A research team wants to investigate whether happier individuals are more productive. They carry out an experiment with 700 university students. After filling out a survey questionnaire, the students see a short film clip and are then asked to add up as many sets of five two-digit numbers as possible in 10 minutes (which is a simple but taxing task under time pressure). The participants are told before the task that they would receive bonus payments (performance-related) for each correct addition. For the film clip, the students are randomly selected to see either a comedian telling jokes or a film clip with calming abstract images and music. The researchers construct the following variables: (i) Additions the number of correct additions performed; (ii) Happiness - answers to a question how happy they feel on a 7-point scale where 7 is completely happy and 1 is completely sad, asked immediately after seeing the film clip; (iii) Comedy -a variable equal to 1 if the respondent is shown the comedy clip, 0 otherwise; (iv) Male - a variable equal to 1 if the respondent is male, 0 otherwise; (v) High School Grades-their average grades when leaving high school; and (vi) Test Score - the score on a short math test, administered as part of the questionnaire. The researchers then produce the following table of results, with the robust standard errors reported in the parentheses. Regressor Comedy Happiness Male High School Grades Test Score Dependent Variable and Estimation Method Happiness In(Additions) In(Additions) OLS OLS (1) 2SLS (2) (3) 1.168 (0.374) 0.154 (0.229) 0.321 (0.119) 0.038 (0.276) 0.216 (0.034) -0.055 (0.057) 0.431 (0.113) 0.097 (0.026) 0.101 (0.040) -0.027 (0.061) 0.477 (0.114) 0.100 (0.023) Comedy is instrument for Happiness (a) Carefully explain why we cannot interpret the coefficient on Happiness in column (2) as the causal effect of happiness on productivity. Describe the sources of bias and the direction of the bias. (b) What is the effect of happiness on productivity in column (3)? Describe the assumptions which are necessary to interpret the coefficient on Happiness in column (3) as the causal effect of happiness on productivity. Discuss whether these assumptions are likely to be satisfied in this case. (c) Carefully discuss how the bias(es) you identified in part a) and the conclusions from part b) explain the difference in the coefficients on Happiness in columns (2) and (3).