pqf1 - Econ 410 - Introduction to Econometrics Practice...

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Econ 410 - Introduction to Econometrics Practice Questions for the Final Exam 1. Consider the following nonlinear regression model: wage i = β 0 + β 1 exp i + β 2 college i + β 3 exp i college i + u i where wage i is the hourly wage of individual i , exp i is a continuous variable measuring work experience while college i is a binary variable taking value 1 if the individual has a college degree and 0 otherwise. From a random sample composed of 5000 observations, you estimated the following regression function: d wage i =7 . 22 (2 . 91) +0 . 87 (0 . 29) exp i +3 . 17 (1 . 21) college i 0 . 11 (0 . 04) exp i × college i R 2 =0 . 38 Assume that all the least squares assumptions hold. (a) Write the predicted wage of an individual who has a college degree as a function of work experience. Also, write the predicted wage of an individual who doesn’t have a college degree as a function of work experience. Draw a picture of both lines; put exp i in the horizontal line and d wage i in the vertical line. What is the interpretation of your picture? (b) Test 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. Use a 5% signi f cance level. (c) Test 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. Use a 5% signi f cance level. (d) How would you test the null hypothesis that the population regression function for a person with college degree is the same as the population regression function for a person without college degree? De f ne the null hypothesis and mention the test statistic that you would use to test this null hypothesis. What is the approximate distribution of this test statistics in large samples? (e) According to the estimated model, after how many years of experience the predicted wage of a person without college degree equals the predicted wage for a person with college degree? 2. You want to estimate the e f ect of living in di f erentareaso fMad isononstuden ts ’GPA .Youd iv ide Madison into three areas, Downtown, West and East, and you consider the following multiple regression model: Y i = β 0 + β 1 W i + β 2 E i + u i where Y i is GPA of observation i , W i is a binary variable that is equal to 1 if the observation lives in theW es ts ideand 0
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pqf1 - Econ 410 - Introduction to Econometrics Practice...

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