voting for a school budget 3

8/14/2019 Voting for a School Budget 3

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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 annualhousehold income, amount of property taxes, number of years ofresidency, number of children in public and private school, the status ofbeing employed as a teacher (public or private), has effect on theprobability of voting for a school budget or not. The hypothesis I have test isthere is no relationship between one of such variables with the probability ofvoting for a school budget. The results, derived from the test of statisticalsignificance, that support to the rejection of this hypothesis lead us to theconclusion that the probability of voting for a school budget cal be explainedby these variables.

Review of Literature

When children are of school age, households are most likely to beaware of the costs and benefits associated with a vote for higher schooltaxes. The presence of at least one child in public school is expected anddoes have a significant positive impact on the probability of yes vote. Thepresence of additional school-age children does not increase the probability ofa yes vote until beyond the fifth child the marginal gain of reallocating thehousehold budget toward private expenditures outweighed the gain from thepublic expenditures and the probability of a yes vote decline.The number oryears in residence is also included as explanatory variable in the model. As the

time of residence increases, voters tend to vote no, either in criticism of theeducational system or possibly in opposition to the growing burden oftaxes.The school variable is included to account for the fact that the sample ofrespondents is overrepresented by schoolteachers and their spouses.Schoolteachers are more likely to vote yes in the election relative toindividual with otherwise similar attributes.On the assumption that localschool education is a normal good, we expected, other things being equal,that income and the demand for public schools will be positively correlated.Asprice of schooling (property tax payments) rises, other things being equal, weexpected that the quantity of educational expenditures per pupil demand willfall, as will the probability of voting 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

---- +


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PRIV 1 if I or more children attend privateschoo

SCHOOL 1 if being employed as a teacher (public orprivate)

Data set is as follows:

Table-2

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

1.000000 10.46300 7.047500 11.00000 0.000000 1.000000 0.000000 0.000000 1.000000


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21

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

27

1.000000 9.770001 6.745200 5.000000 1.000000 0.000000 0.000000 0.000000 1.000000

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

31

1.000000 10.02100 6.745200 2.000000 0.000000 1.000000 0.000000 0.000000 0.000000

320.000000 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

38

1.000000 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

1.000000 10.02100 6.745200 12.00000 0.000000 0.000000 0.000000 0.000000 0.000000


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51

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

57

0.000000 9.433500 7.047500 20.00000 1.000000 0.000000 0.000000 0.000000 0.000000

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

61

1.000000 10.02100 7.047500 2.000000 1.000000 0.000000 0.000000 1.000000 0.000000

620.000000 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

68

0.000000 10.02100 7.047500 20.00000 1.000000 0.000000 0.000000 0.000000 0.000000

691.000000 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

75

0.000000 9.770001 7.047500 12.00000 0.000000 0.000000 0.000000 0.000000 0.000000

761.000000 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


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81

1.000000 10.02100 7.279300 2.000000 0.000000 0.000000 0.000000 0.000000 0.000000

82

1.000000 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

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

Log income ($)


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


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the values of log income range from 8.29 to 10.82, with a standard deviation of0.411. The median is 10.021. The skewness of - 0.89 tell us that the lower tailof 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 logincome 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 2df, that is 5.99. Therefore, the null hypothesis that the log income values arenormally 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 aboveinformation, the values of log property taxes range from 5.99 to 7.49, with astandard deviation of 0.31. The median is 7.047. The skewness of 0.31 tell usthat the upper tail of the distribution is slightly thicker, with more observationthan the lower tail. The kurtosis of 4.68 is much greater than 3, telling usthat the distribution of log property taxes has tail that is higher and longerthan normal. The JB statistic of 26.81 is more than the critical value of the chi-square distribution with 2 df, that is 5.99. Therefore, the null hypothesisthat the log propert; taxes values are normally distributed can be rejected.


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Model Estimation and Hypothesis Testing

The regression results of Linear ProbabilityModel are:


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The hypothesis I have tested is:

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

H0: 1 2 3 4 5 6 7 8 0

In the results of three models, only )3t and 132 are significant at 95% levelof confidence, as their probabilities are less the 5%. However, in the results ofLinearity 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., allexplanatory variables together have effect on probability of voting yes for aschool budget. In Logit and Probit models, LR statistics (8 df) are 19.46 and19.78 respectively. Comparing these values to the 5% critical chi-squarevalue with 8 df of 15.5073, the null hypothesis that all the slope coefficientsare simultaneous equal to zero is rejected, i.e., all explanatory variablestogether 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 asfollows:

E(Yi / Xi) = - 0.38 + 0.37 LOGINCi - 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 and the numb 3r of years of residency will vote yes for aschool bidget. Since this value is negative, and since probability cannot benegative, 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 unitchange in log income ($), log property taxes ($) and year of residency (year),on average, the probability of voting yes for a school budget increases by


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37%, decreases by 41% and decreases by 0.5% respectively. The number ofchildren in the public school increase the yes probability by 10.6%, 21.6%and 10.1% for 1 or 2, 3 or 4 and 5 or more children in the public schoolrespectively, while one or more children in the private school decrease theyes probability by 6.7%. The status of being employed as a teacher (public

and private) increases the yes probability by 31 %.

The regression results of Logit Model are as follows:

Log rob(yes) = 5.19 + 2.18 LOGlNCi- 2.39 PTCONi - 0.026 YEARSi + 0.58PUB12i +

1se = (7.55 (0.78) (1.08) (0.026) (0.68)z = (- (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 heldconstant, that if log income increases by a unit, on average the estimatedlogit increases by about 2.18 units. For log property taxes, if it increasesby a unit, the estimated logit decreases by 2.39 units. Increasing inyears of residency by a unit cause the estimated logit to decrease by 0.026unit. For the number of children, 1 or 2, 3 or 4 and 5 or more children inthe 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 by0.34 unit. The estimated logit can increase by 2.62 unit as to the status ofbeing 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 income increases by a unit, on average the estimated probit


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increases by about 1.31 units. For log property taxes, if it increases by aunit, the estimated probit decreases by 1.46 units. Increasing in years ofresidency by a unit cause the estimated probit to decrease by 0.015 unit. Forthe number of children, 1 or 2, 3 or 4 and 5 or more children in the publicschool increase the estimated probit by 0.36, 0.69 and 0.29 unit

respectively, while 1 or more children in the private school decrease it by0.21 unit. The estimated logit can increase by 1.58 unit as to the status ofbeing employed as a teacher (public or private).

Comparing the values of YESVM and the probabilities fromthree models.

Table-3


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obs YESVM LMP PROBIT LOGIT

1 1.000000 0.795538 0.851226 0.860401

2 0.000000 0.713714 0.729725 0.738597

3 1.000000 0.501486 0.490557 0.488591

4 0.000000 0.721922 0.749317 0.745865

5 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 0.762297

15 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 0.571597

26 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 0.597021

38 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 0.668388


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Robert S. Pindyck and Daniel L. Rubinfeld, Econometric ModelsEconometric Forecasts NewYork: McGraw-Hill, 1997

voting for a school budget 3

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