Density Delay and Organizational Survival - Springer Link

P1: VBI Computational & Mathematical Organization Theory

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Computational & Mathematical Organization Theory 3:4 (1998): 219–247 c 1998 Kluwer Academic Publishers. Manufactured in The Netherlands °

Density Delay and Organizational Survival: Computational Models and Empirical Comparisons ALESSANDRO LOMI Faculty of Economics, University of Bologna, Piazza Scaravilli 1- 40137 Bologna, Italy email: [email protected] ERIK REIMER LARSEN European Union Marie Curie Fellow, Faculty of Economics, University of Bologna, Piazza Scaravilli 1- 40137 Bologna, Italy email: [email protected]

Abstract Research on the ecological dynamics of organizational populations has demonstrated that competitive conditions at the time of founding have enduring effects on organizational survival. According to ecological theories, organizational life chances are systematically affected by density (the number of organizations in a population) at the time of founding because the lower resource endowments that characterize organizations appearing in periods of high population density tend to become self-reinforcing, and—over time—amplify differences in mortality rates of organizations founded under different conditions. However, credible arguments have been offered that could justify both positive and negative effects of the delayed effects of population density on organizational mortality rates, and received empirical research in part reflects this ambiguity. To develop new insight into this issue and to explore the boundaries of received empirical results, in this study we present a computational model of organizational evolution according to which the global dynamics of organizational populations emerge from the iteration of simple rules of local interaction among individual organizations. We use the synthetic data produced by simulation to estimate event history models of organizational mortality, and compare the parameter estimates with those reported in the most recent empirical studies of actual organizational populations. The conclusions supported by the model qualify and extend received empirical results, and suggest that delayed effects of density are highly sensitive the details of local structure of connections among members of organizational populations. Keywords: computational models of organizations, organizational ecology, cellular automata, simulation

1.

Introduction

How do conditions at the time of founding affect the vital dynamics of organizations? This question raises relevant theoretical concerns because it brings into focus the role of historical processes in the evolution of organizational populations, and therefore, the relationship between organizations and social structure (Stinchcombe 1965). Issues related to the effects of founding conditions are also practically important because—if new organizations are assembled to satisfy current needs and demands—questions arise about how fast established organizations can change to adapt to new circumstances, and/or inhibit the birth and diffusion of new social formations (Hannan and Freeman 1989).


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One of the most pervasive—if implicit—assumptions in current theories of organizations and institutions is that observed organizational arrangements are the (unique) outcome of systematic processes, such as competition at the population level, learning at the individual level, or some combination of the two (Barnett et al. 1994; Carroll and Harrison 1994; Levinthal 1991). This equilibrium assumption rests on a hypothesis of “historical efficiency” of organizational evolution, i.e., on the belief that (March and Olsen 1989: 5): “Institutions and behavior [. . .] evolve through some form of efficient historical process. An efficient historical process [ . . . ] is one that moves rapidly to a unique solution, conditional on current environmental conditions, and is independent of the historical path [ . . and of . . .] the details of historical events leading to it.” Under conditions of “historical efficiency” organizations structures can be seen as reflecting of a more or less extensive list of current “contingencies”, both internal as well as external to individual organizations. However, if organizational survival chances are permanently affected by conditions imprinted at the time of founding, then it could be argued that some form of historical path-dependence is at work to shape the evolution of organizational populations over long periods of time (Carroll and Harrison 1994; Stinchcombe 1965). If supported, this conclusion would significantly complicate our understanding of organizations and institutions as transaction cost minimizing collective entities (Williamson 1991, 1994). Against this general background, in this paper we examine the effects of density at time of founding (or “density delay”) on organizational survival. Density delay represents a specific way in which historical conditions may affect the vital dynamics of individual organizations because research in the population ecology of organizations has shown that competitive conditions at the time of founding have persistent effects on organizational mortality. Specifically, empirical evidence exists that shows that organizations founded in periods of high density experience a higher cohort-specific probability of failure (Carroll and Hannan 1989). This findings have great theoretical value because if organizational mortality is systematically affected by density at founding, then we could claim to have identified a specific type of historical process affecting the ecological dynamics of organizational populations. To explore the implications for organizational survival of alternative hypotheses about the effects of density delay, in this paper we propose a specific computational model of organizational evolution. According to this model, the ecological dynamics of organizational populations emerge from the iteration of simple rules of local interaction which regulate the appearance, survival and demise of individual organizations. We simulate the model under a variety of evolutionary conditions to search for sets of structural features that can generate organizational life histories that are qualitatively consistent with those observed in empirical organizational populations. Using event history analysis, we compare the survival experience of organizations in our artificial populations with those implied by the estimates reported in empirical studies that have analyzed the role of density delay in the evolution of organizational populations. We organize the paper as follows. In the next section we offer a reinterpretation of density delay as a specific instance of path-dependence in the evolution of organizational populations, we review the specialized literature on the delayed effect of density on organizational


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mortality, and we argue that the effects of density delay documented by empirical studies can be seen as induced by patterns of local interaction among members of an organizational population. In the third section we establish the basic modeling framework, provide details of the simulation methods that we adopt, and discuss the inferential procedures that we use to analyze the data. In the fourth section we report the results of the study. We conclude the paper by discussing the value and limits of the results in the context of the main questions addressed. 2. 2.1.

Theoretical Background Density Delay and Organizational Mortality

How does density at founding affect organizational mortality? In the context of contemporary population ecology theories of organizations, this somewhat narrower version of our opening question, is important for at least two reasons. The first has to do with the fact that until very recently ecological theories were unable to offer a convincing explanation for the decline in the number of organizations in a population, and density delay could be seen as a possible source of decline in age-structured organizational populations (Hannan 1997; Hannan and Carroll 1989). The second reason is related to organizational inertia, one of the core assumptions in population ecology theories of organizations, because the existence of a systematic connection between organizational life chances and conditions at founding would provide indirect evidence that some form of environmental imprinting is at work to shape the evolutionary dynamics of organizational populations (Stinchcome 1965; Hannan and Freeman 1977). Although other dimensions of organizational environments at founding—such as, for example, political turmoil (Carroll and Huo 1986; Swaminathan 1996)—obviously affect organizational mortality rates, in this paper we concentrate on organizational density because we want to learn more about how the presence of other organizations affects the mortality of individual members of a population through processes of legitimation and competition—a highly controversial point in the current debate on ecological models of organizations (Baum and Powell 1995; Hannan and Carroll 1995). Population ecology theories of organizations have suggested three plausible—but partially conflicting—explanations for the relationships between density at founding and organizational mortality (Carroll and Hannan 1989). According to the first explanation, periods of high density are likely to be characterized by resource scarcity because new entrants find themselves competing against established organizations for a pool of resources that cannot be easily expanded in the short run. Resource scarcity may leave organizations founded in this period weak and underdeveloped, consuming the limited energies that characterize young organizations in securing the conditions for survival. This “liability of resource scarcity” resulting in a positive relationship between density at founding and organizational mortality rates may also emerge from the lack of incentive for individual members to invest in organization-specific skills, and from the obvious difficulty of establishing a framework of cooperation and trust under conditions of uncertainty about organizational survival. According to the “liability of resource scarcity” hypothesis, adverse founding conditions operate through density primarily on the founding rate of new firms.


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Carroll and Hannan (1989) were probably the first to document the detrimental effects of high density at founding on organizational survival. Their study of five organizational populations reported that the level of cohort-specific density increases organizational mortality rates significantly. The predicted age-specific mortality rate of organizations founded at peak density was 147% higher than the rate of those founded at half the peak for Argentinean newspapers, 107% higher for San Francisco newspapers, 31% higher for Irish newspapers, 338% higher for American Labor Unions, and 99% higher for American breweries. More recently, Hannan and Carroll (1992) reported similar results for the population of American Life insurance companies and Manhattan banks, Barron et al. (1994) found a significantly positive relation between density at founding and the mortality rate of New York City Credit Unions during the period 1914–1990. Additional indirect evidence for the link between the liability of resource scarcity and density at founding comes from a study by Suarez and Utterback (1995) according to which firms entering an industry after the high density period in which a dominant design has emerged suffered a relatively higher failure rate. Carroll and Hannan (1989: 415) suggested a second explanation according to which the delayed effects of density at founding on organizational mortality manifest themselves because “when density is high resources are subject to intense exploitation and few resources go underexploited”. From the point of view of individual organizations arriving in a population at times of high density, competitive intensity during early stages of resource accumulation imply both a lower absolute level of resources available, as well as a lower relative quality of resources available for growth (Winter 1990). According to this “tight niche packing” hypothesis, adverse founding conditions permanently affect the failure rate of organizations founded in such periods, because organizations appeared during periods of intense resource exploitation may be forced to operate at the margin of resource spaces already occupied by established competitors. According to this strong version of Stinchcombe’s (1965) imprinting argument, organizational life chances are permanently affected by high density at the time of their founding because tight niche packing has a strong influence on strategic orientation, and hence it shapes core dimensions of the organizational form that may prove exceptionally hard and risky to alter at later stages (Amburgey et al. 1993; Boeker 1989; Hannan et al. 1996; Hannan and Freeman 1977, 1989; Romanelli 1993). Both the “liability of resource scarcity”, as well as the “tight niche packing” hypotheses imply a positive relation between density at founding and organizational mortality, but only a limited number of empirical studies are available that separate out the transitory effects of resource scarcity, from the longer-term effects of “tight niche packing”. While studies are available that demonstrate how the level of initial resource endowments has significant implications for organizational survival (Brüderl et al. 1992; Levinthal and Fichman 1988), and simulation experiments have been performed to show how the delayed effects of density induce sharp decline in population density (Hannan and Carroll 1992), only Swaminathan (1996) has addressed the problem explicitly in the context of his study on organizational mortality rates in the population of US breweries, and Argentinean newspapers. He reported no evidence for the hypothesis of permanent effects of density at founding on asymptotic death rates, and some evidence for the hypothesis of transitory effects of density at founding on organizational mortality rates.


