Provider Retention in High Need Areas. Two-Location Choice Model with NHSC Programs

12/22/2014

We now turn to simulations of choices under an NHSC LRP.  As discussed above, there are four distinct groups to consider:

  1. Group 1 – individuals with outstanding loans who apply for NHSC and are accepted;
  2. Group 2 -- individuals with outstanding loans who apply and are rejected;
  3. Group 3 -- individuals with outstanding loans who do not apply and
  4. Group 4 – individuals without outstanding loans and not eligible to apply.

To determine these groups, we randomly assign half of the 20,000 cohort to have outstanding debt and thus be eligible for application for LRP.  Group 4 thus contains 10,000 individuals.  Each of the 10,000 individuals with outstanding debt decides to apply or not apply depending upon whether the inequality in equation (9) holds.  The NHSC then evaluates the individual’s application.  According to equation (11), the applicant’s unobservable value to the program is based on his (standardized) net preference for location 1 and a random shock that is uncorrelated with preferences.  Once a random shock is generated and the applicant’s value to the program (A) is computed, the NHSC is assumed to rank-order applicants and select half of them for acceptance into the program.  Accepted applicants thus form Group 1 and rejected applicants form Group 2.  In all simulations, there were 1,644 accepted applicants and 1,643 rejected applicants.  The remaining are 6,713 individuals with outstanding debt form Group 3.

The following two tables (Tables VI.3 and Table VI.4) contain means of key outcome variables in the simulations for groups 1, 2 and 4.  Group 3 outcomes are ignored because everyone in this group goes to location 2 and stays there in period 2.  Since groups 2 and 4 together represent all non-participants who located in the HPSA, the table shows rates and means for these two groups combined.  Each table contains five scenarios that vary the correlation between preferences and other factors that influence selection into NHSC.  The correlations range from 0 to 0.98.  In the first scenario, selection into the program is independent of location preferences.  In the last scenario, applicants are selected into the program almost completely on the basis of the strength of their location preferences.

First inspect scenario 1 in Table VI.3.  Obviously, everyone in group 1 must go to location 1, the HPSA, in period 1.  After completing their NHSC service, however, only 53.4% decide to remain in the HPSA for period 2.  This retention rate is much lower than the retention rates of groups 2 and 4.  About 90% of both groups choose to remain in the HPSA for period 2.  These much higher retention rates are explained by the fact that the individuals in the latter two groups did not receive an inducement to locate in the HPSA (in the form of LRP); consequently the smaller percentages that did locate there had much higher average net preferences for the location than the NHSC participants.  Measured by their average preferences for the HPSA, the two groups of non-participants who locate in the HPSA appear relatively homogeneous.  As we shall see, these groups become more heterogeneous the more the NHSC selects applicants on the basis of their location preferences.

Table VI. 3: Means of Key Outcomes with NHSC Program in Five Scenarios (Simulation Set 1)

Migration Patterns

Group

Overall

1

2

4

2 & 4

Scenario 1: Corr(ua, ub)=0

% Choosing Location 1 in Period 1

1.000

0.548

0.174

0.227

0.214

% Retained in Location 1 in Period 2

0.534

0.897

0.907

0.906

0.762

% Moving from Location 2 to 1

 

