A Project Paper on Voting for a School Budget

8/14/2019 A Project Paper on Voting for a School Budget

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Masters in International Economics and Finance

Faculty of Economics,

Chulalongkorn University, Phayathai Road,

Bangkok-10330,Thailand.Tel: (662) 218 6295, (662) 218 6218,Fax:(662) 218 6295,

E-mail: [email protected], http://www.econ.chula.ac.th/programme/ma_inter.html

Paper#3

Application of Qualitative response

regression models

2940605: Quantitative Methods in Economic Analysis

BY

SK. ASHIQUER RAHMANID#4585974929

A Thesis Submitted In Partial Fulfillment of the Requirement for the Degree of Masters in

International Economics and Finance

TO,

DR.BANGORN TUBTIMTONGASSISTANT PROFESSOR

A PaperOn

Voting for a School Budget (Application of QualitativeResponse Regression Models)


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Voting for a school budget 2002

ii

Letter of TransmittalJune 9, 2002

Dr.Bangorn TubtimtongAssistant Professor,Masters in International Economics and FinanceFaculty of Economics,Chulalongkorn University,Phayathai Road, Bangkok, Thailand

Subject: Letter of Transmittal.

Dear Madam,

Here is my paper on Voting for a School Budget (Application of Qualitative Response Regression

Models) that I was assigned. It was a great opportunity for me to acquire practical knowledge of

the Quantitative Methods in Economic Analysis and forecasting

I have concentrated my best effort to achieve the objectives of the report and hope that my

endeavor will serve the purpose.

I believe that the knowledge and experience I have gathered during my paper preparation will

immensely help me in my professional life. I will be obliged if you kindly approve this effort.

Sincerely yours,

Sk. Ashiquer RahmanId#4585974929Chulalongkorn UniversityMasters in International Economics and FinanceBangkok, Thailand


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PrefaceAny institutional education would not be completed if it were confined within theoretical aspects.

Every branch of education has become more competed by their practical application and

accomplishment of full knowledge. We shall be benefited by our education if we can effectively

apply the institutional education in practical fields. Hence, we all need practical education to apply

theoretical knowledge in real world. By considering this importance faculty of economics

arranges the Quantitative Methods in Economic Analysis courses for the students of Masters in

International Economics and Finance. As a part of this program my topic was selected as Voting

for a School Budget (Application of Qualitative Response Regression Models)

I tried my best to conduct an effective study by arrange and analysis data. There may be some

mistakes, which are truly unintentional. So, I would request to look at the matter with merciful

mind.



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AcknowledgementFirst, all praises go to almighty Allah, the most gracious, the most merciful to give me the ability for

all these I have done.

Then I would like to thank Ms. Wanwadee Wongmongkol. Now I would like to thank

Dr.Bangorn Tubtimtong Assistant Professor, Chulalongkorn University, Phayathai Road,

Bangkok,Thailand to give me the opportunity to do this project.

I would also like to thank Professor. Paitoon Wiboonchutikula, Ph.D ,Associate professor and

Chairperson of Faculty of Economics, Chulalongkorn University & Professor Salinee. Secretatery

international economics and finance. My striking thanks go to honorable sir Dr. MN.Sirker who

has helped me in all aspect to prepare the report.

I would like to thank lab incharge Ms. Mink . Last but not the least I wish to thank my

friends, William Lloyed ,Nakarin and Athipat, for their very helpful discussions.



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Table of ContentTitle Page

Letter of Transmittal iiPreface iiiAcknowledgement ivTable Of Content vList Of Tables viList Of Figures viiAcronyms And Abbreviation/ Contraction/Symbols viii

Statement Of The Problem 1-1Literature Review 1-1Formulation Of General Model 1-2Data Sources &Description 2-10Model Estimation And Hypothesis Testing 11-14Interpretation Of The Results And Conclusions 14-18Limitations Of The Study And Possible Extensions 18-18References 18-18


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Title Page

Table1. variablesanddefinition 2Table2. Data set 13Table 3 ComparingthevaluesofYESVMandtheprobabilitiesfromthreemodels

