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Question 1 The company Phiten makes necklaces that Major League Baseball players commonly wear during games. The company claims that the necklaces improve performance. Suppose the MLB want to test this claim. On a particular day, all managers randomly instruct some players to wear a Phiten necklace and others not to wear one using a coin flip. Each player gets a separate and independent coin flip. Let the coin flip be denoted by H (the managers assign the necklace if the coin flip comes up heads). Not all players comply. Some players who were not assigned the necklace wear one anyway and some players who were assigned the necklace do not wear one Let the variable X denote whether a player wore a necklace and R denote the number of runs the player scores during the game. Answer the following questions a) If you regress runs on H, is H exogenous? b) Suppose that the cov(H,R)-0 in the population, does that mean the causal effect of the necklace on runs is zero? c) If you regress runs on X, is X exogenous? d) Suppose that the cov(X,R)-0 in the population, does that mean the causal effect of the necklace on runs is zero? e) Suppose you run a regression of runs on H and X. Will you get consistent estimates of the causal effect of the necklace on runs? If so, which coefficient is that effect? f) What is the first stage of a 2SLS estimate of the causal effect of the necklace on runs? g) What is the second stage ofa 2SLS estimate of the causal effect of the necklace on runs? h) Suppose better batters are more likely to wear the necklace (perhaps because they are trying everything possible to improve their swing) and suppose OLS estimates suggest that a batter who wore the necklace scores an extra 0.2 runs per game. Would that likely be an overestimate, underestimate, or unbiased estimate of the true effect?

Question 1 The company Phiten makes necklaces that Major League Baseball players commonly wear during games. The company claims that the necklaces improve performance. Suppose the MLB want to test this claim. On a particular day, all managers randomly instruct some players to wear a Phiten necklace and others not to wear one using a coin flip. Each player gets a separate and independent coin flip. Let the coin flip be denoted by H (the managers assign the necklace if the coin flip comes up heads). Not all players comply. Some players who were not assigned the necklace wear one anyway and some players who were assigned the necklace do not wear one Let the variable X denote whether a player wore a necklace and R denote the number of runs the player scores during the game. Answer the following questions a) If you regress runs on H, is H exogenous? b) Suppose that the cov(H,R)-0 in the population, does that mean the causal effect of the necklace on runs is zero? c) If you regress runs on X, is X exogenous? d) Suppose that the cov(X,R)-0 in the population, does that mean the causal effect of the necklace on runs is zero? e) Suppose you run a regression of runs on H and X. Will you get consistent estimates of the causal effect of the necklace on runs? If so, which coefficient is that effect? f) What is the first stage of a 2SLS estimate of the causal effect of the necklace on runs? g) What is the second stage ofa 2SLS estimate of the causal effect of the necklace on runs? h) Suppose better batters are more likely to wear the necklace (perhaps because they are trying everything possible to improve their swing) and suppose OLS estimates suggest that a batter who wore the necklace scores an extra 0.2 runs per game. Would that likely be an overestimate, underestimate, or unbiased estimate of the true effect?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Question 1 The company Phiten makes necklaces that Major League Baseball players commonly wear during games. The company claims that the necklaces improve performance. Suppose the MLB want to test this claim. On a particular day, all managers randomly instruct some players to wear a Phiten necklace and others not to wear one using a coin flip. Each player gets a separate and independent coin flip. Let the coin flip be denoted by H (the managers assign the necklace if the coin flip comes up heads). Not all players comply. Some players who were not assigned the necklace wear one anyway and some players who were assigned the necklace do not wear one Let the variable X denote whether a player wore a necklace and R denote the number of runs the player scores during the game. Answer the following questions a) If you regress runs on H, is H exogenous? b) Suppose that the cov(H,R)-0 in the population, does that mean the causal effect of the necklace on runs is zero? c) If you regress runs on X, is X exogenous? d) Suppose that the cov(X,R)-0 in the population, does that mean the causal effect of the necklace on runs is zero? e) Suppose you run a regression of runs on H and X. Will you get consistent estimates of the causal effect of the necklace on runs? If so, which coefficient is that effect? f) What is the first stage of a 2SLS estimate of the causal effect of the necklace on runs? g) What is the second stage ofa 2SLS estimate of the causal effect of the necklace on runs? h) Suppose better batters are more likely to wear the necklace (perhaps because they are trying everything possible to improve their swing) and suppose OLS estimates suggest that a batter who wore the necklace scores an extra 0.2 runs per game. Would that likely be an overestimate, underestimate, or unbiased estimate of the true effect?
Transcribed Image Text:Question 1 The company Phiten makes necklaces that Major League Baseball players commonly wear during games. The company claims that the necklaces improve performance. Suppose the MLB want to test this claim. On a particular day, all managers randomly instruct some players to wear a Phiten necklace and others not to wear one using a coin flip. Each player gets a separate and independent coin flip. Let the coin flip be denoted by H (the managers assign the necklace if the coin flip comes up heads). Not all players comply. Some players who were not assigned the necklace wear one anyway and some players who were assigned the necklace do not wear one Let the variable X denote whether a player wore a necklace and R denote the number of runs the player scores during the game. Answer the following questions a) If you regress runs on H, is H exogenous? b) Suppose that the cov(H,R)-0 in the population, does that mean the causal effect of the necklace on runs is zero? c) If you regress runs on X, is X exogenous? d) Suppose that the cov(X,R)-0 in the population, does that mean the causal effect of the necklace on runs is zero? e) Suppose you run a regression of runs on H and X. Will you get consistent estimates of the causal effect of the necklace on runs? If so, which coefficient is that effect? f) What is the first stage of a 2SLS estimate of the causal effect of the necklace on runs? g) What is the second stage ofa 2SLS estimate of the causal effect of the necklace on runs? h) Suppose better batters are more likely to wear the necklace (perhaps because they are trying everything possible to improve their swing) and suppose OLS estimates suggest that a batter who wore the necklace scores an extra 0.2 runs per game. Would that likely be an overestimate, underestimate, or unbiased estimate of the true effect?
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