11

F- Test ApplicationsF- Test Applications

22

Time Series ApplicationsTime Series Applications

Chow Test for structural changeChow Test for structural change

33

Ratio of California General fund Expenditures to Personal Income, 68-69 through 07-08

y = 0.0003x + 0.0567

R2 = 0.2535

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

68-6

9

70-7

1

72-7

3

74-7

5

76-7

7

78-7

9

80-8

1

82-8

3

84-8

5

86-8

7

88-8

9

90-9

1

92-9

3

94-9

5

96-9

7

98-9

9

00-0

1

02-0

3

04-0

5

06-0

7

Fiscal Year

Pe

rce

nt

44

55

66

-1.0

-0.5

0.0

0.5

1.0

1.5

4

5

6

7

8

70 75 80 85 90 95 00 05

Residual Actual Fitted

Actual, Fitted, Residual graphActual, Fitted, Residual graph

77

The Gann InitiativeThe Gann Initiative

1977-Limit Government in Real Terms Per 1977-Limit Government in Real Terms Per CapitaCapita

Two periodsTwo periods1968-69 through 1977-781968-69 through 1977-781978-79 through 2007-081978-79 through 2007-08

88

Genr periodone=0, type in ones

Genr periodtwo=1, type in zeros

99

Genr timeone=periodone*time

Genr timetwo=periodtwo*time

1010

1111

RegressionRegression

Ratio = c(1)*periodone + c(2)*timeone + Ratio = c(1)*periodone + c(2)*timeone + c(3)*periodtwo + c(4)*timetwo +e(t)c(3)*periodtwo + c(4)*timetwo +e(t)

1212

1313

-1.5

-1.0

-0.5

0.0

0.5

1.0

4

5

6

7

8

70 75 80 85 90 95 00 05

Residual Actual Fitted

1414

F-TestF-Test

FF2, 36 2, 36 = [SSR= [SSR2 2 - SSR- SSR4 4 ]/2 ]/2 ÷ SSR÷ SSR44/(40-4)/(40-4)

FF2, 36 2, 36 = [13.31 – 7.40]/2 ÷ 7.40/36= [13.31 – 7.40]/2 ÷ 7.40/36

FF2, 36 2, 36 = 2.96/0.206 = 14.4= 2.96/0.206 = 14.4

1515

Genr: Fvar=@rfdist(2, 36)

Genr: Density=@dfdist(Fvar, 2, 36)

1616

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10

FVAR

DE

NS

ITY

F-density for 2 and 36 degrees of freedom

F density for 2 and 36 Degrees of F density for 2 and 36 Degrees of FreedomFreedom

3.27

5%

14.4

1717

Can you go from 2 parameters to 4 Can you go from 2 parameters to 4 parameters?parameters?

Yes, there is a significant increase in Yes, there is a significant increase in explained variance, indicating a structural explained variance, indicating a structural change after the passage of the Gann change after the passage of the Gann Initiative in 1977Initiative in 1977

1818

Alternatively, can you estimate a Alternatively, can you estimate a single time trend instead of two single time trend instead of two

time trends?time trends?

No, two time trends fits the data No, two time trends fits the data significantly bettersignificantly better

1919

2020

Wald TestWald Test

2121