Medicaid is a publicly funded health insurance program for low-income individuals. To qualify for Me Show more Medicaid is a publicly funded health insurance program for low-income individuals. To qualify for Medicaid an individual had to have income below certain thresholds.
Recently Oregon wanted to expand its Medicaid program but did not have enough funds to expand Medicaid to all low-income individuals who applied (even if they met the eligibility thresholds). Consequently Oregon used a random lottery to allocate Medicaid. Let the variable L denote whether an individual won the Medicaid lottery. Not everyone who won the lottery ended up being covered by Medicaid (since applying they may have gotten health insurance through their employer). In addition some who did not win the lottery later obtained Medicaid (perhaps after the lottery they obtained Medicaid because of a new pregnancy and states are more likely to grant pregnant women Medicaid). However lottery winners were more likely to obtain Medicaid coverage than non-winners were. Indicate whether an individual had Medicaid with the dummy variable M. Seeing this as an opportunity to analyze the effects of health insurance on health researchers decided to collect the following data for all who applied for Medicaid: whether they won the lottery (L); whether they obtained Medicaid (M); body mass index (BMI); a dummy variable indicating whether the individual was depressed (D). 1) If you run a regression of BMI on M is the variable M likely to be exogenous or endogenous? 2) If you run a regression of BMI on L is the variable L exogenous or endogenous? 3) How would you interpret the coefficient on L? 4) If you regress D on BMI are the predicted values for all individuals guaranteed to be between 0 and 1? 5) If you regress D on L are the predicted values for all individuals guaranteed to be between 0 and 1? 6) Carefully explain how to use this experiment to construct an instrumental variables estimate of the effect of Medicaid coverage on BMI. Carefully write out what the first and second stages are. 7) From part (f) what assumptions do you need? Are they likely to hold true in this context? 8) Another researcher is interested in the effects of BMI on depression (D) and decided to instrument for BMI using L. Are the IV assumptions likely to be satisfied? For full credit carefully explain why or why not. Show less
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