22. What is the null hypothesis when performing anF-test to test the strength of multiple instrumentsj= 1, ..., J?(a) the instruments are weak, with no coefficientθjon the instruments in the first stage differentfrom 0.(b) the instruments are strong with all coefficientsθjon the instruments significantly differentfrom 0.(c) the instruments are sufficiently strong with a coefficientθjon at least one instrument sig-nificantly different from 0.(d) the instruments are weak with all coefficientsθjon the instruments different from 0.ANSWER: APlease refer to the definition of the F-test and the first-step of the 2SLS estimation.23. When you are implementing an instrumental variable regression, you are worried about8
PartII—PracticalandComputationalQuestions(eachquestionworth2points):Consider the following regression model:yi=β1+β2x2i+· · ·+βKxKi+ei,24. You have estimated the following simple regression modely= 379 + 1.44x3(1)What is the elasticity when x = 8.49?xydydx= 1.44*3*x2= 4.32x2x= 8.49 =⇒y= 379 + 1.44(8.49)3= 1260.22=⇒Elasticity= 4.32(8.49)28.491260.22= 2.1025. You have estimated a two variable model, i.e.,K= 2, and your printout includes the followinginformationsxy=3614.00sx=12.72sy=394.61SST=758,912Then theR2for this regression model is:2. For the numbers of the question, we get thatrxy= 0.72, such thatr2xy= 0.52. Hence, (d) is the correct answer. Note that in the final eitherexact values will be given, or it will be stated explicitly that the result is approximate.26. Suppose thatK= 3,y= 9,x2= 3,b2= 1.2,x3= 2,b3= 1.3, then the estimate forβ1,b1is9
(a) 2.8(b) 3.8(c) 8.3(d) 2.5ANSWER: AFor any regression model we know that evaluating the estimated equation at the means will returnthe mean.Mathematically,y=b1+b2x2+b3x3=⇒9 =b1+ 1.2(3) + 1.3(2) =⇒b1= 2.8
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