World Bank Reprint Series: Number 307
Mateen Thobani
A Nested Logit Model
of Travel Mode to VVork
and Auto Ownership
Reprinted with permission from Journal of Urban Economics, vol. 15 (1984), pp. 287-301.
Copyrighted by Academic Press.



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JOURNAL OF URBAN ECONOMCS 15, 287-301 (1984)
A Nested Logit Model of Travel Mode to Work and
Auto Ownership1
MATlEEN Th1OBANI
The World Bank, 1818 H Street, N. W., Washington, D. C. 20433
Received April 23, 1982; revised August 24, 1982
INTRODUCTION
Estimating the demand for urban passenger travel is useful in transport
planning. An appropriately specified model may be used not only to predict
the demand for various travel models but also to examine the effect of
policy changes on the welfare of individuals. Such policies may include
changing the public transport fare structure, changing the tax on petrol,
adding more buses to the existing fleet, or making a certain travel mode
accessible to more people. When the choice of mode to work and auto
ownership is jointly modeled, the effect of, say, an increase in bus fares on
the demand for various travel modes, as well as the effect on the demand for
car ownership, can be predicted.
This paper estimates a probabilistic joint choice model of travel mode to
work and auto ownership. The probabilistic models consider the probability
that an individual makes a certain choice (e.g., the choice of mode to work)
as a function of attributes of the choice and socioeconomic characteristics of
the individual. Such models are behavioral, based on disaggregated data,
and policy oriented in that they are sensitive to changes in policy variables.
An important advantage of the probabilistic models is that under certain
assumptions, they can be derived from a theory of stochastic utility maximi-
zation. Further the decision set may include several modes and allows for
joint decisions such as buying a car and going to work in a bus. If the joint
nature of a decision is ignored it may bias coefficient estimates in addition
to decreasing their efficiency. Decisions such as whether to make a trip or
the time of day to make the trip can also be handled although they are
usually difficult to model and data are often unavailable.
'This paper is a refinement of the author's Ph.D. thesis at Yale University. He is grateful to
his advisors John Quigley and T. N. Srinivasan for guidance. Support for data collection was
provided by the International Labour Office, Geneva. Office space and research assistance
during the data collection period were kindly provided by the Applied Economics Research
Centre, Karachi University. The author thanks Valerie Kozel who suggested many of the
refinements in this paper and Eric Swanson with whom he has had many useful discussions, He
is also grateful to a reference for pointing out an important error and making useful
suggestions.
287
0094-1190/84 $3.00
Copyright © 1984 by Acadermic Prcss, Inc.
All rights of reproduction in any form reserved.



288                       MATEEN THOBANI
While the probabilistic models are typicaly laid out within a framework
which allows for elaborate joint decisions, few studies estimate the joint
decisions. Studies of the latter sort include Adler's and Ben-Akiva's [1]
study on shopping trips and Lerman's [6] study on choice of residential
location, type of housing, automobile ownership, and mode to work. More
recently Train [12] estimates a joint choice model of auto ownership and
mode to work 'Lased on a sample of households in the San Francisco area.
Using Train's -pproach, this paper estimates a joint choice model of auto
owner.6i4' and; mode to work based on household survey data from Karachi.
There are several reasons for choosing to model this set of joint decisions.
The trip to work is a large percentage of total trips made by the household
and the primary use of public transport is for work trips. It is made to a
fixed destiation at a relatively fixed time of day and demand for the trip is
inelastic. This allows one to ignore the effect of a price change on the
decision to go to an alternate location or not make the ftip at all.
One would expect that the decision to buy a car or motorcycle is
determined simultaneously with the decision to choose a particular mode to
work. If so, and the simultaneity is ignored, coefficient estimates are biased.
By correctly modeling the joint decision it is possible to see the effect, for
example, of an increase in petrol price not only on demand for a mode to
work, but also on demand for car ownership.
Fitting the model to household data from Karachi is interesting because
Karachi has a rich variety of modes. Further, it is relevant because all fares
in Karachi and the petrol prices are regulated by the govermment so that
policy instruments are readily available. It is instructive to compare travel
behavior in a city in a developed country (San Francisco) with Karachi. Are
values of time and price and time elasticities different between these cities?
This paper extends Tra's paper in that it explicitly shows how one could
use such a model to make welfare comparisons under different policies.
THE NESTED LOGIT MODEL
The nested logit model is a generalized version of the multinomial logit
model.2 An outline of the model as it applies to the problem at hand is
given below.
The consumer is assumed to face a joint decision of choice of auto
ownership indexed c = 1,... C and mode to work indexed n = 1,... Nc.' The
consumer derives utility Ucn which is a function of the attributes of the
alternative cn. The attributes may be variables related to the consumer, such
as family size and household income; auto ownership, such as maintenance
2See Domencich and McFadden [4] and McFadden [10].
3The set Nc will vary according to c since it is assumed that a person cannot decide not to
own a car but to go to work in one,