13

List of Tables


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Title Page

Fig:1: loginc 6

Fig:2: ptcon 3

Fig:3: Linear Probability Model 11

Fig:4: logit Model 4

Fig:5: probit 5

List of Figure


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Title Page

Graph:1: loginc 7

Graph :2: ptcon 8

Graph :3: group 10

Graph: 4. Residual, Actual, Fitted 11-14

Graph: Result 18

List of Graph


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Title Page

Chat:1: loginc 7

Chat :2: ptcon 8

Chat :3: group 10

List of Chat


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1

STATEMENT OF THE PROBLEM

I have studied the problem about voting for a school budget. The questions I ask are whether each of

the following independents variables: level of annual household income, amount of property taxes,number of years of residency, number of children in public and private school, the status ofbeing employed as a teacher (public or private), has effect on the probability of voting for aschool budget or not. The hypothesis I have test is there is no relationship between one of such variables with the probability of voting for a school budget. The results, derived from the test ofstatistical significance, that support to the rejection of this hypothesis lead us to the conclusion thatthe probability of voting for a school budget cal be explained by these variables.

REVIEW OF LITERATUREWhen children are of school age, households are most likely to be aware of the costs and

benefits associated with a vote for higher school taxes. The presence of at least one child in publicschool is expected and does have a significant positive impact on the probability of yes vote. Thepresence of additional school-age children does not increase the probability of a yes vote untilbeyond the fifth child the marginal gain of reallocating the household budget toward privateexpenditures outweighed the gain from the public expenditures and the probability of a yes votedecline.The number or years in residence is also included as explanatory variable in the model. Asthe time of residence increases, voters tend to vote no, either in criticism of the educational systemor possibly in opposition to the growing burden of taxes.The school variable is included to accountfor the fact that the sample of respondents is overrepresented by schoolteachers and their spouses.Schoolteachers are more likely to vote yes in the election relative to individual with otherwisesimilar attributes.On the assumption that local school education is a normal good, we expected,

other things being equal, that income and the demand for public schools will be positivelycorrelated.As price of schooling (property tax payments) rises, other things being equal, we expectedthat the quantity of educational expenditures per pupil demand will fall, as will the probability ofvoting yes in the election.

The yes probability of voting for a school budget function is

+ ---- ---- +Yes probability = (income Property taxes, Years of residency, Number of children in public ---- +School, number of children in private school, the status of being employed as a teacher)

FORMULATION OF A GENERAL MODEL

I use three following models in my study:


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LINEAR PROBABILITY MODEL

LOGIT MODEL

PROBITY MODEL

DATA SOURCES AND DESCRIPTION

Table1Variables DefinitionE (Yi / Xi) probability of yesLOGINC log of annual household income ($)PTCON log of property taxed ($)YEARS the number of years of residency (year)PUB12 1 if 1 or 2 children attend public school

0, otherwise

PUB34 1 if 3 or 4 children attend public school0, otherwise

PUBS I if 5 or more children attend public school0, otherwise

PRIV 1 if I or more children attend private schoo0, otherwise

SCHOOL 1 if being employed as a teacher (public or private)0, otherwise

E (Yi / Xi)=0+1LOGINCi+2 PTCONi+3YEARSi +4PUB12i +5PUB34i+6PUB5i+7PRIi+8SCHOOLi+i

Prob(yes)

LOG = 0+1 LOGINCi+2 PTCONi+3 YEARSj+4 PUB12i+5PUB34i1 - Prob (yes)

+6 PUBS; +7 PRIi +8 SCHOOLi+i

Pi = F(D +1LOGINC; + 2PTCON; + 3 YEARS, + 4 PUB12 + 5PUB34, +6PUB5; +7PRI; +

8SCHOOL; )


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DATA SET IS AS FOLLOWS:

