Question

It is easy to construct a case that the US spends way too much money on health care. The US spends twice as much as the average OECD 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 $6000. The author starts the analysis by considering a very simple question: are outcomes better for newborns that receive more care? The author takes a sample of newborns and regresses whether the child died within 28 days of birth (y = 1 if they die, y = 0 otherwise) on the hospital expenditures for the newborn right after their birth (x). This basic regression is defined as equation (1) yi = β0 + β1xi + ei and the model is estimated by OLS.

a) Is the OLS estimate of βˆ 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.

Answer 1