MODE TO WORK AND AUTO OWNERSHP                      289
and depreciation; the choice of mode to work such as commuting time; or
interaction variables, such as cost of the mode divided by the individual's
wage rate. The consumer then chooses the alternative that gives the highest
utility. All consumers are assumed to have the same stochastic utility
function.
Not all attributes of the utility function are observed. Unobserved vari-
ables have some probability distribution conditioned on the values of the
observed variables. If the observer knows the foim of the utility function
and the probability distribution of the unobserved variables, he can make a
probabilistic statement of the expected choice, namely
Pr,, = Prob[ U,, > Ubm for bm ¢ cn] (1)
where Prcn denotes the probability of choosing cn.
The joint probability above may be estimated by specifying a functional
form for Uc,, and by using the identity
Pr,, =      Prc                        (2)
where Prcn is the joint probability that the individual chooses mode n to
work and the household choses the auto ownership category c, Prnlc is the
conditional probability of the worker choosing mode n given auto owner-
ship c, and Pr, is the marginal probability of the household choosing auto
ownership category c.
The utility function Uc,, can be decomposed into three components as
shown below
Uc. = Ax + (xaYc + X;cn                     (3)
where xn is a vector of observed attributes which vary with mode attributes
of the work' trip4 (e.g., in-transit time), y, is a vector of observed attributes
which vary only with auto ownership (e.g., depreciation cost), and /3' and a'
are vectors that may be estimated using maximum likelihood methods by
specifying a structure for the stochastic error term Xck.
If the A?, are identically and independently distributed having a Weibull
distribuition, then Prc, is multinomial logit. However, McFadden [10] has
shown that if the Ac, have a particular generalized extreme value distribu-
tion, then the conditional and marginal probabilities described above are
4We have assumed that the nonstochastic compnnent of the utility function is linear in
parameters. In addition, whereas the general model allows for x,, to vary with both mode
ownership and mode to work attributes, in this model xe,, equals x, since the variables such as
in-transit time by bus are independent of whether the household owns a car.



290                      MATEEN THOBANI
given by
,Be'xA/(l-c)                       (4)
elc
and
Pr    y<lal                          (5)
, ea Yb+(1 G)1b
b=1
where
Nc
c     =  log E  ' - a)                 (6)
n=1
A more intuitive interpretation of inclusive value in this model is that it is
the aggregate utility (summed over all available modes) from the trip to
work in each of the auto ownership categories. It is the " utility" from each
of the available public modes and walking, plus the "utility" from taking
the car to work. Both (4) and (5) are in the logit form and hence easy to
estimate. If the coefficient of I in (5) is estimated to be 1 (i.e., a = 0) then
the joint model is multinomial logit. However, in general, the joint model is
not restricted to be multinomial logit. It is an advantage when one suspects
that the assumption of the independence of error terms in the multinomial
logit model is violated. In this case a gives an estimate of the degree of
dependence between the error tenns. In addition, the two-step procedure
results in computational savings since there are fewer alternatives and fewer
parameters to be estimated at each stage. The gain comes at the expense of
some l6ss in efficiency.
It is worth noting that the model is consistent with stochastic utility
maximization only for 0 c a � 1 with one extreme a= 0 giving us the
multinomial logit case and the other extreme a = 1 implying that the two
decisions are in fact independent-that the mode to work decision is
independent of the auto ownership decision.
The best way to proceed is to first estimate (4), obtain f3'/(1 - a), and
calculate 4. Using these estimates of I, estimate (5) to obtain a' and
(1 - a) and test for the coefficient of 1, being different from 1. If it is not
different from 1 then we are in the multinomial logit world (a 0-- ). If it is
between 0 and 1 we have a nested logit model which is consistent with
stochastic utility maximization. Other values of the coefficient lead us to
reject the joint choice model.