Table2

obs YESVM LOGINC PTCON YEARS PUB12 PUB34 PUB5 PRIV SCHOOL

1

1.000000 9.770001 7.047500 10.00000 0.000000 1.000000 0.000000 0.000000 1.000000

2

0.000000 10.02100 7.047500 8.000000 0.000000 1.000000 0.000000 0.000000 0.000000

3

1.000000 10.02100 7.047500 4.000000 1.000000 0.000000 0.000000 0.000000 0.000000

4

0.000000 9.433500 6.396900 13.00000 0.000000 1.000000 0.000000 0.000000 0.000000

5

1.000000 10.02100 7.279200 3.000000 0.000000 1.000000 0.000000 0.000000 1.000000

6

0.000000 10.46300 7.047500 5.000000 1.000000 0.000000 0.000000 0.000000 0.000000

7

0.000000 10.02100 7.047500 4.000000 0.000000 0.000000 0.000000 0.000000 0.000000

8

1.000000 10.02100 7.279300 5.000000 0.000000 1.000000 0.000000 0.000000 0.000000

9

0.000000 10.22200 7.047500 10.00000 1.000000 0.000000 0.000000 0.000000 0.000000

10

1.000000 9.433500 7.047500 5.000000 0.000000 1.000000 0.000000 0.000000 0.000000

11

1.000000 10.02100 7.047500 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

12

0.000000 9.770001 6.396900 30.00000 1.000000 0.000000 0.000000 0.000000 0.000000

13

1.000000 9.770001 6.745200 1.000000 1.000000 0.000000 0.000000 0.000000 0.000000

14

1.000000 10.02100 7.047500 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

15

1.000000 10.82000 6.745200 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

16

1.000000 9.770001 6.745200 42.00000 0.000000 1.000000 0.000000 0.000000 0.000000

17

1.000000 10.22200 7.047500 5.000000 0.000000 1.000000 0.000000 0.000000 1.000000

18

0.000000 10.02100 7.047500 10.00000 1.000000 0.000000 0.000000 0.000000 0.000000

19

1.000000 10.22200 7.047500 4.000000 1.000000 0.000000 0.000000 0.000000 0.000000

20

1.000000 10.22200 6.745200 4.000000 1.000000 0.000000 0.000000 0.000000 0.000000

21

1.000000 10.46300 7.047500 11.00000 0.000000 1.000000 0.000000 0.000000 1.000000

22

1.000000 10.22200 7.047500 5.000000 0.000000 0.000000 0.000000 0.000000 0.000000

23

1.000000 9.770001 6.745200 35.00000 0.000000 1.000000 0.000000 0.000000 0.000000

24

1.000000 10.46300 7.279300 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

25

1.000000 10.02100 6.745200 16.00000 1.000000 0.000000 0.000000 0.000000 0.000000

26

0.000000 10.46300 7.047500 7.000000 0.000000 0.000000 0.000000 1.000000 0.000000

1.000000 9.770001 6.745200 5.000000 1.000000 0.000000 0.000000 0.000000 1.000000


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28

0.000000 9.770001 7.047500 11.00000 1.000000 0.000000 0.000000 0.000000 0.000000

29

0.000000 9.770001 6.745200 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

30

1.000000 10.22200 7.047500 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

311.000000 10.02100 6.745200 2.000000 0.000000 1.000000 0.000000 0.000000 0.000000

32

0.000000 9.433500 6.745200 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

33

0.000000 8.294000 7.047500 2.000000 0.000000 1.000000 0.000000 0.000000 1.000000

34

1.000000 10.46300 7.047500 4.000000 0.000000 0.000000 0.000000 0.000000 0.000000

35

1.000000 10.02100 7.047500 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

36

0.000000 10.22200 7.279300 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

37

1.000000 10.22200 7.047500 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

381.000000 10.22200 7.495500 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

39 0.000000 10.02100 7.047500 10.00000 0.000000 1.000000 0.000000 0.000000 1.000000