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Finally, Carroll and Hannan (1989) suggested an alternative—but equally plausible—exante explanation for the existence of an empirical relationship between density at founding and organizational mortality rates. This third explanation rests on what Carroll and Hannan called a “trial by fire” hypothesis according to which adverse founding conditions weed out the more frail organizations during the early stages of population history, thus leaving only the strongest organizations. According to this Spartan image of the organizational world, organizations founded in difficult periods that survive early selection pressures may actually come to be longer-lived. As Swaminathan recently put it (1996: 1355): “[O]rganizations founded in a high-adversity period [...] may have a higher initial mortality rate than organizations founded in a low-adversity period, but survivors of this early trial may ultimately experience a lower death rate.” Thus, the “trial by fire” hypothesis leads to qualitatively different predictions than the “liability of resource scarcity”, and the “tight niche packing” hypotheses. Swaminathan (1996) has documented the effects the “trial by fire” process on the ecological dynamics of US brewers between 1633 and 1989, and Argentinean newspapers between 1800 and 1900. He found that adverse founding conditions determine higher organizational mortality rates in both populations. However, after the initial selection period, surviving organizations tend to be stronger competitors, i.e., to experience a lower force of mortality at later ages. This finding suggests that in population whose members are heterogeneous with respect to the distribution of unobservable characteristics associated to “frailty”, early selection due to adverse environmental conditions may produce—on average—stronger organizations. To sum up our discussion on density delay, it is probably fair to say that it is unclear whether high density at founding (i) temporarily increases the chances of organizational failure rates because resource scarcity will make the early organizing attempts more difficult, (ii) permanently increases the risk of organizational failure because tight niche packing will lock newly founded organizations into marginal areas of their environment, or (iii) decreases the risk of organizational failure for organizations surviving early selection pressures. It is important to discriminate among these alternative hypotheses, because they have very different implications for age-dependence in processes of organizational mortality. In the first case (“liability of resource scarcity”), mortality operates in an organizational population mostly through newly founded organizations, but the adverse effect of high density at founding declines with organizational age. In the second case (“tight niche packing”), high density at founding will induce a permanently higher risk of failure for organizations throughout their lifetime, i.e., the risk of failure due to tight niche packing will not decline with organizational age. In either case, as density rises the fraction of organizations founded at high density tends to increase, and the average force of mortality for the population increases. In the third case (“trial by fire”), the effect of high density at founding on organizational failure fluctuates with organizational age depending—for example—on the duration of the early selection period. Specifically, there could be a positive relation between organizational age and density at founding induced by a particular (unobservable) distribution of frailty in the population. Both the ambiguity of theoretical predictions, as well as the ambivalence of empirical evidence in this particular area of ecological theories of organizations signal that the different


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possible hypotheses about the role of density delay in organizational mortality are better seen as post hoc explanations for the effects of more fundamental processes underlying the evolution of organizational populations. In the following section we argue that one class of these processes may be related to the micro-structure of organizational populations defined in terms of local connectivity among individual organizations. 2.2.

Population Dynamics and Local Interaction

Recent refinements of the theory of density-dependent organizational evolution have shown that processes of competition and legitimation which control long-term changes in organizational populations are localized, and that processes of organizational founding and disbanding vary systematically across levels of analysis (Carroll and Wade 1991; Freeman and Lomi 1994; Hannan and Carroll 1992; Hannan et al. 1995; Singh 1993). In the study of the ecological dynamics of organizational populations, levels of aggregation—and therefore units of analysis—can be defined on a spatial (Barnett and Carroll 1987; Baum and Mezias 1992; Carroll and Wade 1991; Lomi 1995a; Swaminathan and Wiedenmayer 1991), or temporal basis (Hannan 1997), in terms of abstract sets of connections among individual organizations (Lomi and Larsen 1996), or using any other dimension of organizational domains that can be considered useful for the purpose at hand, like—for example—overlap in product-market combinations (Baum and Haveman 1997; Swaminathan and Delacroix 1991), membership in strategic groups (Carroll and Swaminathan 1992), similarity in patterns of resource consumption (Carroll 1985; Freeman and Lomi 1994), niche overlap (Baum and Singh 1994; Hannan and Freeman 1977; McPherson 1983), or underlying dimensions of the organizational form (Freeman 1990; Hannan and Freeman 1989; Lomi 1995b). These are all examples of ways in which the interaction among the members of an organizational population across multiple networks can be said to be ‘localized’. Despite their problematic commensurability, studies that have explored the various implications of the local character of competition within organizational populations are useful because they suggest that local structures of interaction—and therefore imperfect connectivity—have enduring implications for organizational vital rates. For example, in a study of organizational evolution in the European auto industry Hannan et al. (1995) have produced strong evidence for the hypothesis that competitive environments are more localized than institutional environments—particularly in the early stages of the proliferation of an organizational form (in particular see Hannan et al. 1995: 513), and Baum and Haveman (1997) have shown that localized competition among individual organizations eventually leads to differentiation in the Manhattan hotel industry. These recent results raise a number of complex issues related to how organizational populations evolve in sub-systems of larger systems (Hannan 1997), and to the permeability of the boundaries around organizational populations (Barnett and Carroll 1987; DiMaggio 1994). In terms of the main theoretical issue that we address in this paper, this literature suggests that—for each individual organization—the delayed effects of population density at the time of founding may be significantly influenced by the details of populations microstructure. Specifically, it is conceivable that the life chances of an individual organization will only


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be affected by a limited number of neighboring organizations because it is unlikely that the structure of interaction among the members of a population will resemble a complete regular graph in which every single organization depends on every other. Members of organizational populations may be connected to one another in many complex ways (Kephart 1994), and the microstructure of this emergent population-level network may have substantial implications for organizational life chances. From this perspective, the delayed effects of density on organizational survival could be reconceptualized as emergent consequences of patterns of local interaction among individual members of an organizational population. To clarify how localized interaction affects the link between processes of (organizational) mortality and the delayed effects of ( population) density at founding, in the next section we present a computational model of organizational evolution according to which the vital dynamics of an individual organization have a direct impact on that organizations immediate neighborhood (i.e., on organizations that are “close” to the focal organizations in some sense), and a diffuse effect on organizations operating in more distant sites. In this model, neighborhoods have partial overlap and share only some of their members. Thus the effect of density at founding on the vital dynamics of an individual member of the population can propagate to more distant sites by influencing (increasing or decreasing) competitive pressures in locally connected neighbors through a chain of indirect linkages (Cowan and Miller 1990). Finally, we simulate the qualitative behavior of the discrete dynamical system implied by the model, and analyze the synthetic data produced by simulation to demonstrate the sensitivity of the relationship between density at founding and organizational mortality to small changes in the local structure of interaction among individual organizations. 3.

Models and Methods

In this section we describe the main structural features of the computational model of population dynamics that we use to generate the data that we then analyze in the fourth section. The specific model that we use is a variation of the Game of “Life” (Berlekamp et al. 1982), a cellular automata (CA) model that has been shown to capture a number of salient features of the population ecology of organizational founding (Lomi and Larsen 1996). Since one of the distinctive features of ecological theories of organizations is their symmetry with respect to processes of mortality and founding (Hannan et al. 1991), by exploring the link between density delay and organizational mortality in the context of this specific model we hope to learn more about the extent to which the same model can meaningfully represent important—if partial—aspects both processes. 3.1.

Simulating the Ecological Dynamics of Organizational Populations

Once we abandon the assumption that every organization in a population is equally likely to interact (compete, exchange, or—in general—exchange ties) with any other, we are forced to acknowledge that members of an organizational population may be connected


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to one another in many possible ways. A typical source of complexity in this network of relationships is related to the fact that individual units respond only to the behavior of a limited number of alters with whom they have direct contact without being necessarily aware of the diffuse consequences of their actions (Schelling 1972, 1978: Ch. 4; Hannan and Carroll 1992). We start by assuming that the connectivity among the members of an organizational population can be represented as a two-dimensional regular lattice of size n × n, where every cell in the lattice represents a site potentially or actually occupied by an organizational entity. At any given time each cell can be in only one of two states that for simplicity are coded as 0 for “dead”, and 1 for “alive”. An organizational birth occurs whenever a cell changes its state from 0 to 1. An organizational death occurs when a cell changes its state from 1 to 0. The state assumed by each unit is synchronously and homogeneously updated in discrete steps following a fixed rule defined in terms of the states assumed by cells in neighboring sites (Packard and Wolfram 1985). In this discrete dynamical system there are several ways of defining the neighborhood structure. In this paper we adopt a simple Moore neighborhood, according to which each cell or site has eight neighbors (Packard and Wolfram 1985). To avoid the problem of creating a rule for every possible combination of states, we use a totalistic model, i.e., we assume that the state of each site in the lattice depends only on the sum of the values in neighboring sites (including its own value) in the previous period.1 The size of each local neighborhood is determined by a parameter k. For k = 1 the neighborhood includes the eight cells that touch a given cell. For k = 2 the number of cells in each neighborhood is 24, i.e., the eight cells that touch a given cell plus any cell that touch any of these eight. Similarly, k = 3 increases the number of cells in each neighborhood to 48. In this way k defines the local environment of any given agent and determines how localized is interaction in the system. More formally: Ã ai,t j