MODE TO WORK AND AUTO OWNERSHP                    291
It is apparent from (5) that if the model is estimated without the term Ic,
the coefficient a' may be biased depending on the correlation of I, with Y,.
In addition, standard errors on the estimated coefficients a' will be larger.
Thus if one is interested in modeling the decision to buy a car, but neglects
to take into account the additional utility that an individual may obtain
from taking the car to work, coefficient estimates may be biased and have
larger standard errors.
THE SURVEY
Four hundred households throughout Karachi were interviewed for the
purpose of this study. Of these, 330 were households where at least one
household member made a trip to work. A description of the sampling
methodology is given below.
To ensure enough variation in mode choice, it was important to have
sufficient observations within various income categories. Accordingly, the
city was divided up into certain similar areas depending on the area's
median household income, as reported in a study previously carried out by a
UNDP mission to the Master Plan Office [7]. In addition to income, the
groups were similar with respect to literacy levels, water and sewerage
connections, and percentage of brick or concrete (pucca) houses. The
Master Plan income figures were used only as a basis for sampling-the
subsequent analysis uses income levels reported by the survey.
It was also considered important to have sufficient observations on
households that live near the city center as well as those that live at a
distance. Therefore these income areas were further split into three distance
categories-zero to 3 miles, 3 to 5 miles, and 5 or more miles from the
center of the city. Some areas were then discarded for various reasons such
as for being red-light districts or for having moved significantly from their
income groups since the UNDP study. Two areas were randomly selected
from the list of areas in each cell. Since random sampling within these
relatively large areas was not feasible, a sample of about 50 households
within each of the areas was chosen by the author after inspection to ensure
that the block of houses selected was not atypical for the area. Interviewers
were then sent out to interview at least 13 households in each of the 30 areas
selected.
The richness of the data comes from information not only on the trips
made by each individual of the household on the day prior to the interview,
but also on demographic characte.ristics of the household, income, hours
worked, expenditure by various categories, assets, availability of public
modes, present and purchase price for owned modes, and maintenance
expenditures on these modes. The questions on trips made included origin
and destination, purpose, mode used, in-transit and waiting time, distance



292                       MATEEN THOBANI
covered, number of pcrsons in mode, cost (if public mode), and trip
frequency.
MODAL SPLIT ANALYSIS
The N choices for the mode to work for a consumer include car, taxi,
rickshaw (three-wheeled motorcycles which carry two passengers in addition
to the driver), minibus (14-passenger wagons), walking, and bus. Not all
modes are available to all consuimers. A car is considered available either if
the consumer rode to work in one or if the household owns a car. Other
public modes are considered available either if the consumer used it to get
to work or if he answered yes to the question "is the mode readily available
in your area?" The frequencies of the available and chosen altematives are
g&iven in Table 1.
The dependent variable for the modal split analysis Js the probability of
the consumer choosing a mode conditional on the availability of the mode.
The multinomial logit model was estimated using maximum likelihood
methods, A description of the independent variables along with their means
is given in Table 2.
To calculate values for time and cost, a regression of reported time or cost
by mode on reported distance was run using income and area dummies. The
resulting coefficients were then used to predict values for time and cost both
for the modes not chosen as well as for the chosen model. The hourly wage
rate was calculated by taking the reported pretax monthly wage income and
dividing by the hours worked per week times the 4.28 weeks per month.
Income taxes are not an important component of total income for most
individuals, and it is doubtful whether using post-tax wage rates if they were
available would change the results significantly. A cross tabulation of
household income category by household expenditure category shows that
almost all households lay either along the diagonal or below it leading one
to have some faith in the reported income figures. The estimation results are
TABLE 1
Modal Split Analysis of Frequencies of Alternatives
Percent    Frequency    Percent
Frequency .  of cases    chosen      chosen
Car         104        33,23        90         86.54
Taxi        208        66,45         8          3.85
Rick        237        75.72        14          5,91
Mini        218        69.65        36         1651
Walk        313        100.0        44         14,06
Bus        245         78.27       121         49.39



