where subscript i indexes counties and subscript t indexes year. The dependent variable is one minus the ratio of the survey estimate of total Medicaid enrollment in a county to the administrative data estimate of total Medicaid enrollment in that county. The independent variables include a constant, Medicaid Managed Care Penetration (MMCP), and a linear time trend. MMCP is equal to the number of MMC enrollees divided by all Medicaid enrollees for a given county as reported in California administrative data. The final term, [epsilon], is a regression residual, implicitly assumed orthogonal to the included regressors. We return to whether that orthogonality assumption is plausible below. Chattopadhyay and Bindman estimate equation (1) using weighted least squares (WLS), where the weights equal the estimated population of each county from the CPS. Chattopadhyay and Bindman used data from 1995 to 1999.
To estimate equation (1), we used Medicaid enrollment information from the California Medicaid Monthly Enrollment Files (MMEF) (California Department of Health Care Services 2008) and the Medi-Cal (i.e., the Medicaid program in California) Annual Statistical Reports (California Department of Health Care Services 1997a, b, 1998). Appendix SA2 details how we used these data in the analysis.
For survey counts of county-level Medicaid enrollment and overall population, Chattopadhyay and Bindman use the CPS Annual Social and Economic Supplement. We note that CPS California samples are small (roughly between 4,000 and 6,000 households). While in net there is a large Medicaid Undercount, small samples in any given county induce a Medicaid Overcount in some county-year combinations. Because smaller counties are somewhat more likely to have a Medicaid Overcount, the approach of Chattopadhyay and Bindman to use WLS should help account for this. Appendix Table SA 1 compares the data we collected to the data reported by Chattopadhyay and Bindman. The Medicaid and MMC enrollment numbers we found are generally consistent with Chattopadhyay and Bindman. Some differences arise because we use a different source of data than Chattopadhyay and Bindman from 1995 to 1997. However, our estimates of the Medicaid Undercount from 1995 to 1999 and MMCP from 1998 to 1999 are similar to the estimates of Chattopadhyay and Bindman. Our estimates of MMCP from 1995 to 1997 are slightly lower.
The left panel of Figure 1 shows a scatterplot of Medicaid Undercount rates by county and MMC penetration rates. As predicted by Chattopadhyay and Bindman’s theory, the scatterplot in Figure 1 and the corresponding simple regression line show a positive correlation between the MMC penetration rate and the Medicaid Undercount.