describes the actual radii calculated for the hospitals in our nine-state sample. For urban hospitals, 75 percent radii range from less than 1 to 78 miles, and the mean is 10.4 miles. Among rural hospitals, 75 percent radii have a larger mean (14.2 miles) compared to urban hospitals, and range from less than 1 to 259 miles. Ninety percent radii are larger than 75 percent radii. Among urban hospitals, 90 percent radii range from less than 1 to 179 miles and have a mean of 21.5 miles. Radii are again larger for rural hospitals, with a range from 1 to 283 miles and a mean of 25.2 miles.
75 Percent and 90 Percent Radii for Urban and Rural Hospitals: Descriptive Statistics
and provide regression results for urban and rural hospitals respectively. For urban hospitals, we explain 39.6 percent of the variance in the radii that captures 75 percent of patients, and 44.7 percent of the variance in the 90 percent radii. We are less successful in explaining the variance in rural hospitals' radii (adjusted R-squared = 8.3 for 75 percent radii and 9.6 for 90 percent radii). The circular approximation of hospitals' markets may be less well suited for rural hospitals. The results are largely robust to whether the 75 or 90 percent measure is used. For ease of exposition, our discussion focuses on the 75 percent measure.
Regression Results for Urban Hospitals
Regression Results for Rural Hospitals
For urban and rural hospitals alike, we find that higher population density is correlated with a smaller hospital radius. Hospitals in the most densely populated areas in the country (density in the top five percent of all metropolitan areas) have radii 6.5 miles shorter than hospitals in the least dense of urban areas. Likewise, hospitals in the most dense of rural areas have radii on average 9.2 miles shorter compared to those in the least dense areas.
The presence of other hospitals also is related to the market size of both urban and rural hospitals: Radii are 3.4 to 4.9 miles shorter among urban hospitals surrounded by more than three other hospitals within 15 miles and are 7 miles shorter among rural hospitals surrounded by more than six other hospitals within 30 miles. For urban hospitals, specific characteristics of nearby hospitals also matter: The existence of a COTH hospital within 100 miles of an urban hospital is associated with a radius on the order of 4 miles shorter compared to a hospital with no nearby COTH hospital. For the 90 percent radii, the magnitude of the association varies depending on whether the hospital itself was a COTH member or not: COTH competition is associated with radii 13 miles shorter if the reference hospital is a non-COTH hospital, compared to 9 miles if the hospital is itself a COTH hospital.
Other hospital characteristics were also associated with market size among urban hospitals. In particular, radii were larger among teaching hospitals (+1.9 miles for hospitals affiliated with a medical school and +3.3 miles for major teaching hospitals), and markets were larger among private compared to public hospitals (+2 miles for private nonprofit, +2.5 miles for private for-profit). Special services offered by urban hospitals are also related to market size: A burn unit is associated with radii 3.1 miles longer; likewise for transplant services (3.8 miles) and psychiatric services (1.2 miles). Hospitals offering one or more of specialized outpatient services (physical rehabilitation services, urgent care services, outpatient surgical services, or hospital-based outpatient center services) have radii more than 7 miles larger than hospitals that do not provide any such services. Urban hospitals that serve a relatively large proportion of Medicaid patients have smaller radii. Finally, case mix is a highly important correlate of hospital market area—hospitals with more severely ill patients (high case-mix values) have larger radii. Severely ill patients may have, or be willing, to travel farther to find highly specialized medical services, and thus the case-mix variable may be capturing the influence of unmeasured hospital service offerings. We caution, however, that the case-mix variable is only for the Medicare population; whether a measure of the case mix of hospitals' general population would show similar results is uncertain.
In comparison, and as foreshadowed by the difference in the R-squared statistics between the urban and rural regressions, few measured factors contribute to explaining the market size of rural hospitals. Beyond population density and local area hospital competition, only hospitals' service offerings have an additional explanatory role. Neonatal, psychiatric, and outpatient service offerings all are associated with a larger reach of a rural hospital.9
provides predictions for the 75 percent and 90 percent radii for short-term, nonfederal, general hospitals in the United States and descriptive statistics for the two measures of competition calculated (number of competing hospitals and HHI). Hospital market size as defined by the 75 percent radii averages 12.2 miles, with a range from 0.04 miles to 44.2 miles. The average number of competing hospitals is 3.2, with more than half of hospitals in the United States having either zero or one competitors. Mean and median HHI were similar, at .65 and .62 respectively.
Predicted Radii and Competition Measures for U.S. Short-Term General Hospitals
Markets defined by 90 percent radii are larger and thus more hospitals are considered competitors. Ninety percent radii average 22.8 miles and range between 0.21 and 105.1 miles and these markets have on average 8.2 competitors, with half of hospitals having between zero and three competitors. Likewise, the HHI for the market as defined by the 90 percent radii was smaller—indicating more competition—compared to the market defined by the 75 percent radii. The average HHI was .44 and half of hospitals had an HHI of .34 or lower.
The market sizes we predict are larger, exhibit more variability, and span a wider range compared to those that Phibbs and Robinson (1983) estimate. Despite the differences in estimated market size, our mean HHI estimates are nearly equivalent to Phibbs and Robinson's. However, we estimate a smaller average number of competitors (3.2 versus 3.9 for the 75 percent radii and 8.2 versus 9.7 for the 90 percent radii) and a smaller median HHI for markets defined by the 75 percent radii (.62 versus .84).