Document11

THE 4TH INTERNATIONAL

MANAGEMENT SYSTEM AND SOCIAL

4th

International Conference on Water Supply Management System and Social Capital

Makassar, Indonesia, 16-17 Juli 2012

A Trip Mode Choice Model with Endogeneity in

Explanatory Variables

Kakuya MATSUSHIMA

1. INTRODUCTION

1.1 Endogeneity and Sorting

The importance and the complexity of the

relationship between land use and travel behavior

has been recognized for long years in the field of

transportation planning. In conventional

transportation mode,transportation system

are often treated as exogenous variables in models

and the emotional

Part of utility for travel has been ignored. In

reality, each individual has own preference for travel

mode and obtains the emotional utility if they

choose the mode consistent with their preference.

The preferences also affect residential choice

behavior of households. The tendency of people to

choose locations based on their preferences, referred

to residential sorting would be occurred. Therefore,

travel mode choice behavior and residential choice

behavior are considered to be mutually interrelated.

If residential sorting effects are ignored when

estimating mode choice of individuals, the

estimation results would be biased because of the

endogeneity in the model.

In this paper, the mechanism of residential sorting

and its effect on the economy are analyzed

building a theoretical model that explicitly treats

emotional part of utility for choosing specific

mode. We also verify the residential sorting effects

by using person trip survey data in Japan.

concludes with a discussion of model findings for

policy planning. In particular, we found

implementing soft transport policy measures that

effects of individuals’ preference for travel mode

have to be considered as one of the tools of city

planning policy measures.

INTERNATIONAL CONFERENCE ON WATER SUPPLY

MANAGEMENT SYSTEM AND SOCIAL CAPITAL

Makassar, Indonesia, July 16-17, 2012

ional Conference on Water Supply Management System and Social Capital


Explanatory Variables

MATSUSHIMA Kiyoshi KOBAYASHI Hiroshi FUKUI



recognized for long years in the field of


transportation mode,transportation system attributes


art of utility for travel has been ignored. In

reality, each individual has own preference for travel

mode and obtains the emotional utility if they

with their preference.

preferences also affect residential choice

behavior of households. The tendency of people to

locations based on their preferences, referred

to residential sorting would be occurred. Therefore,

and residential choice

behavior are considered to be mutually interrelated.

If residential sorting effects are ignored when

estimating mode choice of individuals, the

results would be biased because of the

, the mechanism of residential sorting

and its effect on the economy are analyzed by

building a theoretical model that explicitly treats

emotional part of utility for choosing specific travel

mode. We also verify the residential sorting effects

rson trip survey data in Japan. The paper

concludes with a discussion of model findings for

policy planning. In particular, we found

implementing soft transport policy measures that

effects of individuals’ preference for travel mode

s one of the tools of city

1.2 Endogeneity Bias

When the error term and explanatory variables

correlated each other, estimated parameters may be

biased without any consideration of endogeneity

problem. This type of bias is called

bias. Researchers should pay attention to the

endogeneity because implemented policies form the

analysis without any consideration of the

endogeneity issues. Let us start from an example in

linear regression model in order to understand the

endogeneity bias. See the following linear

regression equation.

y X β ε= +

Here y is a dependent variable with

X=(X1,X2) is a matrix of explanatory variables with

(n × k), and ϵ is an error term vector with

The conditional expected value of estimated

parameters β is derived as follows by the least

square method.

1( )E X X X X E y Xβ − ′ ′ = ɶ

1( ) XX X X E Xβ ε−′ ′= +

The estimated parameters are

when 0E Xε = holds.

explanatory variables X2((n × k

the error term, that is, E Xε not true. X2 is called as entogenous explanatory

variable in this case.

Observational error, Omitted variable,

112


FUKUI

When the error term and explanatory variables

correlated each other, estimated parameters may be

biased without any consideration of endogeneity

problem. This type of bias is called as endogeneity

bias. Researchers should pay attention to the

endogeneity because implemented policies form the

analysis without any consideration of the

Let us start from an example in

linear regression model in order to understand the

bias. See the following linear

(1)

Here y is a dependent variable with ( 1)n×2) is a matrix of explanatory variables with

is an error term vector with (n × 1).

