- B 2 In Does Hospital Crowding Matter Evidence From Trauma And Orthopedics In England American Economic Journal Econo 1 (251.52 KiB) Viewed 35 times
B.2 In “Does Hospital Crowding Matter? Evidence from Trauma and Orthopedics in England (American Economic Journal: Economic Policy. forthcoming). Thomas Hoe examines the in- pact of hospital crowding on medical treatment outcomes exploiting variation in emergency admissions. For simplicity, we abstract from some of the details examined in the paper. One possible outcome of interest is the length of the illness (measured in days) for a particular patient i. Let this be denoted by yi. Suppose one focusses on the following model relating this outcome for an individual i admitted to a particular hospital: In(x) = 30 + x 3, +4. where x; comprises variables such as the individual's age, race and disease stage at the time of admission. As indicated in the article, other elements that might affect the outcome of interest relate to patient composition and hospital operation details (such as capacity constraints and utilisation) at the hospital where the individual is admitted, among other factors. Note that the unit of observation in items (a)-(e) below are the individual whereas in items (d)-(e) relates to a time period (day) for a particular hospital. (a) Suppose that one is interested in estimating (7) with data from a particular hospital. Let e > 0 denote the number of days an individual is at the hospital. This variable and x is observed for every patient in the hospital. If individual is discharged after recovering from the illness (i.e., g > yı), y, is known, but otherwise we only know c and that y > g. What additional assumptions would one need to estimate (7) by maximum likelihood? Write down the log-likelihood function for this regression and explain your answer.