Econometrics I Midterm Solutions_475106409.pdf

Econometrics I Midterm Solutions_475106409.pdf -...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
(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.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern