1. 1 F- Test Applications

2. 2 Time Series Applications Chow Test for structural change Chow Test for structural change

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6. 6 Actual, Fitted, Residual graph

7. 7 The Gann Initiative 1977-Limit Government in Real Terms Per Capita 1977-Limit Government in Real Terms Per Capita Two periods Two periods 1968-69 through 1977-78 1968-69 through 1977-78 1978-79 through 2007-08 1978-79 through 2007-08

8. 8 Genr periodone=0, type in ones Genr periodtwo=1, type in zeros

9. 9 Genr timeone=periodone*time Genr timetwo=periodtwo*time

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11. 11 Regression Ratio = c(1)*periodone + c(2)*timeone + c(3)*periodtwo + c(4)*timetwo +e(t) Ratio = c(1)*periodone + c(2)*timeone + c(3)*periodtwo + c(4)*timetwo +e(t)

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14. 14F-Test F 2, 36 = [SSR 2 - SSR 4 ]/2 ÷ SSR 4 /(40-4) F 2, 36 = [SSR 2 - SSR 4 ]/2 ÷ SSR 4 /(40-4) F 2, 36 = [13.31 – 7.40]/2 ÷ 7.40/36 F 2, 36 = [13.31 – 7.40]/2 ÷ 7.40/36 F 2, 36 = 2.96/0.206 = 14.4 F 2, 36 = 2.96/0.206 = 14.4

15. 15 Genr: Fvar=@rfdist(2, 36) Genr: Density=@dfdist(Fvar, 2, 36)

16. 16 F density for 2 and 36 Degrees of Freedom 3.27 5% 14.4

17. 17 Can you go from 2 parameters to 4 parameters? Yes, there is a significant increase in explained variance, indicating a structural change after the passage of the Gann Initiative in 1977 Yes, there is a significant increase in explained variance, indicating a structural change after the passage of the Gann Initiative in 1977

18. 18 Alternatively, can you estimate a single time trend instead of two time trends? No, two time trends fits the data significantly better No, two time trends fits the data significantly better

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20. 20 Wald Test

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