0.140

0.022

0.038

0.018

Average Δθ | Location 1 in Period 1

1,636

5,308

5,197

5,213

3,854

Scenario 2: Corr(ua, ub)=0.447

% Choosing Location 1 in Period 1

1.000

0.474

0.174

0.216

0.208

% Retained in Location 1 in Period 2

0.609

0.872

0.907

0.902

0.783

% Moving from Location 2 to 1

0.000

0.126

0.022

0.036

0.018

Average Δθ | Location 1 in Period 1

2,878

4,129

5,197

5,046

4,081

Scenario 3: Corr(ua, ub)=0.707

% Choosing Location 1 in Period 1

1.000

0.408

0.174

0.207

0.203

% Retained in Location 1 in Period 2

0.679

0.842

0.907

0.898

0.804

% Moving from Location 2 to 1

0.000

0.112

0.022

0.034

0.018

Average Δθ | Location 1 in Period 1

3,859

3,066

5,197

4,896

4,302

Scenario 4: Corr(ua, ub)=0.894

% Choosing Location 1 in Period 1

1.000

0.324

0.174

0.195

0.196

% Retained in Location 1 in Period 2

0.766

0.795

0.907

0.892

0.833

% Moving from Location 2 to 1

0.000

0.095

0.022

0.032

0.018

Average Δθ | Location 1, Period 1

4,855

1,851

5,197

4,725

4,598

Scenario 5: Corr(ua, ub)=0.98

% Choosing Location 1 in Period 1

1.000

0.216

0.174

0.180

0.187

% Retained in Location 1 in Period 2

0.880

0.685

0.907

0.876

0.874

% Moving from Location 2 to 1

0.000

0.078

0.022

0.029

0.017

Average Δθ | Location 1, Period 1

5,857

103

5,197

4,478

5,003

Now let us examine collectively the other scenarios.  Notice, as the NHSC selects applicants more and more on the basis of their net preferences for service in the HPSA, the retention rate among NHSC participants in period 2 increases.  In fact, by scenario 5 the retention of the participants converges to the retention of the non-participants without student loans (group 4) and the average retention of all non-participants (groups 2 & 4 combined).  As we move from scenario 1 to scenario 5, however, the retention of group 2 declines significantly.  This decline is due to the fact that, as the NHSC selects applicants more on the basis of preferences, the pool of rejected applicants consists more of individuals with weaker net preferences for location 1.

An important take-away from these scenarios is that retention of NHSC participants in a HPSA is never likely to exceed the retention of non-participants and will likely be less than the retention of non-participants unless applicants are selected into the program almost exclusively on the basis of preferences for service in a HPSA.

Table VI.4 repeats the five scenarios assuming a larger standard deviation of shocks to location decisions.  The overall pattern of outcomes remains the same as in Table VI.1, but (as discussed above) larger shocks have the effect of inducing a higher rate of selection of location 1 in period 1 but higher rates of movement out of and into location 1 in period 2. The lower overall retention in location 1 is also explained by the fact that the average net preference for location 1 in period 1 among the people choosing that location in period 1 is smaller in simulation set 2 with the higher variance in the random shock.

Table VI. 4: Means of Key Outcomes with NHSC Program in Five Scenarios (Simulation Set 2)

Migration Patterns

Group

Overall

1

2

4

2 & 4

Scenario 1: Corr(ua, ub)=0

% Choosing Location 1 in Period 1

1.000

0.578

0.184

0.184

0.220

% Retained in Location 1 in Period 2

0.546

0.816

0.832

0.832

0.723

% Moving from Location 2 to 1

 

0.175

0.038

0.038

0.030

Average Δθ

1,012

1,068

-9,979

-9,979

-10,008

Average Δθ | Location 1, Period 1

1,012

4,274

4,476

4,476

3,152

Scenario 2: Corr(ua, ub)=0.447

% Choosing Location 1 in Period 1

1.000

0.507

0.184

0.229

0.410

% Retained in Location 1 in Period 2

0.626

0.776

0.832

0.824

0.743

% Moving from Location 2 to 1

0.000

0.147

0.038

0.053

0.030

Average Δθ

2,426

-347

-9,979

-8,620

-10,008

Average Δθ | Location 1, Period 1

2,426

3,039

4,476

4,273

3,421

Scenario 3: Corr(ua, ub)=0.707

% Choosing Location 1 in Period 1

1.000

0.450

0.184

0.221

0.210

% Retained in Location 1 in Period 2

0.688

0.730

0.832

0.817

0.758

% Moving from Location 2 to 1

0.000

0.136

0.038

0.052

0.030

Average Δθ

3,533

-1,454

-9,979

-8,776

-10,008

Average Δθ | Location 1, Period 1

3,533

1,752

4,476

4,092

3,635

Scenario 4: Corr(ua, ub)=0.894

% Choosing Location 1 in Period 1

1.000

0.370

0.184

0.210

0.203

% Retained in Location 1 in Period 2

0.766

0.667

0.832

0.808

0.781

% Moving from Location 2 to 1

0.000

0.124

0.038

0.050

0.030

Average Δθ

4,697

-2,619

-9,979

-8,940

-10,008

Average Δθ | Location 1, Period 1

4,697

185

4,476

3,871

3,928

Scenario 5: Corr(ua, ub)=0.98

% Choosing Location 1 in Period 1

1.000

0.297

0.184

0.200

0.197

% Retained in Location 1 in Period 2

0.835

0.593

0.832

0.798

0.804

% Moving from Location 2 to 1

0.000

0.113

0.038

0.049

0.030

Average Δθ

5,552

-3,475

-9,979

-9,061

-10,008

Average Δθ | Location 1, Period 1

5,552

-1,474

4,476

3,636

4,191

 

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