Please focus on part (b), part (a) is just presented for background information
rawing a causal diagram. (a) Draw a causal diagram for the research question ?do long shift hours make doctors give lower-quality care?? that incorporates the following features (and only the following features): i. Long shift hours ( "Long Shift") affect how tired doctors are ("Tiredness") affects the quality of care ("Quality of Care"). ii. How long shifts are is often decided by the characteristics of the hospital the doctor works at ("Hospital Characteristics"). There are plenty of things about a given hospital that also affect the quality of care, like its funding level, how crowded it is, and so on. iii. A new policy that reduces shift times may be implemented at a hospital (assumed to be determined by some unobservable change in policy preferences) but this policy does not affect the quality of care ("Policy"). b) Suppose we have a cross-sectional data set across different hospitals. This data set contains the hospital-level observations about (1) the quality of care ("Quality of Care"), (2) the average shift hours of doctors ("Shift hours"), (3) the survey result on how tired doctors are on average at the hospital, (4) various hospital characteristics ("Hospital Characteristics"), (5) Measurement of a policy that regulates shift-times, which is assumed to be randomly determined ("Policy"). We assume that the causal relationship between shift hours to the quality of care can be described with a linear regression model (In reality, they may be non-linear). 1. Suppose we regress "Quality of Care" on constant and "Shift Hours." Can we estimate the causal effect of changing shift hours on the quality of care? Why or why not? 2. Suppose we regress "Quality of Care" on constant, "Shift Hours," and "Hospital Characteristics." Can we estimate the causal effect of changing shift hours on the quality of care? Why or why not? 3. Suppose we regress "Quality of Care" on constant, "Shift Hours," "Tiredness," and "Hospital Characteristics." Can we estimate the causal effect of changing shift hours on the quality of care? Explain what the estimated coefficients on "Shift Hours" and "Tiredness" represent. 4. Suppose we regress "Quality of Care" on constant and "Policy." Can we estimate the causal effect of changing a shift-hours policy on the quality of care? Why or why not? 5. Suppose we do not observe "Hospital Characteristics" in the data set. Discuss how we can estimate the causal effect of changing the shift hours on the quality of care. [Hint: can we use the instrumental variable estimation?] rawing a causal diagram. (a) Draw a causal diagram for the research question ?do long shift hours make doctors give lower-quality care?? that incorporates the following features (and only the following features): i. Long shift hours ( "Long Shift") affect how tired doctors are ("Tiredness") affects the quality of care ("Quality of Care"). ii. How long shifts are is often decided by the characteristics of the hospital the doctor works at ("Hospital Characteristics"). There are plenty of things about a given hospital that also affect the quality of care, like its funding level, how crowded it is, and so on. iii. A new policy that reduces shift times may be implemented at a hospital (assumed to be determined by some unobservable change in policy preferences) but this policy does not affect the quality of care ("Policy"). b) Suppose we have a cross-sectional data set across different hospitals. This data set contains the hospital-level observations about (1) the quality of care ("Quality of Care"), (2) the average shift hours of doctors ("Shift hours"), (3) the survey result on how tired doctors are on average at the hospital, (4) various hospital characteristics ("Hospital Characteristics"), (5) Measurement of a policy that regulates shift-times, which is assumed to be randomly determined ("Policy"). We assume that the causal relationship between shift hours to the quality of care can be described with a linear regression model (In reality, they may be non-linear). 1. Suppose we regress "Quality of Care" on constant and "Shift Hours." Can we estimate the causal effect of changing shift hours on the quality of care? Why or why not? 2. Suppose we regress "Quality of Care" on constant, "Shift Hours," and "Hospital Characteristics." Can we estimate the causal effect of changing shift hours on the quality of care? Why or why not? 3. Suppose we regress "Quality of Care" on constant, "Shift Hours," "Tiredness," and "Hospital Characteristics." Can we estimate the causal effect of changing shift hours on the quality of care? Explain what the estimated coefficients on "Shift Hours" and "Tiredness" represent. 4. Suppose we regress "Quality of Care" on constant and "Policy." Can we estimate the causal effect of changing a shift-hours policy on the quality of care? Why or why not? 5. Suppose we do not observe "Hospital Characteristics" in the data set. Discuss how we can estimate the causal effect of changing the shift hours on the quality of care. [Hint: can we use the instrumental variable estimation?]
