1. It is easy to construct a case that the US spends way too much money on health care. The U5 spends twice as much as the average DEED country, 90% more than the Canada and 150% more than the UK, yet the US has one of the lowest life expectancy rates and one of the highest infant mortality rates in the developed world. Some have suggested these numbers indicate that at the margin, additional health care dollars generate little in the way of better health outcomes. An author is interested in examining whether greater health care spending produces better outcomes for newborns. The author focuses on newborns because childbirth is the most frequent reason for a hospital admission and the average hospital stay for childbirth costs about $E. The author starts the analysis by considering a very simple question: are outcomes better for newborns that receive more caretI The author takes a sample of newborns and regresses whether the child died within 28 days of birth {y =1 ifthey die, y = [1 otherwise] on the hospital expenditures for the newborn right after their birth {x}. This basic regression is dened as equation {1} y} = pa + 51x. + Er and the model is estimated by DLS. (a) {5 points} Is the GL5 estimate of ,1 from the simple bivariate model above an unbiased estimate of the impact of health care spending on infant mortality? Why or why not? If the estimate is biased, provide an equation for the omitted variable bias are argue whether the estimate is biased up or down. Consider the following Regression Discontinuity Design model constructed to esti- mate the impact of greater health care spending on newborn health. The author's exploit the fact that many hospitals have rules requiring greater care for newborns with particular characteristics. The average child weighs 35oo grams at birth and low birth weight is a good predictor of later outcomes. As a result' in some hospitalsI newborns with very low weight infants [those -=: 15110 grarns] are sent to directly to the neonatal intensive care units {NIEU} or hospital wards with greater nurse super- vision. The authors hope to exploit the difference in health care use at 15er grams in a 'regression discontinuity' model to estimate the benets of greater health care on child outcomes. The authors collect data on a large sample of children with low birth weights [1350 to 155!) grams}. The outcome of interest {y} is a dummy variable that equals 1 if a child dies within 28 days of birth. The key covariate is x [hospital spending in dollars for the newborn]. In the rst stage and reduced-forms, the authors control for the birth weight in grams tow} and a dummy variable {D} that equals 1 ifthe newborn is less than 1soo grams in weight. First Stage: xi = or + o1BWf + oil]j + uf Reduced Form: y}. = y + ~,r1lrv'j + i'zr + \"r Table 1: Results for Question X (X) (Y) Hospital The newborn Charges in died within dollars 28 days Constant 260.250 0.168 (23.000) (0.021) BW (in grams) -115 -0.000083 (15.1) (0.00002) D(BW