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# pqf1_ak - Econ 410 - Introduction to Econometrics Practice...

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Econ 410 - Introduction to Econometrics Practice Questions for the Final Exam - Answer Key 1. (a) For a person with college degree ( college i =1) , the predicted wage is: d wage i =7 . 22 + 0 . 87 exp i +3 . 17 0 . 11 exp i =10 . 39 + 0 . 76 exp i For a person without college degree ( college i =0) , the predicted wage is: d wage i =7 . 22 + 0 . 87 exp i The f rst line has a higher intercept, but it is F atter (the slope is lower). The interpretations is that, in the sample used to obtain the OLS coe cients, people with a college degree start with a higher wage, but as they gain experience, the increase in their wage happens at a lower rate compared to people who do not have a college degree. (b) The expected wage of an individual with exp i =0 and college i =1 is: E ( wage i | exp i =0 ,college i =1)= β 0 + β 2 The expected wage of an individual with exp i =0 and college i =0 is: E ( wage i | exp i =0 ,college i =0)= β 0 Then: E ( wage i | exp i =0 ,college i =1)= E ( wage i | exp i =0 ,college i =0) if β 2 =0 so we need to test: H 0 : β 2 =0 . The t-statistic is: t = 3 . 17 0 1 . 21 =2 . 61 > 1 . 96 . The null hypothesis that the expected wage of an individual with no work experience but with a college degree is the same as the expected wage of an individual with no work experience and without a college degree is rejected at the 5% signi f cance level. (c) When college i =1 , the expected change in wage following some exp i is: E ( wage i | exp i ,college i =1)= β 0 + β 1 ( exp i + exp i )+ β 2 + β 3 ( exp i + exp i ) β 0 β 1 exp i β 2 β 3 exp i =( β 1 + β 3 ) exp i When college i =0 , the expected change in wage following some exp i is: E ( wage i | exp i ,college i =0)= β 0 + β 1 ( exp i + exp i ) β 0 β 1 exp i = β 1 exp i Then: E ( wage i | exp i ,college i =1)= E ( wage i | exp i ,college i =0) if β 3 =0 so we need to test: H 0 : β 3 =0 . The t-statistic is: t = 0 . 11 0 0 . 04 = 2 . 75 < 1 . 96 The null hypothesis that the expected change in wage when work experience is increased is the same for a person with college degree and for a person with no college degree is rejected at the 5% signi f cance level. (d) The population regression functions for a person with college degree and a person without college degree are de f ned as: E ( wage i | exp i ,college i =1)= β 0 + β 1 exp i + β 2 + β 3 exp i =( β 0 + β 2 )+( β 1 + β 3 ) exp i E ( wage i | exp i ,college i =0)= β 0 + β 1 exp i So ,theya rethesamei fbo th β 2 =0 and β 3 =0 . Then, we need to test the joint hypothesis H 0 : β 2 =0 and β 3 =0 and we need to use the F-statistic to test this null hypothesis. Since the restrictions in this joint hypothesis are 2, the approximate distribution of the F-statistic in large samples is F 2

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## This note was uploaded on 07/28/2010 for the course ECON 410 taught by Professor Staff during the Fall '08 term at Wisconsin.

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pqf1_ak - Econ 410 - Introduction to Econometrics Practice...

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