Econometric take home APPS_Part_10

Econometric take home APPS_Part_10 - ?= Application 6.4?=...

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39 ?======================================================================= ? Application 6.4 ?======================================================================= According to the full model, the expected number of incidents for a ship of the base type A built in the base period 1960 to 1964, is 3.4. The other 19 predicted values follow from the previous results and are left as an exercise. The relevant test statistics for differences across ship type and year are as follows: (3925.2 - 660.9)/4 type :F[4,12] = =14.82, 660.9/12 (1090.3 - 660.9)/3 year :F[3,12] = = 2.60 660.9/12 . The 5 percent critical values from the F table with these degrees of freedom are 3.26 and 3.49, respectively, so we would conclude that the average number of incidents varies significantly across ship types but not across years. Regression Coefficients Full Model Time Effects Type Effects No Effects Constant 3.4 6.0 8.25 10.85 B 27.75 0 27.75 0 C –7.0 0 –7.0 0 D –4.5 0 –4.5 0 E –3.25 0 –3.25 0 65–69 7.0 7.0 0 0 70–74 11.4 11.4 0 0 75–79 1.0 1.0 0 0 R 2 0.84823 0.0986 0.74963 0 e e 660.9 3925.2 1090.2 4354.5
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40 Chapter 7 Specification Analysis and Model Selection Exercises 1. The result cited is E[ b 1 ] = β 1 + P 1.2 β 2 where P 1.2 = ( X 1 X 1 ) -1 X 1 X 2 , so the coefficient estimator is biased. If the conditional mean function E [ X 2 | X 1 ] is a linear function of X 1 , then the sample estimator P 1.2 actually is an unbiased estimator of the slopes of that function. (That result is Theorem B.3, equation (B- 68), in another form). Now, write the model in the form y = X 1 β 1 + E[ X 2 | X 1 ] β 2 + ε + ( X 2 - E[ X 2 | X 1 ]) β 2 So, when we regress y on X 1 alone and compute the predictions, we are computing an estimator of X 1 ( β 1 + P 1.2 β 2 ) = X 1 β 1 + E[ X 2 | X 1 ] β 2 . Both parts of the compound disturbance in this regression ε and (X 2 - E[X 2 |X 1 ]) β 2 have mean zero and are uncorrelated with X 1 and E[ X 2 | X 1 ], so the prediction error has mean zero. The implication is that the forecast is unbiased. Note that this is not true if E[ X 2 | X 1 ] is
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This note was uploaded on 11/13/2011 for the course ECE 4105 taught by Professor Dr.fang during the Spring '10 term at University of Florida.

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Econometric take home APPS_Part_10 - ?= Application 6.4?=...

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