The conditional expected value of estimated

is derived as follows by the least

E X X X X E y X

1( )X X X E Xβ ε′ ′ (2)

The estimated parameters are consistent estimator

However, when some

((n × k2)) correlated with

2 0E Xε ≠ , this result is

is called as entogenous explanatory

Observational error, Omitted variable,

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synchronization are main factors to bring about the

endogeneity issues. Dataset used for the estimation

may contain observational error when those are the

result after taking means or approximation. The

following equation holds with observational error

X X u= +ɶ (3)

Here Xɶ is a matrix with observed explanatory

variables, X is the matrix of true explanatory

variables, and u is a vector with error term. Let us

assme that reseachers try to esstimate the following

relation.

y X β ε= + (4)

As we may have observational error, the following

equation will be used for the estimation.

y X uβ ε β= + −ɶ (5)

X β ε= +ɶ ɶ

In this case, the error term ϵ is correlated with

explanatory variables Xɶ , which gives us a biased

estimated parameters βɶ because it is eqipped with

the endonegeity. If we apply general the least square

estimation for these cases, attenuation may occur

(Green 2007). Next, let us consider omitted variable

with the following equation.

y X Uβ α ε= + + (6)

Here 0E XUε = holds. Let us assme that U are

not observed and taken as omitted variable. The

error term is caluclated as Uε α ε= +ɶ , which

brings about 0a ≠ . The estimation result of β is

biased when U and X are correlated. Thirdly,

consider the case with synchronization. It may

happen when at least one explanatory variable and

the dependent variable are simultaneously chosen.

For example, we can observe this phenomenon in

the relation which shows the demand and supply in

markets. If we estimate parameters by ignoring the

structure, estimated parameters are biased.

2 ENDOGENEITY IN DISCRETE CHOICE

MODEL

2.1 A Case of Linear Regression Model

One of the most general methodology which

consider the endogeneity in linear regression model

is the control function method. A control function

(IV: Instrumental Variable) will be found when we

estimate parameters by this methodology. It plays an

important role when we consider the case with

discrete choice model. The control variable shoud

satisfy the following conditions.

(I) It should not have any correlation with the error

term.

(II) It should be correlated with the endogenous

variable.

Let us consider the following linear regression

model.

, 1,...,i i iY X i nβ ε= + = (7)

Assume that an explanatory variable Xi is correlated

with the error term ϵi. The endogeneity bias can be

observed if we apply the general OLS estimation.

Researches get a variable Zi which satisfies the

conditions above and estimate parameters by the

control variable method. The following equation is

satisfied by the condition (I).

1

( )i i iZ Y Xn

β−∑ (8)

The estimated control variable is diffined as follows.

( )( )

( )( )

i iIV

i i

Z Z Y Y

Z Z X Xβ

− −=

− −∑∑

S

S

Z

ZX

εβ= + (9)

When we take a limitation of estimated control

variable, the following equation is derived with

conditions (I) and (II).

( , )

lim( , )

IV Cov Zp

Cov Z X

εβ β= +

β= (10)

Then the estimated control variable satisfied

consistency. The problem is which data is used for

the control variable. Researches should explain the

appropriateness about the adopted control variable.

2.2 Endogeneity in Discrete Choice Models

Generally speaking, the methodology cannot be

applied to the case of discrete choice models due to

the non-linearity. Several alternative methodologies

to estimate parameters in discrete choice models are

proposed to conquer it (Louviere et al. 2005). the

BLP approach and the control function approach are

proposed as major methodologies. Berry(1994).

Berry. Levinsohn and Pakes(1995) proposed a

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methodology (hereafter BLP) to estimate parameters

with endogeneity issues. The consumption behavior

to purchase differentiated goods is estimated by

BLP approach based upon the discrete choice

model. Let us explain about BLP model with the

following. Assume that a good in market m = 1, · · ·

,M is supplied by firms j = 1, · · · , J. A consumer n

in each market purchases a good from one of the

firms. The utility when households purchase a good

in firm j at market m is shown as follows.

u

n jm jm jm njmnjm q xα β ξ ε= + + + (11)

where qjm is the price of good n, xjm is the

observed characteristics of the good, ξjm is the

unobservedcharacteristics, αn, βn are unknown

parameters to be estimated, and ϵnjm is an error

term. αn,βn are expressed as follows.

n

n n

n

D vα αβ β

= + Π +

∑ (12)

Here Dn is a vector with d dimension about social

economic variables for households, and Π is a

matrix with (K + 1) × d, and Σ is an adjusted matrix

with (K + 1) × (K + 1). Let us assume that θ = (θ1,

θ2) is a vector which contains all parameters to be

estimated. Then θ1 = (α, β)·θ2 = (Π,Σ, η) is satisfied.