=φ

j+k i=i+k X j= X

! ai,t−1 j

,

(1)

i=i−k j= j−k

where a t is the state of the site i, j at time t. The global evolution of the population is determined by the number of organizations alive around any given cell, i.e., by the iteration of a rule strictly defined in terms of local interaction. If the number of organizations alive in a given neighborhood is below a threshold El , the central organization will die because of “solitude”—a mechanism designed to capture the main intuition behind the ecological notion of density-dependent legitimation. On the other hand, if the number of organizations alive in a neighborhood is greater than E u , the central organization will die because of “over-crowding”—a mechanism designed to represent the qualitative implications of density-dependent competition. As the survival band (E u − El ) defined over a neighborhood becomes smaller, individual entities become more sensitive to changes in their local environment. Birth (or “arrival”) processes in the population are modeled in a similar fashion. A “birth” occurs only if the number of organizations in the k-neighborhood of an “empty” cell is above a threshold value that is above λl , but below λu . In this way is the evolution of the population determined by the width of a “survival-band” (E u − El ), the “founding-band”


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(λl − λu ) defined over the each k-neighborhood. To formalize this argument αi,t j =

j+k i=i+k X j= X

ai,t−1 j ,

and

(2)

i=i−k j= j−k

ai,t j

 t−1 t   1 if El < αi, j < E u | ai, j = 1, = 1 if αi,t j = λ | ai,t−1 j = 0,   0 ohterwise,

(3)

where (2) defines the number of cells alive in a k-neighborhood around cell ai, j at time t, and (3) describes the updating mechanism that determines the evolution of each individual site in the automata. Without loss of generality, throughout the paper we assume that λ = λl = λu . This assumption makes the model a variation of Conway’s well known “Game of Life” (Berlekamp et al. 1982). The diagram contained in figure 1 summarizes the internal operation of the model as defined in Eqs. (2) and (3). Figure 2 illustrates the first four time steps in the evolution of the nearest neighbor (k = 1) model simulated under the evolutionary regime: λ = 2, El = 3 and E u = 7. The five cells active at time t = 0 represent the initial conditions of the system. Each time step the state of every cell in the lattice is synchronously updated according to the rules that define

Figure 1.

Summary description of model operation.

Figure 2.

Ecological dynamics of local structure in a nearest-neighbor model.


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the evolutionary regime. For example, in figure 2 the first cell from the left that is alive in period 1, dies out by period 2 because in period 1 density in its 8-neighbor square fell below El = 3. The same cell (organization) became active (was founded) in period 1, because there were exactly two other cells alive in its 8-neighbor square at time t = 0. Before we can actually simulate this model, we need to establish (i) its boundary conditions, and (ii) the initial conditions needed to set the system in motion. There are several ways of determining the boundary conditions of a CA, ranging from folding the automata on itself and arranging the cells on a torus, to assigning fixed or random values to the cells nearest to the boundary (Wolfram 1983). For simplicity, we decided to assign a fixed value to the m nearest cells to the boundary. If the CA has a size of n x × n the number of active cell is reduced down to (n − 2m)2 . In the model analyzed below we have used n = 100 and m = 5, which makes the maximum number of potential organizations in the population 8100. Alternative solutions also exist for determining the initial conditions, ranging from a random matching of states to sites, to starting from a “fixed” seed (Wolfram 1983). Since we are interested in the ecological dynamics of organizational populations during their complete evolutionary history, we chose to initialize the system by placing a small cluster of organizations in the center of the lattice. In the framework that we have established, any delayed effect of density on organizational mortality is genuinely “emergent” in the sense that individual entities are not programmed to be sensitive—in any obvious way—to the delayed effects of density at founding.

3.2.

Quantitative Analysis of Organizational Survival Rates

To explore possible links between the computational model that we propose and empirical studies of actual organizational populations, we estimate the delayed effects of density on the mortality rates of individual organizations using the synthetic data produced by our simulations. We designed the simulations to produce data that have the typical event history structure used in empirical studies to analyze the ecological dynamics of actual organizational populations (Tuma and Hannan 1982). Event history (or “failure time”) data have the following form: h = (o, d, s, t, X), were s is the starting time of each episode (or spell), t is its ending time, o is the origin state (or sets of origin states in case of multiple transitions), d the destination state (or set of destination states in case of multiple transitions) and X is a set of covariates that may change during the episode with which they are associated, or remain constant. In our case (t − s) is the lifetime of each individual cell, and for every cell o = 0, d = 1, and X contains information on density at time τ = s, plus a constant term (intercept). A sample of organizational event histories can be summarized by its associated survivor function which expresses the probability that an event of interest (in our case “death”) will not occur before t: G(t) = Pr{T > t}, where T is a random variable that denotes the waiting time in the current state (in our case “alive”). The rate at which transitions from the origin state “alive” to the destination state “dead” occur is called the hazard rate, and is defined as r (t) = lim

1t→0

G(t) − G(t + 1t) d log G(t) =− . G(t)1t dt

(4)


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To make the estimates comparable to those reported in the most recent empirical literature we adopt an accelerated lifetime framework with a Gompertz-Makeham specification of age-dependence (Freeman et al. 1983; Hannan 1988; Swaminathan 1996). The transition rate of the Gompertz-Makeham model is given by the expression:2 r (t) = a + b exp(ct),

a, b ≥ 0.

(5)

The corresponding density and survivor functions are ¾ ½ b f (t) = exp −at − [exp(ct) − 1] [a + b exp(ct), c ¾ ½ b G(t) = exp −at − [exp(ct) − 1] . c

and

(6) (7)

Because it is defined in terms of three different parameters (henceforth referred to as the A-term, B-term and C-term of the model), the Gompertz-Makeham model offers a variety of opportunities to explore the effects of covariates on the transition rate, hence it allows to explore different aspects of the organizational mortality process. In the model we estimate below the parameters in Eq. (5) are defined in terms of functions that link covariates to the transition rate. Specifically: a = exp{α0 + α1 N f }; b = exp{β0 + β1 N f }, c = (γ0 + γ1 N f )

and

(8)

so that—by substitution into (5)—the rate becomes: r (t) = exp{α0 + α1 N f } + exp{β0 + β1 N f } exp(γ0 + γ1 N f ),

(9)

where α0 , β0 and γ0 are constant terms, N f is the density at founding for the ith organization, and the associated coefficients α1 , β1 and γ1 are the model parameters to be estimated. As we mentioned, the parameters in the Gompertz-Makeham model have different substantive interpretations because they capture different aspects of the delayed effects of density on organizational mortality. Specifically, α1 is associated with the effect of density at founding on the asymptotic mortality rate. Therefore, a significantly positive estimate of α1 would be consistent with the “tight niche packing” hypothesis (particularly if β1 = 0). The parameter β1 is associated with the effects of density at founding on the initial mortality rate. Therefore, a significantly positive estimate of β1 would be consistent with the “liability of resource scarcity hypothesis” (particularly if α1 = 0). Obviously, the “tight niche packing” and the “liability of resource scarcity” hypotheses are not mutually exclusive, i.e., it is conceivable that α1 6= 0, and β1 6= 0 in the same model. Finally—if the C-term in Eq. (8) remains negative over the range of values for N f — then γ1 captures the effects of density at founding on the speed at which an individual organization reaches its asymptotic mortality rate. Significantly positive estimates of γ1


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imply that organizations born under conditions of high density experience a prolonged liability of newness (Freeman et al. 1983). Significantly negative estimates of γ1 suggest that organizations founded under conditions of high density will tend to fail at higher rates during the initial stages of their life. Hence, the “trial by fire” hypothesis is supported when γ1 < 0, and β1 > 0. In this case, beyond a given value of organizational age the mortality rate of organizations founded in high density periods will be lower than that of firms founded under less adverse conditions.3 3.3.

Estimation

The models discussed above are estimated using the method of maximum likelihood after splitting the episodes in unit spells and coding as (right) censored those cases for which the state at the start of the spell is equal to the state at the end of the spell.4 Using the conditional survivor function: ¾ ½ b (10) G(t | s) = exp −a(s − t) − [exp(cs) − exp(ct)] c it is possible to derive the log-likelihood l=

X i∈E

log{a + b exp(cti )} +

X i∈N

b a(si − ti ) + [exp(csi ) − exp(cti )] c

(11)

where E is the set of all uncensored episodes, and N is the set of all censored episodes. In words, uncensored episodes contribute to the likelihood the density function evaluated at their (observed) ending time. Right-censored episodes contribute to the likelihood the survivor function evaluated at their (known) censoring time. The results that we report below were produced by using the iterative maximum likelihood routines implemented in TDA (Röhwer 1994). 4.