MODE TO WORK AND AUTO OWNERSHIP                       293
TABLE 2
Modal Split Analysis
Description of Variables
OVTT Out of vehicle travel time in minutes-it includes waiting time and walk time.
IVTT Time (in minutes) spent in-vehicle for all modes except walk.
IVTT(mode) Alternative specific IVTT; equals IVTT for alternative (mode); else zero.
COSTWA    Monetary cost in rupees divided by wage in rupees/minute.
DHEAD    Equals one if alternative is car and person is head of household; else zero.
D(mode) Altemative specific dummy; equals one for alternative (mode); else zero.
Means of Variables
OVTT          IVTT          COSTWA            DHEAD
Car                  0             18.30          27.36            0.644
Taxi                12.50          19.92          82.39            0
Rick                 15.80         24.76          60.09            0
Mini                 12.27        24.97           17,60            0
Walk                 79.57          0              0               0
Bus                  10.58         29.83           8.75            0
given in Table 3. Two models are presented. The first model considers IVTT
to be a generic variable or implicitly assumes that a minute spent traveling
in a car is as onerous as a minute spent in a bus. The second model with
mode-specific IV1T aSlows the disutility of time'to vary across modes.
Recall that the parameter estimates are coefficients . the linear utility
function and so the coefficient of an attribute is simply the marginal utility
of the attribute. The ratio of any pair of coefficients is the marginal rate of
substitution between their respective attrioutes. Therefore the ratio of the
coefficient of OVTT to that of I T of 2.8 implies that OVYT is about three
times as onerous as IVTT. This result is similar to those reported in studies
done in developed countries using multinomial logit techniques as well as
other methods.
The cost-divided-by-wage (COSTWA) variable was used rather than cost
to allow the value of time to vary directly with an individuals's wage. The
variable is expressed in units of time and can be considered to represent the
number of minutes a person has to work to earn the cost of his transporta-
tion. (The cost for a car includes gasoline and maintenance while the cost
for public modes is the fare.) The marginal rate of substitution between
IVTIT and COSTWA is the value of time spent in the vehicle as a function
of wage and is seen to be 3.8. While one could conceive of reasons why the
value of time spent in a model might be greater than the wage rate, a value
four times as great seems excessively high. However, most studies that



294                          MATEEN THOBANI
TABLE 3
A Modal Choice Model Conditional on Auto AvailabiLty
Model with            Model with mode-
generic IVTT             Specific IVTT
Estimated   Asymptotic   Estimated   Asymptotic
coefficient  t statistic  coefficient  t statistic
OVTT                   - 0.1920     - 6.323     - 0.2017    - 5.640
IV'T                   -0.0698      -2.406        -            -
IVTTCAR                  -           -          -0.0596     -0.7859
IYVTAXI                  -           -          -0.0106     -0.2434
IVTTRICK                 -           -          -0.0666     -1.651
IVTTMINI                 -           -          -0.0957     -1.572
IVITBUS                  -           -          -0.0929     -2.147
COSTWA                 -0.0184      -3.369      -0.0259     - 3.346
DHEAD                   2.455        3.325       2.541        3.657
DCAR                   -2.285       -3.067      -2.639      -2.977
DTAXI                  - 2.673      -4.878      - 3.623     -4.8iI6
DRICK                  -1.721       -3.801      -1.770      -2.969
DMINI                  -2.146       -5.132      -1.756      -2.1'J0
DBUS                   -1.056       -2.287      -0.7492     -1.498
Likelihood ratio index          0.5832                   0.5898
Log likelihood at
convergence               --182.4                  -179.5
Log likelihood at zero      -437.6                   -437.6
Degrees of freedom           1003                      999
Values of time as a percentage of wage
IVIT (all modes)                  379
Car                               230
Taxi                               41
Rickshaw                          257
Mini                              369
Bus                               358
OVTT (includes walking)   1043 and 779
employ multinomial logit methods to estimate the value of time5 find such
unrealistically high ratios; in addition, these ratios differ widely from values
obtained by earlier studies using other cruder techniques. Further work
needs to be done to determine why modal split models estimated by
multinomial logit techniques yield unrealistically high values of time.
The variable DHEAD was used as a way to decide who gets use of the car
when there are competing demands on the car. The positive valiue of the
5Sec, for example, Train [12] Kozel [51, and Anas [2).