Eq. (11) can be rewritten as follows.

, , 1 , , , 2 ,( ; ) ( ; )njm jm jm jm jm jm jm n n njmu q x q x D vδ ξ θ θ ε= + +

where .jm njmvδ are expressed as follows.

, (jm jm jm jm njm jm jm n nx q v q x D vδ β α ξ = + + = Π + ∑ (13)

δjm is a mean utility which households in market

purchase “outside good” , which is homogenous for

all households in the market. Each household has an

option to purchase other goods. It means that

households prefer to purchase ”outside good”. The

utility which she/he gets by purchasing it can be

normalized as follows.

un0m = ϵn0m (14)

Households purchase a good which gives the

highest utility. Define a set of households’

characteristics

who purchase good j in market m as follows.

. . . 2 0( , , ; ) {( , , ,..., ) 0,... }jm m m m n n n m nJm njm nlmA x q D v u u l Jδ θ ε ε= ≥ ∀ = (15)

. 1( ,..., )m m Jmx x x= , . 1( ,..., )m m Jmq q q= , and

. 1( ,..., )m m Jmδ δ δ= are satisfied. Let us also assume

that D, v, and ϵ are independent. The market share of

good j in market m can be derived as follows.

. . . 2ˆ( , , ; ) ( , , ) ( ) ( ) ( )

jm jm

m

jm m m m v D

A A

s x q dP D v dP dP v dP Dεδ θ ε ε= ∫ ∫ (16)

P shows the distribution of population for each. By

assuming ϵnjm follows Gumbel distribution with

i.i.d., the following will be derived.

. . . 2

1

exp( )ˆ( , , ; ) ( ) ( )

1 exp( )

jm njm m

jm m m m D vJ

v D lm nlml

vs x q dP D dP v

vλ

δδ θ

δ=

+=

+ +∫ ∫ ∫ ∑

(17)

2.3 The Estimation of Parameters

Only the error term in the equation isjmξ as

( , , )n nD v nε are already integrated in equation (17).

A factor jmξ which is not observed in market m are

correlated withe the endogenous variable qjm, that’s

why an estimation methodology with considering

endogeneity issues is necessary to be adopted. One

of the advantages of BLP methodology for

parameter estimation is to treat this type of issues

explicitly. A control variable matrix Z is introduced

for the estimation, which satisfies the following

condition.

*( ) 0E Z ω θ′ = (18)

Here ω(·) is a function of parameters to show the

error term. θ∗ is the true value for parameters. The

GMM estimator is expressed as follows.

1ˆ arg min ( ) ( ),Z Zθθ ω θ ω θ−′ ′= Φ (19)

where Φ is a consistent estimator for [ ]E Z Zωω′ ′

which is callsed as a weight matrix, an inverse

matrix of variance-covariance matrix of the

moment. It is necessary to express the error term as

a function of parameters in order to derive the

GMMestimator by equation (19). Berry(1994)

defines jmξ as an error term, which is different form

the difference between the observed share S and the

estimated share s. The meaning is easily

interpretedeconomically by defining jmξ as an error

term. The mean utility is a function of ξ defined in

equation (13). It is necessary to derive the mean

utility jmδ to have ξjm. In order to achieve it, let us

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solve thefollowing equations where the observed

share and the estimated share of goods in each zone

are equal.

. . . . 2 .( , , ; )m m m m ms x q Sδ θ = m = 1, · · · ,M (20)

BLP methodology is not applied to cases with small

samples as market share should be observed. It

cannot be applied when a share for each product is

small enough, because market share should be

observed with only small sample error. In the field

of demand estimation models (e.g. Fox(2007)),

there are also other cases which BLP estimation

cannot be applied to models which are not

consistent with the framework of BLP. Control

function method is effective for these cases. It is

widely adopted compared with BLP approach, and

parameters are easily estimated. Hereafter, the

outline of controlfunction method is explained

followed by Petrin et al.(2010). Assume that

household n select one of the choices J. Her utility

by choosing the choice j is expressed as follows.