Analysis

We present the analysis in three steps. First, we illustrate the qualitative behavior of the model, and describe the survival experience of organizations in different simulated populations. Second, we report the estimates of the coefficients in Eq. (9) obtained by fitting the Gompertz-Makeham specification of a pure density delay model to the synthetic data produced by all meaningful combinations of the parameters that define the lower (El ) and upper (E u ) limits of the survival band as defined in Eq. (3). Specifically, we concentrate on the results produced by simulating the nearest neighbor model (i.e., k = 1) when the number of organizations (λ) that must be alive in any 1-neighborhood at time t − 1 for a new birth to occur at time t, is 1 and 2, respectively. Finally, we assess the conformity of the estimates to alternative predictions of the delayed effects of density on organizational mortality in the light of received empirical results.


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Figure 3.

4.1.

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Organizational proliferation and the aggregate dynamics of local interaction in a simulated population.

Results

The six space-time frames reported in figure 3 illustrate the population growth path according to a nearest neighbor model (k = 1) defined in terms of evolutionary conditions: λ = 2, El = 3, and E u = 7 regulating the vital dynamics of individual organizations in overlapping 8-neighbor squares. For this specific rule, the sequence of frames shows the two-dimensional configurations emerging after the indicated numbers of time periods. We recorded the mortality experience of all the members of the population in terms of state transitions of the cells on the lattice. Table 1 reports the average duration, average density, the sample size, and the number of censored observations for all the possible combinations of El , and E u over which the nearest neighbor model with founding threshold λ = 1 is defined. As the width of the survival band (E u − El ) increases the average duration increases. For example, for El = 2, the average duration when E u = 9 is 20 times longer than the average duration when E u = 4. This feature of the model reflects the fact that—as the upper limit of the survival band increases—the requirements for survival become less stringent because overcrowding becomes less likely.


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Table 1.

Nearest-neighbor models with λ = 1: Descriptive statistics. Average duration (SD)

Average density (SD)

(2, 4)

1.3488 (0.6905)

(2, 5)

(El , E u )

Cases

Censored

1922.9 (465.2)

111343

2168

3.7367 (8.1132)

2455.6 (735.4)

52826

3015

(2, 6)

16.4835 (28.0266)

2575.7 (1159.7)

15011

3584

(2, 7)

25.3747 (35.9550)

2612.4 (1253.6)

10385

3823

(2, 8)

25.9699 (33.1541)

2608.0 (1262.0)

10176

3833

(2, 9)

26.0213 (33.1742)

2613.5 (1264.0)

10176

3840

(3, 5)

1.2391 (0.5086)

1874.9 (462.3)

116971

2060

(3, 6)

2.4058 (0.9621)

2208.9 (685.4)

73935

2799

(3, 7)

4.9078 (13.6703)

2472.6 (962.5)

43710

3344

(3, 8)

5.8827 (15.9066)

2555.5 (1033.7)

38340

3480

(3, 9)

6.1013 (16.2845)

2579.4 (1052.9)

37444

3516

(4, 6)

0.9867 (0.1187)

1481.8 (389.9)

113520

1623

(4, 7)

1.2122 (0.5095)

1834.0 (446.7)

117720

2075

(4, 8)

1.2611 (0.6372)

1872.9 (453.1)

115318

2151

(4, 9)

1.3035 (0.7496)

1911.5 (465.6)

114173

2043

(5, 7)

1.0365 (0.2522)

1619.5 (419.9)

118855

1853

(5, 8)

1.0580 (0.2923)

1662.0 (422.0)

120286

1807

(5, 9)

1.0622 (0.3086)

1659.4 (419.5)

120012

1804

(6, 8)

1.0012 (0.1740)

1542.9 (401.0)

117229

1790

(6, 9)

1.0051 (0.1870)

1552.2 (401.4)

117578

1840


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233

As the lower limit of the survival band increases, the average duration decreases because the organizational turnover increases independent of the width of the survival band. For example, the average duration of an organization in a population in which El = 2 and E u = 7 is 25.37 periods, while the average duration of an organization in a population in which El = 4 and E u = 9 is 1.30 periods, i.e., approximately 19 times shorter. Thus, organizational survival chances are strongly affected by the lower limit of the survival band, independent of its width. This is consistent with the notion of density-dependent legitimation (Hannan and Carroll 1992) because—as El increases—the survival of each individual organization becomes increasingly dependent on the survival of other neighboring organizations. For sufficiently high values of El , the disappearance of a single organization can generate a wave of failures that will diffuse throughout the population. Table 2 suggests that similar results are obtained when λ = 2, i.e., when the founding threshold is doubled. As before, when the lower limit of the survival band reaches 4 the demographic turnover increases dramatically and it is difficult to find organizations surviving more than two periods. However, when El = 2 the average lifetime is more than two times longer than that observed in the λ = 1 case (50 vs. 26) while the average density does not change significantly. As it could perhaps be expected, when El > 2 the λ = 2 model produces results that are closer to those of the λ = 1 model. After computing the survival time for each cell, we estimated accelerated lifetime models of organizational mortality with the Gompertz-Makeham specification of the transition rate (Blossfeld and Röhwer 1995; Freeman et al. 1983; Tuma and Hannan 1982). Table 3 reports the estimates of the delayed effects of density on organizational mortality across different combinations of El and E u in the nearest neighbor models with λ = 1. According to these estimates, density at founding does not affect the long-term (“permanent”) mortality rate because α1 is never statistically different from 0. We found no case in which density at founding induces a permanent liability. This is perhaps not too surprising given that none of the elements through which “tight niche packing” operates (such as—for example—differentiation, concentration , and resource partitioning) are represented in our models.The hypothesis that density at founding affects only the initial mortality rate (β1 6= 0) is supported 80% of the times, although in 3 cases density at founding seems to increase organizational life chances against theoretical predictions (because β1 < 0). In 50% of the cases, organizations born under conditions of high density experience a prolonged liability of newness (because γ0 > 0), while—according to our estimates—organizations founded under conditions of high density will tend to fail at higher rates during the initial stages of their life only in 4 cases (because γ1 < 0). According to Stinchcombe’s (1965) liability of newness hypothesis, organizational age has a negative effects on mortality. This prediction is only verified 50% of the times (because γ0 < 0). However, as the lower limit of the survival band increases above 3, organizational mortality processes are consistently characterized by positive agedependence (because γ0 > 0). Thus, the tendency of young organizations to fail early in their life—and the associated tendency of the risk of failure to decline with organizational age—appear to be very sensitive to the width of the local survival band around individual organizations. The estimates support the “trial by fire” hypothesis in 6 cases. For example, the model defined in terms of the rules of local interaction (El = 5, E u = 9, k = 1, l = 1) generates data that are consistent with the trial by fire hypothesis because higher density at


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11:39

LOMI AND LARSEN Table 2.

Nearest-neighbor models with λ = 2: Descriptive statistics. Average duration (SD)

Average density (SD)

(2, 4)

1.3532 (0.7389)

(2, 5)

(El , E u )

Cases

Censored

1676.5 (571.3)

80542

2308

2.2985 (2.1065)

2119.8 (764.8)

60093

2947

(2, 6)

18.8932 (24.4490)

2272.2 (1194.9)

10483

3964

(2, 7)

30.0589 (27.8570)

2520.9 (1402.5)

7786

4616

(2, 8)

47.7731 (21.9551)

2627.5 (1556.5)

5634

5361

(2, 9)

50.4065 (20.1747)

2768.8 (1623.1)

5622

5615

(3, 5)

1.2559 (0.6092)

1600.0 (563.7)

75630

2216

(3, 6)

1.6754 (1.3132)

1775.8 (674.7)

63253

2622

(3, 7)

5.1145 (10.6356)

2309.4 (1206.2)

31167

4047

(3, 8)

8.7831 (17.0003)

2457.4 (1323.8)

20767

4603

(3, 9)

8.3610 (16.5658)

2509.8 (1355.8)

22164

4715

(4, 6)

1.0535 (0.3334)

1246.6 (518.1)

63452

1912

(4, 7)

1.0965 (0.4318)

1296.8 (499.0)

66960

1954

(4, 8)

1.1157 (0.5108)

1266.7 (530.6)

61566

1838

(4, 9)

1.1148 (0.5124)

1266.3 (530.4)

61590

1886

(5, 7)

1.0152 (0.1183)

32.3 (15.6)

565

78

(5, 8)

0.9968 (0.2268)

1081.0 (442.1)

60381

1629

(5, 9)

0.9968 (0.2213)

1081.0 (442.1)

60381

1629

founding increases the initial mortality rate (β1 > 0), but organizations surviving the trial will eventually experience a lower mortality rate (γ1 < 0). Finally, we compare our estimates to those obtained by Swaminathan (1996) who used a similar approach to estimate the effects of density at founding on the mortality rates of American beer producers (between 1633 and 1989), and Argentinean newspaper organizations (between 1800 and 1900). We report these estimates in the bottom two rows of Table 3.


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DENSITY DELAY AND ORGANIZATIONAL SURVIVAL Table 3. λ = 1.

