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
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?

Image Transcription

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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