( , , ) ,nj nj nj n njU V y x β ε= + (21)

where ynj is the observed endogenous variable (e.g.,

prices) and xnj, βn are observed exogenous

parameter vector which shows the preference, and

ϵnj is unobservable error. Assume also that the

endogenous variable ynj are correlated with the error

term ϵnj. Control function approach tries to create

substitutable variables for endogenous variable ynj

correlated with the error term ϵnj. The rest of the

endogenous variable is independent from the

unobserved error term, so the general estimation

methodology can be applied. The endogenous

variable ynj is expressed as the function of

exogenous variables, the control variable and the

error term.

( , , )nj n n ny W x z µ= (22)

in which ,n njµ ε are independent from ,n nx z and

dependent on ,n njµ ε . Let us consider a simple case

where the unovserved error is a function with single

varialbe µnj.

( , ; )nj n n njy W x z γ µ= + . (23)

Here γ is a parameter. As a control variable satisfies

the condition for exogenous variables, the following

equation is satisfied.

( , , )nj nj nj n n nje y E W x zε ε γ µ = + (24)

nj njE ε µ =

The error term njµ explains some parts of the

endogenous variable njy which is correlated with

njε

Divide the error term ϵnj into the condtitional mean

and its difference.

nj nj nj njE uε ε ε = + ɶ (25)

The conditional mean of ϵnj, E[ϵnj|µnj], is called as a

control function which is represented by CF(µnj; λ).

CF(µnj; λ) = E[ϵnj|µnj] (26)

λ is a parameter for estimation. When a household

select a choice j, her utility is derived as follows.

Unj = V (ynj, xn, βn) + CF(µnj; λ) + njεɶ (27)

The probability for household n to choose j is

represented by

Pr ( )nj nj nkP ob U U= >

( ) ( , )

nj nj nk nk nk n n nnj

I V CF V CF k j f d dε ε β ε ε β= + + > + + ∨ ≠∫∫ ɶ ɶ ɶ ɶ (28)

Where nεɶ = ⟨ nεɶ ∀j⟩, µn = ⟨µnj∀j⟩, and the

simultaneous density function is f(·).

Vnj = V (ynj, xnj, βn) (29)

CFnj = CF(µnj, λ)

is also satisfied. Equation (28) represents the

probability in general choice models except for that

a control function is introduced as an explanatory

variable. It should be pointed out that the integration

in equation (28) is taken for the conditional

distribution εɶ , not for the error ϵ. ϵ is correlated

with the endogenous variable ynj, but εɶ is not

correlated with that. We can estimate the model with

the following procedure.

1. A control function CF(µnj; λ) is specified.

2. the residual µnj is estimated.

3.Equation (28) where a control function is

introduced as one of explanatory variables is

estimated.

Take a simple example to specify a control function

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CF(·; λ). If we assume that ϵnj and µnj follows the

normal distribution with mean 0, the following

equation is satisfied form the characteristic of

normaldistribution.

CF(µnj; λ) = E[ϵnj|µnj] (30)

= λµnj (31)

When the household choose j, her utility is discribed

as follows

Unj = V (ynj, xn, βn) + λµnj + εɶ nj (32)

In order to estimate parameters in equation (32), µnj

should be ovserved. As it is not ovserved ingeneral,

it is substituted by the estimated ynj. Regard the

endogenous variable ynj as the dependent variable

in equation (35a), and take a regression by taking

exogenous variables and the control variable as

explanatory variables. The residual µnj = ynj −W(xn,

zn; γˆ) is used for estimation.

2.4 Adjustment of standard error with Bootstrap

Method

As a generated regressor (Pagan 1984) ˆµ is used for

the second estimation in control function method,

the standard error of estimated parameters are

under-estimated if the general methodology is

applied to derive the standard error. The effect of

additional error should be considered by applying

the generated regressor. The standard error is

adjusted by applying the bootstrap method (Pertin

and Train (2010)) in this paper. After the residual is

calculated with samples thorough bootstrap method,

parameters in a discrete choice model with the

residual are estimated. This process is repeated and

then derive the variance of estimated parameters for

each. Here is the procedure.

(1) The least square method is applied to yn = γzn+µn,

n = 1, · · · ,N at the first step of the control

function method, and derive the residual { u n, n

= 1, · · · ,N}.