Maximum likelihood estimates of models of organizational mortality in nearest-neighbor models with α0

(El , E u ) (2, 4) (2, 5)

−13.5515 −6.2418∗

α1

β0

β1

γ0

γ1

−0.018562

−0.9911∗

0.000034∗

0.6136∗

−0.000022* −172936 −124976

0.000364

−0.9242∗

−0.000064∗

−0.0885∗

−0.000018∗ −125999 −104223

LL0

LL p

(2, 6)

−24.7418

−0.028252

−1.4734∗

0.000347∗ −0.4048∗

0.000008

−43012

−23488

(2, 7)

−25.3743

−0.038065

−1.5351∗

0.000341∗ −0.8399∗

0.000111∗

−29556

−13829

(2, 8)

−17.8396

−0.000324

−1.5569∗

0.000345∗ −0.8548∗

0.000114∗

−28263

−13442

0.000346∗

−0.8553∗

0.000114∗

−28855

−13431

0.000404∗

1.6653∗

−0.000429∗ −174104 −108280

−0.3473∗ −0.000010

−0.1653∗

0.000008∗ −135692 −113035

0.000075∗

−0.2606∗

(2, 9)

−16.9233

−0.000640

−1.5646∗

(3, 5)

−15.5489

−0.000024

−1.7815∗

(3, 6)

−17.2150

0.000437

(3, 7)

−15.5734

−0.000211

−0.5395∗

0.000004

−96792

−69350

(3, 8)

−15.8645

−0.000323

−0.5254∗

0.000084∗ −0.3473∗

0.000024∗

−88544

−58901

(3, 9)

−15.0174

−0.000311

−0.5255∗

0.000081∗ −0.3575∗

0.000026∗

−87356

−57711

(4, 6)

−17.6213

−0.003500

−1.3000

0.000110

(4, 7)

−13.5101

−0.000867

−1.0453∗ −0.0552∗

0.8962∗

0.000060∗ −172599 −105080

0.002927

−0.8261∗

−0.000011

0.5331∗

0.000035∗ −172453 −122402

−0.000011

0.3108∗

0.000036∗ −172820 −132609

(4, 8)

−21.1090

0.6625

−0.000011

−172759 −105090

(4, 9)

−24.4621

0.005009

−0.6637∗

(5, 7)

−15.4151

−0.000068

−2.0026∗

0.000068∗

2.6363∗

−0.000139∗ −159784

−41671

0.0557∗

2.0630∗

−0.000092∗

(5, 8)

−15.0285

−0.000063

−1.6454∗

−163098

−59788

(5, 9)

−33.4032

0.010093

−1.5575∗

0.000119∗

1.9188∗

−0.000158

−163029

−67899

(6, 8)

−14.9243

−0.000061

−2.3752∗

0.000008

3.2626∗

−0.000013

−153783

−7794

(6, 9)

−14.7906

−0.000158

−1.9793∗ −0.000095∗

0.000125∗ −154572

−17288

Mean

−17.7123

−0.003636

−1.2558

(Std)

(5.7472)

(0.011419)

(0.5771)

2.7223∗

−0.000011

0.000108

0.6652

(0.000158)

(1.2938)

(0.000125)

Max val −6.2418

0.010093

−0.3473

0.000404

3.2626

0.000126

Min val −33.4032

−0.038065

−2.3752

−0.000064

−0.8553

−0.000429

American breweries

0.0007

0.00085•

−0.00514• −0.000016•

Argentine newspapers

0.00164

0.01885•

−0.222•

* p < 0.001;

•

−0.00217

p < 0.05.

Three main points emerge from this comparison. First, the estimates obtained by fitting the model to actual organizational populations are always within the numerical boundaries of the estimates obtained by fitting the model to synthetic data. Second, the mean estimate of γ1 (−0.000011) is very close to the corresponding estimate of γ1 obtained on the population of American beer producers (−0.000016). Third, estimates of α1 that are reported as not significant in the empirical study, are never significant in our data. Estimates of γ0 that are always reported as significant in the empirical study, are always significant in our data except for one case (El = 4, E u = 6).


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236 Table 4. λ = 2.

LOMI AND LARSEN Maximum likelihood estimates of models of organizational mortality in nearest-neighbor models with α0

α1

β0

β1

γ0

γ1

0.007941

−0.9133∗

0.000018

0.5327∗

−0.000016∗

−124557

−0.7951 −0.049355

−0.9842∗

0.000012

0.0408∗

−0.000003

−117504 −107353

(El , E u ) (2, 4) (2, 5) (2, 6) (2, 7)

11:39

−30.5977 −140.1073∗

0.035112∗

LL0

LL p −92562

−1.7434∗

0.000142∗

−0.2131∗

−0.000018∗

−27932

−20129

−17.9930 −0.000266

−2.3427∗

0.000340∗

−0.2741∗

−0.000074∗

−16893

−10222

−0.000271∗

−0.3540∗

0.000008

−2231

−1639

−0.201935

0.1059

−0.093023

−83

−20

(5, 8)

−16.3233 −0.000076

−3.4675∗

(5, 9)

−16.3233 −0.074133

0.7282

(3, 5)

−13.9021 −0.000903

−0.8526∗ −0.000076∗

0.6096∗

0.000073∗

−112384

−76370

(3, 6)

−15.2694

0.001204

−0.6468∗ −0.000061∗

0.0655∗

0.000037∗

−107175

−92965

(3, 7)

−11.2959∗

0.002187∗

−0.6406∗

−0.1591∗

−0.000039∗

−70211

−57572

−0.3777∗

−0.000002

−50833

−34040

−0.5354∗

−0.000008

(3, 8)

−9.4280∗ −0.001219

(3, 9)

−15.9109 −0.000431

−0.4485∗ −0.000011

(4, 6)

−13.6692 −0.000265

−1.3204∗ −0.000100∗

(4, 7)

−14.3808 −0.000026

−0.8552∗

−0.000051∗

0.9031

0.000052

−91965

−53852

(4, 8)

−25.8236

0.007339

−0.6743∗

0.000036

0.6931∗

−0.000092

−85134

−57874

(4, 9)

−16.9924 −0.015384

−0.6371∗

0.000027

0.6479∗

−0.000079

−85100

−58325

(5, 7)

−152.6997 −0.006256

−2.3106∗ −0.007576

3.7663∗

−0.015979

−720

−75

0.000165∗

2.9038∗

−0.000214∗

−78623

−12447

0.000165∗

2.9038∗

−0.000214∗

−78623

−12447

(5, 8)

−16.3233 −0.012635

−2.1270∗

(5, 9)

−16.3233 −0.012635

−2.1270∗

Mean

−30.6252 −0.006658

−1.2166

(Std)

(41.4296) (0.022468)

Max val

−0.7951

0.0000002

−0.011621

−0.4004∗

0.0000005

−53673

−35449

1.5998∗

0.000112∗

−85291

−34500

0.7219

0.0060819

(0.9431)

(0.046190)

(1.2291)

(0.021399)

0.0351125

0.7282

0.0003407

3.7663

0.000112

Min val −152.6997 −0.0741335

−2.3427

−0.4004

−0.093023

−0.201936

American breweries

0.0007

0.00085•

−0.00514• −0.000016•

Argentine newspapers

0.00164

0.01885•

−0.2222•

−0.00217

* p < 0.001; • p < 0.05.

When we modify the local founding threshold, the analysis reveals similarly complex patterns of delayed effects of density on organizational failure rates. Table 4 contains the estimates of the Gompertz-Makeham model when the number of units that must be active in neighborhood for a new organization to arrive into the population (λ) is increased from 1 to 2. The hypothesis that density at founding affects only the initial mortality rate (β1 > 0) is now supported only 22% of the times, but we found that density at founding significantly increases organizational life chance in 28% of the cases. In only slightly less than 2% of the times, organizations born under conditions of high density experienced a prolonged liability of newness (because γ1 > 0), while our estimates show that organizations


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founded under conditions of high density will tend to fail at higher rates during the initial stages of their life only in 33% of the cases (because γ1 < 0). When λ = 2, the liability of newness hypothesis (γ0 < 0) is verified 33% of the times, but evidence of positive duration dependence was found the 56% of the times (γ0 > 0). We found no evidence of liability of newness whenever El ≥ 4. Parameter combinations that can be interpreted as supportive of the trial by fire hypothesis (i.e., α1 = 0, β1 > 0, and γ1 < 0) are produced only in three cases [(El , E u ) = (2, 7), (5, 8), (5, 9)]. As before, we compare our estimates to those obtained by Swaminathan (1996) which are reported in the bottom two rows of Table 4. This time we found that the estimate of β1 obtained for the population of American beer producers (0.00085) is approximately 2.5 times larger than the largest β1 that we could find (0.0003407). All the other empirical estimates are well within the range of the estimates obtained on synthetic data, despite the fact that the mean estimates and the empirical point estimates have opposite signs. The γ1 estimated for the population of American beer producers (−0.00016) is very close to the estimate of γ1 obtained when El = 2 and E u = 6 (−0.00018). The γ0 estimated for the population of Argentinean newspaper organizations (−0.222) is very close to the estimate of γ0 obtained when El = 2 and E u = 6 (−0.213). 4.2.

Qualitative Implications

Figure 4 plots the multiplier of the transition (“mortality”) rate due to density at founding for organizations founded at the highest (N f MAX ) and mean (N f MEAN ) density in the population

Figure 4. Qualitative implications of estimated effects of density at founding on transition rates in selected populations: Trial by fire.


