tiểu luận kinh tế lượng FACTORS THAT INFLUENCE THE LEVEL OF USING BUS AS a MEANS OF TRANSPORTATION IN THE URBAN AREAS

Describe statistical sample data Source: we calculated it based on the statistic in the Gretl software Where: - BUSTRAVL : the number of people using the bus in an hour in a locality.. C

FOREIGN TRADE UNIVERSITY FACULTY

OF INTERNATIONAL ECONOMICS

=====000=====

ECONOMETRIC REPORT

FACTORS THAT INFLUENCE THE LEVEL OF

USING BUS AS A MEANS OF

TRANSPORTATION IN THE URBAN AREAS

Instructor: Assoc Prof Tu Thuy Anh

Group 3 - JIB – K57

1815520167 Le Thuy Hang English 06

1815520164 Nguyen Thi Thu Ha English 06

1815520194 Nguyen Phuong Linh English 06

Hanoi - October 2019

TABLE OF CONTENTS

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I INTRODUCTION 2

II THEORETICAL BASIS 3

3 RESEARCH METHOD 4

3.1 Model Research: 4

3.2 Information source: 4

3.3 Estimation method: 4

4 ESTIMATION OF THE ECONOMETRIC MODEL 5

4.1 Data description: 5

4.1.1 Statistical description table 5

4.1.2 The table describes the correlation among variables 6

4.2 Estimated result and disussion: 6

4.2.1 Estimated result: 6

4.2.2 Discussion 15

CONCLUSION 16

1 INTRODUCTION

Buses have been a very important and convenient means of transportation for people Especially, nowadays, public transport becomes a global trend because more and more people want to protect the environment and save materials In addition, along with the increasing demand for public transportation, buses take priority over the vehicles on the road In developed countries in the world: USA, Western Europe, Japan, buses become the main means of transportation These developed countries often have hundreds

of kilometers length bus routes in order to meet the requirements of transport of the citizen The citizen goes to school by bus, goes to work by bus and hangs out by bus too Besides, using personal vehicles makes you pay a lot of money for gasoline, oil, repair costs, equipment maintenance, car wash, even pay the monthly parking fee, taking bus if different Using bus can greatly reduce our costs compared to using personal vehicle For many people, using motorbikes is much more convenient and time-saving, but we always have to bring a raincoat or a sundress, or have a mask in the trunk We also suffered standing for 15 minutes outdoors in the 40 degree Celsius on the road and standing for hours inhaling dust and smoke Instead, we can enjoy cool conditioning when taking the bus Therefore, the using bus as a means of transportation brings many benefits and widespread But not everyone chooses the bus to move Many people don’t want to take the bus for objective reasons such as hustle and bustle on the bus on rush hour or subjective reason is car sickness

In order to find out more about this issue, our team decided to study the topic: “Factors that influence the level of using bus as a means of transportation in the urban areas.”

To the extent of purpose and resources, there are still deficiencies in this econometrics assignment but we look forward to providing readers with a decent view of the overall of the data set given and the knowledge that we have gained through Dr Tu Thuy Anh’s Econometrics course

2 THEORETICAL BASIS

Bus is a very popular transportation these days, especially to student and the low income Number of bus user depends on some factors which can be mentioned as:

 Fare: when increase the price will facilitate the innovation of transportation and the

extension of the service network, the bus routes will be covered throughout and near

to people Then, there will be a higher proportion of bus user

 Income: to the low or medium income, they tend to take public transportation in order

to minimize the moving cost Relative to microeconomic, pertain to the medium or high class goods, rise in consumer income drags along higher level of use in goods and contrariwise

 Population: higher popupation results to the overload of private transpotation, and it’s

when people switch to public transportation as bus to decrease number of vehicles as well as to minimize the moving cost as mentioned above

Furthermore, there are many other factors affect to the number of bus user every single hour but in this survey, we only consider the paradigm of three factors are ticket price, per capita income and population that have affection to the number of bus user each hour

