Instrumental Variables and Measurement Error, Suppose we are interested in estimating the effect of a child's health on their score on a math test. We have two measures of the child's health - health1health1 is reported by the child's mother and health2health2 is reported by the school nurse. Suppose we estimate the following regression using health2 as an instrumental variable for health1: mathscore = β0 + β1health1 + β2female + u a. What assumption regarding Corr(health1, health2) must we make for health2 to be a valid instrument? Do you think this assumption is likely to be satisfied? Explain b. What assumption regarding Corr(health2, u) must we make for health2 to be a valid instrument? Do you think this assumption is likely to be satisfied? Explain c. If health2 is a valid instrument, should it be includ
Instrumental Variables and Measurement Error,
Suppose we are interested in estimating the effect of a child's health on their score on a math test. We have two measures of the child's health - health1health1 is reported by the child's mother and health2health2 is reported by the school nurse.
Suppose we estimate the following regression using health2 as an instrumental variable for health1:
mathscore = β0 + β1health1 + β2female + u
a. What assumption regarding Corr(health1, health2) must we make for health2 to be a valid instrument? Do you think this assumption is likely to be satisfied? Explain
b. What assumption regarding Corr(health2, u) must we make for health2 to be a valid instrument? Do you think this assumption is likely to be satisfied? Explain
c. If health2 is a valid instrument, should it be included in the main regression? (just YES or NO)
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