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LOMI AND LARSEN

with local rule of interaction: [(El , E u ) = (2, 5); λ = 2]. The multiplier of the transition rate tells the relationship between density at founding (N f ) and organizational age (t) implied by the estimates. In terms of the notation introduced in Section 3, the multiplier of the transition rate is defined as: MR = exp[(βˆ1 N f ) + (γˆ0 t) + (γˆ1 N f t)]

(12)

The results represented in figure 4 are consistent with the trial by fire hypothesis because— during the first four years of their life—organizations founded in high density environments experience a higher mortality rate than organizations founded in mean-density environments. However organizations founded in high density environments that survive more than 4 years will enjoy a significantly lower mortality rate than organizations founded in mean-density environments. For example, at 35 years of age the mortality rate of organizations founded in mean-density environments is 3 times the mortality rate of organizations of the same age founded in high density environments.5 Apparently marginal changes in the rule of local interaction among individual organizations have substantial implications for the relationship between density at founding and organizational mortality rates. For example, figure 5 shows three cases in which the numerical estimates imply positive age dependence. In terms of the parameters in Eq. (9), the “tight niche packing” hypothesis is supported when α1 > 0 (and possibly also γ1 = β1 = 0). The “liability of resource scarcity” hypothesis, which implies only a transitory effect of density at founding on the mortality rate, requires

Figure 5. Qualitative implications of estimated effects of density at founding on transition rates in selected populations: Positive age dependence.


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DENSITY DELAY AND ORGANIZATIONAL SURVIVAL Table 5. Qualitative implications of the estimated effects of density delay on organizational mortality rates in nearest-neighbor models with λ = 1. (El , E u )

α1

β1

γ1

Results

(2, 4)

0

+

−

Trial by fire

(2, 5)

0

+

−

Trial by fire

(2, 6)

0

+

0

Liability of resource scarcity

(2, 7)

0

+

+

Positive age dependence

(2, 8)

0

+

+


(2, 9)

0

+

+


(3, 5)

0

+

−

Trial by fire

(3, 6)

0

0

0

No effects

(3, 7)

0

+

0

Liability of resource scarcity

(3, 8)

0

+

+


(3, 9)

0

+

+


(4, 6)

0

0

0

No effects

(4, 7)

0

−

+

Inconclusive

(4, 8)

0

0

+

No effects

(4, 9)

0

0

+

No effects

(5, 7)

0

+

−

Trial by fire

(5, 8)

0

+

−

Trial by fire

(5, 9)

0

+

−

Trial by fire

(6, 8)

0

0

0

No effects

(6, 9)

0

−

+

Inconclusive

that β1 > 0 (and possibly also γ1 = α1 = 0). Finally the “trial by fire” hypothesis implies that β1 > 0, and γ1 < 0. The pattern of results induced by small changes in the rules of local interaction is illustrated in Table 5 which reports the signs of the parameter estimates contained in Table 3, and gives an overall picture of the complex relationship between population density at founding, organizational mortality rates, and the structure of local connectivity among individual organizations. Although we found no evidence of permanent liability associated with high density at founding (the “tight niche packing” hypothesis) all the other hypotheses are supported in mixed proportions, with a slight prevalence of the “trial by fire” hypothesis (which is supported in 6 cases in the λ = 1 population, and in 3 cases in the λ = 2 population) over the liability of resource scarcity—which is supported only in 2 cases (when λ = 1) and not at all supported (when λ = 2). Finally, we note that when λ = 1 the model predicts positive age dependence in 25% of the cases. 5.

Discussion and Conclusions

We started the paper by interpreting density at founding as a concrete instance of how historical processes affect organizational life chances, and shape the evolution of organizational


240

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populations. Following current ecological theories of organizations, we argued that the lower resource endowments that typically characterize organizations founded in periods of high population density tend to become self-reinforcing, and—over time—amplify differences in evolutionary paths of organizations founded under different conditions. If this is the case, then population density at founding could be seen as a specific historical factor that affects the ecological dynamics of organizational populations, and that has and an enduring influence on organizational-level processes of resource accumulation. We reviewed the different explanations that have been offered of the relationship between density at founding and organizational mortality rates, and we suggested that the non-uniqueness of available theoretical justifications—together with the associated ambiguity of received empirical results—can be interpreted as a signal that more fundamental processes are at work to shape the ecological dynamics of organizational populations. Building on recent results according to which density-dependent processes of competition and legitimation operate at different scales (Hannan et al. 1995), and their effects on organizational mortality rates vary systematically across levels of aggregation (Lomi 1995a), we argued that the delayed effects of density are mediated and qualified by local structures of interaction among individual organizations in the early stages of proliferation of the organizational form. Our argument suggests that the various qualitative relationships between (population) density at founding and (organizational) mortality rates could be more usefully seen as post-hoc rationalizations of the effects of micro-connectivity among members of organizational populations, rather than genuine ex-ante predictions. Building on our prior experience with a computational model of local interaction that has been shown to capture salient features of the ecological dynamics of organizational founding (Lomi and Larsen 1996), we explored the extent to which the same model is able to generate helpful insights into processes of organizational mortality. According to this model the global dynamics of organizational populations emerge from the iteration of simple rules of local interaction among individual organizations represented as cells in a two-dimensional lattice. Since no structural element in the formal set up of the model links density at founding to transition probabilities of individual cells, we treated the data obtained by simulating the model under a variety of local rules as data generated by a series of virtual experiments, and analyzed them accordingly. In terms of the theoretical issues that we addressed, our study supports two general conclusions. First, although our models tend to confirm the existence of a systematic relationship between organizational mortality rates and population density at the time of founding, the specific form that this relationship takes is extremely sensitive to changes in rules of local interaction among individual organizations. Unsurprisingly, in the lack of any element of differentiation among individual organizations in the data generating model, we could not find any support for the “tight niche packing” hypothesis. However, the “trial by fire” hypothesis was more frequently supported than the “liability of resource scarcity” hypothesis. Organizations founded under adverse conditions (defined in terms of relatively higher population density) have higher initial mortality rates than organizations founded in lower-density environments. However, our models support the hypothesis that organizations surviving the early “trial” tend to experience lower mortality rates later in their life course. This conclusion is broadly consistent with the results reported by Swaminathan


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(1996) who found that density at founding affected the mortality rates of both American beer producers, as well as Argentine newspaper organizations according to the predictions of the “trial by fire” hypothesis. According to this study, American breweries founded in high-density periods have higher mortality rates than breweries founded in mean-density periods until approximately 55 years of age. However, organizations surviving beyond 55 suffered a lower probability of disbanding. Swaminathan estimated that the duration of the trial by fire period for Argentine newspapers is seven years. As we illustrated in figure 4, when El = 2, E u = 5, l = 2, and k = 1, our model predicts that organizations founded in high-density environments will suffer lower mortality rates than organizations founded in mean-density environments after four years. Second, although we found some support for the “trial by fire” hypothesis under a variety of rules of local interaction, the estimates that we reported frequently imply a kind of “liability of senescence”, i.e., a tendency of organizational failure rates to increase with organizational age. This result is in contrast with earlier research on age dependence (Aldrich and Marsden 1988; Singh and Lumsden 1990), but is qualitatively consistent with more recent empirical results. For example, Barron et al. (1995) found that the mortality rate of Credit Unions in New York increased with age at almost all ages, and that the mortality rate of 40-year-old organizations was 10 times that of newly founded organizations. Barnett (1990) reported a positive and significant effect of age on mortality rates of telephone companies in Pennsylvania, and Amburgey et al. (1994) found a positive effect of age on the mortality rate of US Credit Unions during the decade 1980–1990. What makes our current results interesting in the context of the ecological research on age dependence is that certain structures of local interaction induce positive age dependence in organizational mortality rates even in the absence (by design) of any individual heterogeneity in terms of size or growth rates. When excluded from empirical models, size or growth rates are typically identified as sources of misspecification that bias estimates of age-dependent mortality rates in favor of the liability of newness hypothesis. Our analysis illustrated how positive age dependence in organizational mortality rates can arise as a consequence of local structures of interaction among members of a population, independent of the existence of any inter-organizational size and growth rate differentials. We believe that this results can be a useful starting point for a more systematic exploration of the relationship between structures (and range) of local interaction, and age dependence in processes of organizational mortality. In discussing the limitations of our current modeling effort, we find it useful to distinguish between those limitations that are inherent to the modeling framework we adopted, and assumptions that are restrictive in the present context, but which do not necessarily imply a loss of generality. The first basic limitation of the modeling framework is its synchronous updating mechanism. The state of every site on the lattice is updated at the same discrete time steps. While this computational structure is generally considered a reasonable assumption in models of physical and chemical systems (Wolfram 1986), its realism for modeling the mechanics of social and ecological processes can be questioned (Hogeweg 1988). Despite this inherent limit, models inspired by the theory of cellular automata are beginning to be applied to traditional social science problems like, for example, macroeconomic cycles (Albin 1987), market structure, collusion and competition (Albin and Foley 1992; Keenan and O’Brien 1993) and the emergence of political elites (Brown and McBurnett 1993).