(2) Calculate likelihood distribution F where the

probability 1/N are allocated for each point of the

residual. Then extract the bootstrap sample { u n,

i = 1, · · · ,N} with size N.

(3) Calculate the bootstrap sample yn , i = 1, · · · ,N

of the endogenous variable yn with yn = n+ u n.

(4) Derive the residual {ˆµ∗n(b), n = 1, · · · ,N} by

the first step of the control function method with

{ y n , zn}, n = 1, · · · ,N.

(5) Parameters of the discrete choice model are

estimated by adding the residual in (4) as an

explanatory variable. Define the estimated

parameter vector as β *(b).

(6) Calculate the estimated values { β ∗(b)}, b = 1,

· · · ,B by repeating B times from (1) to (5).

2. A CASE STUDY

3.1 Background

A large variety of policies for sustainable urban

development are investigated in developed countries

to attack important issues like global environmental

problems, and sprawl in urban area. The concept of

compact city is proposed in Europe, which plays an

important role for the discussion about the

sustainable regional structure. In Japan, in which

population started to decrease with an ageing

society, the development of sustainable area and the

intensive style of regional structure are key issues

when we consider policies for urban and regional

development. Japanese central government supports

municipalities to develop policies for low-carbon

society by introducing the guideline for them.

Policies, such as the change of regional structure to

more intensive way and the equipment of public

transportation system are taken as examples in the

guideline. The discussion where the regional

structure will be changed from that highly depend

on automobiles by navigating the urban structure

more compact assumes one way casual relation that

living environment affects travel behavior of

households. However, it is not clear whether this

relation holds or not because the relation between

the living environment and travel behavior. Most of

proposed trip mode choice models do not consider

the households’ preference for trip mode.

Households may decide their residence by

considering their preference toward trip mode,

which is a different assumption from that where

they decide trip behavior given the living

environment. They may decide their residence

where they can enjoy their preferable travel mode

easily. We may define it as ”residential sorting”. In

this case, the service level of transportation which

they enjoy is interpreted as the result of their

selection about the residence. Observed data are

considered as endogenous (not exogenous) variables

which are correlated with the error term as a result.

If we estimate parameters without any consideration

of residential sorting, estimated parameters might be

biased.

3.2 Target Area

We may develop a trip mode choice model with

dataset derived from the 4th person trip survey in

Kansai area, Japan. We had extract trip data with

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origins as Suma, Tarumi, and Nishi ward in Kobe

city and destination as Chuo ward in Kobe city.

Here we consider two type of trip mode (railway

and automobile) for simplicity. Only individuals

who have the driver license are extracted. The

sample size is 758.

3.3 The Model

Consider a discrete choice model for commuting

trip. By setting her utility when individual n choose

railway as Un1, and that for automobile as Un2, the

probability to choose raiwaly is expressed as

follows.

Pn(1) = prob{Un1 − Un2 > 0} (33)

We assume a linear utility function as follows.

Unj = V (ynj, xnj, βn) + ϵnj, (34)

where ynj is an endogenous variable, β is an

estimated parameter vector, xn is explanatory

variable vector, and ϵn is the error term. The

following explanatory variables are considered;

Sex(Male:0 and Female:1), Age(More than 50:0 and

less than 50:1), a dummy variable to show the

possession of cars(households without cars:0, those

with cars:1), trip time, access time, and egress time.

Trip time is a common variable for both modes,

while a dummy variable for car possession is only

for automobiles, access time and egress time are

only for railways. We assume that individuals have

their own preference toward trip mode which is not

observed. They may choose their residence given

their preference, which may bring about self-

selection mechanism about their residence.

Individuals with the preference toward railway may

select their residence which is close to stations.

Access time is considered as one of endogenous

variables in this case. Assume that the unobservable

error term which affects the endogenous variable is

expressed as µnj and that ϵnj and µnj follows the

normal distribution with mean 0. The following

equations are satisfied.

ynj = W(xn, zn; γ) + µnj (35a)

CF(µnj; λ) = E[ϵnj|µnj] = λµnj (35b)

Her utility when she choose mode j is

Unj = V (ynj, xn, βn) + λµnj + εɶ nj. (36)

The control function CFnj is considered as a

psychological utility for the trip mode choice. µ

explains the effect to the choice of access time by

considering the preference for trip mode.