40

1.000000 10.22200 7.047500 2.000000 0.000000 0.000000 0.000000 0.000000 0.000000

41

0.000000 10.02100 7.047500 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

42

0.000000 10.82000 7.495500 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

43

1.000000 10.02100 7.047500 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

44

1.000000 10.02100 7.047500 3.000000 1.000000 1.000000 0.000000 0.000000 0.000000

45

1.000000 10.02100 6.745200 6.000000 0.000000 0.000000 0.000000 0.000000 1.000000

46

1.000000 10.02100 7.047500 2.000000 1.000000 1.000000 0.000000 0.000000 0.000000

47

0.000000 9.770001 6.745200 26.00000 0.000000 0.000000 0.000000 0.000000 0.000000

48

0.000000 10.22200 7.495500 18.00000 1.000000 0.000000 0.000000 0.000000 0.000000

49

0.000000 9.770001 6.745200 4.000000 0.000000 0.000000 0.000000 0.000000 0.000000

50

0.000000 10.02100 7.047500 6.000000 0.000000 0.000000 0.000000 0.000000 0.000000

51

1.000000 10.02100 6.745200 12.00000 0.000000 0.000000 0.000000 0.000000 0.000000

52

1.000000 9.433500 6.745200 49.00000 0.000000 0.000000 0.000000 0.000000 0.000000

53

1.000000 10.46300 7.279300 6.000000 1.000000 0.000000 0.000000 0.000000 0.000000

54

0.000000 9.770001 7.047500 18.00000 1.000000 0.000000 0.000000 0.000000 0.000000

55

1.000000 10.02100 7.047500 5.000000 0.000000 0.000000 0.000000 0.000000 0.000000

56

1.000000 9.770001 5.991500 6.000000 1.000000 0.000000 0.000000 0.000000 0.000000

0.000000 9.433500 7.047500 20.00000 1.000000 0.000000 0.000000 0.000000 0.000000


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57

58

1.000000 9.770001 6.396900 1.000000 1.000000 0.000000 0.000000 1.000000 1.000000

59

1.000000 10.02100 6.745200 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

60

0.000000 10.46300 7.047500 5.000000 1.000000 0.000000 0.000000 0.000000 0.000000

611.000000 10.02100 7.047500 2.000000 1.000000 0.000000 0.000000 1.000000 0.000000

62

0.000000 10.82000 7.279300 5.000000 1.000000 0.000000 0.000000 0.000000 0.000000

63

0.000000 9.433500 6.745200 18.00000 0.000000 0.000000 0.000000 0.000000 0.000000

64

1.000000 9.770001 5.991500 20.00000 1.000000 0.000000 0.000000 0.000000 1.000000

65

0.000000 8.922700 6.396900 14.00000 1.000000 0.000000 0.000000 0.000000 0.000000

66

0.000000 9.433500 7.495500 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000

67

0.000000 9.433500 6.745200 17.00000 0.000000 0.000000 0.000000 0.000000 0.000000

680.000000 10.02100 7.047500 20.00000 1.000000 0.000000 0.000000 0.000000 0.000000

69

1.000000 10.02100 7.047500 3.000000 1.000000 1.000000 0.000000 0.000000 0.000000

70

1.000000 10.02100 7.047500 2.000000 0.000000 1.000000 0.000000 0.000000 0.000000

71

1.000000 10.22200 7.047500 5.000000 0.000000 0.000000 0.000000 0.000000 1.000000

72

1.000000 9.770001 7.047500 35.00000 0.000000 0.000000 0.000000 0.000000 0.000000

73

0.000000 10.02100 7.279300 10.00000 1.000000 1.000000 0.000000 0.000000 0.000000

74

1.000000 9.770001 7.047500 8.000000 0.000000 1.000000 1.000000 1.000000 0.000000

750.000000 9.770001 7.047500 12.00000 0.000000 0.000000 0.000000 0.000000 0.000000

76

1.000000 10.22200 6.745200 7.000000 1.000000 1.000000 0.000000 0.000000 0.000000

77

1.000000 10.46300 6.745200 3.000000 0.000000 0.000000 0.000000 0.000000 1.000000

78

0.000000 10.22200 6.745200 25.00000 1.000000 1.000000 1.000000 0.000000 0.000000

79

1.000000 9.770001 6.745200 5.000000 0.000000 0.000000 0.000000 1.000000 1.000000

80

1.000000 10.22200 7.047500 4.000000 1.000000 1.000000 0.000000 0.000000 0.000000

81

1.000000 10.02100 7.279300 2.000000 0.000000 0.000000 0.000000 0.000000 0.000000

821.000000 10.46300 6.745200 5.000000 1.000000 1.000000 0.000000 0.000000 0.000000

83

0.000000 9.770001 7.047500 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000

84

1.000000 10.82000 7.495500 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

85

0.000000 8.922700 5.991500 6.000000 1.000000 0.000000 0.000000 1.000000 0.000000

86

1.000000 9.770001 7.047500 3.000000 0.000000 0.000000 0.000000 1.000000 0.000000


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87

1.000000 9.433500 6.396900 12.00000 1.000000 0.000000 0.000000 0.000000 0.000000

88

1.000000 9.770001 6.745200 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000

89

1.000000 10.02100 7.047500 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

90

1.000000 10.02100 6.745200 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000

