Provider Retention in High Need Areas. Generic Two-Location Choice Model

12/22/2014

Table VI.1 shows the key assumed values of variables or distribution parameters for the two sets of simulations.  We endow each of 20,000 hypothetical individuals with a preference for location 1 drawn from a normal distribution with a mean of -10,000 and a standard deviation of 7,500 and a preference for location 2 drawn from a normal distribution with a mean of 0 and a standard deviation of 7,500.  Location 1 is obviously less desirable on average than location 2.  But the relatively large standard deviation of each preference factor indicates that there is significant heterogeneity of preferences in the population.  Wages are set at 30,000 in both locations, and the LRP amount is set at 5,000.  Simulation set 1 assumes a relatively low standard deviation of random shocks to decisions in each period (1,000).  Simulation set 2 doubles this standard deviation.

Table VI. 1: Assumed Values of Variables or Distribution Parameters

Variable or Distribution Parameter

Simulation Set 1

Simulation Set 2

Location 1 Wage (W1)

30,000

30,000

Location 2 Wage (W2)

30,000

30,000

Loan Repayment Amount (L)

5,000

5,000

Mean Preference Location 1 (μ1)

-10,000

-10,000

Mean Preference Location 2 (μ2)

0

0

Standard Deviation of Preferences (σθ)

7,500

7,500

Standard Deviation of Random Shocks (σε)

1,000

2,000

The model is first run under the assumption of no NHSC program.  In simulation set 1, 17.7% of the individuals choose location 1 (the HPSA location).  But although the individuals in the cohort of 20,000 have an average net preference for location 1 of -10,000, the 17.7% that actually select location 1 in period 1 have an average net preference for the location of 5,300.  Because the average preference of those choosing location 1 to begin with is so high, 90.2% of these individuals chose to remain in the location in period 2; the other 9.8% received a location shock that induced them to move to location 2.  Finally, note that 2.2% of the individuals who chose location 2 in period 1 chose to move to location 1 in period 2.

Table VI. 2: Means of Key Outcomes without a NHSC Program

Migration Patterns

Simulation Set 1

Simulation Set 2

% Choosing Location 1 in Period 1

0.177

0.185

% Retained in Location 1 in Period 2

0.902

0.826

% Moving from Location 2 to 1 in Period 2

0.022

0.037

Average Δθ | Location 1 in Period 1

5,300

4,417

Table VI.2 indicates that a larger standard deviation of random shocks (Simulation Set 2) increases the fraction of the initial cohort that choose location 1 in period 1.  Intuitively, larger shocks induce more individuals to choose location 1 even though they have a negative preference for it.  But larger random shocks also induce more individuals to move away from location 1 in period 2; larger shocks also induce more movement in period 2 from location 2 to location 1.

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