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

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

FOREIGN TRADE UNIVERSITY FACULTY OF INTERNATIONAL ECONOMICS

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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

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(X2, X3, X4)

- Estimation form: BUSTRAVL = β1+ β2 𝐅𝐀𝐑𝐄 + β3 𝐈𝐍𝐂𝐎𝐌𝐄 + β4 𝐏𝐎𝐏 + ui Inside:

Yi BUSTRAVL The level of using bus in

urban area

Thousand people/ hour

Dependent variable

variable

variable

X4 POP Population in the urban area Thousand

people

Independent variable

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

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 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 + ei

* From the result, it can be inferred that:

β̂ 1 = 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

β̂ 2 = − 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

β̂ 3 = − 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

β̂ 4 = 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

H1: βi ≠ 0

- From exhibit 4, it can be inferred:

P-value(β2)= 0,23519 > 5% => Not evident to reject H0 P-value(β3)= 0,11159 > 5% => Not evident to reject H0 P-value(β4)= 1,00e-017 < 0,00001< 5% => Reject H0, β4 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

coefficient std error t-ratio p-value - const 1214,48 1378,42 0,8811 0,3845 FARE 186,713 593,256 0,3147 0,7549 INCOME −0,0310650 0,0776781 −0,3999 0,6917 POP −0,0711677 0,958716 −0,07423 0,9413 yhat^2 0,000248918 0,000109830 2,266 0,0299 **

yhat^3 −1,32053e-08 5,66970e-09 −2,329 0,0259 **

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 interval midpt frequency rel cum

< -1400,5 -1719,7 1 2,50% 2,50%

-1400,5 - -762,18 -1081,4 7 17,50% 20,00% ******

-762,18 - -123,83 -443,00 12 30,00% 50,00% **********

-123,83 - 514,52 195,35 6 15,00% 65,00% *****

514,52 - 1152,9 833,70 11 27,50% 92,50% *********

1152,9 - 1791,2 1472,0 2 5,00% 97,50% * >= 1791,2 2110,4 1 2,50% 100,00%

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)

 P-value = 0,66870 > 0,05 At the 5% significant level, the model has a standard distribution

c Multicollinearity test

 Signal 1: High 𝑅2 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

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 𝑹𝟐 = 0.88001

Additional regression models:

 FARE regression according to INCOME and POP:

Model 2: OLS, using observations 1-40

Independent variable: FARE

Coefficient Std Error t-ratio p-value

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)

 𝑅2 < 𝑅𝑚𝑎𝑖𝑛2 (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

Coefficient Std Error t-ratio p-value

R-squared 0,118778

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 𝑅2 < 𝑅𝑚𝑎𝑖𝑛2 (0,118778 < 0,88001) so multicollinearity does not exist

 POP regression according to FARE and INCOME:

Model 4: OLS, using observations 1-40

Independent variable: POP

Coefficient Std Error t-ratio p-value

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)

 Vì 𝑅2 < 𝑅𝑚𝑎𝑖𝑛2 (0,113930 < 0,88001) so multicollinearity does not exist

 The signal 3 inferred that the model does not have multicollinearity

 Singal 4: Use the variance increment factor VIF

Variance Inflation Factors Minimum possible value = 1.0 Values > 10.0 may indicate a collinearity problem

FARE 1,008 INCOME 1,135 POP 1,129

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

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:

ei2 = α1+ α2 FARE + α3 INCOME + α4 POP + α5 FARE2 + α6 FARE INCOME

+ α7 FARE POP + α8INCOME2 + α9 INCOME POP + α10 POP2 + vi

- The result shown in the table:

White's test for heteroskedasticity OLS, using observations 1-40

Dependent variable: uhat^2

coefficient std error t-ratio p-value - const 5,19333e+06 8,74264e+06 0,5940 0,5570 FARE −1,84745e+06 6,22686e+06 −0,2967 0,7687 INCOME −455,497 949,072 −0,4799 0,6348 POP 2455,89 5105,07 0,4811 0,6340 sq_FARE −1,84226e+06 2,16245e+06 −0,8519 0,4010 X2_X3 297,210 368,212 0,8072 0,4259 X2_X4 116,104 734,557 0,1581 0,8755 sq_INCOME 0,00541227 0,0259041 0,2089 0,8359 X3_X4 −0,112996 0,319942 −0,3532 0,7264 sq_POP −0,0440935 0,207512 −0,2125 0,8332 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)

- Hypothesis: {H0: PSSS unchanged

H1: 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

Coefficient Std Error t-ratio p-value