Based on Decker (2012):
The national average of observed proportion of office-based physicians accepting Medicaid patients in 2011 (P0) is 0.694.
The Observed value of the Medicaid-to-Medicare fee index (I0) 2008 is 0.742.
We have already derived that the logit coefficient of the Medicaid-to-Medicare fee ratio (B1) is 1.88. This implies that OE is approximately 0.576 (based on equation (13)).
Now consider a 10 percent increase in the Medicaid-to-Medicare fee index from the national average in 2008. This implies that the new value of the Medicaid-to-Medicare fee index (I1) is 0.8162.
This further implies that the predicted log-odds of the proportion of office-based physicians accepting new Medicaid patients is equal to about 0.958 (using equation (14)).
Thus, using the expression in equation (15) the predicted proportion of office-based physicians accepting new Medicaid patients (P1) is equal to 0.723 or 72.3 percent.
The same methodology is applied while calculating the predicted proportions for each state and the US in Exhibit 25.