MODE TO WORK AND AUTO OWNERSHIP                  295
coefficient suggests that heads of household are more likely to get the car (or
get greater utility from the use of the car). This result is also borne out by
Train [12].
The models estimated in Table 3 assume that a minute spent walking is as
onerous as a minute spent waiting for a mode. It is a plausible assumption
that can be supported by other studies6 and was necessary because walking
time to the mode and waiting time for the mode could not be distinguished
in the questionnaire.
The hypothesis of the value of time being different in the various modes
was tested in the second model of Table 3. As the reader can verify by
means of a likelihood ratio test, the hypothesis that the value of time is
equal in all modes was not rejected at the 5% level of significance. The
results have been presented here because it is interesting to note that the
values of time are ranked according to our expectations. Contrary to Train's
model where the- value of time spent in a car is much higher than that in a
bus, in this model there is no significant difference and, in fact, the
estimated coefficients point toward car travel time being less onerous than
bus travel time. This is understandable because, unlike transit in San
Francisco, buses in Karachi are very uncomfortable and extremely crowded.
Kozel [5] also finds cars to be less onerous than transit modes in Bogota.
Two other hypotheses of interest (not shown in Table 3) are that income
is not a significant variable in the decision to choose a mode to work and
that people who locate away from the center of town have the same value of
time as those near the Central Business District. At the 5% level of
significance, the hypothesis that the coefficients of income are equal to zero
was not rejected. The hypothesis that individuals who live more than 5 miles
from the center of town have the same value of IVTT as those who live
,within 5 miles from the center was rejected at the 5% level. This supports
Train's result that suburban dwellers have lower values of time as compared
to urban dwellers. Although the inclusion of this result would improve the
fit of the model slightly, it was decided to stay with the simpler formulation
for simplicity and ease of comparison with other models. The hypothesis
that these two groups of residents have the same value of OVTT was not
rejected at the 5% level of significance (it was rejected at the 10% level).
The elasticities of demand for various travel modes with respect to time
and cost are valuable to the planner who contemplates a change in these
variables. In this paper, it was decided to simulate changes in variables to
obtain arc elasticities rather than evaluate the point elasticities at the means
of the independent variables. This is because point elasticities are very
sensitive to where they are evaluated; arc elasticities are more relevant in
6See Bruz.lius [3] for a survey.



296                        MATEEN THOBANI
TABLE 4
Modal Split Analysis of Simulated Demand Elasticities for Select Variables
Car    Taxi   Rick    Mini   Walk     Bus
OVTT(mini)       0.01   0.02   0.05   -0.06    0.06    0.45
OVTT(bus)        0.03   0.05   0.16     0.35   0.14   --0.74
IVTT(mini)       0.01   0.02   0.04   -0.43    0.02    0.35
IVIT(bus)         0.03  0.06   0.17     0.45   0.06   -0.77
TVT(car)        -0.04    *      *       0.01    *       0.02
COSTWA(mini)      *      m     0.01   -0.10    0.01    0.08
COSTWA(bus)       *      *     0.01     0.04   0.01   -0.06
*Less than 0.01.
this study of the effect on welfare of discrete changes in the attributes. The
elasticities are given in Table 4.
All elasticities are based on a 10% change in the independent variables in
the first model of Table 3. For example, to obtain the elasticity of waiting
time for a bus [OYTI (bus)I, the waiting time for each trip in the bus
alternative was decreased by 10%. The new predicted probability shares
were then compared with those of the original model. The difference in the
probabilities was divided by 10 to yield the relevant arc elasticity for the
individual. Next, these elasticities were weighted to reflect the number of
such individuials in the population and then averaged across all trips. Note
that, while the results presented here consider only the effect of a change in
the attributes of one mode on the demand for various modes, this method
can readily be extended to reflect simultaneous changes in a combination of
variables as will be seen in the last section of the paper.
Since the value of OVTT was revealed to be very high, it is not surprising
to find elasticities with respect to OVTT to be relatively high. Cross
elasticities tend to be low except between bus and minibus which are close
substitutes. The implication of the high OVT    elasticities and low cost
elasticities is that higher gains are more likely to come as a result of
decreasing waiting time for public modes (adding more buses or minibuses)
than by making public transport cheaper. A welfare exercise which consid-
ers raising bus fares while simultaneously decreasing waiting time for a bus
is described in the last section of the paper.
AUTO OWNERSHIP ANALYSIS
The model of the decision to own a car is estimated using binary logit.
The two alternatives are to own a car or not own a car. Twenty-seven
percent of our stratified sample owned a car. A description of the indepen-
dent variables along with their means is given in Table 5,