3 RESEARCH METHOD

This research based on Quantitative research method, specifically as following:

3.1 Research Model:

- Structural form: Y = f(X 2 , X 3 , X 4 )

- Estimation form: BUSTRAVL = β1 + β 2 + β 3 + β 4 + u i

Inside:

Y i

BUSTRAVL The level of using bus in Thousand Dependent

variable

variable

X4 POP Population in the urban area Thousand Independent

Table 1 Variables of model

3.2 Information source:

The data above was taken by authors from Data warehouse Ramanathan, data

4-4, Gretl software.

3.3 Estimation method:

- The model above was estimated by Ordinary Least Square (OLS)

- Then, authors conducted tests , including:

+ Missing variable test

+ Normal distribution test

+ Multicollinearity test

+ Error Variance

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4 ESTIMATION OF THE ECONOMETRIC MODEL

4.1 Data description:

4.1.1 Statistical description table

Summary Statistics, using the observations 1 – 40

Variable Median Minimum Maximum Std Dev Missing

obs.

Exhibit 2 Describe statistical sample data

(Source: we calculated it based on the statistic in the Gretl software)

Where:

- BUSTRAVL : the number of people using the bus in an hour in a locality The

difference between the lowest value and the highest value is quite high: on average 1.589.600 people/hour

- FARE : the bus fares used in the metropolitan areas are 0.5 USD with the lowest

price and 1.5 USD with the highest price The difference is not significant The average price is 0.8 USD

- INCOME : The average annual income of urban bus users is at an average level

in the US, with the difference between the highest value (21 886 USD) and the lowest

value (12 349 USD) is not large It can be seen that this is the average salary in the US, with the highest salary of 21 886 USD is still not high in the US

- POP : The average population of the US is about 555 000 people, and it can be

considered as a high population level However, the difference between the largest value (7

323 300 people) and the smallest value (167 000 people) is substantial In the US, there are many cities with a high population, up to 7 323 300 people such as New York, Los Angles Meanwhile, the bus users are just about 18 000 people We can conclude that: in the big, densely populated and developed cities, the more income people get, the less they use the

bus In the sparsely populated city, for example about 167 000 people, maybe the infrastructure has not been developed yet, the demand for traveling is not high so people don’t use the bus often

4.1.2 The table describes the correlation among variables

Correlation coefficients, using the observations 1 - 40 5% critical value (two-tailed) = 0, 3120 for n = 40

1,0000 -0,0755 0,0149 FARE

1,0000 POP

Exhibit 3 Correlation matrix

(Source: we calculated it based on the statistic in the Gretl software)

From the matrix, it can be inferred that the correlation between bustravl and each of the independent variables Specifically:

r (BUSTRAVL,FARE) = - 0,0480  low correlation level, negative correlation

r (BUSTRAVL,INCOME) = 0,2287  low correlation level, posittive correlation

r (BUSTRAVL,POP) = 0,9313  high correlation level, postitive correlation

4.2 Estimated result and disussion:

4.2.1 Estimated result:

Model 1: OLS, using observations 1-40 Independent variable: BUSTRAVL

R-squared 0,880001 Adjusted R-squared 0,870001

Excluding the constant, p-value was highest for variable 2 (FARE)

Exhibit 4 Estimated result based on OLS method

(Source: we calculated it based on the statistic in the Gretl software)

From the exhibit 4, we have a random sample regression model:

BUSTRAVL = 2683,59 − 609,126 FARE − 0,116272 INCOME + 1,88836 POP + e i

* From the result, it can be inferred that:

β̂1 = 2683,59: the level of traveling by bus in urban areas is 2683,59 thousand people/hour in case of not being influenced by the other factors.

β̂2 = − 609,126: If the bus fares increase 1 USD, the people traveling by bus decrease by 609,126 thousand people/hour, in case of the other factors not changed.