91

1.000000 10.22200 7.279300 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000

92

1.000000 10.02100 7.047500 3.000000 1.000000 1.000000 0.000000 1.000000 1.000000

93

1.000000 10.02100 7.047500 5.000000 0.000000 0.000000 0.000000 0.000000 0.000000

94

1.000000 8.922700 5.991500 35.00000 0.000000 0.000000 0.000000 1.000000 1.000000

95

0.000000 10.46300 7.495500 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

Number of observations

Logincome($)


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The mean of log income is 9.97 $ per year. Seen from the above information, the values of log


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income range from 8.29 to 10.82, with a standard deviation of 0.411. The median is 10.021. The

skewness of - 0.89 tell us that the lower tail of the distribution is slightly thicker, with more

observation than the upper tail. The kurtosis of 5.62 is much greater than 3, telling as that the distribution

of log income has tail that is higher and longer than normal. The JB statistic of 39.85 is more than

the critical value of the chi-square distribution with 2 df, that is 5.99. Therefore, the null

hypothesis that the log income values are normally distributed can be rejected.Log Property Taxes


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The mean of log property taxes is 6.93 $ per year. Seen from the above information, the values of logproperty taxes range from 5.99 to 7.49, with a standard deviation of 0.31. The median is 7.047. Theskewness of 0.31 tell us that the upper tail of the distribution is slightly thicker, with moreobservation than the lower tail. The kurtosis of 4.68 is much greater than 3, telling us that thedistribution of log property taxes has tail that is higher and longer than normal. The JB statistic of26.81 is more than the critical value of the chi-square distribution with 2 df, that is 5.99.Therefore, the null hypothesis that the log propert; taxes values are normally distributed can berejected.


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MODEL ESTIMATION AND HYPOTHESIS TESTING

The regression results of Linear Probability Model are:


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The hypothesis I have tested is:

H0: 1= 2 =3 =4 = 5 = 6 =7 =8 = 0H0: 12345678 0

In the results of three models, only )3t and 132 are significant at 95% level of confidence, as

their probabilities are less the 5%. However, in the results of Linearity probability Model, F-statistic

of 2.21 with less than 5% probability (3.35%) tells that there is overall significance of the model,

i.e., all explanatory variables together have effect on probability of voting yes for a school budget. In

Logit and Probit models, LR statistics (8 df) are 19.46 and 19.78 respectively. Comparing these

values to the 5% critical chi-square value with 8 df of 15.5073, the null hypothesis that all the slope

coefficients are simultaneous equal to zero is rejected, i.e., all explanatory variables together have

effect on probability of voting yes for a school budget.

INTERPRETATION OF THE RESULTS AND CONCLUSION

The regression results of Linearity Probability Model are as follows:

E(Yi / Xi) = - 0.38 + 0.37 LOGINC i - 0.41 PTCON i - 0.005 YEARS i + 0.106 PUB12 i + 0.216

PUB34 i +

se = (1.48) (0.14) (0.18) (0.005) (0.14) (0.16)t = (-0.26) (2.68) (-2.24) (-1.003) (0.72) (1.33)

0.101 PUB5 i - 0.067 PRI i + 0.31 SCHOOL i + i

(0.26) (0.16) (0.15)(0.38) (-0.40) (1.97

The intercept of -0.38 gives the probability that zero value of log income, log property taxes andthe numb 3r of years of residency will vote yes for a school bidget. Since this value is negative, andsince probability cannot be negative, we treat this value as zero, which is sensible in the presentinstance. The slope values of 0.37, -0.41 and -0.005 mean that for a unit change in log income ($),log property taxes ($) and year of residency (year), on average, the probability of voting yes for a

school budget increases by 37%, decreases by 41% and decreases by 0.5% respectively. The numberof children in the public school increase the yes probability by 10.6%, 21.6% and 10.1% for 1 or2, 3 or 4 and 5 or more children in the public school respectively, while one or more childrenin the private school decrease the yes probability by 6.7%. The status of being employed as ateacher (public and private) increases the yes probability by 31 %.

