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F- Test Applications. Time Series Applications. Chow Test for structural change. Actual, Fitted, Residual graph. The Gann Initiative. 1977-Limit Government in Real Terms Per Capita Two periods 1968-69 through 1977-78 1978-79 through 2007-08. Genr periodone=0, type in ones - PowerPoint PPT Presentation
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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
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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
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Genr: Fvar=@rfdist(2, 36)
Genr: Density=@dfdist(Fvar, 2, 36)
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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
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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
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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
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2020
Wald TestWald Test
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