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The second limitation concerns the fact that the same set of evolutionary conditions is used to update the state of every cell in the lattice. In principle, it is possible to think of different rules competing for sites, or to design individual cells which draw a set of evolutionary rules from a distribution of possible configurations (or combinations of k, L l , L u , El , and E u ), but we are not aware of any work that has implemented such a model, possibly because—if the number of possible combinations is left unconstrained—the computational burden quickly becomes prohibitive. Only recently we made some progress in this direction by experimenting with a one-dimensional automata in which individual cells are probabilistically assigned to different rules at time t = 1 (Lomi and Larsen 1997). Some may consider as a further limitation of our model the fact that we made no attempt to associate specific sets of local rules of interaction to alternative hypotheses about the delayed effects of density on organizational mortality rates. Although this is a legitimate claim, in this paper we preferred to follow a different analytical strategy. We specified the model strictly in terms of local interaction, without building into the simulations any structural relationship between density at founding (a population-level quantity) and organizational failure (an organization-specific event). The disadvantage of this analytical strategy is that we do not know which structure of local interaction is responsible for which process. The advantage is that we can now claim that the connection between density at founding and mortality rates is an emergent feature of the evolution of organizational populations, and that this connection is—at least in part—independent from assumptions about behavior at lower levels of analysis. Empirical studies that have addressed issues of density delay have captured selected aspects of this emergent property of organizational populations. There are a number of assumptions embedded in the models presented that are restrictive in the present context, but need not imply loss of generality of the results reported. The first of these assumptions concerns the specific tessellation structure chosen, i.e., the structure of the lattice. Hexagonal and triangular arrays are less commonly used than square lattices, but they are equally plausible (Gutowitz and Victor 1987). A second set of apparently arbitrary assumptions embedded in the model, concerns the specific rules of local interaction that we have selected. In selecting the rules of local interaction that we used to simulate the model and generate the data, we chose to be constrained by prior research that has demonstrated that the iteration of these local rules produces an aggregate behavior that is consistent with what we know about the population ecology of organizational founding (Lomi and Larsen 1996). A third set of contextual limitations is related to the deterministic nature of the models. The models simulated here contain no random component, and this could attract allegations of lack of realism. Random perturbations are easy to incorporate in our models and there are several ways for doing so. For example, a stochastic time-varying component could be added to λ (the founding threshold), and/or to (E u − El ) (the survival band). Lomi and Larsen (1995) have implemented a similar solution in the context of a one-dimensional model of voting behavior by drawing a random quantity from a uniform distribution, adding it to the underlying rule for local interaction, and then using the new time-varying rule to update the state of each cell of the lattice at each time period. In the present context


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we limited our attention to deterministic models because we wanted to show that simple rules of local interaction are capable of producing a wide range of population-level implications even in the absence of any random disturbance. Obviously, our models do not imply that random variation plays no important role in the evolution of organizational populations. Finally, the parametric form imposed on the transition rate is only one of many possible forms that we could have used. While this obviously restricts the interpretation of the results to a specific class of transition rate models (within the exponential family), a careful assessment of distributional assumptions was not one of our objectives. We chose the Gompertz-Makeham specification because it allowed us to address core theoretical concerns in organizational ecology, and because we wanted to compare our results with those produced by the most recent empirical research on density delay that is based on the same model. Of course, nothing prevents alternative specifications the transition rates— provided the existence of some theoretical guidance. For example, according to Fichman and Levinthal (1991) transition rates vary non-monotonically with organizational age. To test this hypothesis, log-logistic, log-normal, or Sickle models might prove more adequate than those estimated in this paper. In spite of these limitations, we believe that—by exploring specific aspects of the role of historical processes in the ecological dynamics of organizations—the present work adds an important dimension to our understanding of the ecological dynamics of social and economic institutions, and points out specific ways in which computational models can be used to illuminate core issues in contemporary theories of organizations. Acknowledgments A prior version of this paper was presented at the 1997 Academy of Management Meetings (OMT Division), Boston, Ma. The authors would like to thank Kathleen Carley for her help and advice, and two anonymous reviewers for their constructive criticism. The programs used to produce the data analyzed in this paper were written in Turbo Pascal, Version 7.0. The code and an executable version of the program can be obtained simply by writing to the authors. Notes 1. Otherwise the number of possible rules would be 29 = 512 just in a simple two-state totalistic automata, i.e., in a model in which the value of a site depends only on the sum of the values in the neighborhood. 2. Note that when a = 0 the model reduces to the Gompertz without the Makeham term, and that when b or c = 0 the model reduces to the simple exponential model. 3. An additional constraint that the estimates have to satisfy in order for the trial by fire hypothesis to be supported is that |γ1 t| > |β1 | for at least some t < tmax , where t is organizational age. This condition is easy to verify for population in which the maximum observed age (tmax ) is greater than 1 period. 4. The spells correspond to simulation (or time) periods. So for example, one cell on the lattice that remains active between period t and period t + k will contribute k observations to the data set. 5. In this discussion, we assume—conventionally—that what we have called “simulation period” throughout the paper corresponds to 1 year of historical time.


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References Albin, P. (1987), “Microeconomics Foundations of Cyclical Irregularities or ‘Chaos’,” Mathematical Social Sciences, 13, 185–214. Albin, P. and D. Foley (1992), “Decentralized, Dispersed Exchange without an Auctioneer. A Simulation Study,” Journal of Economic Behavior and Organization, 18, 27–51. Aldrich, H. and P. Marsden (1988), “Environments and Organizations,” in N. Smelser (Ed.) Handbook of Sociology, Newbury Park, CA: Sage, pp. 361–392. Amburgey, T., D. Kelly and W. Barnett (1993), “Resetting the Clock: The Dynamics of Organizational Failure,” Administrative Science Quarterly, 38, 51–73. Amburgey, T., T. Dacin and D. Kelly (1994), “Disruptive Selection and Population Segmentation: Interpopulation Competition as a Segregation Process,” in J. Baum and J. Singh (Eds.) Evolutionary Dynamics of Organization, NY: Oxford University Press, pp. 240–255. Barnett, W. (1990), “The Organizational Ecology of a Technological System,” Administrative Science Quarterly, 35, 31–60. Barnett, W. and G. Carroll (1987), “Competition and Mutualism among Early Telephone Companies,” Administrative Science Quarterly, 32, 400–421. Barnett, W., H. Greve and D. Park (1994), “An Evolutionary Model of Organizational Performance,” Strategic Management Journal, 15, 11–28. Barnett, W.P. and G. Carroll (1995), “Modeling Internal Organizational Change,” Annual Review of Sociology, 21, 217–236. Annual Review Press. Barron, D., E. West and M. Hannan (1994), “A Time to Grow and a Time to Die: Growth and Mortality of Credit Unions in New York City,” American Journal of Sociology, 100, 381–421. Baum, J. (1996), “Organizational Ecology,” in S. Clegg, C. Hardy and W. Nord (Eds.) Handbook of Organization Studies, London: Sage, Chapter 13. Baum, J. and C. Oliver (1991), “Institutional Linkages and Organizational Mortality,” Administrative Science Quarterly, 36, 187–218. Baum, J. and S. Mezias (1992), “Localized Competition and the Dynamics of the Manhattan Hotel Industry,” Administrative Science Quarterly, 37, 580–604. Baum, J. and J. Singh (1994), “Organizational Niches and the Dynamics of Organizational Mortality,” American Journal of Sociology, 100, 346–380. Baum, J. and W. Powell (1995), “Cultivating an Institutional Ecology of Organizations,” American Sociological Review, 60, 529–538. Baum, J. and H. Haveman (1997), “Love Thy Neighbor? Differentiation and Agglomeration in the Manhattan Hotel Industry, 1898–1990,” Administrative Science Quarterly, 42, 304–338. Berlekamp, E.R., J. Conway and R. Guy (1982), Winning Ways for Your Mathematical Plays, Vol. II. New York: Academic Press. Blossfeld, H.-P. and G. Röhwer (1995), Techniques of Event-Hystory Modeling. Mahwah, NJ: LEA Publishers. Boeker, W. (1989), “Organizational Origins: Entrepreneurial and Environmental Imprinting at the Time of Founding,” in G. Carroll (Ed.) Ecological Models of Organizations, Cambridge, MA: Ballinger, pp. 33– 51. Brittain, J. (1994), “Density-Independent Selection and Community Evolution,” in J. Baum and J. Singh (Eds.) Evolutionary Dynamics of Organizations, New York: Oxford University Press, pp. 355–378. Brown, T. and M. McBurnett (1993), “The Emergence of Political Elites,” Paper Presented at the European Conference on Artificial Life, Brussels, Belgium. Brüderl, J., P. Preisendorfer and R. Ziegler (1992), “Survival Chances of Newly Founded Business Organizations,” American Sociological Review, 57, 227–242. Carroll, G. (1985), “Concentration and Specialization: Dynamics of Niche Width in Populations of Organizations,” American Journal of Sociology, 90, 1262–1283. Carroll, G. and P. Huo (1986), “Organizational Task and Institutional Environment in Evolutionary Perspective: Findings from the Local Newspaper Industry,” American Journal of Sociology, 91, 838–873. Carroll, G. and M. Hannan (1989), “Density Delay and the Evolution of Organizational Populations: A Model and Five Empirical Tests,” Administrative Science Quarterly, 43, 411–430.


