Lab EightLab Eight

Econ 240CEcon 240C

Per Se LegislationPer Se Legislation

• Introduced in Great Britain in October 1967

• Before driving dangerously while intoxicated led to a conviction only if you were found guilty in court

• After October 1967, if your blood alcohol content, BAC, was 0.08 or greater you were per se guilty

Capturing an event with a step functionCapturing an event with a step function

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60 62 64 66 68 70 72 74

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60 62 64 66 68 70 72 74

No visual impact

Two Approaches to Seasonal DataTwo Approaches to Seasonal Data

• Regression of kill(t) = a –b*step(1967.10) + seasonal dummies + e(t)

Regression with Seasonal dummiesRegression with Seasonal dummies

Actual, fitted, residualActual, fitted, residual

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60 62 64 66 68 70 72 74

Residual Actual Fitted

Actual, fitted, residualActual, fitted, residual

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62 64 66 68 70 72 74

Residual Actual Fitted

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-160 -120 -80 -40 0 40 80 120 160

Series: ResidualsSample 1960:04 1975:12Observations 189

Mean 6.68E-09Median -3.352202Maximum 169.0330Minimum -166.0877Std. Dev. 43.97311Skewness 0.177571Kurtosis 4.364645

Jarque-Bera 15.65850Probability 0.000398

The Alternative ApproachThe Alternative Approach

• Box Jenkins– Seasonal difference instead of seasonal

dummies

Model:

Kill(t) c ar(1) ar(2) ar(3) step

(1-Z12) Kill(t) c ar(1) ar(2) (1-Z12) step(1967.10)

Sdkill(t) c ar(1) ar(2) sdstep(1967.10)

Seasonal differenceSeasonal difference

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62 64 66 68 70 72 74

Residual Actual Fitted

Residual is White NoiseResidual is White Noise

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-160 -120 -80 -40 0 40 80 120 160

Series: ResidualsSample 1961:03 1975:12Observations 178

Mean 1.888725Median 0.375867Maximum 162.6580Minimum -156.3048Std. Dev. 46.53823Skewness 0.113472Kurtosis 3.510213

Jarque-Bera 2.312674Probability 0.314637