ECO 310  Econometrics Dr. Robert Jantzen

Homework 9


Objective:  Analyze the cost structure of Westchester's hospitals using the hospital.csv file.  The data pertain to the 15 private Westchester hospitals’ average costs per bed (AVGCOST), their size (BEDS), the number of full-time staff per bed (FTPERBED), and their occupancy rates (OCCUP).  All data were measured in 1992, and average costs refer to annual spending levels per bed (in $) and the occupancy rate shows the percentage of hospital beds filled.

I.   EALimdep Programming:

     A.  You will have to create five new variables (namely, BEDDSQ, LOGCOST, LOGBEDS, LOGFTES AND LOGCC) from the existing variables in the Excel worksheet.  To do so:

  • Start up the Gretl program.
  • Import the hospital.csv file.
  • Create the BEDDSQ variable by clicking on <Project><New><Variable>, typing in BEDSSQ in the Name box and BEDS*BEDS in the Expression box, and then clicking on OK.  Then create the LOGCOST variable by clicking on <Project><New><Variable>, typing in LOGCOST in the Name box and LOG(AVGCOST) in the Expression box,   and then clicking on OK.  Then create the LOGBEDS variable by clicking on <Project><New><Variable>, typing in LOGBEDS in the Name box and LOG(BEDS)  in the Expression box, and then clicking on OK.  Then create the LOGFTES variable by clicking on <Project><New><Variable>, typing in LOGFTES in the Name box and LOG(FTPERBED) in the Expression box, and then clicking on OK.  Then create the LOGOCC variable by clicking on <Project><New><Variable>, typing in LOGOCC   in the Name box and LOG(OCCUP) in the Expression box, and then clicking on OK.
  • Run the following three regression models:

    •  

     
     
     

    #1   AVGCOSTi  = b0 + b1BEDSi  + b3FTPERBEDi  + b4OCCUPi  + ei
    #2   AVGCOSTi  = b0 + b1BEDSi  + b2BEDSSQi  + b3FTPERBEDi  + b4OCCUPi  + ei
    #3   AVGCOSTi  = b0 + b3FTPERBEDi  + b4OCCUPi  + ei
     

  • Run the following two regression models:
        #4   LOGCOSTi  = b0 + b1LOGBEDSi  + b3LOGFTESi  + b4LOGOCCi + ei
        #5   LOGCOSTi  = b0 + b1BEDSi  + b3FTEPERBEDi  + b4OCCUPi  + ei

II.   Assignment:

a.   What do the newly created variables measure?

b.    Looking at the first three regression results, does hospital bed size influence average hospital costs?  Do the appropriate test(s).

c.   Looking only at the second regression results, find which bed size maximizes/minimizes average hospital costs.

d.   Conduct t-tests and interpret the coefficients for the 4th regression (exclude the constant).  What is the underlying non-logged model that you have estimated coefficients for?

e.   Conduct t-tests and interpret the coefficients for the 5th regression (exclude the constant).

BONUS:  Using the coefficients in the 4th regression, find how much of the variation in the dependent variable (namely AVGCOST, not log of AVGCOST), is explained by variation in the explainers.  In other words, use the logged value regression to find the R squared for the underlying, non-logged value of the dependent variable.  In order to get the R squared:

       a.  rerun the 4th logged equation and keep the predicted values for the logged dependent variable (click on the <OUTPUT> tab when you run the regression and click on <keep predictions as variable> and type in LOGCOST2 as the variable name).
       b.  to obtain non-logged predicted values for the dependent variable, compute the antilog of the predicted values in the logged equation, i.e., create the COST2 variable by clicking on <Project><New><Variable>, typing in COST2 in the Name box and EXP(LOGCOST2) in the Expression box, and then clicking on OK.
     c.  to compute the logged model's "implied" R squared for the non-logged cost variable, run a regression of the actual average cost values (AVGCOST) using the predicted cost values that were generated by the logged model (COST2).