To simplify the general location choice model for the purpose of analyzing the NHSC, consider the case of only two locations. With only two locations, an individual chooses location 1 if . This implies
A further assumption significantly simplifies the condition for choice of location, namely that is independent of location in period t. This assumption is reasonable if job skills are perfectly transferable and the experience gained in one location is just as valuable in other locations as in the current location. To a first approximation, this assumption is plausible in the case of health care providers.29 With this assumption, equation (4) can be rearranged as:
The individual thus chooses location (1) if the location 1 preference differential plus the location 1 wage differential exceeds the (location 2) random shock differential, . Equation (6) implies that individuals may choose location 1 in the face of a negative wage differential if their preference differential is high enough; conversely, individuals with a negative net preference for location 1 may choose it if they receive a wage premium for working there.
In the case of two locations, and with our simplifying assumptions, the probability of choosing location 1 reduces to
Equation (7) makes it clear that probability of choosing location 1 increases with the net preference for location 1, , and the wage differential between location 1 and location 2, . Notice that, for any given wage differential, there is a preference differential that makes individuals indifferent between location 1 and location 2 (in an expected value sense). According to equation (7), an individual whose preference differential is equal to will have a 50% chance of choosing either location.
29 If the future wage path is dependent on the period t location choice, the choice differential in equation (6) would need to include a term for the difference in expected future earnings due to period t choice. For simplicity, we assume that the on both sides of equation (4) is the same.