answer e and f

Question 1 (100 marks Because cognitive skills affect many economic and health-related outcomes, it is important to under- stand how such skills can be fostered. Video game developers advocate that playing video games can improve cognitive skills such as problem solving, abstract reasoning, and spatial logic. Using a survey of 4,534 randomly sampled age 10 children, an economist aims to estimate the causal effect of time spent playing video games on cognitive skills. The survey includes various characteristics of the families, the parents (education, ethnicity, in- come, age, occupations, etc.), and the children themselves. The time spent playing video games is measured using a time diary. A child (or his/her parent) is asked to randomly choose a weekday and list all his/her activities in the 24 hour time diary, importantly they record the times at which the activity started and ended. The economist obtains three variables representing how a child spent his/her 24 hours in a random weekday: 0) Video Games the number of hours spent playing video games, (*) Productive Activities the number of hours spent on activities that are conventionally deemed to positively affect cognitive skills such as reading educational books, doing homework, or exercising, and (W) Unproductive Activities the number of hours spent on unproductive activities that might possibly have little effect on cognitive skills, for example, travelling, watching television, shopping, or eating. These variables are defined such that any activity would fall into one of the three categories although it is possible that mistakes are made when recording data. The data are only recorded once a week To measure cognitive skills, the economist uses an international mathematics test, which as- sesses children's ability to solve mathematical reasoning problems. The score for each child, recorded as Maths Scores, has been standardised to have a mean of O and a standard deviation of 1. (a) The economist specifies a baseline regression equation with Maths Scores as the outcome and Video Games on the right side. He also insists on including either Productive Activities or Unproductive Activities in any regression. Explain whether or not including one of the vari- ables benefits the estimation. Should he include both Productive Activities and Unproductive Activities in the regressions? Explain 120 marks) The economist runs several regressions and obtains the following table, with robust standard errors reported in the parentheses Dependent Variable and Estimation Method Regressor Maths Scores Maths Scores Reading Maths Scores OLS OLS OLS 2SLS (1) (2) (3) (4) Video Games 0.089 0.038 0.010 0.093 (0.018) (0.013) (0.011) (0.037) Productive Activities 0.065 0.021 0.101 0.091 (0.007) (0.004) (0.004) (0.033) Other Covariates Not included Included Included Included Notes: In Column (4). Games on Weekend is the instrument for Video Games. The coefficients for the intercept and the other covariates are not reported. LSE LT 2022/EC220 Page 2 of 3 (e) A research assistant suggests that the economist should include the variable Reading as a covariate in the regression in column (2). Carefully explain whether or not the economist should follow the suggestion. [15 marks) () The economist has another variable Games on Weekend that measures the number of hours per day a child spent playing video games over weekends. He uses the variable as an instrumen- tal variable for Video Games and reports the result in Column (4). Carefully explain whether he can interpret the coefficient on Video Games in Column (4) causally now. To begin your an- swer, explain the intuition behind this approach and evaluate any necessary assumptions this strategy requires. What type of bias(es) might this approach help overcome? Discuss whether the economist can test the validity of the assumptions. If your answer is yes, explain how to perform such test(s) [25 marks)