Econometrics I Midterm Solutions_475106409.pdf

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Introductory Econometrics I Midterm Exam Suggested Solutions Spring, 2013 Points: Problem 1: 25 Problem 2: 30 Problem 3: 25 Problem 4: 20 Total: 100 1. Your goal is to forecast the amount of rainfall that we will have in May based on the amount of rainfall we have had in April. Let a i denote the amount of rainfall in April and m i the amount of rainfall in May (both measured in centimeters). Suppose you have a friend that works for the weather channel. For Beijing in the last N years she tells you 1 N N i =1 a i = ¯ a = 20 , 1 N N i =1 m i = ¯ m = 35 , 1 N N i =1 ( a i - ¯ a ) 2 = 30 , and 1 N N i =1 ( m i - ¯ m ) 2 = 37 . 5 , 1 N N i =1 ( m i - ¯ m ) ( a i - ¯ a ) = - 6 . Further suppose that you know that the rainfall in April this year was 18 cm. Using these data: (a) Run a simple linear regression of m on a . Calculate ˆ β 1 , the OLS estimator of the slope coefficient. (10 points) ˆ β 1 = 1 N N i =1 ( m i - ¯ m ) ( a i - ¯ a ) 1 N N i =1 ( a i - ¯ a ) 2 = - 6 30 = - 1 5 . 1

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(b) Calculate ˆ β 0 , the OLS estimator of the intercept. (8 points) ˆ β 0 = ¯ m - ˆ β 1 ¯ a = 1 N N i =1 35 - - 1 5 × 20 = 39 . (b) Forecast the amount of rainfall in May this year. (7 points) ˆ m = ˆ β 0 + ˆ β 1 · a = 39 + - 1 5 × 18 = 35 . 4 2. Suppose you have data on people’s education level ( edu i , measured in years of schooling) and monthly income ( income i , measured in thousands of dollars). Suppose that you run a regression of monthly income on education level, and find that income i = 0 . 5 + 0 . 36 edu i + ˆ u i . (1) (a) Thinking about the model in term of a descriptive manner, explain what it means that the slope coefficient is 0.36. (4 point) Suppose I randomly picked two people from the data and it turned out that one had 1 more year of schooling than the other. I would expect the person that had more years of schooling to earn an extra amount of \$360 per month. (b) Thinking about the model in term of a causal manner, explain what it means that the slope coefficient is 0.36. (4 point) If I acquire 1 extra year of schooling, my monthly income will go up by \$360.
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