β̂3 = − 0,116272: If per capita income increases by 1 USD/ person, the level of travel by bus in the city decreases by 0,116272 thousand

people/hour in case of the other factors unchanged.

β̂4 = 1,88836: If the population in the metropolitan areas increases 1 thousand people, the level of traveling by bus increases 1,88836

thousand people/hour in case of the other factors unchanged.

* The level of relevance of the model

Ta có: R2 = 0,880001

 The level of relevance of the model is 88,0001 %: the variations of the FARE, INCOME, and POP variables explain 88,001% of the average variation of the BUSTRAVL dependent variable

* Testing regression coefficients

Testing hypothesis:

- We have: {H0: βi = 0 H 1 : β i ≠ 0

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- From exhibit 4, it can be inferred:

P-value(β 2 )= 0,23519 > 5% => Not evident to reject H 0 P-value(β 3 )= 0,11159 > 5% => Not evident to reject H 0

P-value(β 4 )= 1,00e-017 < 0,00001< 5% => Reject H 0 , β 4 is significant.

* Tests of hypothetical violations:

a Test omitted variables bias:

Auxiliary regression for RESET specification

test OLS, using observations 1-40 Dependent

variable: BUSTRAVL

p-value

-

Test statistic: F = 2,753232,

with p-value = P(F(2,34) > 2,75323) = 0,0779

Exhibit 5 Ramsey’s RESET

(Source: we calculated it based on the statistic in the Gretl software)

 P-value > 0,05 so at the 5% significant level, the model does not suffer from omitted

variables bias.

b Test the normal distribution:

Frequency distribution for uhat1, obs 1-40

number of bins = 7, mean = -1,42109e-014, sd = 876,78

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Test for null hypothesis of normal distribution:

Chi-square(2) = 0,805 with p-value 0,66870

Exhibit 6 Test the normal distribution

(Source: we calculated it based on the statistic in the Gretl software)

c Multicollinearity test

 Signal 1 : High 2 and low t-statistics

Low t-ration of variables FARE, INCOME meanwhile t-ration of variable POP is high Therefore, regression coefficients of independent POP are statistically significant, the rest are not

 The model maybe exist multicollinearity

 Signal 2 : Correlation between independent variables:

Correlation coefficients, using the observations 1 - 40 5% critical value (two-tailed) = 0,3120 for n = 40

Exhibit 7 Matrix of correlation between independent variables

(Source: we calculated it based on the statistic in the Gretl software)

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Because cov between variables has an absolute value of less than 0.8, the model does not have multicollinearity

 The model does not have multicollinearity.

 Signal 3 : Conduct additional regression

The main regression has = 0.88001

Additional regression models:

 FARE regression according to INCOME and POP:

Model 2: OLS, using observations 1-40

Independent variable: FARE

INCOME −1,20666e-05 2,31427e-05 −0,5214 0,6052

Exhibit 8 Estimated the regression model of FARE independent variable according to INCOME and POP

(Source: we calculated it based on the statistic in the Gretl software)

 2 < 2(0.007515 < 0.88001) so multicollinearity does not exist

 INCOME regression according to FARE and POP:

Model 3: OLS, using observations 1-40

Independent variable: INCOME

Exhibit 9 Estimated the regression model of INCOME independent variable according to FARE and POP

(Source: we calculated it based on the statistic in the Gretl software)

 Vì 2 < 2 (0,118778 < 0,88001) so multicollinearity does not exist

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 POP regression according to FARE and INCOME:

Model 4: OLS, using observations 1-40

Independent variable: POP

Exhibit 10 Estimated the regression model of POP independent variable according to FARE and INCOME (Source: we calculated it based on the statistic in the Gretl software)

 Singal 4 : Use the variance increment factor VIF

Variance Inflation Factors

Minimum possible value = 1.0

Values > 10.0 may indicate a collinearity problem

VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple

correlation coefficient

between variable j and the other independent variables

Properties of matrix X'X:

