PA 581 Homework 4, Spring 2025
In 2008, Goldman and Romley studied hospital demand by analyzing how 8,721 Medicare-covered pneumonia patients chose from among 117 hospitals in the greater Los Angeles area. The authors concluded that clinical quality (as measured by a low pneumonia mortality rate) played a smaller role in hospital choice than did a variety of other factors.
Let’s focus on a subset of the Goldman-Romley sample: the 499 patients who chose either the UCLA Medical Center or the nearby Cedars Sinai Medical Center. Typically, economists would expect price to have a major influence on such a choice, but Medicare patients pay roughly the same price no matter what hospital they choose. Instead, factors like the distance the patient lives from the hospital and the age and income of the patient become potentially important factors:
Where
Di = 1 if the ith patient chose Cedars Sinai, 0 if they chose UCLA
DISTANCEi = the distance from the ith patient’s home (according to zip code) to Cedars Sinai minus the distance from that point to the UCLA Medical Center (in miles)
INCOMEi = the income of the ith patient (as measured by the average income of their zip code in thousands of dollars)
OLDi = 1 if the ith patient was older than 75, 0 otherwise
Part I: Interpretation
a. Create and test appropriate hypotheses about the coefficient of DISTANCE.
b. Carefully state the meaning of the estimated coefficient of DISTANCE in terms of the “per mile” impact on the probability of choosing Cedars Sinai Medical Center
c. Think about the definition of DISTANCE. Why do you think we defined DISTANCE as the difference between the distances as opposed to entering the distance to Cedars and the distance to UCLA as two different independent variables?
Part II: Stata
d. Load the “HOSPITAL13” data into Stata to estimate the linear probability model (LPM) version of this equation. What is the coefficient of DISTANCE in your estimate? Which do you prefer, the logit or the linear probability model? Explain.
e. (OPTIONAL/EXTRA CREDIT) Now create a slope dummy by adding OLD x DISTANCE to the original equation and estimating the new logit equation. Why do you think we’re suggesting this particular slope dummy? Create and test the appropriate hypothesis about the slope dummy. Which equation do you prefer, the original or the new slope dummy logit? Explain.