MODE TO WORK AND AUTO OWNERSHIP                      297
TABLE 5
Auto Ownership Analysis
Description of Variables
AGGUTIL      Aggregate household utility in the trip to work-see Eq. (10) for a precise definition.
COSTINC      Annual depreciation and maintenance cost of a car divided
by annual household income.
INCOME       Annual household income in thousands of rupees in the own car altermative; else zero.
NMEMBER      Number of members in the household in the own car alternative; else zero.
DCAR         Dummy; equals one in the own car alternative; else zero.
Means of Variables
AGGU3IL       COSTINC       INCOME        NMEMBER        DCAR
Own car         -0.1297        0.2058       42.34          6.392        1.000
Own no car      -2.749         0             0             0            0
In the joint choice model, the marginal probability of owning a car
depends on, among other factors, the aggregate utility obtained by the
household in its trip to work. This variable, which has been called "inclusive
value 7 and a "measure of work place accessibility,"8 is what links the auto
ownership decision with the choice of mode to work. In this model the
aggregate utility measure is taken to be the inclusive value for the primary
earner. The term is defined in (10). For the alternative own no car, it is
constructed under the assumption that only the available public modes can
be used for the trip to work. For the own car alternativc, the accessibility
measure assumes that in addition to the available public n1odes, a car is also
available for primary earner's trip to work.
An alternative way of defining aggregate utility is to take the sum of
individual inclusive values for all earners. A sufficient condition for this
definition is that the car owned by the household can be taken to work by
each of the earners and that the household utility function for the work trip
is the sum of independent utility functions of each earner. This variable
proved insignificant leading one to believe that it is unrealistic to expect
either that every earner is able to take the car to work or that the household
utility function is the sum of independent earner utility functions. The
inclusion of the primary worker, however, proved significant suggesting that
the primary worker is the person who has exclusive access to the car in the
trip to work.
In the unconstrained estimation of Table 6, the coefficient of AGGUTIL
lies between 0 and 1 which indicates that the decision to buy an auto and
the choice of mode to work are indeed made simultaneously. Since the
7See McFadden [9].
8See Ben-Akiva and Lerman (1979).



298                       MATEEN THOBANI
TABLE 6
An Unrestricted Model of Auto Ownership
Estimated   Asymptotic
coefficient  t statistic
AGGUTIL          0.3938      2.137
COSTINC        -17.02       -2.877
INCOME           0.0124      1.327
NMEMBER        -0.0159      -0.2274
DCAR           -0.5028      -0.3664
Likelihood ratio index        0.5083
Log likelihood at convergence  -75.66
Log likelihood at zero      -153.9
Degrees of freedom            222
coefficient is different from 1, it suggests that the joint choice model is not
multinomial logit. The degree of dependence between the error terms of the
first level of the model is 0.61. Since the coefficient of AGGUTIL is not zero
and the variable is not expected to be exactly orthogonal to the other
variables, estimation of the auto ownership decision without this variable
should yield biased coefficients. When the auto ownership decision was
estimated without the AGGUTIL variable; the model yielded different
coefficients and a significantly worse fit. However, when the auto ownership
model was reestimated with the coefficients of the other variables being
constrained to those of the biased model, but AGGUTIL (and the dummy)
being free to take on any value, a likelihood ratio test showed that the
hypothesis that the coefficients of the biased model are not different from
those of the unconstrained model could not be rejected at the 5% level. This
implies that the loss in terms of bias would not have been large if the
jointness of the decision were ignored.
The cost variable for the auto ownership decision (COSTINC) is assumed
to be zero in the own no car alternative and equal to the average annual cost
of owning a car in the own car cat.gory. It is divided by the annual
household income to reflect the diminishing utility of income. Although the
coefficient is negative and significant indicating that the variable is an
important determinant in the decision to own a car, care must be taken in
interpreting the coefficient. Since cost does not vary between individuals the
coefficient actually reflects the reciprocal of income.
Income enters the model not only indirectly via its effect on COSTINC,
but also directly as a proxy for certain unobserved variables such as social
status. Its sign is found to be positive but not very significant. This is
because its effect is predominantly captured by the COSTINC term de-
scribed above.



MODE TO WORK AND AUTO OWNERSHP                  299
A priori, the sign of the number of members in the household variable
(NMEMBER) cannot be ascertained. One would expect it to be negative
since, other things being equal, a larger household would have less money
left over to own a car. On the other hand, a larger household would better
utilize a car. In this model, the former effect barely outweighed the latter
yielding a small and insignificant coefficient.
As in the last section, it was decided lo simulate changes in variables to
obtain the arc elasticity of car ownership with respect to income. The
elasticity was found to be 1.4, which is not very different from those in other
studies. In Kozel [5] the income elasticities lay between 1 and 1.3.
POLICY ANALYSIS AND CONCLUSIONS
Since the nested logit model has been derived from a theory of stochastic
utility maximization where the model estimates coefficients of the nonsto-
chastic components of a utility function, it would appear that a statement
concerning the expected utility of a given situation can be made.
McFadden [10] has derived an expression for the expectation of the utility
function used in generalized extreme value models of which our nested logit
model is a special case. The expression for our model is
li[(evll/(1-a) + eVl2/(1-a) +  + eV16/1(1))1-a
+ (eV2z/(1 e) + . .. + eV26AL-a))l-e]             (6)
where VJ, the nonstochastic component of the utility function obtained by
choosing mode ownership category i and choosing mode j to work, is given
by
Vij=8'x1+ a'yi.                        (7)
(Note: V21 does not exist since a person is not allowed to choose not to buy
a car but to take a car to work.)
The expected utility from a situation is the most meaningful measure of
welfare. To compare the welfare from two situations one has simply to
evaluate the above expression at each situation and see which is greater. If
desired, such an exercise could be repeated for various feasible changes in
independent variables to arrive at a maximum expected utility.
Here this method is used to evaluate a policy whereby the OVTT for a
bus is decreased by 10% while the bus fare is simultaneously increased by
20%. In Karachi, where the majority of buses are privately owned, it is quite
possible that the increased bus fare would induce enough additional invest-
ment in buses so as to result in a 10% decrease in OVTT for a bus.
Therefore such a scheme may be a feasible way to improve the overall utility
of consumers without using scarce government funds.



