Health Practitioner Bonuses and Their Impact on the Availability and Utilization of Primary Care Services. C.2. DID model and derivation for estimating the impact of HPSA bonus

12/22/2014

Equation (5) below shows the empirical specification that we used to estimate the effect of HPSA status on the outcome variables discussed above:

(5)

 

The model is specified based on the physician level data in each year.  Here, the dependent variable, is one of the other potential outcomes of interest of a primary care physician i, in county c, at time t; is an indicator of whether physician i’s county is a HPSA at time t; is an indicator variable taking the value of 1 if the physician’s county ever gained the HPSA status (from a non-HPSA) during the sample period and zero otherwise;  is an indicator variable taking the value of 1 if the physician’s county ever lost the HPSA designation during the sample period and zero otherwise; the vector includes variables reflecting the physician characteristics, their geographic locations etc., and is a vector of time-specific fixed effect terms.

The term represents random unobserved factors affecting outcomes. If the change of HPSA status is associated with any changes in the volume of services provided by primary care physicians in those areas, then we should expect estimated values of and in equation (5) will reflect them. If the outcome of interest is the volume of services then a positive significant estimated value of would imply higher volume of services due to gaining HPSA designation.

For simplicity, assume that we have physicians in the following four types of counties: counties that are always HPSA (type C1); counties that are always non-HPSA (type C2) ; counties that gained HPSA status and remained HPSA afterwards (C3); and counties that lost HPSA status and remained non-HPSA afterwards (C4). Also, consider the number of E&M claims submitted under Medicare as the outcome variable of interest. Now for given values of , , , , and , let us focus on the first 7 terms of the above equation for a representative provider in each of these 4 types of counties:

Equation (6) shows the expression of the model, excluding the last three terms, for County Type C1 (always HPSA):

(6)

 

Equation (7) shows the expression of the model, excluding the last three terms, for County Type C2 (always non-HPSA):

(7)

 

Equation (8) shows the expression of the model, excluding the last three terms, for County Type C3 (gained HPSA status) when these counties have HPSA status:

(8)

 

Equation (9) shows the expression of the model, excluding the last three terms, for County Type C3 (gained HPSA status) when these counties have Non-HPSA status:

(9)

 

Thus in equation (6) shows the estimated average number of claims per physician in HPSA counties (after controlling for other factors); while in equation (7) represents the estimated average number of claims per physician in non-HPSA counties. Thus, captures the persistent difference in the average number of claims between the HPSA and non-HPSA counties.

On the other hand comparing equation (8) and (9), the model indicates that in counties that gained the HPSA status shows the difference between the estimated average number of claims per physician when the counties have the HPSA status and the average number of claims when they do not have the HPSA status. However, already captures the persistent difference in the average number of claims between the HPSA and non-HPSA counties. Therefore, the parameter shows the additional impact of HPSA status on the average number of claims per physician in the counties that gained HPSA status. If gaining HPSA status encourages physicians to increase the availability of primary care services, then we expect to be positive.

Similarly equation (10) shows the expression of the model, excluding the last three terms, for County Type C4 (lost HPSA status) when these counties have HPSA status:

Type C4 and HPSA:

(10)

 

Equation (11) shows the expression of the model, excluding the last three terms, for County Type C4 (lost HPSA status) when these counties have Non-HPSA status:

(11)

 

Once again, comparing equation (10) and (11), the model indicates that in counties that lost the HPSA status shows the difference between the estimated average number of claims per physician when they have the HPSA status and the average claims when they do not have the HPSA status. However, already captures the persistent difference in the average number of claims between the HPSA and non-HPSA counties. Therefore, the parameter shows the additional impact of HPSA status on the average number of claims per physician in the counties that lost HPSA status. If losing the HPSA status induces physicians to decrease the availability of primary care services, then we expect to be positive implying higher average claims when the counties had the HPSA status.

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