For simplicity, assume there are only two location types: HPSAs and non-HPSAs, and each individual has a certain preference for locating in HPSAs, θi. The correlation between the unobservable factors that affect admission to the LRP program and choice of geographic location (i.e., the correlation between γi and θi) has implications for observed retention patterns of NHSC participants and non-participants.
Under normal circumstances, there will be a number of participants with negative values for θi who will locate in HPSAs only because of the program. As a result of these providers going to HPSAs, the average preference of participants is lower than the average preference of non-participants and therefore the retention of participants in HPSAs will always be lower than the retention of non-participants. The difference between the retention rates is larger when the correlation between γi and θi is lower. As discussed above, the limiting case is when the correlation is zero, meaning that preferences for HPSAs play no role in the acceptance process. In this case, the number of NHSC participants with negative preferences for HPSAs will be the highest and therefore, the average retention rate in the population of participants will be at its lowest point relative to any other scenario when the correlation between γi and θi is strictly positive.11
In the unlikely case when there are more individuals with positive values for θi than the number of available program positions and the correlation between γi and θi is positive, all program participants will be individuals who have a preference for locating in HPSAs. Such individuals will have a higher average preference for HPSAs than program non-participants who were attracted to HPSAs anyway. Because they have a higher average preference for HPSAs than non-participants, program participants will tend to have higher retention in HPSAs after completion of their service obligations than non-participants. However, given that not all candidates are accepted into NHSC, this case cannot be encountered in reality.
Finally, the magnitude of the program effect on HPSA provider supply also depends on how sensitive location choices are to the presence of the program and the LRP amount. As in the general case, the impact depends on the mean preferences for various locations (the μj), the standard deviation of preferences (σθ), and the standard deviation of the random shocks (σε). Choices are more sensitive the more homogeneous location preferences are (i.e., the smaller is σθ) and the smaller the role of random shocks to location decisions (i.e., the smaller isσε).
11 A case of negative correlation between and would mean that the NHSC purposefully selects into the program providers who do not want to there.