1-norm = 1,2059628e+010

Determinant = 1,1108538e+018

Reciprocal condition number = 3,3049137e-011

Exhibit 11 Test the variance increase factor

(Source: we calculated it based on the statistic in the Gretl software) The variance increase factor of all 3 variables is less than 10

 The model does not have multicollinearity

CONCLUSION: The model does not suffer from multicollinearity

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d Testing the error variance:

 Signal 1: Using qualitative methods (visual methods)

Graph of ei according to BUSTRAVL

Comment: From the graph, the values on the graph are not evenly distributed

 Have the sign of disease error variance

 Signal 2: UsingWhite-test

- Conduct regression of sub-model:

e2i = α 1 + α 2 FARE + α 3 INCOME + α 4 POP + α 5 FARE2 + α 6 FARE INCOME + α 7 FARE POP + α 8 INCOME2 + α 9 INCOME POP +

α 10 POP2 + v i

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- The result shown in the table:

White's test for heteroskedasticity

OLS, using observations 1-40

Dependent variable: uhat^2

Unadjusted R-squared = 0,145698

Test statistic: TR^2 = 5,827904,

with p-value = P(Chi-square(9) > 5,827904) = 0,757011

Exhibit 12 Testing error variance with the quantitive method White-test

(Source: we calculated it based on the statistic in the Gretl software) H0: PSSS unchanged

- Hypothesis: { H 1 : PSSS changed

- p-valute = 0.757011 > 5% so reject H0

 The model suffers from PSSS at 5% significant level

* Solution: Using verification Robust

Model 5: OLS, using observations 1-40 Independent variable: BUSTRAVL Heteroskedasticity-robust standard errors,

variant HC1

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Mean dependent var 1933,175 S.D dependent var 2431,757 Sum squared resid 27674784 S.E of regression 876,7805

Log-likelihood −325,7006 Akaike criterion 659,4012 Schwarz criterion 666,1567 Hannan-Quinn 661,8438

Recalibrating the model (used Robust Test) by White test, we get the following results:

White's test for heteroskedasticity

OLS, using observations 1-40

Dependent variable: uhat^2

Unadjusted R-squared = 0,145698

Test statistic: TR^2 = 5,827904,

with p-value = P(Chi-square(9) > 5,827904) = 0,757011

H0: PSSS unchanged

- Hypothesis: {

H 1 : PSSS changed

- p-valute = 0.757011 > 5%, so rejectH0

 The model still suffers from PSSS at 5% significant level

However, because the Robust test has controlled the error variance, we can still use the model after the Robust without affecting the deductive

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4.2.2 Discussion

The model we used to interpret is:

BUSTRAVEL = 2683.59 – 609.126.FARE – 0.116272.INCOME + 1.88836.POP (1) From the above model estimation, tests and solutions, we have drawn the best model available:

BUSTRAVEL = 2683.59 – 609.126.FARE – 0.116272.INCOME + 1.88836.POP (2) Model (2) has been applied with Robust to control the error: Heteroscedasticity

 Model (1) has the error: Heteroscedasticity.

 For the Heteroscedasticity, our team implemented Robust test and obtained the model (2), although it could not fix the errors but was controlled and the model could still be used to infer without being affected by errors

 The used model is consistent with economic theory Firstly, taking bus is a secondary commodity, so when the income of passenger increases to a certain extent and bus fare increases they tend to reduce bus consumption , instead, they use other alternative means such as motorcycles, taxis, cars, Therefore, the regression coefficients of the two variables INCOME, negative FARE are appropriate Secondly, with the growth of population, more and more people using bus as a means of transportation is reasonable, so the regression coefficient of positive POP variables is appropriate

 The significance level of the model is 88,0001%, although not higher than 95% but this level of significance is quite high and this is the best current model

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