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February 17, 1998


11:39

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Carroll, G. and J. Wade (1991), “Density Dependence in the Organizational Evolution of the American Brewing Industry Across Different Levels of Analysis,” Social Science Research, 20, 217–302. Carroll, G. and A. Swaminathan (1992), “The Organizational Ecology of Strategic Groups in the American Brewing Industry from 1975 to 1990,” Industrial and Corporate Change, 1(1), 65–97. Carroll, G. and J. Harrison (1994), “On the Historical Efficiency of Competition between Organizational Populations,” American Journal of Sociology, 100, 720–749. Carroll, G. and M. Hannan (1995), “Automobile Manufacturers,” in G. Carroll and M. Hannan (Eds.) Organizations in Industry: Strategy, Structure and Selection, New York: Oxford University Press, pp. 195–214. Delacroix, J., A. Swaminathan and M. Solt (1989), “Density Dependence versus Population Dynamics: An Ecological Study of Failings in the California Wine Industry,” American Sociological Review, 54, 254–262. DiMaggio, P. (1994), “The Challenge of Community Evolution,” in J. Baum and J. Singh (Eds.) Evolutionary Dynamics of Organizations, New York: Oxford University Press, pp. 444–450. Fichman, M. and D. Levinthal (1991), “Honeymoons and the Liability of Adolescence: A New Perspective on Duration Dependence in Social and Organizational Relationships,” Academy of Management Journal, 16, 442–468. Freeman, J. (1990), “Ecological Analysis of Semiconductor Firm Mortality,” in J. Singh (Ed.) Organizational Evolution, Beverly Hills, CA: Sage, pp. 53–77. Freeman, J., M. Hannan and G. Carroll (1983), “The Liability of Newness: Age Dependence in Organizational Death Rates,” American Sociological Review, 48, 692–710. Freeman, J. and A. Lomi (1994), “Resource Partitioning and the Founding of Banking Cooperatives in Italy,” in J. Baum and J. Singh (Eds.) Evolutionary Dynamics of Organizations, Oxford University Press, pp. 269– 293. Gutowitz, H. and J. Victor (1987), “Local Structure Theory in More than One Dimension,” Complex Systems, 1, 57–68. Hannan, M.T. (1988), “Age Dependence in the Mortality of National Labor Unions: Comparisons of Parametric Models,” Journal of Mathematical Sociology, 14, 1–30. Hannan, M.T. (1997), “Inertia, Density, and the Structure of Organizational Populations: Entruies in European Automobile Industries, 1886–1981,” Organisation Studies, 18, 193–228. Hannan, M. and J. Freeman (1977), “The Population Ecology of Organizations,” American Journal of Sociology, 83, 929–984. Hannan, M. and J. Freeman (1989), Organizational Ecology. Cambridge, MA: Harvard University Press. Hannan, M.T., D. Barron and G. Carroll (1991), “The Interpretation of Density Dependence in Rates of Organizational Mortality: A Reply to Petersen and Koput,” American Sociological Review, 56, 410–415. Hannan, M. and G. Carroll (1992), Dynamics of Organizational Populations, Density, Legitimation, and Competition. New York: Oxford University Press. Hannan, M. and G. Carroll (1995), “Theory Building and Cheap Talk about Legitimation,” American Sociological Review, 60, 539–544. Hannan, M., G. Carroll, E. Dundon and J. Torres (1995), “Organizational Evolution in a Multinational Context: Entries of Automobile Manufacturers in Belgium, Britain, France, Germany, and Italy,” American Sociological Review, 60, 509–528. Hannan, M., D. Burton and J. Barron (1996), “Inertia and Change in the Early Years: Employment Relations in Young High Technology Firms,” Industrial and Corporate Change, 5, 503–536. Hogeweg, H. (1988), Cellular Automata as a Paradigm for Ecological Modeling. Applied Mathematics and Computation, 27, 81–100. Kalbfleisch, J. and R. Prentice (1980), The Statistical Analysis of Failure Time Data. New York: Wiley. Keenan, D. and M. O’Brien (1993), “Competition, Collusion, and Chaos,” Journal of Economic Dynamics and Control, 17, 327–353. Kephart, J. (1994), “How Topology Affects Population Dynamics,” in C. Langton (Ed.) Artificial Life III, AddisonWesley, pp. 447–463. Levinthal, D. (1991), “Organizational Adaptation and Environmental Selection—Interrelated Processes of Change,” Organization Science, 2, 140–145. Levinthal, D. and M. Fichman (1988), “Dynamics of Interorganizational Attachments: Auditor-Client Relations,” Administrative Science Quarterly, 33, 345–369.


246

KL564-01-Lomi

February 17, 1998

11:39

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Lomi, A. (1995a), “The Population Ecology of Organizational Founding: Location Dependence and Unobserved Heterogeneity,” Administrative Science Quarterly, 40, 111–144. Lomi, A. (1995b), “The Population and Community Ecology of Organizational Founding: Italian Cooperative Banks, 1936–1989,” European Sociological Review, 11, 75–98. Lomi, A. (1997), “The Population Ecology of Danish Commercial Banks, 1846–1990. Data Coding and Data Analysis,” University of Bologna. Unpublished manuscript. Lomi, A. and E.R. Larsen (1995), “The Emergence of Organizational Structures,” in R. Burton and B. Obel (Eds.) Design Models for Hierarchical Organizations: Computation, Information and Decentralization, Kluwer, pp. 209–232. Lomi, A. and E. Larsen (1996), “Interacting Locally and Evolving Globally: A Computational Approach to the Dynamics of Organizational Populations,” Academy of Management Journal, 39, 1287–1321. Lomi, A. and E. Larsen (1997), “Evolutionary Models of Local Interaction: A Computational Perspective,” in Variations in Organization Science: A Conference in Honor of Donald T. Campbell, University of Toronto. March, J. and P. Olsen (1989), “The New Institutionalism: Organizational Factors in Political Life,” American Political Science Review, 78, 734–749. McPherson, M. (1983), “An Ecology of Affiliation,” American Sociological Review, 48, 519–532. Packard, N. and S. Wolfram (1985), “Two-Dimensional Cellular Automata,” Journal of Statistical Physics, 38, 901–946. Petersen, T. and K. Koput (1991), “Density Dependence in Organizational Mortality: Legitimacy or Unobserved Heterogeneity?” American Sociological Review, 56, 399–409. Ranger-Moore, J., J. Banaszak-Holl and M. Hannan (1991), “Density-Dependent Dynamics in Regulated Industries: Founding Rates of Banks and Life Insurance Companies,” Administrative Science Quarterly, 36, 36–65. Romanelli, E. (1993), “Organizational Imprinting: Initial Conditions and Constraints on Subsequent Organizational Strategies,” Working Paper. School of Business Administration, Georgetown University, Washington, DC. Scott, W. and J. Meyer (1983), “The Organization of Societal Sectors,” in J. Meyer and W. Scott (Eds.) Organizational Environments: Ritual and Rationality, Beverly Hills, CA: Sage, 129–153. Singh, J. (1993), “Density Dependence Theory: Current Issues, Future Promise,”American Journal of Sociology, 99, 464–473. Singh, J. and C. Lumsden (1990), “Theory and Research in Organizational Ecology,” Annual Review of Sociology, 16, 161–195, Palo Alto, CA: Annual Reviews. Stinchcombe, A. (1965), “Social Structure and Organizations,” in J. March (Ed.) Handbook of Organizations, Chicago: Rand McNally, pp. 142–193. Suárez, F. and J. Utterback (1995), “Dominant Design and the Survival of Firms,” Strategic Management Journal, 16, 514–430. Swaminathan, A. (1996), “Environmental Conditions at Founding and Organizational Mortality: A Trial-by-Fire Model,” Academy of Management Journal, 39, 1350–1377. Swaminathan, A. and J. Delacroix (1991), “Differentiation within an Organizational Population: Additional Evidence from the Wine Industry,” Academy of Management Journal, 34, 679–692. Swaminathan, A. and G. Wiedenmayer (1991), “Does the Pattern of Density Dependence in Organizational Mortality Rates Vary Across Levels of Analysis? Evidence from the German Brewing Industry,” Social Science Research, 20, 45–73. Trussell, J. and T. Richards (1985), “Correcting for Unmeasured Heterogeneity in Hazard Models Using the Heckman-Singer Procedure,” Sociological Methodology, 15, 242–276. Tuma, N. and M. Hannan (1982), Social Dynamics: Models and Methods. New York: Academic Press. Williamson, O. (1991), “Comparative Economic Organization: The Analysis of Discrete Structural Alternatives,” Administrative Science Quarterly, 36, 269–296. Williamson, O. (1994), “Transaction Cost Economics and Organization Theory,” in N. Smelser and R. Swedberg (Eds.) Handbook of Economic Sociology, Princeton NJ: Russell Sage Foundation, pp. 77–107. Winter, S. (1990), “Survival, Selection and Inheritance in Evolutionary Theories of Organizations,” in J. Singh (Ed.) Organizational Evolution: New Directions, Newbury Park, CA: Sage, pp. 269–297.


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Wolfram, S. (1983), “Statistical Mechanics of Cellular Automata,” Review of Modern Physics, 55, 601–644. Wolfram, S. (1986), “Cellular Automaton Fluids: Basic Theory,” Journal of Statistical Physics, 45, 471–526. Alessandro Lomi is a member of the Strategy and Organization Group at the School of Economics of the University of Bologna (Italy). Previously he was Assistant Professor at the London Business School (London, UK) and NATO Advanced Science Fellow at Syracuse University (Syracuse, New York). He received his MS and Ph.D. degrees from Cornell University (Ithaca, New York). His main research interests include ecological model of organizations, the simulation of organizational processes and the analysis of social networks. Erik Reimer Larsen is EU Marie Curie Fellow at the School of Economics of the University of Bologna (Italy). Previously he held positions at London Business School (London, UK) and Copenhagen Business School. He received his Master of Engineering from the Technical University of Denmark, and his Ph.D. degree from the Institute of Economics at the Copenhagen Business School. His research focuses on computational organizational theory the use of system dynamics to model the transition from monopoly to competition in energy markets. He is the co-editor of “Systems Modelling for Energy Policy” published by Wiley in 1997.