(Solved): please solve it in 20 mins I will thumb you up just need b part B.2 In "Does ...

just need b part

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 8, +4. (7) 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 c >> 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., cy), y, is known, but otherwise we only know ci and that y > 4. 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. (b) Suppose that individual i opts to go to a hospital according to the following choice model: h = 1(70+ nad + v, 20) (8) where hi = 1 if individual i goes to the hospital and = 0, otherwise. The variable de records i's distance to the closest hospital and v marks idiosyncratic unobservable factors informing this decision. Assume that t; follows a standard normal distribution. One is interested in estimating (7) and information on yi is only available for those who go to the hospital. Assume that OLS estimates are obtained for those observations. First, if & and ; are not necessarily independent, but d = 0, would the OLS estimator above be consistent? Explain. What if yd is not necessarily zero, but d, and x are independent? Explain.