Question 2 Application (25 marks) You have been asked by the university to learn the causal effect of owning a personal laptop computer on college GPA. Some claim that owning a laptop makes a student more productive, while others argue that it does not matter or may make a student less productive (for example if they use a laptop computer for computer games etc.). a) (5 marks) Suppose you observe data on GPA and Laptop ownership for many individuals in their 4th year of studies at the University of Calgary. In particular, let Y, represent the GPA of individual i, and let X, be a binary indicator variable of whether individual i owns a laptop or not. Do you think you can identify the causal effect of having a personal laptop on GPA by comparing the sample average GPA between those who own a laptop and the rest (i.e. estimating E|Y|X; = 1] - E|Y|X; = 0))? Why/why not? Explain using logical argument. b) (5 marks) To study this question, you decide to use a linear model. In particular, you consider the regression: Y = B + 3X + t (4) Assuming B1 is the causal effect of laptop ownership on GPA, do you expect that OLS will deliver an unbiased estimator of B? Why/Why not? c) (5 marks) Suppose that, four years ago, the university gave scholarships to buy computers (in the form of say a coupon to be used at the computer store) to one half of the incoming students, and the recipients were randomly chosen. Let the indicator of whether an individual received the grant be given by S. Explain carefully how you would use S, as an indicator for X, (write down a regression model that allows us to recover the causal effect of our interest). d) (5 marks) Now, suppose that the university awarded cash instead of a coupon specifically for a computer. Compared to the rule in part c), would this setup be better or worse for answering your causal question of interest (i.e. As a researcher whose interest is to learn the causal effect of laptop ownership on college GPA, would you prefer the rules the university uses to award the coupon or cash)? Explain. e) (5 marks) Suppose now that the policy used by the University to award the coupon changes. Instead, the University awards the coupon to all students with a high school average grade of at least 85 percent. Students with an average of less than 85 do not receive a coupon. Explain how you may use this rule to identify the causal effect of laptop ownership on GPA. Explain any assumptions you must make. Question 2 Application (25 marks) You have been asked by the university to learn the causal effect of owning a personal laptop computer on college GPA. Some claim that owning a laptop makes a student more productive, while others argue that it does not matter or may make a student less productive (for example if they use a laptop computer for computer games etc.). a) (5 marks) Suppose you observe data on GPA and Laptop ownership for many individuals in their 4th year of studies at the University of Calgary. In particular, let Y, represent the GPA of individual i, and let X, be a binary indicator variable of whether individual i owns a laptop or not. Do you think you can identify the causal effect of having a personal laptop on GPA by comparing the sample average GPA between those who own a laptop and the rest (i.e. estimating E|Y|X; = 1] - E|Y|X; = 0))? Why/why not? Explain using logical argument. b) (5 marks) To study this question, you decide to use a linear model. In particular, you consider the regression: Y = B + 3X + t (4) Assuming B1 is the causal effect of laptop ownership on GPA, do you expect that OLS will deliver an unbiased estimator of B? Why/Why not? c) (5 marks) Suppose that, four years ago, the university gave scholarships to buy computers (in the form of say a coupon to be used at the computer store) to one half of the incoming students, and the recipients were randomly chosen. Let the indicator of whether an individual received the grant be given by S. Explain carefully how you would use S, as an indicator for X, (write down a regression model that allows us to recover the causal effect of our interest). d) (5 marks) Now, suppose that the university awarded cash instead of a coupon specifically for a computer. Compared to the rule in part c), would this setup be better or worse for answering your causal question of interest (i.e. As a researcher whose interest is to learn the causal effect of laptop ownership on college GPA, would you prefer the rules the university uses to award the coupon or cash)? Explain. e) (5 marks) Suppose now that the policy used by the University to award the coupon changes. Instead, the University awards the coupon to all students with a high school average grade of at least 85 percent. Students with an average of less than 85 do not receive a coupon. Explain how you may use this rule to identify the causal effect of laptop ownership on GPA. Explain any assumptions you must make