size, indicating that these relationships are essentially linear in form. For local government health
organizations, the signs of the two coefficients are reversed. Further examination of this case
suggests that the positive estimate for the squared term dominates so that this relationship is also
nearly linear. In sum, then, the results are generally supportive of the ESA model expectations,
but with a third or so of the models showing little density dependence.
The real issue for our present purpose, however, concerns variations in these response
functions across the 14 sub-guilds. Comparisons of these differences across polynomial
coefficients are not easy. To make these differences more apparent, the curvilinear response
functions were first examined graphically, although these are not shown. The curvilinear
response functions vary markedly in their initial steepness and their degree of curvilinearity or
density dependence. Among the more notable variants, lobby registrations in the direct care
providers, treatment facilities, health advocacy, and health product sub-guilds respond in a nearly
linear fashion to change in the numbers of their constituent units in the states. In contrast, lobby
registrations representing nursing homes, pharmaceutical firms, and HMOs seem to respond in an
especially density dependent manner to change in the numbers of their constituents. Indeed, the
predicted number of nursing home registrations is expected to actually decline as states become
very large. Between these extremes, the remaining sub-guilds generated varying degrees of
response to change in constituent numbers, but all are moderately density dependent with number
of lobby registrations flattening among the larger states. In short, the several sub-guilds respond
quite differently to numbers of potential constituents in terms of generating lobby registrations.
How should this pattern of responses be interpreted? Perhaps the first explanation many
will think of concerns variations in free riding, with incentives to free ride being especially strong
in guilds evidencing more severe density dependence. That is, in guilds with many constituents,
free riding might depress lobby registrations (Olson 1965). We do not find this explanation
Simply put, there is no clear relationship between the average number of
13
It is also true, however, that at the aggregate level, results generated by free riding and density
dependence associated with resource scarcity can be largely indistinguishable. For a discussion of this
problem and ways in which to distinguish the two effects, see: Lowery, Gray, and Monogan (2006).
15
Convention