destination choice. These impacts are not modeled here.

11 As indicated in the footnote on page 8, the exogeneity of M is maintained because of data limitations.

12 The t-statistic is computed for the null hypothesis that the satiation parameter is equal to 1. Equivalently, the t-statistic is for the test that there are no satiation effects or that the utility structure is linear.


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