THE REGRESSION RESULTS OF LOGIT MODEL ARE AS FOLLOWS:


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Log rob(yes) = 5.19 + 2.18 LOGlNCi- 2.39 PTCONi - 0.026 YEARSi + 0.58 PUB12i +1 - Probse = (7.55) (0.78) (1.08) (0.026) (0.68)z = (-0.68) (2.77) (-2.21) (-0.96) (0.84)1.12 PUB34 i + 0.52 PUB5 i -0.34 PRI i + 2.62 SCHOOL i + i

(0.76) (1.26) (0.78) (1.41)(1.46) (0.41) (-0.43) (1.86)The 2.18 coefficient of log income means, with other variables held constant, that if log

income increases by a unit, on average the estimated logit increases by about 2.18 units. For

log property taxes, if it increases by a unit, the estimated logit decreases by 2.39 units.

Increasing in years of residency by a unit cause the estimated logit to decrease by 0.026 unit.

For the number of children, 1 or 2, 3 or 4 and 5 or more children in the public school

increase the estimated logit by 0.58, 1.12 and 0.52 unit respectively, while 1 or more children

in the private school decrease it by 0.34 unit. The estimated logit can increase by 2.62 unit as to

the status of being employed as a teacher (public or private).

THE REGRESSION RESULTS OF PROBIT MODEL ARE AS FOLLOWS:

Pi= F( -2.95 + 1.31 LOGING- 1.46 PTCON; - 0.015 YEARS; + 0.36 PUB12; +0.69 PUB34; +0.29 PUB5;

se = (4.50) (0.46) (0.64) 0.015) (0.42) (0.47) (0.75)z = (-0.65) (2.83) (-2.28) (-1.03) (0.85) (1.46) (0.38)- 0.21 PRI; + 1.58 SCHOOL)(0.48) (0.82)(-0.43) (1.92)

The 1.31 coefficient of log income means, with other variables held constant, that if log incomeincreases by a unit, on average the estimated probit increases by about 1.31 units. For logproperty taxes, if it increases by a unit, the estimated probit decreases by 1.46 units.Increasing in years of residency by a unit cause the estimated probit to decrease by 0.015 unit. For thenumber of children, 1 or 2, 3 or 4 and 5 or more children in the public school increase theestimated probit by 0.36, 0.69 and 0.29 unit respectively, while 1 or more children in theprivate school decrease it by 0.21 unit. The estimated logit can increase by 1.58 unit as to thestatus of being employed as a teacher (public or private).

COMPARING THE VALUES OF YESVM AND THE PROBABILITIES FROMTHREE MODELS.

Table3

obs YESVM LMP PROBIT LOGIT1 1.000000 0.795538 0.851226 0.8604012 0.000000 0.713714 0.729725 0.738597


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3 1.000000 0.501486 0.490557 0.4885914 0.000000 0.721922 0.749317 0.7458655 1.000000 0.837365 0.875463 0.8832106 0.000000 0.665035 0.694005 0.6980597 0.000000 0.597170 0.604833 0.6092358 1.000000 0.637445 0.637049 0.6514739 0.000000 0.545291 0.552493 0.55374010 1.000000 0.505538 0.472957 0.47661211 1.000000 0.506999 0.496729 0.49492012 0.000000 0.522635 0.550823 0.53807213 1.000000 0.543054 0.545345 0.53793414 1.000000 0.741278 0.754696 0.76229715 1.000000 1.167924 0.981167 0.96912716 1.000000 0.551309 0.570284 0.57427917 1.000000 0.995988 0.953308 0.94659018 0.000000 0.468410 0.453627 0.45076119 1.000000 0.578367 0.588930 0.59091420 1.000000 0.699402 0.734418 0.73217021 1.000000 1.055092 0.970142 0.96152722 1.000000 0.668538 0.691065 0.69681123 1.000000 0.589898 0.612331 0.61694724 1.000000 0.817532 0.823271 0.82994225 1.000000 0.556367 0.576168 0.57159726 0.000000 0.886284 0.870345 0.87734927 1.000000 0.709857 0.794735 0.80179228 0.000000 0.366892 0.329155 0.32319229 0.000000 0.532028 0.533060 0.52532330 1.000000 0.589393 0.600924 0.60309931 1.000000 0.867825 0.865691 0.86159032 0.000000 0.408832 0.375421 0.36230733 0.000000 0.275081 0.254924 0.26612034 1.000000 0.766231 0.791677 0.79464235 1.000000 0.512512 0.502901 0.50125236 0.000000 0.725351 0.735650 0.74829937 1.000000 0.583880 0.594938 0.59702138 1.000000 0.410024 0.367238 0.37122239 0.000000 0.891543 0.911809 0.91172240 1.000000 0.685076 0.707222 0.71261841 0.000000 0.512512 0.502901 0.50125242 0.000000 0.633241 0.649721 0.66319843 1.000000 0.506999 0.496729 0.49492044 1.000000 0.645595 0.655346 0.66275145 1.000000 0.896033 0.920332 0.91514746 1.000000 0.651107 0.661026 0.66838847 0.000000 0.500918 0.506645 0.50216048 0.000000 0.321819 0.278693 0.28248349 0.000000 0.622199 0.639469 0.63779250 0.000000 0.586144 0.592870 0.59711251 1.000000 0.674102 0.706620 0.706700


