Density-dependent dynamics in regulated industries: founding rates of banks and life insurance companies

Administrative Science Quarterly,  March, 1991  by James Ranger-Moore,  Jane Banaszak-Holl,  Michael T. Hannan

• E-mail
• Print
• Link

Unlike the two kinds of banks, stock and mutual life insurance companies conducted the same kinds of business in the same consumer markets, differing only in form of ownership.

The similarity of business practice presumably meant tighter links between the two subpopulations than was the case for commercial and savings banks. The links may have been either positive or negative, depending on whether growth of one population tended to legitimate the other or to exhaust its resource base. The literature does not offer any clear indications on this issue.

In addition to testing the hypothesis of nonmonotonic density dependence, Hannan and Freeman (1987, 1989) modeled the interactions between subpopulations. We follow their approach herel. Let [C.sub.ij] denote the competitive pressure on the ith subpopulation in the (possible) presence of subpopulation j. Then we assume that

[Mathematical Expression Omitted]

If subpopulation j competes with i, then [[delta].sub.ij] < 0. But if the relationship is symbiotic, then this coupling parameters is positive. Finally, if the two subpopulations do not interact, then the coupling parameter is zero. Substituting this expanded specification of the competition process into the model gives as the founding rate for the ith subpopulation:

[Mathematical Expression Omitted]

We also explored the fit of models that allowed quadratic dependence of rates on the density of the other subpopulation. However, in no case did allowing such a more complicated cross-effect improve the fit of a model significantly. Therefore, we report estimates of models with only monotonic cross-effects, as in equation (7).

Methods of Analysis

Founding of banks and insurance companies can occur at any time during the year. Therefore, it makes sense to model foundings as realizations of continuous-time stochastic processes even when available data do not contain exact timing of events during years. As has been discussed by Hannan and Freeman (1989, chap. 8) and Hannan (1989a, 1991), foundings can usefully be be considered an instance of an arrival process. Let the cumulative number of foundings in a population by time t be denoted by the random variable Y(t). The stochastic process of interest, the founding process, is {Y(t)[bar] t [is less than or equal to 0}, with state space equal to {0, 1, 2, . . .}. The fundamental parameter of such a process is the founding rate, the rate of arriving at state y + 1 at (just after) time t. This rate can be defined as

[Mathematical Expression Omitted]

The well-known Poisson process serves as a natural baseline model for arrival processes. This is a continuous-time, discrete-state stochastic process that assumes that the rate of arrival does not depend on the history of previous arrivals, including the number of previous arrivals and time of the last arrival. If the rate at which organizations enter a population follows a Poisson process, the rate of arriving at state y + 1 at time t is a constant: [[lambda].sub.y](t) = [lambda]. The theory under test implies that founding rates are not a constant because they depend on density, which varies over time. Therefore we re-express the model to allow the rate to depend on a vector of time-varying convariates, [x.sub.t]; to simplify the notation at this point, we regard this vector as containing both density, the square of density, and the covariates and period effects. So we concentrate on a process whose reate has the general form