3.4 Control Function

As we have only one endogenous variable, we need

to install a control variable other than

thesevariables. In this paper, declared land price of

thier residence is used as the control variable

Figure1 Correlation between the endogenous

variable and the control variable

Figure1 shows the relation between the endogenous

variable and the control variable. We can observe

negative correlation where residential area with high

land price is close to the nearest station. See the area

with its land price 20 thousand yen/m2. We can see

that access time to the closest station is distributed

from 10 to 20 minutes from the figure. Some areas

are far from the station, while the others are close to

the station, which shows that households choose

their residence by considering their preference

toward trip mode given the same land price. the

residual in the regression analysis is interpreted as a

variable about the preference to trip mode as

households who live in areas with shorter access

time may prefer to choose railway for commuting.

Households who has positive the residual (it means

longer access time) may have preference toward

automobiles, while those with negative the

Table1 The Comparison of Two Methodologies

Normal Estimation Control function method

Estim

ated

Standa

rd Param

eter

t-

valu

e Erro

r

Estim

ated Param

eter

Standard

Error

t-valu

e

Sex (Female:1

) 1.559 0.295

5.27

7 1.696 0.303 5.6

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Age (More tha

n 50:1) 0.248 0.225 1.10

5 0.086 0.235 0.36

4

Possesion of c

ars

0.89

8

0.36

8

2.4

4

1.02

4

0.37

4

2.7

42

Trip time -

0.349 0.141

-2.476 0.698

0.173 -4.0

Access time -

1.383 0.167

-8.274 0.104

0.287

0.363

Egress time -0.2 0.223

-0.897

-0.296

0.239

-1.239

Constant 4.175 0.513 8.14 2.796 0.559

5.005

The residual

-2.476

0.453

-6.153

residual (it means shorter access time) may prefer to

use railway. This hypothesis will be examined by

checking the sign in the estimation.

3.5 The Result of Estimation

Table{1 summarizes the result of estimation both by

general methodology and control function method.

The estimated parameter about access time is

different for both cases. The parameter is not

significant by the control function method in

addition. As the residual µ is significant, this

variable is found to be endogenous variable. The

sign of the parameter is also appropriate as we

assume that positive the residual shows the

preference toward automobile and negative residual

shows the preference for public transportation.

3.6 Policy Implications

We can say form the estimated result that Access

time is an endogenous variable for the trip mode

choice model and correlated with unobservable

variable such as the preference toward public

transportation. It is effective to ally control function

method for the estimation in order to get rid of the

endogeneity bias. Households may choose their

residence by considering the preferable trip mode in

advance. That is, the residential sorting can be

observed thorough the mechanism of residential

selection. It means that intensive regional structure

may not be realized only by introducing policies to

decrease access time, such as the increase in the

frequency of public transportation to the station. It is

also necessary to introducing policies which affect

their preference in order to change the regional

structure thorough residential sorting mechanism.

Some municipalities may attract individuals with

strong preference toward public transportation,

which brings about the increase in population who

are possibly commute by public transportation.

Thanks to the scale economy, such municipalities

can supply rich public transportation service with

cheaper cost, which also attract more individuals

with the preference toward public transportation.

4 Conclusion



has been recognized for long years in the field of


transportation mode, transportation system attributes


and the emotional part of utility for travel has been

ignored. In reality, each individual has own

preference for travel mode and obtains the

emotional utility if they choose the mode consistent

with their preference. The preferences also affect

residential choice behavior of households. The

tendency of people to choose locations based on

their preferences, referred to residential sorting

would be occurred. Therefore, travel mode choice

behavior and residential choice behavior are

considered to be mutually interrelated. If residential

sorting effects are ignored when estimating mode

choice of individuals, the estimation results would

be biased because of the endogeneity in the model.

This paper proposes a methodology to tackle with

endogeneity issues in discrete choice models. Two

methods, BLP approach and control function

approach are explained and their characteristics are

summarized. The hypothesis that access time in trip

mode choice model is endogenous is proposed and

tested with empirical analysis with person trip

survey data in Kansai area, Japan. The estimation

result shows that access time for the public

transportation is endogenous variable, which

explains

the importance of control function method to prove

the existence of ”residential sorting”. A political

implication is derived from the result, that is,

policies which try to attract individuals who has

similar preference toward trip mode.

REFERENCES

Berry, S. : Estimating Discrete-Choice Models of

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