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52 1.000000 0.245415 0.225075 0.21995953 1.000000 0.566715 0.572972 0.58020254 0.000000 0.328302 0.290970 0.28568955 1.000000 0.591657 0.598863 0.60318956 1.000000 0.817255 0.850229 0.83422457 0.000000 0.188568 0.159270 0.15987858 1.000000 1.007951 0.956326 0.94903159 1.000000 0.628034 0.652927 0.64967260 0.000000 0.665035 0.694005 0.69805961 1.000000 0.649103 0.644106 0.66716762 0.000000 0.708777 0.739149 0.74709163 0.000000 0.416311 0.391453 0.38205764 1.000000 0.928930 0.944279 0.93138265 0.000000 0.286753 0.250761 0.23418666 0.000000 0.198599 0.149215 0.15653567 0.000000 0.421824 0.397408 0.38805368 0.000000 0.413282 0.393109 0.38916069 1.000000 0.645595 0.655346 0.66275170 1.000000 0.746791 0.759537 0.76685671 1.000000 0.857392 0.897924 0.89834572 1.000000 0.330268 0.300130 0.29792473 0.000000 0.514198 0.493487 0.50228974 1.000000 0.516035 0.490941 0.50539275 0.000000 0.457062 0.433224 0.43174876 1.000000 0.821459 0.838376 0.83556377 1.000000 1.081633 0.977256 0.96653478 0.000000 0.483965 0.509059 0.49460879 1.000000 0.942131 0.929852 0.92941180 1.000000 0.716963 0.736564 0.74338581 1.000000 0.515388 0.495614 0.50140082 1.000000 0.924665 0.906024 0.89769683 0.000000 0.506677 0.488463 0.48830384 1.000000 0.638754 0.655436 0.66883185 0.000000 0.629760 0.637658 0.63729786 1.000000 0.643268 0.630531 0.65556687 1.000000 0.493156 0.496119 0.47910488 1.000000 0.627712 0.645245 0.64362189 1.000000 0.741278 0.754696 0.76229790 1.000000 0.723717 0.752629 0.75163291 1.000000 0.586756 0.587843 0.59716492 1.000000 0.971040 0.937352 0.93777793 1.000000 0.591657 0.598863 0.60318994 1.000000 0.754427 0.832479 0.84101195 0.000000 0.730970 0.739175 0.755652


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LIMITATION OF THE STUDY AND POSSIBLE EXTENSIONS

There are many limitations of my study. First, I cannot understand the concept very well, so it

may be difficult for me to develop the perfect study. Second, I face some difficulties in using the

Eviews Program as the program is complicated and I am not quite well in using computer. Last,

as the time is constraint, I cannot get more information I should have to do a perfect study.As the

RZ is not meaningful in binary regressand model, one can use Count R2 tomeasure goodness of fit.

The R2 can be computed as number of correct predictions divided by total number of observations.

Also, in Linearity Probability Model, the hetroscedasticity exists, dividing the original equation by

~Wi can correct this problem, whereas ~wi is equal to aPi(1-Pi) .

References

Damodar N. Gujarati, Basic Econometrics, New York: McGraw-Hill, 2000

Karl E. Case and ray C. fair, Piinciples of Economics, New Jersey: Prentice-Hall, Inc.,

1996

Robert S. Pindyck and Daniel L. Rubinfeld, Econometric Models Econometric

ForecastsNewYork: McGraw-Hill, 1997

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A Project Paper on Voting for a School Budget

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