300                       MATEEN THOBANI
TABLE 7
Daily Gain to Consumers Caused by Decreasing Waiting Time for a Bus by 10%
and Increasing Fare by 20%
Income group
I       II      III     IV       V     Total
Sample gain         2.91     12.05   16.60   13.40   12.01   56.97
Trips in sample     29       60      84      75      65     313
Gain/trip (Rs)       0.1003  0.2008  0.1976  0.1787  0.1848  0.1820
Total trips (000/day)  604  1618    293     253     132    2900
Total gain (RSOOO/day)  60.6  324.9  57.9    45.2    24.4   513.0
To perform this exercise, the individual inclusive values were evaluated at
the current level of the variables and then again with the new fare and
OVJT figures for the bus. The difference in expected utility for each
individual was converted to rupees by using an application of Roy's
identity.9 The resulting sample gains for each of the five income groups are
given in Table 7. A figure for total trips to work in 1971 was obtained from
the Master Plan survey.10 Under the assumption that trips are proportional
to population and based on income distribution and population growth to
1979, estimates for the total number of trips to work in 1979 were obtained
for each income group. The rupee benefit per trip for each income group
was multiplied by the total trips made per day by each income group, to
obtain the total rupee benefit to consumers. All income groups tended to
gain more from the reduced OVTT than they lost from the increased fare.
This is not surprising when one consider the high marginal rate of substitu-
tion between OVIT and cost revealed by the model.
Before the planner decides on this policy he will need to know its effect
on the demand for various travel modes to examine macro constraints that
may have been ignored in the above exercise. To do this a method similar to
that of calculating elasticities for the modal choice decision was used. The
model was simulated with changes in independent variables induced by
the policy and the predicted probability sums were compared with those in
the earlier model. This particular change in bus attributes was found to
change the demand for cars, taxis, rickshaws, minibuses, walking, and buses
by -0.8, -6.7, -7.2, - 5.3, -2.1, and 3.1%, respectively. Demand for all
modes except the bus decreased.
In summary, the joint choice model estimated here reveals that the
decision to own a car is made simultaneously with the decision of which
mode to take to work. However, this study shows that had this simultaneity
been ignored, the loss in terms of bias in the estimated coefficients would
9See Small and Rosen [11].
°0Master Plan Office [8].



