This question asks you to interpret the following estimates of the effect of individual i’s health insurance status (Di) on their health status (Yi), measured on a ten-point scale (10 = excellent health, 1 = very poor health). Parental education (X1) is measured in years of schooling, and the instrument (Zi) indicates whether individual i was assigned health insurance eligibility through a state-run lottery.
Table 1: Effect of Health Insurance on Health Status
Panel A: OLS (1)
Panel A: OLS + Parental Education (2)
Health Insurance (Di)
0.60
0.45
(0.08)
(0.07)
Parental Education (X1)
0.05
(0.01)
Controls
No
Yes
Observations
1,200
1,200
Panel B: 2SLS (3)
Panel B: 2SLS + Parental Education (4)
Health Insurance (Di)
1.20
1.10
(0.50)
(0.55)
Lottery Assignment (Zi)
0.18
0.16
(0.04)
(0.05)
Controls
No
Yes
Observations
1,200
1,200
(a) Interpret the OLS coefficient in column (1) of Panel A. Is it significantly different from zero at the 5% level?
(b) What concern do you have with interpreting this OLS coefficient causally? In which direction would you expect bias?
(c) Explain why the coefficient changes when parental education is included in column (2) of Panel A.
(d) Interpret the second-stage coefficient in column (3) of Panel B. How does its magnitude relate to the OLS estimates in Panel A?
(e) Interpret the first-stage coefficient for Zi in column (3) of Panel B. Why is relevance of the instrument important?
(f) Approximately, what is the implied effect of a change in Zi on Yi? Do you observe weak instrument concerns when comparing columns (3) and (4)?
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