MODE TO WORK AND AUTO OWNERSHIP                           301
not have been large. The main cause of concern is that the estimated model,
like many other multinomial logit models of modal choice, finds unrealisti-
cally high values of time. Further work needs to be done to determine the
cause of this phenomenon. Otherwise, however the model has many ad-
vantages over the conventional transport demand models. It can be esti-
mated using a small household sample; it is behavioral and responsive to
most important instruments available to a planner; it allows one to make
welfare comparisons between various policy regimes; and it allows one to
calculate the effect of a policy change or change in the attributes of various
modes on the demand for each mode and car ownership.
REFERENCES
1. T. J. Adler and M. Ben-Akiva, "Joint-Choice Model for Frequency, Destination, and
Travel Mode for Shopping Trips," Transportation Res. Rec. 569 (1976).
2. A. Anas, "The Capitalization of Transportation Improvements into Housing Prices in the
Short Run: Empirical Evidence and Policy Analysis with Discrete Choice Models,"
Mimeo, Department of Civil Engineering, Northwestern University (1Q81).
3. N. Bruzelius, "The Value of Travel Tim,e," Croom Helm, London (1979).
4. T. Domencich and D. McFadden, "Urban Travel Demand: A Behavioral Analysis,"
North-Holland, Amsterdam (1975).
5. Valerie Kozel, "Travel Demand Models for Developing Countries: The Case of Bogota,
Colombia," Urban and Regional Report No. 81-26, World Bank, Washington, D.C.
(1981).
6. Steven R. Lerman, "Location, Housing, Automobile Ownership, and Mode to Work: A
Joint Choice Analysis," Transportation Res. Rec. 610 (1977).
7. Master Plan for Karachi Metropolitan Region, "Socio-Economic Homogeneous Areas,"
MP-RR/50 (1972).
8. Master Plan for Karachi Metropolitan Region, "Final Report on Transportation,"
MP-RR/94 (1974).
9. D. McFadden, Conditional logit analysis of qualitative choice behavior, in "Frontiers in
Econometrics," (P. Zarembka ed.), Academic Press, New York (1973).
10. D. McFadden, Modelling the choice of residential location, in "Spatial Interaction Theory
and Planning Models," (A. Karlquist, Ed.), North-Holland, Amsterdam (1978).
11. K. Small and H. Rosen, Applied welfare economics with discrete choice models,
Ecbnometrica, 49(1) (1981).
12. K. Train, A structured logit model of auto ownership and mode choice, Rev. Econ. Stud.,
47 (1980).



No. 287.  Michael A. Cohen, "The Challenge of Replicability: Toward a New Paradigm for
Urban Shelter in Developing Counttries," Regional Development Dialogue
No. 288. Hollis B. Chenery, 'Interaction between Theory and Observation in Developmeit,"
V'hrld Development
No. 289.  J. B. Knight and R. H. Sabot, "Educational Expansion and the Kuznets Effect," The
American Economic Review
No. 290.  Malcolm D. Bale and Urich Koester, 'Maginot Line of European Farm Policies," The
World Economy
No. 291.  Danny M. Leipziger, "Lending versus Giving: The Economics of Foreign Assistance,"
V'- rld Development
No. 292.  Gregory K. Ingram, "Land in Perspective: Its Role in the Structure of Cities," World
Congress on Land Policy, 1980
No. 293.  Rakesh Mohan and Rodrigo Villamizar, "The Evolution of Land Values in the Context
of Rapid Urban Growth: A Case Study of Bogota and Cali, Colombia," World Congress
on Land Folicy, 1980
No. 294.  Barend A. de Vries, 'International Ramifications of the External Debt Situation," The
AMEX Bank Review Special Papers
No. 295.  Rakesh Mohan, "The Morphology of Urbanisation in India," Economic and Political
Weekly
No. 296.  Dean T. Jamison and Peter R. Moock, "Farrner Education and Farm Efficiency in Nepal:
The Role of Schooling, Extension Services, and Cognitive Skills," World Development
No. 297.  Sweder van Wijnbergen, "The 'Dutch Disease': A Disease after All?" The Economic
Journal
No. 298.  Arne Drud and Wafik M. Grais, "Macroeconomic Adjustment in Thailand: Demand
Management and Supply Conditions," Journal of Policy Modeling
No. 299. Shujiro Urata, "Factor Inputs and Japanese Manufacturing Trade Structure," The Review
of Economics and Statistics
No. 300.  Dipak Mazumdar, "The Rural-Urban Wage Gap Migration and the Working of Urban
Labor Market; An Interpretation Based on a Study of the Workers of Bombay City"
Indian Economic Review
No. 301.  Gershon Feder and Roger Slade, "Contact Farmer Selection and Extension Visits: The
Training and Visit Extension System in Haryana, India," Quarterly Journal of Interna-
tional Agrculture
No. 302.  James Hanson and Jaime de Melo, "The Uruguayan Experience with Liberalization
and Stabilization, 1974-1981," Journal of Interamerican Studies and Wrld Affairs
No. 303.  Nancy Birdsall and Dean T. Jamison, "Income and Other Factors Influencing Fertility
in China," Fbpulation and Development Review
No. 304.  Graham Donaldson,"Food SeCcUrity and the Role of the Grain Trade," American Journal
of Agricultural Economics
No. 305.  William F. Steel and Yasuoki Takagi, "Small Enterprise Development and the
Employment-Output Trade-Off," Oxford Economic Papers
No. 306.  Oh Havrylyshyn and Engin Civan, "Intra-Industry Trade and the Stage of Develop-
ment: A Regression Analysis of Industrial and Developing Countries," Intra-Industry
Trade: Empirical and Methodological Aspects
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